ION PAIR FORMATION

IN

ATOM-MOLECULE COLLISIONS

M.M.HUBERS

ION PAIR FORMATION

IN

ATOM-MOLECULE COLLISIONS

ION FAIR FORMATION

IN

ATOM-MOLECULE COLLISIONS

academisch proefschrift

ter verkrijging van de graad van Doctor in

de Wiskunde en Natuurwetenschappen aan de

Universiteit van Amsterdam op gezag van de

Rector Magnificus, Dr. G. den Boef, hoog-

leraar in de Faculteit der Wiskunde en Na-

tuurwetenschappen, in het openbaar te ver-

dedigen in de Aula der Universiteit (tij-

delijk Lutherse Kerk, ingang Singel 411,

hoek Spui) op woensdag 19 mei 1976, des

namiddags te vier uur

MAARTEN MICHIEL HUBERS

geboren te Voorschoten

idoor

Promotor : Prof. Dr. J . Los

Co-referent : Prof. Dr. J.D.W. van Voorst

RECEPTIE NA AFLOOP VAN DE PROMOTIE

De receptie vindt evenals de promotie plaats in de Lutherse Kerkaan het Spui (ingang Singel 411)

S T E L L I N G E N

behorende bij het proefschrift

ION PAIR FORMATION IN

ATOM-MOLECULE COLLISIONS

M.M.Hubers Amsterdam, 19 mei 1976.

'•e'. •

De door Habitz en Schwarz gekonstateerde diskrepantie tussentheorie en experiment voor de elastische verstrooiing 'anlithium ionen aan natrium atomen kan verklaard worden met be-hulp van een drie-toestands benadering. Het minimum in dedifferentiële werkzame doorsnede t.g.v. destruktieve inter-ferentie tussen de partiële golven, die het l2j; resp. 2^Eoppervlak gevolgd hebben, kan teniet gedaan worden door derotatie koppeling tussen de 2^-1 en l̂ n konfiguraties.

P. Habitz and W.H.E. Sahjarz3C7iem.Phys.Lett. 34 (1975) 248.

II

De energie afhankelijkheid van de werkzame doorsnede voor deovergang in H2 (ls*£g •*• 3p^nu) door aanslag met elektronen'tussen 0 en 100 eV, zoals bepaald door Baltayan en Nedelec.is aan bedenkingen onderhevig.

P. Baltayan and 0. Nedelec, J. Quant. Speatrose.Radiat. Transfer 16 (1976) 207.

III

Bindings energieën van alkali atomen aan een polykristallijnwolfraam oppervlak, bepaald via thermische desorptie, kan meninterpreteren als bindings energieën van alkali atomen aanspecifieke kristal vlakken.

W. Körner, Proo. 2nd Int. Conf. on Solid Surfaces, 1974Japan. J.Appl. Phys. Suppl. 2t Pt. 23 1974.

IV

Twee-foton ionisatie van alkali atomen via een resonante tus-sentoestand leidt tot een hoekverdeling der geëmitteerde elek-tronen, die in sterke mate afhankelijk is van de koppeling vanhet totaal elektronisch impulsmoment en de kernspin van hetbetrokken atoom. Lambropoulos en Berry houden hiermee in hunanalyse betreffende twee-foton ionisatie van natrium via de^ / 3/2 niveaus ten onrechte geen rekening.

M'.M. Lambropoulos and R.S. Berry, Phys.Rev. A8 (1973) 855.

De overeenstemming tussen de translatie energie der fragmentenbij fotodissociatie van halogeen molekulen (X2) en de transla-tie energie der reaktie produkten bij de reaktie H+X2 is voorde zwaardere halogenen veel minder goed dan voor de lichtere.Dit wordt veroorzaakt door het afnemende relatieve verschilvan de evenwichts afstanden in X2 en X£~ bij zwaarderehalogenen.

D.R. Herschbach, Faraday Disa. Chem. Soe. SS (1973) 233.

VI

Door de in de vakuum techniek gebruikelijke schoonmaak proce-dures dient men bedacht te zijn op een afnemende detektieefficiëntie van alkali atomen aan hete wolfraam bandjes.

VII

De introduktie van schade in halfgeleidende materialen doorlichte, energetische projectielen wordt mede beïnvloed doorde ligging van het Fermi niveau.

W.H. Kool, proefschrift (Amsterdam, 1976) Hfst. III.

VIII

In atoom - niolekuul verstrsoiings experimenten, gericht op hetonderzoek naar de koppeling tussen verschillende elektronenkonfiguraties, is het noodzakelijk de metingen voort te zettennaar zo hoge energieën dat de rotatie en vibratie bewegingvan het molekuul verwaarloosd mogen worden.

Dit proefschrift, Hfst. III.

IX

Thermische verontreiniging door elektriciteitscentrales is inprincipe drastisch te beperken m.b.v. een passief stralings- <koelsysteem, waarbij gebruik wordt gemaakt van een spektraal jselektief filter, dat transparant is in het infrarode gebied jtussen 8 en 13 ym. ;

5. Catalanotti, V. Cuomo3 G. Piro, D. Ruggi, V. Silvestriniand G. Trotse, Solar Energy 17 (1975) 83. •

Het onderzoekbeleid, in het bijzonder dat voor de exaktewetenschappen, dient in belangrijke mate gevoerd te wordendoor ervaren onderzoekers, die aktief betrokken zijn bijhet onderzoek, hetzij op basis van een gedeelde funktiedan wel OTP basis van een volledige funktie gedurendebepaalde aaneengesloten perioden.

Personeelsadvertentie "de rijksoverheid vraagt1'vac. nr. 6-4160/2731, NHC Handelsblad (27/3/1976) p. 26.

fir

C O N T E N T S

INTRODUCTION

page

9

CHAPTER I

3.

CHEMI-IONIZATION IN ALKALI-HETERONUCLEAR

HALOGEN COLLISIONS: ROLE OF EXCITED MOLECULAR

TON STATES

1. Introduction ..

2. Experimental

Results and discussion

3.1. Electron affinities of IX

3.2. Dissociation energies of IX

3.3. I produation-Role of excited

states of IX~ ..,

3.3.1. Construction of potential energy

curves

3.3.2. Threshold for I production

3.3.3. Simplified model of the collisions

3.3.4. Role of anisotropy of H-p

3.3.5. Role of excited states in homo-

nuclear halogens

References

15

16

16

17

18

19

20

20

22

22

25

26

27

CHAPTER II ION PAIR FORMATION IN ALKALI-SF, COLLISIONS:D

DEPENDENCE ON COLLISIONAL AND VIBRATIONAL

ENERGY 29

1. Introduction 30

2. Experimental method 32

3. Experimental results and data evaluation .. 33

3.1. Nan velocity selected spectra 33

3.2. Velocity selected spectra ., 33

4. Discussion 40

4.1. Threshold measurements (T = 300 K) ... 40

4.2. The collision model ....*.. 47

4.3. The role of internal energy 49

page

5. Conclusions 51

Appendix A. Calculation of p and ƒ 51

Appendix B. The calculation of o 52

References 53

CHAPTER III ION PAIR FORMATION IN ALKALI-HALOGEN COLLISIONS

AT HIGH VELOCITIES 55

1 . Introduction , 56

2. Experimental .

2.1. Description of the apparatus 59

2. 2. Ionization efficiency . 61

2.3. Evaluation of the arose section 63

3. Results 64

4. Discussion 70

4.1. Collision model 73

4.2. Low velocity region 78

4.3. High velocity region 81

4.3.1. Vertical electron affinities 83

4.3.2. Coupling matrix elements 85

4.3.3. H22 - R^ relations 86

5. Conclusions 91

References 93

CHAPTER IV SIMPLE TRAJECTORY CALCULATIONS ON ION PAIR

FORMATION IN ALKALI ATOM-HALOGEN MOLECULE

COLLISIONS.

1. Introduction 95

2. Theoretical method 97

3. Results and discussion '03

3.1. Bondstretching 103

3.2. Total cross sections '05

3.3. Fractions of dissociated ions 109

References Ill

SUMMARY 112

SAMENVATTING 114

The work described in this thesis is part of the research program of

the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for

Fundamental Research on Matter), made possible by financial support

from the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onder-

zoek (Netherlands Organization for the Advancement of Pure Research).

- 9 -

I N T R O D U C T I O N

This thesis deals with a molecular beam study on ion pair formation in

collisions of alkali metal atoms and simple molecules. From a practical

point of view the formation of ions in collisions of neutral species by

electron transfer is a fundamental process in areas like hot atom chemistry,

flames, plasma physics, upper atmosphere and space chemistry. However,

these processes are often inelastic by energies of the order of 1 eV which

is far beyond the range attainable from effusive sources and therefore ex-

perimentally difficult to study. The endothermicity can be surmounted by

electronic or vibrational excitation of one of the reactants and by en-

hancement of the relative kinetic energy.

The last few years this field of research has received much attention

due to the development of special techniques in the late sixties, to produce

hyperthermal neutral beams. The experimental studies concern cross section

measurements for the various reaction pathways as a function of relative

energy, the behaviour of the cross section near threshold, the relative im-

portance of translational and internal energy in promoting processes of

ion pair formation and the dynamics of these ionising collisions as revealed

by the product angle and product energy distrib itions.

The study of ion formation by electron transfer is a natural extension

of the molecular beam research of the past fifteen years on reactive

collisions in the thermal energy range. As for the alkali atom (M)-halogen

molecule (X») reactions the experimental results can be summarized by:

large reaction cross sections (100-300 A ) , high product vibration and sharp

forward scattering of the alkalihalide product. The basic features can be

satisfactorily explained by the so-called harpoon model, originally proposed

by Polanyi already in 1932 to explain his famous sodium flame experiments and

further developed by Magee. The mechanism involves a sudden jump of the

valence electron of the alkali atom to the halogen molecule at an internu-

clear distance R , corresponding with the crossing of the lowest covalent

(M+X2) and ionic (M +X2) potential surfaces. Subsequent dissociatin. of X ?

and formation of a new bond M X complete the reaction, while the remaining

- 10 -

halogen atom X is departing undisturbed (spectator stripping model). The

large cross section simply can be understood from the large R : since the

electron jump occurs with unit probability, the reactive cross section2

equals TTR . The high product vibrational excitation is determined by the

attractive character ("early down hill") of the adiabatic potential surface.

A theoretical description for the electron jump transition probability

between two electronic configurations at the crossing R is given by the

Landau-Zener theory. This theory, which is a two state approximation, in-

deed forecasts adiabatic behaviour of the system at very low velocities;

at higher velocities, however, diabatic crossings 'ill occur. The colliding

particles will separate again untill the crossing radius is passed for the

second time. At relative energies larger than the endothermicity AE, ion

pair formation can occur due to an electron jump at the first crossing

while passing the second crossing diabatically (no change occurs) or vice

versa? Here AE is the difference of the ionization potential I of the donor

atom and the vertical electron affinity EA of the acceptor atom. The

crossing radius in a good approximation is given by R = a /„(I-EA ).

The usefulness of the Landau-^ener formula has been demonstrated in experi-

ments on ion pair formation in Na+I collisions by Moutinho (total cross

sections) and by Delvigne (differential cross sections).

In this thesis studies on ion pair formation are reported which concern

three particle and multi particle interactions, respectively the systems

M+XY (M'= alkali atom, XY = halogen molecule) and M+SF,. Also here the

mechanism of electron transfer is responsible for the ion formation; the

picture, however, is much more complicated because of the number of degrees

of freedom (3N-6) involved. Calculations have to be performed on crossing

potential hypersurfaces instead of crossing (one dimensional) potential

curves; straight forward application of the Landau-Zener formula to cal-

culate the transition probability is not allowed.

At very low velocities quenching (or vibrational relaxation) will ocfir.

Trajectory calculations on K+Br„ show that at the very threshold for ion

formation the highly vibrationally excited Br„ is effectively quenched to

the lowest vibrational levels by the Coulomb interaction with the K ion

during the collision. This means the transfer of vibrational into transla-

tional energy. As a consequence the threshold for parent ion formation ir

said to correspond with the adiabatic electron affinity of the molecule.

- 11 -

Experimental evidence, however, does not exist. If one leaves threshold

phenomena out of consideration but concentrates on processes at higher ve-

locities, an important simplification can be introduced: the motion of

the alkali atom relative to the center of mass of the halogen molecule and

the relative motion of the two particles X-Y or SF5~F in the molecule can

be considered as being completely independent. Thus the Landau-Zaner for-

mula can be applied in calculations of the total cross section, with due

observance of some molecular aspects of the target.

The most important features of a molecular target are:

a) the angular dependence of the coupling matrix element H 1 ? which

describes the interaction between the diabatic potentials at R . For thec

M-X? interaction simple expressions for H.? (R ,0) have b«en derived.

b) excited states of the product molecular ion. The single crossing is

replaced by several crossings.

c) the vibrational motion of the target molecule. In comparison with the

heavy particle motion the electron jump is very fast. According to the

Franck-Condon model a distribution of vibrational states of the molecular

ion is formed which is an exact reflection of the original vibrational

state distribution. In other words one has to do with a distribution of

vertical electron affinities, i.e. of crossing radii.

d) the internal motion of the molecular ion during the passage of the

crossing region ("bondstretching"). As for the M-XY interaction the XY

molecular ions are formed on the repulsive part of the potential due to the

large difference between the internuclear distances of XY and XY (the

electron is promoted to a strongly antibonding orbital). Therefore the

(X-Y) bond will stretch during the collision, which increases drasti-

cally the diabatic behaviour of the system at the second crossing (i.e.

leading to ion pair formation).

The latter is by far the most influential molecular aspect: it plays a very

fundamental role in atom-molecule interactions at velocities where the

collisional time and the vibrational time of the molecular ion are of the

same order. At high velocities (collisional time « vibrational time) this

effect disappears; then the total cross section can be evaluated using the

Landau-Zener formula, only taking into account the molecular aspects a),

b) and c).

- 12 -

The first three chapters deal with experimental results on negative ion

formation in atom-molecule collisions, whereas in the fourth chapter

theoretical calculations are presented which explain in terms of a simple

collision model the features as observed in the alkali atom-halogen mole-

cule collisions (reported in chapters I and III). Chapter I describes the

dependence of the partial (i.e. with respect to the different ions formed)

total cross sections for M-IBr and M-IC1 on the relative energy in the low

energy range (from threshold to about 20 eV c m . ) . Two molecular aspects

are studied here: thf. role of excited molecular ion states (evident from

the I production) and bondstretching (the only mechanism to allow for the

I formation). Chapter II describes the results of measurements on negative

ion formation in M-SF, collisions.performed as a function of both theo

translational and the vibrational energy modes. This experiment again

covers the low energy range, from threshold to at most 30 eV cm.; the vi-

brational excitation of the target molecule is achieved by heating the SF,

source from room temperature to about 850 K. The relative importance of

the translational and vibrational degrees of freedom with respect to ion

formation is discussed; experimental evidence is obtained for the effect ;

of quenching at the very threshold energy. The symmetric SF, molecule has

been chosen due to its large internal energy content (the total vibrational -

energy increase is an order of magnitude larger than in the case of a halo- ;

gen molecule while much higher vibrational levels will be considerably po-

pulated). In Chapter III results are given on especially the high velocity {

dependence of the negative ion formation in M-XY collisions. Objectives of ;

the experiment were in the first instance to obtain information on the upper i

limit of the velocity of bondstretching, on a possible incoming of excited ;;

XY states, to determine the values for the vertical electron affinity of L

the halogen molecules and to study the (Landau-Zener type of) behaviour of \

the total cross section, which might yield information on the coupling ;

element HJ2. The results are surprising; indeed above-mentioned questions |

are answered but at the same time quite new aspects of the total cross sec- \

tion are revealed. In order to explain these a collision model is developed; ]

total cross sections have been calculated using the two state Landau-Zener i

theory but with taking into account, however, the molecular aspects, which i

are active in the high velocity range. In Chapter IV numerical calculations \l

are presented to verify the results of chapters I and III. Total and partial £•total cross sections have been evaluated for the entire velocity range I

- 13 -

covered by these experiments, using the impact parameter method. Threshold

aspects have been left out of consideration. Time dependent bondstretching

has been incorporated in the collision model by solving numerically the

differential equation of motion on the repulsive X~ potential curve with

respect to the collision time.

Literature concerning this introduction:

D.R. Herschbach, Advan. Chem. Phys. 10 (1966) 319;

J.L. Kinsey, Biennal Review of Science3 Technology and Medicine3

Reaction Kinetics Volume, Ch. 6 (J972);

E.E. Nikitin, in: Chemische Elementarprozesse, ed. H. Hartmann,

Springer Verlag (1968), p. 43;

J. Los, in: The Physics of Electronical and Atomic Collisions, '•{

VIII ICPEAC, Inv. Lect., eds. B.C. Cobic and M.V. Kurepa I

(Beograd, 1973), p. 621;

S. Wexler, Ber. Bunsenges. Phys. Chem. 77 (1973) 606;

J.P. Toennies, Phys. Chem., Vol. VIA (1974), p. 228;

A.P.M. Baede, Advan. Chem. Phys. (1975), p. 463.

A.M.C. Moutinho, Ph.D. Thesis (1971), Leiden.

A.P.M. Baede , ..h.D. Thesis (1972), Amsterdam.

G.A.L. Delvigne, Ph.D. Thesis (1973), Amsterdam.

- 15 -

C H A P T E R I

CHEMI-IONIZATION IN ALKALI-HETERONUCLEAR HALOGEN COLLISIONS:ROLE OF EXCITED MOLECULAR ION STATES

- 16 -

CIIFMICAL PHYSiCS 2 (1973) 107 118. © NORTH-HOLLAND PUBLISHING COMPANY

CHEMI-IONIZATION IN ALKALI-HETERONUCLEAR HALOGEN COLLISIONS:ROLE OF EXCITED MOLECULAR ION STATES

D.J. AUERBACH*. M.M. HUBERS, A.P.M. BAEDEt and J. LOSFOM-lnslituut voor Atoom- en Molecuulfysica, Amsterdam, The Netherlands

Received 3 May 1973

Total cross sections have been measured for the production of negaiive halogen ions in collisions between the alka-li atoms K, Na and Li and the heteronuclear halogen molecules IBr and ICI at relative energies from threshold up toabout 20 eV. By means of a mass spectrometer the cross secticns for negative parent ion and fragment ion productioncould be measured separately.

The total cross sections for the IX" and X~ production show features similar to those reported earlier forM + \i -» M+ + XJ, M+ + X + X~. The most striking feature of this work is the presence of the I~ production. Thisis interpreted to occur via an excited state of IX" ( n p . The genera! behaviour of the I" cross section ischaracteristically dependent on the alkali collision partner: for K collisions the 1~ cross section peaks just abovethreshold and falls rapidly, for Na the cross section is just about the experimental uncertainty and for Li negligible.This behaviour will be discussed in terms of a modified Landau -Zcner theory.

From these measurements we have inferred the adiabatic electron affinity of IX (Id: 2,41 eV, IBr 2.55 eV) andthe well depth of 1X~(22;+) (ICr: 0.95 eV, IBr~: 1.05 eV).

1. Introduction

In recent years there has been a growing body ofexperimental work on electronic excitation and ioni-zation in atom—molecule collisions in the thresholdand near threshold energy range. Total cross sectionsfor collisional ionization of I2, Br2 and Cl2 and someother molecules by the alkalis Li, Na and K have pre-viously been studied in this laboratory [1] and recent-ly differential cross sections [2] and total cross sec-tions with mass analysis of the negative ions [3] havebeen measured. The Harvard group has studied bothionization and excitation of K by several diatomicmolecules [4] and has recently also performed experi-ments with mass selection of the negative ions [5].Collisionai ionization of Br2 by Cs has been studied byRothe [6j. who recently has applied the time of flighttechnique to achieve improved energy resolution [7].Other studies of collisional ionization include Na on

O2 by the San Diego group [8] and Cs on NO2, N2Oand O2 by the Oak Ridge group [9]. Excitation ofboth alkali and target molecules has been studied bythe Freiburg group [10].

A common feature of all this work is that largecross sections are observed well below the energiespredicted by the adiabatic criterion and this is inter-preted in terms of non-adiabatic transitions at thecrossing of potential surfaces. The surfaces involvedare those belonging to the covalent M+IX state and theionic M++1X~ state, i.e., the ground states of the ionpair. The formation of ion pairs proceeds directly fromthis crossing, while excitation results from a secondcrossing of the ionic state with an excited state.

We report data on collisional ionization of hetero-nuclear halogens in collisions with alkali atoms whichshows that the crossing of the covalent M+IX surfacewith an excited ionic M++ IX~ (2fli) surface playsan important role in these processes.

* Present address: Dept. of Physics, University of WesternOntario, London 72, Canada.

t Present address: K.N.M.I. (Royal Dutch Meteorological Insti-tute), De But, The Netherlands.

2. Experimental

The apparatus used for this work is the same as

- 17 -

used in earlier work of the negative ions formed in al-kali homonucleur halogen collisions [3], so only avvr> brief description will he given here.

A beam of alkali atoms is produced by sputtering,velocity selected mechanically and crossed with ahalujien beam from a multichannel array. The ionsproduced are extracted in a uniform field, focused,mass analysed with a sector magnet and counted. Theprimary beam is monitored with an Ir surface ioniza-tiois detector treated with O->. Several settings of thevelocity selector were used in this work. For most ofthe work the velocity spread was 9% (fwhm). Forsome threshold measurements we reduced this to 7%while for Li a larger spread (12%) was used to allowhigher velocities to be reached. We encountered a newexperimental problem in this work because of the pre-sence of I2 and X2 due to impurities and dissociationof the target gas IX. IBr contains about 8% I2 and Br2

at ordinary temperatures [11]. That means that theformation of X' is due to two processes:

M + IX - M + + I + X - ,

M + X2 -* M+ + X + X- ,

while the formation of X2 is due to

M + X2 -* M+ + X2 .

(la)

(lc)

Using the X-, ion signal as a measure for the amountof X2 present in the target gas IX, measurements onthe homoiiuclear halogen molecules [3] enabled us tosubtract this latter contribution from the X~ signal.

This correction has been applied also to the I~ pro-duction due to the process

M + IX -• M+ + r + X .

3. Results and discussion

(Id)

The measured total cross sections for negative ionformation for M + IX in which M is K. Na or Li andIX is IBr or IC1, are given in fig. 1 (M-IBr) and fig. 2(M-ICI). The vertical scales are arbitrary in thesense that the parent ion cross sections are normal-ized to ten in their maxima, the mutual ratios be-tween the parent ion cross sections and fragment ioncross sections are absolute within 10%.

Fig. la. Cross sections for the production of negative ions inK-IEr collisions.

C M ENERGY <»V)

Fig. 1 b. Cross sections for the production of negative ions inNa-IBr collisions.

Iry u

nits

1

S

O

1.1

Bf'

LI.IBr

10 16CM ENEKVUV)

Fig. 1 c. Cross sections for the production of negative ions inLi-IBr collisions.

- 18 -

10 IS 20

CM. ENERGY (»V)

Fig. 2a. Cross sections for the production of negative ions inK-ICJ collisions.

10 15

CM. ENERGY<eY)

20

Fig. 2c. Cross sections for the production of negative ions inLi-ICl collisions.

Fig. 2b. CrossNa- IC1 collisions.

15 20

C M ENERGY (*v)

ions for the production of negative ions in

One of the most interesting aspects of these mea-surements is the formation of I~. For K + IX we findan l~ signal about 0.2 of the X" signal, for Na-+ IXthe I~ production is much smaller (approaching thenoise limit of the subtraction procedure used in thedata reduction), and for Li + IX no I" is observed.The experimental features of the I~ cross sections,with respect to relative magnitude, energy depen-dence and dependence of collision partner ar? dis.

cussed below in connection with a model based ontransitions to an excited electronic state of IX~.

The formation of IBr~, IC|-, Br~ and CI~ pre-sents few new features so we will discuss it only brief-ly.

The reactions M + IX •* M+ + I + X~ (i.e., dissoci-ation of the ground state ion to the atomic ion ofgreater electron affinity) show features similar, al-though less pronounced, to those reported earlier forM + X2 -» M+ +X + X~ [3]. The X~ cross sections forNa + IX show a rather smooth behaviour with maximaif at all, at rather large energies whereas those for K+ IX have their maximum at energies near threshold.These results can be explained qualitatively in termsof a modified Landau-Zener model suggested in [3J.

3.1. Electron affinities of IX

From the measured thresholds for formation of theparent ions the adiabatic electron affinities EAad(IX)of [Cl and IBr can be deduced

EAad(IX) = /(M) - ^ „ ( I X " ) , (2)

where /(M) is the alkali ionization potential. We assumethat these threshold energies correspond with the adia-batic electron affinity. This assumption is based uponthe following considerations: Franck-Condon overlapcalculations of Baede (unpublished

- 19 -

l.ihk I

1 lue-.tK.UI eiKTj'.ies A,|lr t«r negative molecular ion produciionand JJI.IIUIK elecimn jttinities l:AJ(j in eV

KNaLi

AverageOilier work

[16]

lltr

'•thr

1.802.552.85

1 A ad

2.542.59-2.54

2.552 7

KI

/;ihr

1 952.69-

'•-Aad

2.392.45-

2.41

Br-.I-M

1 Aad

2.552.51

CN1151

fAad

2.452.38

\j

| 3 |

l A a

2.522.58

results) and recent similar calculations of Kendall andGrice [12] show that a measurable amount of nega-tive molecular ions can be formed via a Franek-Con-don transition in vibrational levels a few tenths of aneV above the lowest vjbrational stale of the molecularion. In view of the uncertainties in the potential para-meters of the molecular ion ground state and thesteepness of the repulsive potential of this state aslight deviation of Franck- Condon behaviour seemsenough to reach the lowest vibrational levels. More-over Zembekov [13] has shown that the M+ ion canact as an effective quencher of the vibrationally ex-cited molecular ion.

The thresholds are determined by fitting to the ex-perimental points the convolution over the distribu-tion in relative energies of a parameterized cross sec-tion (linear energy dependence) [3, 14, 15). The re-sults are presented in table 1, as well as some valuesobtained by Chupka et al. 116].

3.2. Dissociation energies oj'IX

The dissociation energy of the negative molecularion IX" (-2+)can be obtained straightforwardlyfrom the difference of threshold energies for the for-mation of IX and X , using the relation

IX' ) = KAad(IX) - EA(X)

(3)

neutral atoms. In table 2 we have compiled the valuesfor the experimental binding energies for IX andX-,. together with experimental values of Chupka etal. 116] and Lacmann [4], ind estimated values ofPerson [17] based upon rough molecular orbital argu-ments. The figures of Chupka are deduced by us fromhis data on the electron affinities with eq. (3) in itsgeneral form.

In molecular orbital (MO) description the electronconfigurations for the ground states are written as fol-lows for the valence shell electrons

I X ( » S + ) : . . . o V * 4

! X - ( 2 Z + ) : . . . o V i r 4 o .

The two states differ in the additional electron in thestrongly antibondingö MO. The net effect of the n andir MOs is slightly bonding: the actual bond is formedby the pair of electrons in the a MO [18].

In case of IX" , however, the bond strength is con-siderably weakened by the addition of an electron inthe strongly antibonding a MO.

The net result is still a bound molecular ion groundstate IX" (2£+) . On the other hand the excited statesof IX~ are expected to be repulsive since these confi-gurations include two electrons in the a MO. Since Xis more electronegative than I, the coefficients for theX terms and I terms in the valence shell MOs are dif-ferent: the bonding a and n MOs are composed pri-marily of X AOs, whereas the anti-bonding n and aMOs are composed predominantly of 1 AOs. The mea-sured dissociation energies are in agreement with thisorbital asymmetry of the interhaiogen molecules."

Table 2Experimental potential well depth (dissociation energy) ofthe negative molecular halogen ions in eV, compared withsemi-empirical values of Person [17] and experimental valuesof Chupka et al. [16) and Lacmann et al. [4]

Here Dj]( IX) means the dissociation energy of IX into

IBr-

i r rIFBrfCII

O0(XY - ) (

This work

1.050.951.021.151.31

± 0.1iO.I± 0.05± 0.1t 0.15

£(uVPerson1171

0.9 ± 0.41.1 ±0.50.7 s 0.31.0 * 0.5!.2±0.5

Chupka[16]

1.18 ±_1.07 ±1.14±1.28 t

0.2

0.10.J0.1

Lacmann[4]

__

2.1+0.2

- 20 -

the well depths of IBr and I(T are closer to thewell depth ol' I, than to those for Bi, and CI->.

Analogous phenomena giving e\idencc for the orbi-tal asymmetry have been observed for instance in theabsorption spectra {I0! and the anomalous chemicalshift in C1F [201.

3.3. l~ production - Role of excited states of IX ~

The reactions M + IX - M4+ X + I have severalstriking features:

(1)1" is formed although the ground state (22+)of 1X~ dissociates into X~ + I. This leads us to aninterpretation, based upon an electron jump into ex-cited states of IX~. Anoma'ies in the threshold forI" formation are discussed lelow in support of thisinterpretation.

(2) I" is at most 0.25 of the X~ production. Thepreference for X~ formation above 1~ formation isto be expected since the molecular ion state that dis-sociates into I + X" has a larger EA than the excitedmolecular ion state which dissociates into I~ + X;as a consequence curve crossings occur at a larger ra-dius RC(K + IC1 -* IC1- : Rc * 7.5A; K + IC1 ->• I" :

(3) The cross section »"or l~ formation dependsstrongly on the alkali atom used going in the orderaK > aNa > °L. " 0.

(4) The 1~ cross section for K + IX exhibits a peakat rather low energies and falls rapidly to a more orless constant value. At high energies the cross sectionhas decreased to about 1 /3 of its maximum value.

The last two points are discussed below in terms ofa simplified model of the collisions based upon thestretching of the IX~ bond during the collision.

3.3.1. Construction of potential energy curvesLet us consider the potential energy curves for IX

and IX~ (figs. 3 and 4) and also the correspondingMO correlation diagram of the electronic states of theIX~ molecular ion (fig. 5; table 3). The IX and IXpotential curves are approximated by Morse functions,with the parameters determined following the MO ar-guments of Person [17] and using the data available atpresent [211. The parameters are given in table 4. Thecorrelation between the excited repulsive molecularstates and their dissociation products is established by

3-

2-

IBr

-2-

IBr"4030eVi

1 1 1 ' 10 2 4 6 a

MTERNUCLEAR DISTANCE XCE ( )Fig. 3. Potential energy curves for the molecular groundstates of IBr and IBr", and for the excited 2rti state of IBr".

2 4 6 8INTERNUCLEAR DISTANCE d(S)

10

Fig. 4. Potential energy curves foi the molecular groundstates of ICi and \Cl~. and for the excited 2M; state of IC1"

matching equal values of the projection f2 of the totalelectronic angular momentum on the internuciear axis[22]. It is assumed that there is no outer crossing be-tween states of equal SI. Assuming that the presence

- 21 -

T-Mc 3Asynipiniic energy differences in eV bclween the atomic-.tjtes lor lür and K I. I or the meaning of A/see fig. 5

II.Br)

• * ' • :

(1.190.460.3(1

ll.(ï)

0.290.100.55

MO ELECTRON MOLECULARCONFIGURATION STATES

(A.S)G l l ' l t " ? ' £ ' 'ij

, , _< ,_ - Von 1 o' n — _ ii

oVti'ff 2 i * — —'t

I'ig. 5. The MO correlation diagram of the electronic slatesof the IX molecular ion. The values A£ for IBr and 1CI aregiven in table 3.

ATOMIC STATES

(J.J)

\ I - I (?P.,;)-X-("SC)

ij = . "tr,

Table 4Parameters used lor the construction ot the Morse potentials(see fins 3 and 4)

IBr

re(A) 2.49O0 'e V> 1.82ui.icm"1) 268.71

IBr

2.91.05

130

in ICI

2.32 2.82.15 0.95

384.29 200

Table 5The species for the different quasi-molecular states. The pointgroup O2Vand the g and u in brackets are only defined forhomonuclear molecules. The underlined species in the lowestrow belong to one surface; the not underlined species belongto the other. The 2 n species refers to both surfaces

2 A,

of the M+ ion does not severely disturb this diagramwe see that IX~ arising from the crossing of the cova-lent M + IX state with the ionic M+('S) + IX~(2£+)state will yield only X~ on dissociation. The forma-tion of I~ on the other hand can only come from thedissociation of one of the excited -\\ states of IX".

Let us consider the symmetry of the auasi-molecu-lar electronic states, which are involved. Table 5 showsthe species of these states: M(2S) + IXC1 £+) .M+('S) + IX-(2S4) and M+(!S) +IX-(2IT)corre-sponding with the possible configurations. Now as-suming that transitions are possible only betweenstates of equal species, it follows from table 5 thatdiabatic transitions from the IX ground state to the

IX" (-11) state are allowed except in collinear (C^y)collisions. We note that C^v configuration is not de-fined for the interhalogens, however, for the homonu-clear halogens transitions for broadside (C2V) collisionsare not allowed.

Unfortunately there is no experimental data avail-able on the potential energy curves of the excitedstates of IX-. The 2Z+^ 22+ (ultraviolet) and the2 2* -* 2 ng (infrared) transitions are observed in dopedalkali-halide crystals as absorption peaks for the Xjcolour centers [23]. We may expect, however, thatthese transitions will differ from those which wouldbe observed in the "free" X2 molecule, i.e., in the ab-sence of external constraints.

Due to configuration interaction of the excitedstates, with the valence band of the crystal, the energylevels in the X, ion will lower in relation to the X^ground state. This holds especially for the UV transi-tions [24]. Because cf the uncertainties involved inthe construction of the potential curves of the excitedstates, we restrict ourselves to construct the curve forthe 2rii state only.

We have fixed the potential curve for the 2IL stateof 1X~ in three points:

(1) Trie position of the asymptote for dissociationinto I~(1S0) + C1(2P?) relative to the asymptote forI(2Ps) + Cl-( ' So) wfiich is accurately known [27].

(2) The vertical energy difference between the po-tential minimum of the IX~ molecular ground stateand the IX~(2n>) slate corresponds with the

2 + "* Hi optical absorption transition. However,this value is only known for the homonuclear halogens(Clj : 1.65 eV; Brj : 1.65 eV; ij • I -55 eV) [23]. MOarguments indicate the lj value as the best approachfor both IBr- andlCI".

(3) The vertical energy difference between the po-

- 22 -

Iahle6( jKuljied jnd measured threshold energies fur neiiaiive atom-

ic ion production m eV'

K +

Na +K +Na +

K +Na +K +Na +

IBrIBrKIICiBr2

[2 *

h

f l h r<Br ».-

measured

2.803.652.903 652.953.75_

'•«hr«f' >

calculatedIroni cq.(4)

2.793.592.873.682.953.75_

-

' t h r " »

measured

3.35X

3.55X

-

2.823.62

calculatedfrom eq.(4)

3.093.893.434.23-

2.823.62

tential minimum of the IX molecular ground stateand the IX~(3rk) state, i.e., EAV for the formation of(X-(-rii), is determined by the threshold for I~ for-mation (table 6).

In the construction the vibrational motion of IX hasbeen ignored. In later calculations, however, the effectof vi^rational time of IX is taken into account. The re-sulting curves are shown in fiss. 3 and 4. As to this con-struction we remark: In the first place the potentialcurves for these states are indeed repulsive as was pre-dicted by the MO analysis; secondly the ICl~(2rU) po-tential curve is flatter than the one of IBr".

We may expect that the repulsion for IX~(2lli) isless than the corresponding repulsion for If or Xïsince for [X~(2fïi) the electron wii! "feel" the greaterEA of X as I" is brought close. Taking into accountthe greater EA difference of ICI compared to that of IBrthe repulsion for ICI" is smaller than for lBr~ resul-ting in a flatter potential curve for ICI".

3.3.2. Threshold for l~ productionFurther evidence that the IX-(2fh) state is involved

in the I~ production comes from a consideration ofthe threshold energy. From the situation at infinite se-paration we can calculate the threshold for 1~ or X~fragmentation from the relation

^ DgOXJ-EACX). (4)

All these values are accurately known*. Table 6 gives

/:',],,. as measured and calculated from (4) including forcompleteness some values for homonuclear halogens.In ^ase ot the homonuclear ones (he agreement is ex-cellent. Also the Br resp. Cl theoretical thresholdsfor the heteronuelear molecules are in agreement withthe experimental values. For the I" threshold, how-ever, the experiments show a threshold- which is 0.25eV higher than the theoretical one in case of IBr. 0.1eV in case of ICI.

While the subtraction procedure used to correct theI curves does introduce some extra noise in the data,the shift for IBr is well beyond experimental error andfor ICI of the order of experimental uncertainty. Bothvalues are each the result of two completely indepen-dent measurements using different settings of the ve-locity selector.

We assume the explanation for these discrepanciesis that the formation of P" is due to dissociation fromthe slightly repulsive 2 ft, state. Jn the previous sectionwe mentioned the difference of steepness of the 2n±potential curves for IBr" and ICI ~. Assuming that theelectron jump to the 2fli state is a vertical Franck—Condon transition or at least does not deviate toomuch from vertical, the smaller threshold shift in theI~ production for ICI may be due to the larger widthof its lowest vibrational wavefunction, the vibrationaltimes of ICI and IBr are 0.9 X ] 0~ ' 3 sec and1.3 X 10" ! 3 sec respectively.

3.3.3. Simplified model of the collisionsThe role of curve crossings in inelastic collisions

has been extensively explored in terms of the Landau-Zener-Stueckelberg theory (henceforth abbreviatedLZS theory) and its extentions. In this semiclassical ap-proximation it is supposed that transitions are well lo-calized in a very narrow zone around Rc, where thepseudocrossing of the potential surfaces occurs. Incase of a collision a crossing must be traversed twice;in this approach both transitions can be treated inde-pendently, so we can write for the total probabilityfor excitation via an avoided crossing

(5)

* See [251 for ionization potentials, (26) for dissociationenergies, and [271 for electron affinities.

- 23 -

in wh ich / ; is the diabalic tiansition probability, given

by

(6)

where we luve specialized 'he LZS expression to thediabatic potentials near the crossing//j ] = 0 and//-)•> == I,'/? + AA'(au). Heie u is the radial velocity at thecrossing radius/?c.

This theory only holds for a two-particle interactionas said and is too simple Tor treating a three-particleinteraction like the M + IX collision process. In colli-sions with molecules the transition probability strong-ly depends on vibrational excitation and stretching ofthe bond of the molecular ion. For the case whereIX is formed in the repulsive -Hi state, a stretchingof the r - X bond may occur by the repulsive forcein the molecular ion. Since EA(IX) varies appreciablywith the bond length due to the steepness of the po-tential well of IX, p will be quite different at the se-cond crossing (figs. 3 and 4). Furthermore the cou-pling matrix element//], is strongly dependent on therelative orientation of both collision partners due tothe conical intersection of the potential surfaces in-volved. Self-evidently Hi-) is very sensitive for theshapes of the potential surfaces.

In analysing their measurements for negative atom-ic ion formation in the alkali atom-homonuclearhalogen molecule collisions Baede et al. [3] presenteda simple modification of the curve crossing model. Inthis type of collisions two extrema are distinguishedfor the calculation of the total transition probability:on the one hand it is assumed that no stretching of thebond occurs for the formation of the parent molecularion, on the ether that for the formation of the frag-ment atomic ion the bond has stretched completely.This has important physical consequences since there isa very large difference between the diabatic transitionprobabilities for K(or Na) •- X2. K - X and Na - X inthe eV region

(K X 2 ) : / / , , / ? c = 1.75 X 10 2 au [2]

(K - X) : / / | 2 / ? c = 1.15 X 10 3 au [28]

(Na X) : / / I 2 /? c=3.4 X 10" 2 au [2]

The model shows the characteristic difference in the

atomic ion cross sections between K and Na: the com-puted X " cross section peaks sharply for K just abovethreshold - although not that much as has been ob-served experimentally, to which we shall return later— whereas the computed X cross section for Napeaks smoothly at much higher energy.

In our model we also take into account situationsin which the dissociation is not complete. In thismore realistic approximation the stretching of thebond is directly correlated with the velocity of disso-ciation, which is dominated by the force due to therepulsive potential of the 2IL state. Moreover theavailable time for stretching is closely linked up withthe collision time. Our schematic model of the colli-sion is the following one. We assume that at the firstciossing according to the LZS theory, part of the mole-cules make a diabatic transition, the other fraction anadiabatic one. In case of the adiabatic transition IX~(-S+) is formed, which we do not consider further.In case of a diabatic transition, when the impact para-meter is small enough, an ianer crossing with the 2flion state is passed. At this crossing IX-(2I1) may beformed. During collision stretching of the bond of themolecular ion takes place leading to an outer crossingwith different crossing radius than the incoming one.The LZS diabatic transition probability for the out-going crossing is denoted in this case by p j , wherep'bis a function of collision time and the collision part-ners.

We make the following simplifying assumptions:(1) The diatomic molecule remains in its original

electronic and vibrational state if no electron jumpoccurs.

(2) A fraction ƒ of the collisions leads to an innercrossing with the 2I1^ state and this fraction is inde-pendent of energy.

(3) The stretching of the IX" molecular ion is notdisturbed by the field of the M+ alkali ion. Thestretching is only due to the repulsive force of the2H> potential. Initial relative motion of I and X canbe neglected.

(4) The stretching time equals the collision time:'"stretch = r-oU- H e r e TcoUis approximated by putting

where /?Cj and RCQ are the crossing radii belonging tothe inner and outer crossing respectively

- 24 -

and v is ihe radial velocity * constant during the col-lision.

(5) At the outgoing crossing a vertical transitiontakes place between the stretched IX~ and the IX(' Ï )curve.

T!ie second assumption amounts to saying that thediabatic transition at the first crossing is energy inde-pendent. While not strictly true it is a useful simplifi-cation at this level of detail. The third assumption iscertainly an over-simplification but holds in first ap-proximation up to a stretching of about 9 au, i.e.. forthe involved energy region [12]. The fifth assumptionis based upon a comparison of the time needed for theelectron jump ( ~ I0~ ' 5 sec) with the vibrationaltime of the 1X~ molecular ion ( ~ 10~13 sec).

Two passes for I" production are available, thesum of which yields the total transition probability/^:

(1) The electron jump occurs at the second crossing,which means that the total probability Plb for thispass is proportional to pb (1 - pb). But as pb — 0 in-dependent of the restive energy for all alkalis, theincoming crossing is diabatically passed and conse-quently we may neglect this possibility.

(2) The elctron jump occurs at the first crossingwith probability f(\ - pb)\ then assumption 4 im-plies that having reached the second crossing theI ~ - X molecule has stretched its bond length, so thiscrossing is passed diabatically with a modified proba-bility p'b. Thus for this pass the total probability P2b

is given by.

Thus for the total transition probability of bothchannels it follows:

The total inelastic cross section at a certain velocity isobtained by integrating over 6

£maxQ(U)=27TJ Pbbdb . (8)

addition that ph, and p'b are given by the LZS the-ory by (6), where Rc is given by

LA(IX)| J (au). (9)

Here EA(1X) is the electron affinity connected withthe -Ib slate and thus strongly dependent on the in-ternuclear distance d. The coupling matrix element/ƒ,-> may be obtained from the semi-classical relationof Olson, Smith and Bauer [29]

l exp[-0.86*c*] , (10)

Neglecting dipole interactions the diabatic potentialsat the crossing are given by H{](R)=C and H-tfiR)~ 1 IR + At' (au), and thus 6m a x = Rc. We assume in

in whichfl* = ! ( a + 7 ) # c , / , =a 2 /2and / 2 = 72/2./ , and /2 are the ionization potentials of thé transfer-red electron in respectively the reactant state and theproduct state. All quantities are in atomic units.

We have calculated Hn as a function of the stretch-ing of the J'-X bond in the 2iTi state. It appearsthat //j2 as a function of \jRc is strongly dependenton the alkali atom involved. No dependence is shownfor the interhalogen molecule, IBr or Id , which is notsurprising since there arc only minor differences be-tween IBr and Id . In fig. 6 we have plotted (HnRc)

2

as a function of the internuclear distance d for the dif-ferent alkalis: for clearness the plot also shows the cross-ing radius/?cversus</. With arrows we have indicatedthe maximum stretchings for K, Na and Li which self-evidently refer to the threshold energies. According toeq. (6) the plot offers the crucial information on thedifferences of the transition probability function P be-tween K, Na and Li. In the first place we note that atthe equilibrium distance of the molecular ground state(H]2RC)2 - 10~2 au,which implies^ - 0 for K, Naand Li in the entire energy interval. Secondly we notethat at the same stretching of the \~ - X bond the fac-tor (Nl2Rc)

2 differs some orders of magnitude for Kand Na (or Li). Moreover we see that for Li the stretch-ing at threshold is negligible.

Above we have explained the construction of therepulsive potential of the 2rii state. From the poten-tial the repulsive force acting'between the I" and Xatom is calculated. This gives a relation betweenstretching time and internuclear bond distanced orcrossing radiusRc, using eq. (9). Since the stretching

- 25 -

I

I I

O 2 4 6 6 10 121NTERNUCLEAR DISTANCE d ( a u )

Fig. 6. Dependence of//12 and Rc on bond stretching. Theshown arrows are correlated with the maximum stretchings.

time is equal to the collision time, the time scales ofthe M-IX interaction and the stretching are con-nected. According to eq. (7) it follows for our energyrange:

for Li: Ph — 0, since p j - p^ — 0,forK :Pb~p-b.

In case of Na.pj^is not as small as for Li, but still quitesmall. Consequently the I" fragmentation for K. + IXdirectly depends on the diabatic transition probabilityat the second crossing, i.e., with a stretched molecule.For K we do expect I" formation, for Li definitelynot, while Na is an intermediate case.

The calculations performed for K + IC1 and K + IBrhave shown that the energy dependence of p is verysensitive on the behaviour of the repulsive potential,i.e.. both the slope of the curve at the equilibrium inter-nuclear distance of the molecular ground state and theionization potential / (^Pj) of about 0.) eV. An in-crease in J(^Ui) of about 0.1 eV results in a drastic

3 i

f> - 90

* = 60

* = 45'

f-M

CM ENEfiGV teï)

Fig. 7. Calculated total transition probability for the forma-tion of 1 in the collision process K + IC1. For the meaning of<J> see text.

change in the energy dependence. It can be shownthat due to the smaller stretching the velocity scaleis shifted with about a factor of 2 to lower veiocitiei.On the other hand a decrease of/(2n> ) which seems,however, incompatible with the experimentally ob-served threshold value, has a favourable effect on thehigh energy tail. A similar effect for IBr is caused bya steeper slope of the potential curve with say 25%.This is the case when the potential energy above 'heequilibrium molecular ion ground state is about0.1 eV lower.

The calculated P (heavy line) for the 1" formationin K + 1C1 is shown in fig. 7 as a function of relativeenergy E. The LZS theory does not account for thethreshold behaviour in endothermic processes, so wemust fold in a rapid decrease in P as E approaches theinelastic energy loss At' = £ t h r given by eq. (4).

As already mentioned implicitly P appears to dropvery quickly at high energies, which is not in agreementwith the observed I" cross section. It may be thatquenching also occurs at transitions to the -FIL stateas is the case for transitions to the molecular ionground state [13]. In this case the real potential curveof the 2IL state will be sieeper with say 0.1 eV andas said this results in a better agreement with thehigher energies.

3.3.4. Role of'anisotropy }2The simplified model developed above has success-

fully accounted for the alkali dependence of the mea-surements but does not explain the nearly constant

- 26 -

high energy tail found in K + IX -»I . A possiblesource of the discrepancy lies in the neglect so far ofthe anisntropic nature of the interaction matrix ele-ment / / p .

Recent experiments [30J provide evidence that thereaction probability strongly depends on the relativeorientation of the collision partners. Trajectory calcu-lations of Diiren [31 j on K + Br2 have shown thatchemi-ionization is strongly favoured at transitionangles 0 near 90°. in which 0 denotes the ungle of themolecular axis with respect to the alkali atom. Accord-ing to Anderson [32] the covalent-ionic coupling ener-gy / / j , varies as cos2 <p. This relation applies to theconical intersection of the potential surfaces belongingto the covalent M + X2(' Zp state and the ionicM+ +.XJ ( 2 Ins ta t e .

We note that the quasi-molecular complex, whichis formed during die collision will preferably have theiodine, as the least electronegative atom, in the centralposition [33 j . Information about the apex angle of thisconfiguration can be obtained from a consideration ofthe semi-empirical MO analysis of Walsh [34]. His dia-grams show the variation of the orbital energies inchanging the apex angle from 180°(linear) to 90°(bent). In particular for tri-atomic molecules ABC con-taining 15 valence electrons it is shown that they willbe linear in their ground state. So far as is knownthere are no exceptions to this rule. Walsh states thatit is probably a very common feature that the groundstate and the excited states of polyatomic moleculeshave different shapes. Indeed it seems reasonable toassume that the quasi-molecule in case of I~ formationis formed in a bent excited state: the unpaired electronwhich is in an orbital stabilizing the linear form is nowpromoted to the 4a' orbital, which strongly favoursbending. However, the degree of bending is difficultto estimate. We may write now

In particular we put, following Anderson [32] ,/(0)= sin2<£ since this agrees with IIi2

= 0<=^' <t> ~ 0° forcrossings involving the 2 n state (see table 5). In fig. 7the result is given for several values of 0. illustratingthe importance of the effect of the conical curve cross-ing.

A weighted average over 4> would give results for the

high energy tail in closer agreement to the near con-stant value found experimentally. However, there is alack of information for going into more details (com-pare for instance the homonuclear case, in which//|2 = 0 for both the linear and the isosceles configu-ration; that means that the sin20 dependence shouldperhaps be replaced by a sin2 2tj> dependence). Due tothe uncertainties in the angular dependence of Hl2

and the preferred geometry of the reaction complexit is not surprising that the calculated transition prob-ability is not in strict agreement with the experimentbut on the other hand the analysis makes at least clearthe striking difference between K, Na and Li for theenergy range concerned. It seems probable that thecollisions in bent configuration are weighted more'ïeavily.

3.3.5. Role of excited states in homonuclear halogensEvidence for the participation of the excited state

can also be obtained from the studies of type M +X2 -*- M + + X + X- [3].

In the analysis of the fragment ion cross sectionsgiven in [3j, no attention is paid to the possible roleof the excited states. Since / is so much smaller forthese states than for the ground state it was assumedthat they are strongly unfavoured and moreover for-mation of excited X had not been observed before[351.

In the K + X2 experiments it is found that the X~cross sections peak sharply at energies just ibove thres-hold, whereas the sodium cross sections have a smoothmaximum at much higher energies. The explanationbased upon a modified LZS theory indeed forecaststhis different behaviour for K and Na, but in case ofK not the sharp peaks which are observed. If we as-sume that in these processes with K the formation ofX" does not only come from the molecular ion groundstate but also from the excited X2"(2ngi) state, we canroughly correct the fragment ion cross sections usingour results on the interhalogens. This gives fragmention cross sections which are in much better agreementwith the measurements.

Further experimental work on these systems seemshighly desirable. Possible extensions include measure-ments at higher enemies and measurements with Csand Rb. Measurements with vibrationally excited tar-get molecules are in preparation now.

- 27 -

Acknowledgements

The authors wish to thank Mr. A. Mayers for assis-tance with the expeumenf They like to thankDr. A.I. de Vries lor his simulating discussions.This work is part ot" the research program of theStichting voor Fundamenteel Onder/ock der Materie(Foundation for Fundamental Research on Matter)and was made possible by financial support from theNederlandse Organisatie voor Zuiver-WetenschappelijkOnderzoek (Netherlands Organi/ation for the Advance-ment of Pure Research).

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(24) T.L. Gilbert, Nato Summer school in solid state physics,Gent. Belgium (Sept., 1966).

| 2 5 | C.E. Moore, Circ. 467, Nat. Bur. Standards (USA).|26] A.G. Gaydon, Dissociation energies, 3rd Ed. (Chapman

and Hall. London. 1968).|27] R.S. Berry and C.W. Reimann, J.Chem. Phys. 38 (1963)

1540;B. Steiner. M.L. Seman and L.M. Branscomb, in: Atomiccollision processes, Proc. 3rd Intern. Conf. Phys. Electron.Atom. Coll. (London. 1963), ed. M.R.C. McDowell(North-Holland, Amsterdam, 1964).

|28] A.M.C. Moutinho. J. Aten and J. Los. Physica 53 (1971)471.

|29] R.E. Olson. F.T. Smith and E. Bauer, Appl. Opt. 10(1971)1848.

[30] Y.T. Lee. R.J. Gordon and D.R. Herschbach. J. Chem.Phys. 54(1971)2410;J.D. McDonald. P.R. LeBreton, Y.T. Lee and D.R.Herschbach. J. Chem. Phys. 56 (1972) 769;R.K. Preston and J.C. Tully, J. Chem. Phys. 54 (1971)4297;J. Krenos. R.K. Preston, R. Wolfgang and J. Tully,Chem. Phys. Letters 10 (1971) 17.

[31] R. DUren, private communication.[32] R.A. Anderson. Ph. D. Thesis. Harvard University, USA

(1968).[33] S.D. Pcyerimhoff and R.J. Buenker, J. Chem. Phys. 49

(1968)2473.[34] A.D. Walsh. J. Chem. Soc. (London) (1953) 2266;

M. Green a-id J.W. Linnet, Trans. Far. Soc. 57 (1961) 1.[35] D.R. llerschbach. Advan. Chem. Phys. 10 (1966) 384.

- 29 -

C H A P T E R II

ION PAIR FORMATION IN ALKALI~SFg COLLISIONS:DEPENDENCE ON COLLISIONAL AND VIBRATIONAL ENERGY

ï

- 30 -

ChcmiiMl I'hysKs 10(1975» 2 3 5 - 2 5 9' Nnrth-llollaiid Publishing Company

ION PAIR FORMATION IN ALKALI-SF6 COLLISIONS:DEPENDENCE ON COLLISION AL AND VIBRATIONAL ENERGY

MM. HUBERS and J. LOSFOM-Instituut voor Atoom- en Molecuulfysica, Kruislaan 407, AmstcrdamlWgm., The Netherlands

Received 9 April 1975

The dependence of ion paii formation in collisions of fast alkali atoms (K. Na and Li) with SF6 on the initial relativekinetic energy and the internal energy of the target molecule has been studied by the crossed molecular beam method.Using a mass spectrometer we have measured total cross sections for negative ion formation as a function of translationaland internal energy. Collision energies ranged from threshold up to 35 eV and SFj source temperatures were varied from300 K to 850 K.

By means of an inverse Laplace transform of the measured cross sections, we have determined total specific cross sec-tions for each negative ion depending on the SF$ vibrational energy and at fixed relative kinetic energy.

The relative importance of both collisional and internal energy in promoting the electron transfer process is discussedfor the various reaction channels in terms of a collision model. An essential feature of this model is the stretching of theS- F molecular ion bond during the collision. The product ions show complete relaxation in the threshold region, i.e.,vibrational and collisional energy are equivalent: This holds for the SFg" formation only near threshold and for the SFJand F~ formation up to about 2 eV above threshold. In the post-threshold region the effect of the internal energy on thecross section dominates over that of the translational energy.

From these measurements the adiabatic electron affinity ofSFg is inferred to be 0.32 ± 0.15 eV, T= OK. Some otherthermodynamic data are deduced: EA(SFS) > 2.9 ± 0.1 eV (T = 300 K) and Z>0<SFf -F) = 1.0 ± 0.1 eV.

1. Introduction

In reactive collisions between alkali atoms andhalogen compounds the chemical forces are inducedby the transfer of an electron [1]. The electron trans-fer is thought to proceed through coupling of the ion-ic and covalent states at the point, where the diabaticpotentials of these states cross. The prototype of thesecharje transfer reactions is K + Br2 -* KBr + Br. Atenergies exceeding the difference between the ioniza-tion potential and the electron affinity of the two par-ticles involved, this electron transfer might lead to ionpair fortnation. These processes are endoergic withthreshold energies in the range of 0.S up to 20 eV. Thestudy of these electron transfer processes has only be-come possible due to the development of new tech-niques for producing atomic beams in the eV range.

Atom-atom collisions are well described in termsof a two-state approximation by the Landau-Zenertheory. The description for atom—molecule collisions,

however, is much more complicated. Single curvecrossings should be replaced by multiple surface cross-ings and one should take into account the angular de-pendence of both the potential energy surfaces andthe electronic coupling matrix elements.

The translational and angular dependence of thecross section for ion pair formation is being intensive-ly studied at the moment [2J. However, there are fewexperimental data available on the effect of vibration-al or electronic excitation on the cross section. A studyof the modes of energy which have to be activated inorder to initiate reaction is of fundamental importancein chemical reactions. Moreover, tittle is known as towhat extent internal degrees of freedom of the mole-cule play a role in the scattering pattern in fast atom-molecule collisions.

Reactive cross sections are reported to dependstrongly on the excitation of internal energy states.Experiments on ion pair formation might shed somelight upon the influence of internal energy on reactive

- 31 -

processes. Two types of limiting cases can be distin-guished: ('lose to threshold for ion pair formationwhere the nuclei af the molecules involved are notfixed during collision, and at high energies where ro-tational and vibrational motions are "frozen out".The first case provides insight into the questionwhether internal energy leads to enhancement of thecross section, i.e., whether the cross section for ionpair formation in the outgoing channel is a functionof the translational, vibrational or total energy. Thesecond limiting case reveals whether the jumping dis-tance of the electron is a function of internal energy.

Very recently, crossed molecular beam studies ofcollision-induced dissociation of alkali halides [3] andthallium halides [4] have been reported in ."-v<ich thedependence of the polar dissociation on the internalenergy of the target molecules was investigated in thenear threshold energy region. These experiments haverevealed that vibrational excitation in the target mole-cule is far more effective in promoting dissociationthan an equivalent amount of translational energy ofthe reactants. These experimental findings are parallelto results of the endothermic exchange reaction, AB+ C -* A + BC; the analogy is that in both types ofprocesses the barrier to reaction lies "Jong the coordi-nate corresponding to stretching of the bond under at-tack [5].

At the same time similar measurements by theFOM-group (Amsterdam) were reported for the elec-tron transfer reaction of alkali atoms with some halo-gen [6] and methylhalogen [7] molecules. These ex-periments revealed features quite different from thecollision-induced dissociation cross sections. The in-ternal energy is only effective in overcoming the endo-ergicity of the reaction.

In studies of ion pair formation for alkali atom-halogen molecule collisions, it has been argued [17,27]that the electron affinity, which is derived from thethreshold for parent ion formation, is the adiabaticone. because the high vibrational states of the molec-ular ion are quenched [8]. More insight into thismechanism of deactivation near threshold can be ob-tained by studying the dependence of ion formationboth on the internal excitation of the target moieculeand on the translational excitation in the thresholdenergy range in a charge transfer process.

This paper is concerned with molecular beam meas-urements of fast alkali atom-SF6 collisions. SF6 is

known as a very effective quencher; therefore the at-tachment of low energy electrons to SF6 has been thesubject of much research [9]. Recently Fehsenfeld[10] and Chen and Chantry [11] reported that theratio of SF57SFg ion formation at essentially zeroenergy is strongly dependent on temperature. How-ever, these results differ by some orders of magnitude.Spence and Schulz [12] have observed that the energyintegrated cross section for total negative ion produc-tion at low electron energies is temperature indepen-dent. These results are explained by assuming the for-mation of an excited SFg compound state, of whichonly the branching ratios fur dissociation (SF^ , SFJ,F"~) but not the excitation, depend upon the initialthermal energy.

John Ross' group at MIT [13] have recently re-ported a study of the temperature dependence of non-reactive scattering of K atoms, at thermal energiesfrom SFg as a function of scattering angle. They con-cluded that only the stretching vibrational modes ef-fect the reactivity with K. Recently two studies haveappeared on the collisional ionization of SF6 by Cs,both at low collision energies (up to 17 eV) [14] andat higher collision energies (up to 150 eV) [15]. Afterthe completion of this manuscript, Leffert et al.published a short note on the ion pair formation ofCs with SF6 for energies in the threshold region [16].

In this paper we present results on the total crosssections for negative ion formation, produced in elec-tron transfer reactions of fast alkali atoms with SF6.The cross sections have been determined for each neg-ative product ion as a function of translational andinternal energy. Collision energies range from thresh-old up to 35 eV and SF6 source temperatures arevaried from 300 K to about 900 K.

The relative importance of these energy modes tothe various reaction channels, is discussed both forthe threshold and the post-threshold regions.

In the present experiments the cross sections de-pend on the collision energy of the particles and thetemperature of the target gas. We may express themeasured cross section as a summation OVP. all -according to a Maxwell-Boltzmann distribution -populated vibrational energy levels of the SF6 mole-cule times their specific cross section. The latter ischaracterized only by the vibrational energy. From theexperiment, an exponential relationship has beenfound between the cross section and the SFg tempera-

- 32 -

turc. at fixed collision energy.By means of an inverse Laplace transform we then

reduced the experimental total cross sections for ionpair formation to specific cross sections. In this wayinformation is obtained on the role of internal energymodes in the process of ion pair formation. Overallfeatures of the SF6 potential energy curves could thenbe derived as a function of the (S-F) coordinate.This procedure also allows us to determine the realadiabatic electron affinity. The deconvolution of crosssections as a function of internal energy allows theextrapolation to zero internal energy. From the disso-ciative threshold measurements we have deduced alower limit to the electron affinity of SF5 and the dis-sociation energy of SFg.

2. Experimental method

The experimental set up has been published in de-tail elsewhere [17] and therefore only a brief outlineis given here. The apparatus consists of a four-stagedifferentially pumped molecular beam machine (fig. 1):(1) a sputter source, consisting of an Ar+ ion beamsource and ? water-cooled rotating alkali target, (2) amechanical velocity selector, with 10.5% resolutionFWHM, (3) a surface ionization detector, consistingof an iridium wire of 0.1 mm diameter operated atabout 1325 K and which is continuously oxygenated,and (4) an interaction chamber.

I;ig. 1. Schernatir diagram of the apparatus. 1 = unoplasma-tron, 2 = alkali target, 3 = collisnating slits, 4 = mechanicalvelocity selector, 5 = surface ionization detector, 6 = collisionregion, 7 = secondary beam, 8 = extraction field, 9 = magnet,10= multiplier.

In the interaction chamber a well-collimated beamof alkali atoms crosses at right angles with a thermalSF6 molecular beam. The ions formed in the collisioncentre are extracted in a uniform electric field, subse-quently focused and mass-analysed in a magnetic massspectrometer and counted digitally.

The secondary SFg beam effuses from below througha slit aperture (0.1 mm by 4 mm) in a thin-wallednickel capillary tube (outside diameter 1.6 mm). TheNi capillary is electrically heated and the temperature ismeasured using an insulated chromel-alumel thermo-couple, mounted in an AI2O3 capillary tube, insidethe Ni tubing. During the measurements, a chromel-alumel thermocouple which is spot welded to the wallof the tube near the slit was used to monitor andstabilize the oven temperature by electronically con-troling the heating power. The SF6 gas temperatureis given by the insulated thermocouple to within 2.5per cent. The drift of the oven temperature during arun was less than 5 K. Both the oven and the coldtrap located opposite to it were set at the collisioncentre extraction voltage (— 1.8 kV) in order to min-imize the distortion of the homogeneous extractionfield. The ion detection efficiency is independent ofthe SFg molecular speed; because of the high extrac-tion field strength (450 V/cm). This has been checkedby transmission measurements of the extraction-massspectrometer system.

At working conditions the pressure in the interac-tion region was generally about 3 X 10~6 torr. Themass flow of the SFg secondary beam is kept constantby a thermostated needle valve, which has a very largepumping resistance with respect to that of the ovenslit. This makes it possible to use the technique intro-duced by Moutinho et al. [6], to convert the ion sig-nal at a given temperature to a cross section relativeto the room temperature cross section. The densityin the interaction region at constant mass flow isproportional to J " 1 ' 2 .

Of the utmost importance is the pumping speed inthe interaction chamber, as the background SFg pres-sure has to be small with respect to the pressure inthe secondary beam. The maximum contribution ofions due to background SFg is estimated to be at most4 per cent.

- 33 -

3. Experimental results and data evaluation

3.1. Son-velocity selected spectra

The unselected primary alkali atom beam has trans-lational energies up to some hundreds of eV andtherefore it is possible that positive molecular ionsare formed by direct ionization. Fig. 2 gives the posi-tive ion spectrum due to collisions of SFg with an un-selected Li beam. The Li+ peak is due to electrontransfer from Li to SF6. The SF6 spectrum is quitesimilar to a direct electron impact spectrum [18,19];the SF3 peak is dominant, accompanied by a weakSF| peak and a slightly stronger SF5 peak while theSFg ion is missing. The lower mass peaks S+, SF* andSF2 have a relatively strong intensity compared withan electron impact spectrum. Nevertheless the overallfeatures support the suggestion that direct ionizationis responsible for the positive ion spectrum. A secondobservation is that in the negative ion spectrum withan unselected Li beam, the Li" peak has a very lowintensity. This supports the argument that electrontransfer is not the mechanism for the positive molec-ular ion. formation. The Na+ peak is due to a Na im-purity in the Li target.

The negative molecular ion spectrum with an un-selected alkali beam shows all the fragments which areobserved in negative ion mass spectrometry. Here,however, a comparison is rather useless, as negativeion formation due to electron impact occurs by attach-ment or dissociative attachment. This has been clearlyshown by Harland and Thynne [19] and by Lehmann[20], who measured the dependence of the cross sec-tions for the different ions on the electron impactenergy. The energy measurements explicitly show theresonance behaviour of negative ion formation in elec-tron collisions. In the case of collisions of SF6 with analkali atom, however, electron transfer is responsiblefcr the negative ion formation which is rather indepen-dent on the incident energy except close to threshold.The overall mass spectrum shows a group of ions withintensities too small to be measured with velocity se-lected beams, viz. SF~,SF2 and SFJ. The SF4~ peakcould not be found but a weak signal due to this masswould have been masked by the strong SFJ peak. Theother ions, F , F2 , SFj" and SFg" are abundant enoughto be measured with an energy selected primary beam.This is in agreement with the results of Lehmann [20]

Na S SF* SF/SFfSlf SF*

0 K) 25 50 75 100 125 150 200 250»• ion mass (amu)

Fig. 2. Positive ion mass spectruir. of Li + SFj obtained usinga non-velocity selected primary Li beam with the SFj sourceat room temperature.

who showed that the cross sections for the formationof the first group of ions in the electron impact energyrange of 0-25 eV are one to two orders of magnitudesmaller than of the second group.

It should be remarked here that negative ion massspectrometry with a charge transfer source is veryanalogous to positive ion mass spectrometry with anelectron impact source. In both cases the ion yieldstrongly rises above threshold after wich it becomesonly weakly dependent upon energy. This has beenobserved by Rothe even with an atom as heavy ascesium [15].

However, negative ion mass spectrometry with anelectron impact source is strongly dependent on theelectron energy due to the resonance character of theelectron attachment.

3.2. Velocity selected spectra

We have measured total cross sections for ion pairformation in alkali atom-SF6 molecule collisions asa function of the relative kinetic energy and the inter-nal energy of the SF6 target molecule. The alkali,atoms used in these experiments were Li, Na and K.The center of mass energy range extends from thresh-old energy to about 7 eV, 20 eV and 35 eV respective-ly. By changing the temperature of the oven, over arange of 300 K to about 900 K, the internal energy ofthe SFg molecule was varied.

- 34 -

The relative cross sections for the production ofnegative ions at room temperature are shown in figs.3 5. In the cases of K and Na the formation of theparent SF6 ion and the fragment ions SFJ, F2 andF~ are observed; in the case of Li only SFJ and SFJ.A real onset for the production of F~ could not beobserved at room temperature since the endothermic-ity of this reaction is too high. The Li energies are re-latively low because of the use of a mechanical velo-city selector. For all alkalis the F~ cross sectionshows long tailing at low energies. The tailing whichwe observe for both the SFJ and the SFJ productionfor Li + SF6 is most likely due to Na impurities in theLi target. Fn the unselected mass spectrum for the for-mation of positive ions, mass 23 (Na) is discernedwith an intensity of about 1% of the Li+ signal (fig. 2).

The vertical scale is given in arbitrary units. Thecross sections for formation of different ionic species,however, are internally consistent, as all ion signalsare normalized with respect to the maximal SFJ ionyield. We estimate an error of about 5% in the relativecross sections.

The measurements as a function of collision energyat elevated temperatures are shown in figs. 6—10. In

order to compare cross sections which are obtainedat different oven temperatures, the measured ion sig-nals have been multiplied by (7"/rR)1/2, where 7"isthe absolute SF6 gas temperature and 7"R is the abso-lute room temperature. As already stated this correc-tion accounts for the change in particle density in theSFg beam since the molecular velocities are directlyproportional to T1^, while the flux has been keptconstant. The increase in the relative translationalvelocity at elevated temperatures can be neglected aseven at the highest temperature of 845 K this resultsin a correction on the relative energy of the collidingparticles of 0.01 eV in the most unfavourable case ofpotassium.

The measurements have been performed in twoways: (1) as a function of the primary beam energy,at fixed temperature of the secondary beam oven foreach negative ion (300,445,545,650,745 and 845 K);(2) as a function of oven temperature, at fixed prima-ry beam energy. The first method was used to findthe overall features of the cross sections as a functionof t'-jislational energy at different temperatures. Thesecond method, however, yields more accurate meas-urements and has been used for evaluation of the data.

A 6

CM. ENERGY <eV)

Tig. 3. Total cross sections for negative ion formation in Li-SFj collisions as a function of cm. kinetic energy with the SF4

source at room temperature. The vertical scale is given in arbitrary units; however, the same units are u<*d in figs. 6, 7 ,11,14 andIS.

- 35 -

15-

e 12CM ENERGY (*V)

16 20

Fig. 4. Total cross sections for negative ion formation in Na-SF 6 collisions as a function of cm. kinetic energy with the SF6

source at room temperature. The vertical scute is given in arbitrary units; however, the same units are used in figs. >, 9 ,10 ,12 ,16 ,17. 20 and 21.

ir

15-

10-

5

K+SFs T=300K

SFi

DO 0 0 0

SFsW X X X X X X X X X X X X X X X X X X X X X

F2

10 20

CM ENERGY (eV)

30

Tig. S. Total ao&s actions for negative ion formation in K-SF^ collisions as st function of cm. kinetic energy with the SF6 sourceat room temperature The vertical scale is given in arbitrary units; however, the same units are used in figs. 13,18,19 and 22.

- 36 -

15-

~IO-

c3

> .

bit

* 5 -

! " - « T =

^ T =

o T =

SF6" ( « 7 5 )300 K

545 K

8 4 5 K

a

2 i.C M ENERGY (eV)

Fig. 6. Total cross sections for parent ion formation in Li-SFg collisions as a function of cm. kinetic energy at various SF^source temperatures (see fig. 3).

U 6CM ENERGY(eV)

10

Fig. 7. Total cross sections for SFjT formation intemperatures (see fig. 3).

collisions as a function of cm. kinetic energy at various SF« source

- 37 -

j Na • SF6 SF " (x 10)

I x T r 300Xi o T = 845 K

35-1

«XXX»

tv

CM. ENERGY (eV)

o o o o

* i

16 Ir j

Fig. 8. Total cross sections for SFj formation in Na-SFg collisions as a function of cm. kinetic energy at two SF$ source tem-peratures (see fig. 4).

15-

x T = 300Ko T = 445Kv T = 545K" T =845K

CM ENERGY

Fig. 9. Total cross sections for SFj' forma lion in Na -SFj collisions as a function of cm. kinetic energy at various SFj sourcetemperatures (see Tig. 4).

- 38 -

+ SF6- F~U2)

* T = 300Ka T = 4A5KA T = 7A0K" T = 845 K

8C M ENERGY

20

Fig. 10. Total cross sections for F formation in Na-SI;6 collisions as u function of cm. kinetic energy at various SFj souicetemperatures (see fig. 4).

Some features :>f these measurements are ratherobvious. In the near threshold region we observe ashift in the threshold energy for ion formation tolower kinetic energy when raising the SF6 tempera-ture. In this respect the observation of Leffert et al.[16], who measured a threshold shift for Cs+ forma-tion in Cs + SF6 collisions of 0.1 -0.2 eV by changing'the temperature of the secondary SF6 beam from180 K to 380 K, is completely confirmed. In thethreshold energy range we observe striking tailing,which gets more pronounced at higher SF6 tempera-tures. In the post-threshold region a raising of the SFgtemperature yields an increase in the cross section.

The strong temperature dependence of the crosssection is apparently due to the influence of the inter-nal SF6 energy. As already suggested by Ross [13], itis not very likely that rotational excitation is of anyimportance in the electron tranfer process. We mayconsider the internal rotations of the molecule as adia-batic, i.e., these are degrees of freedom which remainin the same quantum state during the collision. Theelectron jump distance, or the crossing radius will notvary drastically with the rotational quantum number.Moreover a rise in the SF6 temperature from 300 K

to 850 K will only result in a rotational energy increaseof 0.07 eV which is negligible with respect to theaverage energy increase stored in the vibrational modes(O.o eV).

Octahedral molecules possess six fundamentalmodes of vibration which include both stretching andbending modes (see table 1). Our measurements clear-ly indicate a threshold shift to lower translationalenergies which is about equal to the average internalvibrational energy (see table 2). Therefore we do notfeel that it is justified to neglect bending modes ascould be inferred from the conclusions drawn by Rossabout the reactive cross sections [13]. In the next sec-tion this will be considered in more detail.

The cross section for the production of a specificion at a given temperature T should then be given by

Q(Eiel,P) = ƒ Wit0) o{EKhEDdfi,.0

(1)

where EIS^ denotes the relative kinetic energy of thecolliding particles, 0 = 1/AT with k the Boltzmannconstant and T the absolute SF6 gas temperature,Ex is the total vibrational energy of the SF6 molecule

- 39 -

Table 1Normal modes of vibiation of SF$ in the vapoui (s = stretch-ing, b= bending) [34]

Mode

(S)

u> (cm )

773.5641.7939614525347

Dcj

123333

and/(£j,/?) is the fraction of SF6 molecules havingvibrational energy E-, u temperature T. We calla(£rel, £"j) the specific cross section. In this approacüit is clear that we do not make any distinction withrespect to different vibrational modes. We only inferthat the cross section is dependent on the internalenergy stored in the vibrational modes.

The energy distribution of internal states at tem-perature J i s given by a Maxwell-Boltzmann distribu-tion:

Table 2Vibrational energies for SF6 in electronvolts at several tem-pexaturcs: f~total> for all vibrational modes and c"stretch-for

only the stretching modes. These energies are in excess of thezero-point vibrational energy, ez = 0.58 eV

Temperature (K)

300 445 545 650 740 845

"[total£stretch

0.07 0.19 0.29 0.40 0.50 0.62Ö.03 0.09 0.14 0.20 0.26 0.33

ƒ (2)

where p(£j) is the density of molecular vibrationalstates at energy £"j.

Provided Q(E[e],f}) has been measured over a largetemperature interval we can unfold o(EKl, E^ fromthe experimental data by an inverse Laplace transform.

10 Iff'300

Fig. 11. Dependence of the total cross sections for resp. SFS and SF« formation from Li > SF6 on the SF6 source temperatureat various cm. kinetic energies (see fig. 3). The dots have been taken from resp. fig. 7 and fig. 6; the crosses have been obtainedby varying the oven temperature at fixed primary beam energy.

- 40 -

When the data is plotted on a semi-logarithmic scaie,In Q versus T at fixed EKl, as is shown in figs. 11, Pand 13, we observe that within experimental errorIn Q is proportional to T, or

= Cexp (A 10), (3)

where Cand^ are only dependent on the collisionenergy. This facilitates the Laplace transform. It thenfollows that

Cexpt4/0)Z(/3)= ƒ(4)

where Z(P) is the partition function JQ p(E{) exp(-£jj3) d£"j. From this the specific cross section a isobtained by means of an inverse Laplace transform:

o(£«,, f j) = [C/piEi)) Z-»[--'4/0) Z0)1 . (5)

This gives us a new set of cro»s sections: in figs. 14—19 a is shown as a function of Ei at fixed EKi, while infigs. 20-22 o is shown as a function of EKi at fixedEy We note that due to the limited temperature range

of the measurements one should be careful in extra-polating the results of the unfolding procedure tointernal SF6 energies, which exceed the r?nge of un-occupied vibrational states involved in the collisi aprocess. We have calculated the specific cross sectionsfor internal energies up to 1.0 eV (in excess of thezero-point energy).

The method is straightforward and has for exam-ple been applied by Tully et al. [3] in a study of polardissociation cross section of alkali halides with Xeatoms. However, in contrast to 'he diatomic case, theBoltzmann distribution function is difficult to evalu-ate. We refer to the appendix for details on the calcu-lation ofpCf,), f{Ei,0) and a(Erei, E{).

4. Discussion

4.1. Threshold measurements (T=300 K)

The energy scale of the primary beam particles hasbeen calibrated by measuring the onset for I" forma-

1 0 -

I O U -

10

Vlhr = 5.80eV

Na.SF6 .SF6(xl0)E,hr=A.65eV

-T(K)900

-T(K)

Fig. 12. Dependence of the total cross sections for resp. SF5 and SF6 formation from Na + SF6 on the SF6 source temperatureat various cm. kinetic energies (see fig. 4). The dots have been taken from resp. fig. 9 and fig. 8; the crosses have been obtainedby varying the source temperature at fixed primary beam energy.

- 41 -

-50

700 900«-T (K)

I ig. 1 3. Dependence ol' the tutul cross sections lor resp. p and Slrs formation from K + ST6 on the SFg sviurce temperature atvarious c.m. kinetic energies (see t"ia. S). Tlie dots IUVC been obtained by varj'ing the primary beam energy at tixucl source tem-ptrjiure. the crosses by varying the source temperature at fixed primary beam energy.

10

VIBRATIONAL ENERGY E (eV)

f ig. 14. Specific cross sections lor Sl'ë" formation from Li +SI15 JS J function ol SI'g vibratiomil energy at various cm.kinctk energies (sec tig. 3).

tion in (he collision process Na + \-> -* Na+ + ! + I .Here the atomic ion threshold is precisely knownfrom thermodynaniic data. The threshold was analysedby fitting to the experimental points the convolutionof a linear model cross section with the center of massenergy distribution f 17]. As the angular distributionof the primary beam is better than 0.5 degrees no cor-rections have to be applied in the threshold convolu-tion procedure for oblique crossing of the beams. An-other method which was used to check the alignmentand calibration of the velocity selector was a meas-urement of the velocity distribution of a potassiumbeam from an effusive oven. The latter gave a slightlyhigher energy (0.05 eV in the lab system) but theagreement was well within the error limits. To cancelerrors, if any, in the convolution procedure we pre-ferred the first method, since the same threshold anal-ysis was applied to the SFg negative ion thresholds.The results for the real threshold energies for the neg-ative ion formation from the reaction M + SF6 atroom temperature (M = K, Na or Li) are presented re-spectively for SF "̂ in table 3 and for SFJ and F~ in

- 42 -

100 0

VIBRATIONAL ENERGY

Fig. IS. Specific cioss sections for Slrj" formation from Li +SFg as J function of ST^ vibrational energy al various cm.kinetic energies (sec fig. 3).

00 05 IBVIBRATIONAL ENERGY E(*V)

Fig. 16. Specific cross sections for SFg formation Trom Na *SF6 as a function oi SF6 vibrational energy at various cm.kinetic energies (see fig. 4).

VIBRATIONAL ENERGYFig. 17. Specific cross sections for SF5 formation from Na +SF$ as a function of SF$ vibraticnal energy at various cm.kinetic energies (see fig. 4).

table 4. As the centre of mass cross section is non-linear (cf. [14,16]), the folding has been performedat the very onset, up till about 0.2 eV above threshold.

It is general practice ÏO assume that E*.d = &E, theasymptotic energy difference between the crossingpotential energy surfaces involved Then the molec-ular electron affinity EA, is found from E^, accordingto

in which 7(M) denotes the ionization potential of thealkali atom M. Anticipating the discussion of the tem-perature dependent threshold measurements we maystate that the onset for parent ion formation corre-sponds with the adiabatic electron affinity. Moreover,all the vibrational energy of the target molecule isavailable for the charge transfer which means the on-set is lowered by this amount. In connection withthis the EA deduced from the parent ion onset shouldbe corrected for the internal energy available. Obvious-ly this correction strongly depends on the sensitivityof the experimental arrangement. A good criterium,however, follows from the experimentally determined

- 43 -

20 -

1000 05 'O

VIBRATIONAl ENERGY e{eV>

Fig. 18. Specific cross sections for SP5 tornwtion from K +SF$ as a function of SV^ vibrational energy at various cm.kinetic energies (see fig. 5).

VIBRATIONAL ENERGY E{eV)

Fig. 19. Specific cross sections for F~ formation from K +SFé as a function of SFg vibrational energy at various cm.kinetic energies (see fig. 5).

50 60CM. ENERGY

7.0

Fig. 20. Specific cross sections for SFê" formalion from Na + SFe as a function of cm. kinetic energy at various SF« vibrationalenergies (see fig. 4). The arrow corresponds with the threshold for SFJ formation with the SF6 source at room temperature.

20

'O'H

'c

n4

'Sco

o.

10"

VIBRATION AL

050

0 75

OIO

'6.0

- 44 -

Na . SF6 : S F "

—To 'C.M ENERGV (eV)

10.0

E!»V)

1120

Fig. 21. Specific cross sections foi SFs formation from Na + SFg as a function of cm. kinetic energy at various SFg vibrationalenergies (see fig. 4). The arrow corresponds with the threshold for SFJ formation with the SF6 source at room temperature.

10

c3

10-

so 7 0 1 8.0 90 COCM. ENERGY

11.0 12.0

Fig. 22. Specific cross sections for F~ forniation from K + SF^ as a function of cm. kinetic energy at various SF$ vibrationalenergies (see fig. 5). The arrow corresponds with the threshold for F~ formation with the SFg source at room temperature.

- 45 -

Table 3J<in pair formation dd'Ui for .M + SI „ in elcclronvolfe. I.A is the adiabatic electron affinity of SF«

Table 4Ion pair

M

LiNaKCs[14]

M

LiN J

K

Cs|14)

formation data for

SFr

(T= 30UK)

4.90 ±0.15-1.65 ±0.103.86 ±0.10

3.35 ±0.10

FA

<r=0.490.490.48

0.54

the production of SFJ and F~

A

(r=300K) (r=3oo

6.10 ±5.80 ±4.85 ±4.40 ±

0.1 0.710.1 0.660.1 0.510.1 0.51

K)

300 K)

±0.15±0.10±0.10+ 0.10-0 .17

fur M + i

EA(7" =

2.92.8

EA(7"= OK)

0.32 ± 0.200.32 ±0.150.31 ±0.15

!F6 in electronvolts

= 300 K)

±0.1±0.2

F "

^thr(r=300K)

8.20 ± 0.17.30 ± 0.1

/)0<SFs-F)

0.93 ± 0.10

1.05 t 0.10

A(r=300K)

3.062.96

threshold shift as a function of temperature. It is ob-served, for example for the two extreme temperatures,300 K and 850 K, that this shift is equal to the energy

difference in the two corresponding internal energydistributions, shown in fig. 23. To be more precise, infig. 23 it is observed that for SF6 at 7 = 300 K f(0>e)

10"

= 300K

VIBRATIONAL ENERGY e (*V)

Fig. 23. The distribution function for ;he internal vibrational ener|y in SF6, calculated t>y the method described in appendix A.The vibrational energy e is the energy in excess of the zero-point energy.

- 46 -

Table 5Llcciron affinity ol SI 6 in ciccuonvolts

1 A Method Investigator

1.49> 1.1» (1.7

0.430.3

> 0.3> 0.6

0.540.750.49

0.32

t 0.21

1.46- 1.2

I O . I+ 0.1

0.17i O J

±0.1

± 0.15

magnetronelectron swarmpulse-samplingflowing jlïcrglowcharge transfer absorptionneg. Jon charge transierneg. ion charge transfer <F= 300 K)charge exchanged Cs; collision chamber (7" = 300 K)charge exchanged Cs; crossed beam (T= 180 K)^puttered K, Na and Li; crossed beam (T - 300 K)

i d e m ( r - O K )

Kay and Page a*Compton et al. *>'Cher, et al. c>lehsenteld d )Hammond e 'Chupka 0Lifshitz et al. S)Compton and Cooper n>Leffert et al. "Present results

Present results

J> J. Kay and P.M. Page. Trans, f'ar. Soc. 60 (1964) 1042.b> R.N. Compton. L.G. Christophorou, G.S. Hurst and W. Reinhardt, J. Chem. Phys. 45 (1966) 4634.c> t . Chen. R.D. George and W.E. Wentwortii. J. Chem. Phys. 75 (1971) 3517.d> r.C. Tehsenfeld, J. Chem. Phys. 54 (1971) 438.e> P R. Hammond, J. Chem. Phys. 55 (1971) 3468.f) W.A. Chupka. quoted in ref. 112).?) C. Lifshitz. T.O. Tiernan and B.M. Hughes, J. Chem. Phys. 59 (1973) 3182.h> See ref. ( I4 | .') Seeref. |16).

has dropped to (1/c) of its maximum value at e = 0.17eV. at T- 850 K at e = 0.97 eV, the difference beingexactly the experimentally observed shift. In table 3the results for EA(SF6) have been given, determinedby the use of relation (6) for K, Na and Li, alongwith the values of the electron affinity in the extra-polation to zero vibrational energy (0 K). A ratherwide range of EA values has been reported using dif-ferent techniques (table 5). The advantage of themethod of crossed molecular beams is that in generalit provides a direct and accurate determination of theEA, due to the relaxation of the negative molecularion [8|.

From the SFJ ion thrc.nold we can deduce the ap-pearance potential A for the formation of SFj + Ffrom the relation

•KM). (7)

The results for A (SF5 ) at room temperature for thealkali atoms studied are given in table 4. The differencesbetween these figures are significant and beyond ex-perimental error: they distinctly increase as K -* Na-* Li, i.e., with increment of the metal ioni2ation poten-tial. It should be noted, however, that the result forthe reaction K + SFg is in excellent agreement with the

appearance potential reported by Compton and Cooperfor Cs + SF6 [14]. By considering the ion pair forma-tion process occurring via a simple one electron transi-tion between crossing potential energy surfaces, thecurve crossing radius is in the first approximation in-versely proportional to the threshold energy, i.e., theendoergicity of the reaction. From a comparison of theinternuclear distances for M-F [21] and the crossingradii roughly corrected for the S-F bond distance [22],it can be argued that in the cases of Na and Li thecrossing radius is shifted to such small distances thatrepulsive forces become important. In this picture theresults for K and Cs seem reliable, i.e., without excessenergy in the products. The appearance potential at300 K of 0.51 eV is in reasonable agreement with theresult of Fehsenfeld (0.43 eV), obtained from tem-perature dependent electron attachment experiments[10]. In comparing with these measurements, how-ever, some care is required as Schulz and Spence havepointed out that only the extrapolated onset of neg-ative ion formation in dissociative attachment meas-urements permits the determination of electron affini-ties or appearance potentials [23]. In dissociativeelectron attachment measurements with SF6 [19] theresonance peak for SFJ formation has been observed

- 47 -

al about 0.5 eV with J halfwidth (FVVIIM) of 0.8 eV;however, the appearance potential for SFjj' is 0.1 eVwhich differs from our observation. We note that inthese mass spectrometric measurements the energyscale is calibrated by the SFg resonance peak at 0 eV.

Assuming that no excess internal or collisionalenergy is released in the fragments at the onset forSFj~ formation (in the case of K), the well depth ofthe parent ion ground state (SF^~, ̂ Ajg) can be deter-mined (see table 3):

i ( S F 6 (8)

Similarly we can deduce a lower limit to the electronaffinity of SF5,

/>0(SF5-F)-EA(SF5). (9)

With the dissociation energy of SF6, D0(SF5-F) =3.4 eV [24] we obtain EA(SFS) > 2.9 + 0.1 eV (atroom temperature, see table 4).

The results for the onsets for F~ formation fromthe reaction M + SF6 at room temperature are listedin table 4 along with the appearance potential data.The F~ threshold could only be observed in collisionswith K and Na; the collisional energy available in theLi-SF6 experiment was not sufficient to overcomethe reaction endoergicity for F~ formation *. Belowthe "real" onsets at which the F~ cross sectionsmarkedly begin to rise, a long tailing is observed downto center of mass energies below the ionization poten-tial of the alkali atom involved. These signals, how-ever, are very low, but above the noise level. Reactivecross section measurements by the Harvard group[25] have revealed that only one set of reaction pro-ducts is possible (MF + SF5) at which MF is formedwith low vibrational energy, fin the case of Li a secondpath is energetically accessible: LiF + F + SF4.) It issurprising that in the collisional i< nization process noF~ is observed at about the alkali metal ionizationpotential according to the reaction M + SF6 -*• M+ +F~ +SF5 , since EA(F)~D0(SF5-F) and EA(F)>EA(SFj) [26]. Very probably the reactive channelaccounts for this phenomenon and is highly competi-tive with the channel for ion pair formation. Thus thesmall F~ signal can be ascribed to dissociation from

1 It appeared that at T= 850 K the total energy (i.e., colli-sional and internal) was sufficient to overcome the thresholdfur F~ formation in Li + SF6.

the reactive channel according to M + SF6 -*• MF +SF^ -> M+ + F~ + SF5. In the dissuciative electronattachment measurements by Marland and Thynne[19] and by Lehmann [20] F~ ion formation was in-deed observed at electron energies near zero. Threeother ionization processes were noted [19] at 4.3,7.8 and 10.5 eV (appearance potentials), the processat 4.3 eV having by far the largest cross section. The"real" onset for F~ production in the collisional ion-ization experiment corresponds to an average appear-ance potential of 3.0 ± 0.1 eV. This result differswith the appearance potential of 4.3 eV from theelectron studies. However, we notice that our resultagrees remarkably well with the minimum enthalpyrequired for the dissociative attachment reactione + SF6 -* SF4 + F + F" , i.e., AH = 3.1 ± 0.4 eV.The bond energies for£>0(SF5-F) andD0(SF4-F)are taken from Hildenbrand [24].

In the reactions with K and Na we have measuredthe cross sections for producing F J . The signals, how-ever, were comparatively small and therefore wecould only roughly determine the threshold energiesfor F2 formation. After applying the convolutionprocedure we found E^iF^)= 6.9 ± 0.4 eV for Na+ SF6 a n d ^ ( F J ) = 5.5 ± 0.6 eV for K + SF6. Wenote that the enthalpy for the reaction e + SFg -*SF4 + FJ is predicted to be 1.9 + 0.5 eV. This is inreasonably good accord with our experimental find-ings for the appearance potential of F2 -

We also note that the formation of SF4" is appar-ently not favoured. Two possible reactions M + SF6

-> M+ + SF4 + F2 and M + SF6 -» M+ + SF4 + 2F areobviously dominated by the reactions leading to M+

+ SF4 + FJ and M+ + SF4 + F + F" , which might beexplained in terms of the electron affinities involved.The EA(SF4) is at most 1.3 eV [but probably muchlower, about equal to EA(SF6)] [24], whereasEA(F2)=*3.0eV [19] and EA(F)=3.44eV [26].

4.2. The collision model

The mass spectrometric studies of dissociativeelectron attachment to SF6 by Harland and Thynne[19] indicate that a rather wide range of vibrational-ly excited SFg" ion states are involved in the attach-ment process e + SF6 -> SFJ + F. They observe onlyone resonance peak at 0.5 eV with a 0.8 eV FWHM.Since in these experiments the electron transitions

- 48 -

are Franck Condon like, M follows thai the potentialiielonging to the SF6 ion state is already very repul-sive at the equilibrium distance of the SF6 groundstate, as a function of the S-F bond distance.

Accordingly the potential weli of SF^ is (shiftedconsiderably with respect to SF6. An approximationof this shift can be deduced from she M + SF6 colli-sional ionization experiment. Here we see that athigher collision energies the SF^/SFJ ratio becomesabout 0.1 which roughly reflects the difference invibrational overlap factors between the SF^ and SFgstates with respect to the formation of SF§ or F +SF5.

A schematic potential energy diagram for theground states of SF6 and SF£ is given in fig. 24, wherewe have plotted the potential energy versus the inter-nuclear S-F distance.

Using this representation of the potential energycurves we can directly explain the ion formation. !r>two recent papers on ion pair formation in alkali-halogen collisions {17,27} we have shown the impor-tance of bond stretching (of the molecular ion) tothe collision dynamics in the energy interval studied.In a calculation we indicated the high sensitivity ofthe ion formation on the steepness of the repulsivestate.

The same considerations apply to SFg. The in-coming crossing will be passed adiabatically, becauseof the large electronic energy splitting between thecovalent and ionic potential surfaces at this distance.Without a stretching of the S-F bond the outgoingcrossing will be passed under the same physical circum-stances, i.e., again adiabatically. However, as shown infig. 24, the SFg potential rises steeply at the equilib-rium distance of the molecular ground state. By theaction of the repulsive force, the S-F bond of the ionis stretched. As a consequence the crossing radius willmove outward (with increasing electron affinity) andcan be passed diabatically due to the much smallercoupling element # 1 2 . A rough calculation, in which//j 2 is estimated using the Olson formula [28], con-firms this. Later when dealing with the role of internalenergy in the process of ion formation we shall comeback to the phenomenon of bond-stretching.

In section 4.1 we have already mentioned that theappearance potentials for the SF5 ion formation dif-fer markedly for the alkali atoms involved (see table 4).This is interpreted by assuming that at least in the cases

<S-F) BCND DISTANCE

Fig. 24. Schematic potential energy diagram for the molec-ular ground states of SFj and SF£~, including also the experi-mental lhumodynamic data.

of Na and Li, the crossing occurs at internuclear dis-tances where the covalent potential energy surface al-ready has become repulsive. The consequence of thisis very instructive and gives insight into the mechanismof F~ formation. Due to the repulsive interaction,momentum is being transferred from the alkali atom tothe SF6 molecule during the approach of the crossingradius. At the moment that the electron jump takesplace the S—F bond distance has been compressed andcorrespondingly the vertical EA has been increased.

This emphasizes that the incoming crossing canonly be passed adiabatically. Diabatic transitions arevery unlikely, the more so as the electronic couplingelement between the potential surfaces only increaseswith decreasing crossing radius. In view of this theformation of F~ cannot be explained by electrontransfer to an electronically excited SFg state, as thiswould imply a diabatic behaviour at the first crossing.Other facts reinforce this statement. In the first placewe have observed that the threshold for F~ formationcorresponds exactly with the minimum enthalpy re-quired for dissociation into F~ + F + SF4. If an ex-cited (repulsive) SF5 state were involved, much moreenergy would be required to form F~, as can be con-cluded already from the SFJ formation. Harland andThynne f 19} have observed in their experiments theformation of F~ (apart from the F~ signal at about0 eV) at 4.3 eV electron energy (appearance potential,with resonance maximum at 5.7 eV). They observedother resonances at 7.8 eV and at 10.5 eV (appearance

- 49 -

. v. KL|] ihey .isi.rihi.'d u> the p- t * li- + SJ-, jiid e + SF6 - F

Ti> (ii*nis-> the f- ï'i.imaiuni. il is ht'lptit] to coit-sidei the -.'CüLTa! shape i)I dn.' nicasuied eioss seitionstor ihc \ jriiuis negjiite product ions. There is a dis-tinct eonneciion between their behaviour. Al collision•.'nerces J! which the fornuian:) o! SFj ;!]id F re-spectively becomes possible, she SF6 and SF5 ion sig-nals level off. Th? product ion cross scciions seein tobe all competitive. On i'ie other hand the diminutionover the cross sections for F . SFJ and SF6 ion for-mation yields J continuously rising cross section as 'jfunction of relative energy. Additional information isobi lined from (he high energy cross section data for(s + SF6 by Ruthe et al. |! 5J, where it is seen thaithe F /SF5 ton ratio becomes unity lor center ofmass energies above about 75 eV'; so no new pathwaysfor ion formation become accessible We conclusivelyslate thai for the energy range up to 200 eV cm. onlythe ground state of SF6 (2Ajp) is involved in the col-hsional ionization process. M + SF6.

In ihe discussion on the formation of SF5 wedemonstrated how momentum (kinetic energy) isbeing transferred to the SF6 molecule due to the re-pu!si\e interaction between M and SF6. by which ;heS F bond distance is reduced and higher vibrationallyexcited stales of SFg can be reached. This mechanismeasily allows for the formation of F" . assuming thatthe F~ signal originates from the excited SF6 groundstate. By increasing the relative kinetic energies, theSF5--F bond distance is compressed more forcefullyand correspondingly due to the steep character of theSF6 potential, higher vibrational ion states becomeaccessible at the moment that the crossing radius isreached and the electron jump takes place. This mech-anism stipulates that more kinetic energy can be storedas potential energy in the molecular ion. In order toallow dissociation into F" + F + SF4. the internallystored potential energy should be redistributed amongthe vibrational modes. As outlined in an extensive pa-per by Steiner et al. 129], a redistribution of vibration-al quanta can occur by energy transfer from mode tomode due to the anharmonicities of the oscillator po-tentials until a reaction coordinate reaches a criticalextension and ihe corresponding dissociation takesplace. This picture of the collision is consistent withthe observation that the F" onset occurs al the mini-

mum energy icquired for ihe electron transfer reactionM + SF6 - M+ + F + F + SF4. Also ihe experimentalobservation that al high relative energies the branchingratio F /SF5 becomes a constant, confirms this.

The production of Fï can be undeisiood in analo-g-ins iernis.

The temperature dependent measurements com-pletely reinforce this collision model as will be dis-cussed in the next section with the help of the specificcross sections.

4.3. Tiie rale of internal energy

In a preceding section we outlined the procedureused to invert the temperature dependent cross sec-tions into specific (i.e., internal energy dependent)cross sections. Lire we will discuss the results.

The specific cross sections for parent ion formationobviously differ from those for the fragmentation pro-ducts. The latter, however, i.e., the specific SF5 andF" cross sections show a strong similarity.

We will first focus our attention on the SF5 crosssections. It is seen (figs. 14 and 16) that near thresh-old a change of internal energy has the same effect onthe cross section as an equal change of the center ofmass energy. This suggests that the process of ion for-mation is completely determined by the total amountof energy of the reactants, i.e.. internal + collisionalenergy. This can be understood in terms of relaxationof the molecular ion formed. In trajectory calculationson K + Br2, Zembekov (8] showed that near thresh-old the highly vibrationally excited parent ion is ef-fectively quenched ("relaxed") to its ground state bythe action of the K+ ion. Very recently the mechanismhas been more fully explained by Zembekov andNikilin [30]. In the alkali atom-halogen molecule re-action M + XY ~* M+ + XY", the XY~ molecular ionis formed via a vertical (Franck—Condon) electronictransition in a higher excited vibrational state. Con-trary to the spectator stripping model, the excited ionis quenched lo its ground state at low relative veloci-ties, due to charge migration in the molecular ion inthe electric M+ field. As a matter of fact the model ofvibralional dcaclivation is invalid at higher collisionenergies as the collision times are too short forquenching. Accordingly the threshold energy for par-ent ion formation in collisional ionization experimentsis supposed to correspond directly with the adiabatic

- 50 -

election jlliruiy 01 the ntokvuie. The model essenfial-l> IL-JVIS to J shift of the parent ion threshold to lowereneipes equal to the JIIKHIIU ot quenching - withrespect it» that expected on the basis of a thresholdbehaviour which is based on Franck-Condon transi-tions.

In these terms a similar shift .'ill occur if internalenergy is present in the molecule in advance, sincethis wiil be quenched in the same way by the alkaliion at low relative velocities.

The observations completely confirm this model.The phenomenon of relaxation occurs in a narrowrange of relative energies ol about 0.5 eV above thresh-old, while internal energies up to about 0.8 eV(in ex-cess of ez) are entirely quenched at threshold. We seethat at higher kinetic energies the quenching is incom-plete.

We may conclude from these measurements thatthe electron affinity deduced for SF6 is indeed theadiabatic EA. It is clear that this value should be cor-rected for the internal energy available at T= 300 K,as the adiabatic EA is referred to the zero vibrationalstates (see table 3).

The specific cross sections for SFj and F~ forma-tion clearly show an equivalence of internal and colli-sional energy of the reactants for center of mass ener-gies up to about 2 eV above threshold. This holds forinternal energies up to 1 eV (in excess of ez). At kinet-ic energies where the F~ channel opens, this equivalenceno longer holds for the SFJ production; the internalenergy becomes much more effective in increasing thecross section than the collisional energy. An analogousbehaviour is observed for the F~ formation. Here theinternal energy begins to dominate the collisionalenergy at approximately 2 eV above iueshold. Thisalready gives an indication that a quenching mecha-nism where a collision partner is involved, does notapply.

We have already stated that the ionization probabil-ity is completely determined by the outgoing (second)crossing. A diabatic transition is only possible, whenduring the collision the SFg can dissociate or almostdissociate into SFj and F. Apart from the fact thatenough energy should be available, this is dependenton the strength of the coupling between the indepen-dent oscillations.

The more energy stored in the SF£" molecule andin the first instance irrespective of whether this energycomes from an electronic transition or is already part-

ly available as vibrational energy in the parent mole-cule, the more effective will be the dissociative stretch-ing in SFS and F. In the limit when the dissociation iscompleted during the collision, the electron affinityrelevant for the outgoing crossing is about 2.9 eV, theEA of SF5, see table 4. The corresponding crossingdistance is large and the electronic coupling element#12 small, so diabatic behaviour will dominate at thecrossing. In terms of this model it can also be under-stood that at energies of some eV above threshold,internal energy becomes more effective than transla-tional energy. The collision time is shortened and asa consequence less time is available for vibrational re-distribution and subsequent dissociation. A less peakedinitial energy distribution might then be favoured asthe first step in redistribution is not necessary.

Both Herschbach et al. (25] and Ross et al. [13]reported a positive effect on the reactive cross sectionof M + SF6 -» MF + SF5 with increasing temperature.Such an effect should be accounted for by an effec-tive increase of Rc for electron transfer. In the pro-cess of ion pair formation, however, this effect of in-creasing Rc will be masked by the relaxation of theexcited molecular ion. This has a much more drasticinfluence on the probability for a diabatic transitionthan the relatively small increase of Rc. The rise ofthe specific cross section as a function of internalenergy at the highest translational energies only givesan indication about the increase of Rc. At these ener-gies, however, the vibrational motions of the molec-ular ion are not frozen out, so that bond stretchingis still effective. This can be concluded from ion pairformation experiments at very high center of massenergies. For Cs + 12 the internal molecular motionsare totally frozen out from about lOOeVc.m. [31 J.

As stated in the beginning, the starting point inthe analysis of the temperature dependent measure-ments was that all vibrational degrees of freedom areinvolved in the process of ion formation. This wasconcluded on the basis of the threshold shift, whichhas been observed for all ions. This shift could be ac-counted for completely when considering all vibration-al degrees of freedom. More specifically these findingshave been confirmed by the results of the Laplacetransform, i.e., by the equivalence of total vibrationalenergy and center of mass energy.

However, these experiments give no decisive answerwhether this procedure is also justified at higher colli-sional energies.

- 51 -

5. Conclusions

In the foregoing we have proposed a simple colli-sion model, which is based on a potential energy dia-gram of SF6 as a function of only the internuclearS F coordinate. However, with this simplification thefeatures of the alkali atom—SF6 molecule ion pairformation are described reasonably well.

We have discerned two mechanisms in the collisionprocess which directly refer to the observations: (a)the equivalence of internal and collisional energy onlynear threshold for the SFg formation, and (b) theequivalence of these energy modes for SF5 and F~formation up to about 2 eV above threshold. Theformer is a relaxation mechanism based on the inter-action of the alkali ion and the highly vibrationallyexcited SF£ molecular ion, as a result of which SFgis quenched. The latter, however, is not a quenchingprocess but an intramolecular mechanism, which alsohas been called relaxation [32]. Both mechanismshave in common that by the relaxation the internuclearS-F bond is stretched, leading to the occurrence ofion formation. We emphasize that the bond stretchingis more generally a dominating mechanism in atom-molecule collisions; in the domain of relative energiesup to lOOeV [31] it should be noted that indeed inthis energy range a two-body approximation is a poorone, since vibrational motions are still non-negligible.

This also means that the energy rang» of our experi-ments is still too small to give reliable information onthe change of the crossing radius as a function oftranslational energy.

In overcoming the threshold for parent ion forma-tion only the total (internal + collisional) energy is im-portant. Consequently, to derive the adiabatic electronaffinity of the parent molecule from ion pair formationmeasurements one has to take into account the vibra-tional energy of all excited vibrational modes. This canbe an important correction for large molecules. In thisrespect we note that our results completely supportZembekov's calculations on K + Br2 [8].

In the post-threshold region the temperature effecton the F~ and SFJ cross sections is larger than forSFg . As the formation of SF5~ and F~ is largely dueto a stretching of the S-F bond in the SFg moleculeduring the collision, it is of no importance whetherthis bond stretching is caused by potential energy dueto the transfer of an electron or to initial vibrational

energy of the molecule. At larger velocities, the lattermight even become more effective. On the other handin the formation of SFg the quenching mechanism isvery important as a vertical electron transition willlargely yield SFJ ions. The amount of energy whichcan be quenched, however, is strongly limited by thecollision time.

In the «iiscussion two assumptions are mads, whichare confirmed by experimental evidence. Firstly theion formation only arises from the molecular ionground state (2A l g); excited SF$ states are not in-volved. Secondly, all vibrational modes contributeequally to the electron transfer process; perhaps amore detailed analysis is required in which the bendingvibrational modes become excluded at higher collision-al energies. However, our measurements give no evi-dence for such a refinement.

Acknowledgement

The authors are indebted to J.A. Aten, ProfessorJ. Kistemaker, Professor J.D.W. van Voorst and Dr.A.E. de Vries for their comments on the ir.muscript.We express our appreciation to F. Vitalis for his con-tinuous interest in this work and his computationalefforts. We are also grateful to A.W. Kltyn andA. Mayers for their enthusiastic assistance at the meas-urements.

This work is part of the research program of theStichting voor Fundamenteel Onderzoek der Materie(Foundation for Fundamental Research on Matter)and was made possible by financial support from theNederlandse Organisatie voor Zuiver-WetenschappelijkOnderzoek (Netherlands Organization for the Ad-vancement of Pure Research).

Appendix A. Calculation of p and ƒ

The density of vibrational energy states p(e) can becalculated to a good approximation at high excitationenergies with the semi-classical expression [33]

is the frequency of the ith of the « harmonic oscilla-

- 52 -

tors and e the energy in excess of the zero-point energyet (for SF6 the vibrationaJ frequencies are given intable 1, ez = £ S|L, hv( = 0.58 eV [34]). At low ener-gies, of the order of ez however, quantum restrictionsbecome important so that a more exact formulationmust be employed. An accurate semi-empirical repre-sentation to p(e) for a set of harmonic oscillators hasbeen developed bv WJiitten and Rabinowitch [35],

(«-!)! [I (Al)

They introduced an "effective" energy dependent ez,characterized by a, along with some other empiricalparameters found by extensive comparison with exactcomputer calculations. The agreement of this approxi-mation with a smoothed true quantum count is with-in a few percent at quite low excitation energies(^ 0.1 ez). We used this approximation to evaluatep(e), since it is valid for the energy interval coveredby our experiments, which corresponds with an exci-tation energy range from almost zero up to 4ez. Wehave compared the results forp(e) for the SF6 mole-cule with a calculation using Haarhoffs formula [36].Fror - rnal energies e of the order ez both methodslead _ same results forp; HaarhofPs formula,how" • ̂ r, appeared to be in error for smaller values ofe, resulting in an apparent increase of p at lower e.

When p(Et) is known, the fraction of moleculeshaving vibrational energy £"j according to a Maxwell -Boltzmann distribution is expressed by:

(A2)

For a system of n independent harmonic oscillatorsthe partition function is given by [37]

/ƒ%(*,

oo

= ƒ p(2Ti)exp(-Z<i0)d/<i

2sinh(/3/H>//2).

Here we have plotted the fraction of molecules withvibrational energies above ez as a function of e, ac-cording to the formula:

/(e,0)de = p(e-)exp[~(e + ez)0] de/Z(0). (A4)

At higher temperatures (above 500 K) ƒ /(e,0)deapproaches unity, which provides a good check forthe correctness of p(e). At lower temperatures, how-ever, discrepancies occur: ƒ/(e,0) de < 1.

However, it should be realized that Z(fi) is evalu-ated from Ex = 0. In a quantized system of harmonicoscillators,/(e,j3) shows a discrete behaviour withnon-zero values below ez, and this gives an importantcontribution to the integral especially at lower tem-peratures where/(e,0)has its maximum at about ez.In the method of Whitten and Rabinowitch p(e) isessentially calculated for vibrational energies in excessof ez. Indeed the discrepancy is removed by correctingZ(fi) for a zero-point contribution Az(fi)= ïl"~ jexp(-*i>,-j3/2),

= ƒ piE

(A3)

ƒ p^exp^fifldEj. (A5)

Appendix B. The calculation of a

In a crossed beam experiment after correction forthe primary beam energy spread, the threshold behav-iour for ion formation is determined by the convolu-tion of the vibrational dependent true cross sectionwith the thermal population of the SF6 vibrationalenergy states. From the experiment we conclude thatthe apparent threshold corresponds with the highestoccupied SF6 states. This means that the specific crosssection o(Eiel, £";) is only defined from a certain"threshold" internal energy Ef" of the SF6 molecule.With the use of the Heaviside unit step function H{E$we define a(EKl, £"j) as

a(EKl, E j) = H(ErEfa)al (Eiei. 5,), (Bl)

whore

In fig. 23 the vibrational distribution functions of SF6

at temperatures T= 300, 550 and 850 K are shown.= 0,= 1,

when £"j < 0when Et > 0.

- 53 -

Hie ti't.il cru.vs section lor ion formation is a convolu-tion v>i' tlii; Sf'6 mternjl eneigy distribution and the«pocific cross section:

(B2)

(B3)

X o, (£„*£• )d£,

= ƒ p(El)H(ErEfa)0

X a!

Since the spectrum of vibrational energy levels isdense, it is possible to replace the summation by inte-gration, considering p and aj as continuous functionsof the internal energy.

Substituting for Q the empirical relation (?(£re],|3)= Cexp(AI0) it follows that

• ƒ

(B4)

With the shift theorem in Laplace transform theory wefind the result already stated:

o(£rcl,

(B5)

We have approximated Z(ff) by a polynomial to inversepowers of (3 for temperatures up to 2000 K. We thenanalytically determine the original function a by theinverse Laplace transform since the image of the gen-eral term of the polynomial is known [38]:

(B6)

where Ifi_ is the modified Bessel function of order0). An analytically derived formula by

Haarhof f for the evaluation of Z(j3) to inverse powersof 0 [39] is only valid ut higher temperatures. There-fore <>ur method is in this case, where the temperaturerange is from 300 till 900 K, niuch more accurate.

In figs. 14 io 19 and figs. 20 to 22 the resultingcross sections a are shown, respectively o(e) ando(£re!). They have been plotted starting with e = 0.However, it should be emphasized that a only exists

for energies above £[*". We also point out that thecross sections o for excitation energies e below~ 0.05 eV have to be considered with some cautiondue to the error in p at these very low energies.

References

[1] D.R. Herschbach. Advan. Chem. Phys. 10 (1965) 319.[2] A.P.M. Baede, Advan. Chem. Phys. (1975), to be

published;S. Wcxlcr, Ber. Bunsenges. 77 (1973) 606;J. Los, in: The Physics of electronic and atomic Colli-sions, VIH ICPEAC, Inv. Lect., eds. B.C. Cobic andM.V. Kurepa (Beograd, 1973) p. 621.

[3] F.P. Tully. Y.T. Lee and R.S. Berry, Chem. Phys. Letters9(1971)80.

[4j E.K. Parks, A. Wagner and S. Wexler, J. Chem. Phys.58(1973)5502.

|5] J.C. Polanyi and W.H. Chong, J. Chem. Phys. 51 (1969)1439;M.H. Mok and S.C. Polanyi, J. Chem. Phj's. 51 (3969)1451.

|6] A.M.C. Moutinho, J.A. «:-n and J. Los, Physica 53(1971)471.

[7] A.M.C. Moutinho, J.A. Aten and J. Los, Chem. Phys. 5(1974) 84.

[8] A.A. Zembekov, Chem. Phys. Letters 11 (1971)415.[9] A.J. Ahearn and N.B. Hanny, J. Chem. Phys. 21 (1953)

119;W.M. Hickam and R.E. Fox, J. Ctem. Phys. 25 (1956)642;J.A.D. Stockdale, R.N. Compton and H.C. Schweinler,J. Chem. Phys. 53 (1970) 1502.

[10] F.C. Fehsenfeld, J. Chem. Phys. 53 (1970) 2000.[1 lj C.L. Chen and PJ. Chantry, Bull. Am. Phys. Soc. 15

(1970)418.f 121 D. Spence and GJ. Schulz, J. Chem. Phys. 58 (1973)

1800.[13] T.M. Sloane, S.Y. Tang and J. Ross, J. Chem. Phys. 57

(1972)2745.114] R.N. Compton and CD. Cooper, J. Chem. Phys. 59

(1973)4140.[15] S.Y. Tang, E.W. Rothe and G.P. Reck, Int. J. Mass

Spectry. Ion Phys. 14 (1974) 79.[16] C.B. Leffert, S.Y. Tang, E.W. Rothe and T.C. Cheng,

J. Chem. Phys. 61 (1974) 4929.I17| A.P.M. Baede, D.J. Auerbach and J. Los, Physica 64

(1973) 134.[18] A.P. Modica, 3. Phys. Chem. ?7 (1973) 2713.[ 19] P. Harland and J.C.J. Thynne, J. Phys. Chem. 73 (1969)

4031;P.W Ilailand and J.C.J. Thynne, J. Phys. Chem. 75(1.971)3517.

[20| B. Lchmann, Z. Naturforsch. 25a (1970) 17.'i

- 54 -

(211 B. Rosen, cd.. International tables of selected cunsljnts.Vol. 1 7. Spectroscopie dala relative to diatomic molc-cüles U'erpamon Press. OVord, 1970).

| 22 | II. Brjune and S. Knoke. Z. Phys. Chem. B21 (1933)297.

| 231 G.J. Sehulz and D. Spence, Phys. Rev. Letters 22(1969)47.

| 24) D.L. Hildenbiand. J. Phys. Chem. 77 (1973) 897.125) S.J. Riley and D.R. Herschbach. J. Chem. Phys. 58

(1973)27:R.P. Manella, D.R. Herschbach and W. Klemperer,J.Chem. Phys. 58(1973)3785.

(26| R.S. Berry and C.W. Reimann. J. Chem. Phys. 35(19&3) 1540.

1271 D.J. Auerbach, M.M. Hubers. A.P.M. Baedc and J. Los.Chem. Phys. 2(1973) 107.

1281 R.L. Olson, I'.T. Smith and L. Bauer, Appl. Opt. 10(1971) 1848.

[29] B. Steincr, C.i". Giese and M.G. Inghiam. J. Chem. Phys.34(1961) 189.

130) A.A. Zembekuv and l..L;. *ikitin. Dokl. Akad. Nauk.SSSR 205 (1972) 1392 (in Russian).

131] M-M- Hubers. A.W. Klcyn and J. Lus (1975). to bepublished:J.A. Aitrn, T. Lantinp and J. Los (1975). to be published.

| 32 | S.Y. Tans:. I..W. Rothe and G.P. Reck. J. Chem. Phys.60(1974)4096.

1331 R.A. MJKUS and O.K. Rice. J. Phys. Colloid Chem. 55(1951) 894.

| 3 4 | II.H. Cbassen, J.Chem. Phys. 53 (1970) 341.(35| G.Z. Whilten and B.S. Rabinowitch. J. Chem. Phys. 38

(1963)2466;D.C. Tardy. B.S. Rabinowitch and G.Z. Whitten. J.Chem. Phys. 48 (1968) 1427.

136) P.C. Haarhotï, Mol. Phys. 7 (1964) 101.(37) R. Kubo. Statistical Mechanics (North-Holland,

Amsterdam. 1965).[38) M. Abranowitz and LA. Stegun. Handbook of

Mathematical Functions (Dover. New York, 1970).[39] P.C. Haarhotï, Mol. Phys. 6 (1963) 337.

- 55 -

C H A P T E R I I I

ION PAIR FOPMATION IN ALKALI-HALOGEN COLLISIONS AT HIGH VELOCITIES*

M.M.Hubers, A.W.Kleyn and J.Los.

ABSTRACT

In a molecular beam apparatus ion pair formation in alkali atom-halogen

molecule collisions has been studied. Total cross sections for negative io"1

production have been measured in collisions of Na,K and Cs with Clo, Bro, '•5

I9, ICl and IBr at relative velocities from threshold to 2x10 m/s. In all3

total cross sections a maximum at about 8x10 m/s is observed. In some

systems a second maximum at about 9x10 m/s is observed, the value of

which is approximately half the first one. The fractions of atomic

ions of the total halogen ion yield are also determined. They strongly

depend on the specific halogen molecule and are less sensitive to the ;i

velocity and to the alkali atom. In case of heteronuclear halogens IX !

the I fractions show a rapid decrease at 7x10 m/s, falling off to zero '

at higher velocities. '\

The results are interpreted in terms of a two state model. The transition ,-'

probability is calculated using the Landau-Zener formula, attention being \

paid to the orientational dependence of the coupling matrix element H „ '-.

and to the increase of the crossing radius R due to stretching of the \

XY bond during the collision. .\

In the calculations performed, for the higher velocities only the ground- i

state of XY is considered. The maximum of the total cross section at low '\

velocity is attributed to bondstretching, while the maximum at high

velocity is considered to be a Landau-Zener maximum. If no second maximum

is observed, it is shown that it is concealed due to bondstretching'„ From i-

the values of the fraction we have deduced the vertical electron affinity =4

of XY (Cl9 : 1.02 eV, Br0 : 1.47 eV, I9 : 1.72 eV, ICl : 1.48 eV and IBr : ',\£ & Z I

: X

) Submitted for publication to Chemical Physics.

- 56 -

1.62 eV). For the Na-XI systems accurate values of the coupling matrix

element H,o are reported (Na-Br0 : 0.42 eV3 Jla-I0 : 0.40 eV3 Na-ICl :

0.44 eV, Na-IBr : 0.41 eV); for the other systems estimates of H-v

are given. Experimental results are presented and oompared with

theoretical predictions on the relation bePJeen U^^ an(^ R • It is shown

that the syrmetria expression of H^9 in terms of the ionization potential

and the electron affinity as given by the relation of Olson et at. is

not valid.

1. INTRODUCTION

During the paït few years much attention has been paid to the under-

standing of electron transfer collisions [1-4]. The development of hyper-

thermal neutral beam sources has considerably stimulated the interest in

these endothermal processes. In particular great effort has been devoted

to studies on ion pair formation in two and three particle interactions,

involving alkali atoms as projectiles

M + X + M+ + X~

M + XY -v M+ + XY~, M+ + X + Y~, M+ + X~ + Y.

In these collisions translational energy is transferred to electronic

excitation. The reaction proceeds via an electron transfer due to the

coupling of the ionic and the covalent states at the point, where the

diabatic potential surfaces cross. The Landau-Zener model applies to the

case of a two particle interaction, in which the motion is described on

one dimensional potential curves. In three particle interactions the

collision process takes place on multidimensional potential energy ;

surfaces. An extension of the Landau-Zener theory to two dimensional \

surfaces has been described by Uikitin [5]. Potential surface calculations !

[6-7] have revealed, that symmetry (geometrical configuration) and '

multiplicity of the quasi molecule strongly affact the electron jump

probability.

Most of the data on ion pair formation refer to measurements in the J

low energy region, from threshold to about 40 eV [8-13]. In these '

experiments especially the threshold behaviour has been studied. The

total cross sections, sometimes measured with mass selection, all show

- 57 -

Che same behaviour as a function of energy: a rapid rise at threshold to

a maximum is followed by a slow leveling off at higher kinetic energies.

On the other hand Bukhteev et al. [14] studied the negative ion formation

by collisions of alkali atoms on Cl_ and 0„ in the lab energy range from

150 to 2000 eV. Their results completely differ from those of Tang et al>

[15]. In this recent work the ion intensity ratios X /X_ from Cs+Cl„,

Br„, I_ were determined for lab energies from threshold up to 350 eV4(2x10 m/s). Kashihira et al. [16] reported on inelastic energy loss

measurements in ionizing collisions of K and Cs with Cl_ and Br« (lab

energy range 50-300 eV). They showed, that the energy loss was nearly

energy independent, about 8-10 eV, irrespective of the reactants. More-

over no energy loss peak was found corresponding with formation of X~ in

the electronic groundstate (about 2-3 eV). These authors suggested that

the predominant process is a transition into an excited electronic state

of X~.

At present relatively little is known about the detailed dynamics of

the alkali atom-halogen molecule collision. It seems appropiate to

discuss the phenomenon of ion pair formation by comparing collisional

time and vibrational time of the halogen molecular ion. Three velocity

regions may be distinguished: a) Threshold region: collisional time ^

vibraiional time. The vibrationally excited molecular ion is effectively

quenched by the alkali ion during the passage of the crossing region. The

threshold of parent ion formation corresponds with the adiabatic electron

affinity rl73. b) Post-threshold region: collisional time ^ vibrational

time. While effective quenching is no longer possible, stretching of the

internuclear XY bond still occurs. The crossing radius is shifted outwards

during the collision, which strongly enhances the diabatic transition pro-

bability (i.e. ion pair formation). This phenomenon may completely conceal

a Landau-Zener type of behaviour of the collision. Apart from the bond-

stretching, energy transfer will occur at the lowest velocities. This will

favour only the dissociative ion production at the cost of the molecular

ion yield, c) High velocity region: collisional time << vibrational time.

The vibrational motion may be considered as frozen during the collision;

the final distribution of XY vibrational states exactly reflects the ori-

ginal XY vibrational state distribution, in agreement with the Franck-

Condon principle.

- 58 -

Measurements in the high velocity region are strongly needed, because

they can provide information on some of the parameters, which determine the

collision process. Measurements of the fraction of dissociated molecular

ions of the total ion yield, i.e. X /(X +Y +XY ), will provide data on the

vertical electron affinity EA of the halogen molecule. Although the

adiabatic electron affinities are accurately known at the moment [2],

only crude estimates of the EA 's by Person [18] are available.

Measurements on the total cross section for ion pair formation possibly

provide information on the values of the coupling matrix element H.„.

The estimation of H.„ will be based on a calculation of the Landau-Zener

type, where some molecular aspects are taken into account. In the calcu-

lation the molecule will be considered to be non-rotating and non-

vibrating. High energy measurements also may give a decisive answer on the

role of excited states in the collision.

This paper describes our results on the partial cross sections for

negative ion formation in collisions of alkali atoms (Na, K, Cs) with

halogen molecules (Cl», Br_, I», IC1, IBr). The measurements were performed

in a crossed beam configuration in the energy range from roughly threshold

to 5000 eV (about 2x10 m/s). By choosing these combinations a set of para-

meters is introduced. The cross section for ion pair formation is to a

high degree determined by the crossing radius R and the coupling matrix

element H-2, which depends exponentially on R . The crossing radius, cor-

responding to the crossing of the ionic and covalent potential curves, is

to a good approximation given by R = !/AE (au) with AE = I - EA , where I

is the ionization potential of the alkali. This relation shows, that the

different ionization potentials (3.89-4.34-5.1A eV for Cs-K-Na) and EA 's, ;

i.e. variations of AE, strongly influence R and H.„(R ) and hence the jC 1 £ C • '

probability of the electron jump. A characteristic parameter in the ii

collision process is the ratio of the collision time and the vibrational Itime of the molecular ion. On the one hand variations in R influence the j

c i

collision time, on the other hand variations in the vibrational time are

obtained when choosing the different halogens. Heteronuclear halogens

have been chosen, because here the importance of excited states can be ï

examined experimentally. •]

- 59 -

The data are presented in two ways, by giving both the fraction of atomic

ions of the total ion yield and the total cross section for ion pair for-

mation as a function of relative velocity. The results will be interpreted

on the basis of the Landau-Zener model, which has been extended to take

into account some molecular aspects of the target.

2. EXPERIMENTAL

P.1 Description of the apparatus

The measurements were performed in a crossed beam apparatus, which is

drawn schematically in Fig. 1. It consists of a charge exchange source, an

inhomogeneous magnet and a surface ionization detector. From the inter-

action region, where the primary alkali beam is crossed at right angle with

a thermal halogen beam, the ions formed are extracted into a mass spectrome-

ter.

Collimation of the primary beam was achieved by the two slits of the

charge exchange source (width 0.3 mm) and a second slit in front of the

inhomogeneous magnet (width 0.1 mm). The beam height was 3 mm.

The charge exchange source is of the same type as constructed by

Helbing and Rothe [12] and has been described elsewhere [19]. The accele-

rating voltage of the ions was directly applied on the cathode, which was

heated by an AC current. The energy spread introduced in this way is

negligible as compared with the high accelerating voltage. The total

energy spread is estimated to be about 1.5 V fwmh at energies lower than

100 V and about 1% at higher energies. Evidence for this is obtained from

the measured intensity as a function of energy (Fig. 2), which shows well

resolved oscillations. The oscillations are due to symmetry interferences

in the charge exchange collision. Comparison of the oscillation pattern

with the measurements of Perel [20] indicates that the energy scale is well

defined. The same oscillation pattern lias been found in the negative ion

yield.

An inhomogeneous Rabi-type magnet has been mounted in front of the

surface ionization detector (SID) in order to remove the thermal alkali

beam from the charge exchange source [21]. Without removing the thermal

- 60 -

Fig. 1. Schematic diagram of the apparatus show-

ing the charge exchange source (I), inhomogene-

ous magnet (2), surface ionization detector (3)

and mass spectrometer system (4).

n=19Pi5C11 9 7 5

umi i i

Fig. 2. Typical fast neutral beam current profile

for K as a function of lab energy. At low energies

the intensity is given by a power law dependence

on the energy, the exponent being 2.3+0.3. The ar-

rows indicate the positions of the maxima in the

oscillation pattern as given by Ferel [20].

- 61 -

beam, the SID is immediately poisoned in case of cold operation or, in

case of heated operation its background is intolerably high.

The SID consists of a W or Ir wire (100 y) which can be heated by a

direct current. Around the wire a collector is placed. The current is DC

measured using a Keithley electrometer. Between wire and collector a

potential difference of 200 V is maintained.

The interaction region and the mass spectrometer have been described

previously [83. Therefore only the effect on the ion yield of the high

collision energies involved in this experiment will be discussed. The

transmission of the extraction system and the mass spectrometer has been

carefully checked, especially in the case of Cs+Cl„, where the largest

momentum transfer to the negative ion might be expected. In all experiments

no evidence for discrimination effects aas been found.

2.2 Ionization efficiency

The ionization efficiency r\ of the SID as a function of impact energy

for alkali atoms on an oxygenated hot W surface is not known for the

entire energy interval studied here (thermal-5 keV). At low energies

(th.-10 eV) n can be obtained from the work of Hurkmans [22]. At higher

energies n has been deduced by performing some experiments for potassium

to relate n of a hot oxygenated surface to the reflection coefficient of

K ions on cold W surfaces. The latter has been studied extensively

[23,24,253.

In order to avoid delay effects high operation temperatures (T 2L '900 K)

were necessary. This was indicated by measurements of the response of the

SID to a sudden change in beam intensity. At high energies reproducible

results were only obtained after an exposure of the SID to the fast beam

during 15 min.

Measurements of the SID signal as a function of temperature and energy

show, that for the entire energy range a plateau is reached at high tempe-

rature [10,12,263. In the energy range 25-100 eV the SID signal is even

completely independent of the surface temperature. At higher energies the

ratio between the signal from a cold and a hot surface is declining as

shown in Fig, 3.

In order to evaluate n we divided the energy range into two parts.

The lower part extends from thermal to about 125 eV. Trajectory calculations

of Hurkmans [273 indicate, that up to this energy penetration of the

- 62 -

'2H

1.0- *

08-

06-

04-

02-

•ttl)

KonW

10' 10J K>3

energy (e V)

Fig. 3. Determination of the ionization efficiency

for K atoms impinging on a hot oxygenated W sur-

face as a function of lab energy.

a) ionization efficiency n for a cold W surface

(Kef. 25).

b) ratio of measured intensities for a cold and

a hot W surface (I c o l d/I h o t>-

c) ionization efficiency for a. hot W surface,

A ~ measurement with normal beam intensity

(cf. Fig. 2).

V - measurement with 5 times lower intensity.

d) product of n and a (see text).

- 63 -

surface can be neglected. Experimental results of Hurkmans [22], which are

in agreement with the theory of Gadzuk [28]» show that n is equal to

unity up to 10 eV< Trapping of the incoming atoms does not play a role

above 25 eVeven on cold surfaces [22]. Therefore we infer from the tem-

perature independence of the SID signal up to 100 eV, that n is equal to

unity.

In the second part of the energy range (150-5000 eV) penetration into •

the bulk plays an important role. Therefore we assume, that n is equal

to the reflection coefficient, as is inferred by the observations of !

Hollstein and Pauly [25]. From 150 eV n has been calculated by dividing

the Hollstein-Pauly value for n of a cold surface by our ratio I . ,/ 1cold J

I, . The resulting n curve is drawn in Fig. 3. A fast decrease of n is Inoc >

observed at about 100 eV (dashed part of the n curve), while n does not

change much at higher energies. We note, that no difference has been ob-

served in this energy interval between measurements with and without

oxygen on the surface. The oxygen partial pressure was about 1x10 Torr,—8

the background pressure about 3x10 Torr. It is clear from Fig. 3, that

in this energy interval a plateau for the SID signal as a function of

temperature does not imply 100% ionization efficiency. This may be ex-

plained by the fact, that the incoming particles do penetrate into the

bulk and only a fraction will diffuse back to the surface and desorb.

Using Na in stead of K n will not be changed considerably. Penetration in-

to the surface will be possible at lower energies [27] and the ionization

potential of Na is higher. We therefore expect n to decrease already below

100 eV. The high energy part of n will not deviate strongly from the X

value, following the simple argument of Brunnée [24], who indicated that

at energies higher than 1 keV the ion reflection coefficient is almost in-

dependent of energy and behaves like (1-m/M), where m is the projectile

mass and M is the surface atom mass. '„

In case of Cs an Ir wire has been used to monitor the beam intensity. j

Using the same arguments r\ for Cs on oxygenated Ir will not differ !

strongly from the K on W results for low energies, but will decrease fas- i

ter for high energies.

2. 3 Evaluation of the cross section

Due to the thermal spread of the ions in the source before charge

exchange, which is a consequence of the ionization on a hot filament, the

- 64 -

beam profile is energy dependent. The beam becomes more forwardpeaked

proportional to the squareroot of the energy. In the centre of the beam

the SID has been placed to allow continuous monitoring of the primary

beam intensity. This means in the first place, that the SID signal correc-

ted for n does not give directly the beam intensity in the interaction

centre and secondly, that an increasing fraction of the primary beam is re-

moved by the SID with increasing energy. By temporarely removing the SID

entirely from the beam and measuring the increase of the number of ions

produced in the interaction centre, the energy dependent correction factor

has been evaluated using a - (I . - I. )/l.out in in

where I is the ion count rate having the SID removed from the beam and

I. is the ion count rate having the SID in the centre of the beam.The total cross section has been evaluated according to

Q = (I. .Ti.ot) / (ICT_.p) where IOT_. is the current to the SID and pin o Lu o J-Dthe inlet pressure of the secondary beam.

By evaluating the product (n«a) as a function of energy, it became

clear that these effects were compensating each other within 15% (Fig. 3).

Because of the uncertainties in n the term was dropped from the formula.

The presented cross sections were calculated by Q = I. /(IOT .p). We note

that due to the drastic decrease of r\ at about 100 eV (dashed part of the

curve (c) in Fig. 3) some uncertainty exists in comparing the value of Q at low

velocity and at high velocity. It has been checked, that the predominant

features of the cross sections were not due to beam profile or SID effects.

In case of the heteronuclear halogens the cross sections for I , Cl

an<f Br formation have been corrected for the presence of homonuclear

halogens X„ in the inlet gas, due to thermal dissociation of the hetero-

nuclear halogens into two homonuclear ones. The X signal is corrected by

subtracting the X from X„, which is calculated from the measured X ? signal

and the fraction X measured in the homonuclear case.

3. RESULTS |t

ïMeasurements of partial total cross sections for negative ion formation :{

i

have been, performed for alkali atom-halogen molecule collisions in the I

energy range from roughly threshold to 5000 eV. The alkalis studied were J

Na, K and Cs and the halogens involved were Cl», Br», I-, IC1 and IBr.

- 65 -

The actually measured partial total cross sections are presented in two

ways. At first the total cross sections for negative ion formation, which

have been derived by adding the corresponding partial total cross

sections, will be given. Next the fractions of dissociated molecular ions

of the total ion yield will be presented. In case of the iieteronuclear

halogens the fractions are given for both atomic ions formed. The partial

total cross sections have been evaluated as indicated in the previous

section.

The total cross sections for negative ion formation are presented as a

function of relative velocity in the Figs. 4-8. The Na and Cs results have

been shifted vertically with respect to those of K for the sake of clarity,

respectively by the constants +1 and -2. The total cross sections in the

low velocity region, which are given by the solid curves, are taken from

Refs. [8,92. The present measurements have been fitted to these results in

the overlap range. The resulting cross sections have been normalized to

ten in their maxima. In the case of Na+ICl both measurements have been

normalized independently to ten since no overlap exists. A common

feature of all systems is a sharp rise at low velocities, which is

followpd when increasing the velocity by a pronounced decline. This de-

cline starts at a velocity of about 10 m/s. In a few systems a second

maximum in the cross section is observed. These systems are Na+Er„,

Na+I„, Na+ICl, Na+IBr, K+Cl- and K+IBr. In the case of Na the minimum be-

tween the two maxima is situated at about 4x10 m/s, in the case of K at

about 2.2x10 m/s. In a few other systems some structure is observed at

velocities of about 2x10 m/s. In the case of Cs the decline at 2x10 m/s

is less pronounced and instead a broader maximum is observed, which shows

some structure.

The fraction of atomic ions of the total ion yield is presented as a

function of velocity in the Figs. 9-14 for all systems studied. It is

clear that these results are independent of SID effects. The accuracy is

estimated to be 5% at velocities above 10 n/s and about 10% for lower

velocities. For the homonuclear halogens the fraction depends strongly on

the halogen involved and is less sensitive to both velocity and alkali

atom. At velocities lower than 2x10 m/s the fraction decreases for K and

Cs and is constant for Na. At higher velocities the fractions behave al-

most alike for all alkali atoms. In case of CI2 the fraction increases,

- 66 -

10«-O0)K i 4 o4

M*CI,

•O0)C*

It 6-1

s

Ct

Fig. 4. Total cross sections for negative

ion formation in M-Cl- collisions as a

function of relative velocity. The ordi-

nates for Na and Cs have been shifted.

The symbols indicate the alkali involved.

The same notation is used in Figs. 5-13.

o - Na + XY

A - K + XY

D - Cs + XY

2

O'rriitivr «docily m/s

Fig. 5. Total cross sections for negative

ion formation in M-Br„ collisions as a

function of relative velocity. The full

lines show the experimental data by

Baede et al. [8]. The dashed Na line is a

result of the calculations (Section 4.3.3).

See Fig. 4 for the scaling and the sym-

bols used.

raMiv* velocity rry'»

Pig. 6. Total cross sections for negative

ion formation in M--I? collisions as a

function of relative velocity. The full

lines show the experimental data by Baede

et al.[8].

See Fig. 4 for the scaling and the

symbols used.

niitiv* vtlocity tn/t

- 67 -

M*IClJig. 7. Total cross sections for negative

ion formation in H-IC1 collisions as a

function of relative velocity. The full

lines show the experimental data by

Auerbach et al. [9].

See Fig. 4 for the scaling and the sym-

° bols used.o

to1

rdativt vttocitj trjt

• (10) N«

10-

1

O.«*°-W.p N.o o

o

%«*»••*. K" 4 4 W 4 4

\

M*IBr

IB»

'Fig. 8. Total cross sections for negative

ion formation in M- IBr collisions as a

function of relative velocity- The full

lines show the experimental data by

Auerbach et al. [9].

See Fig. 4 for the scaling and the sym-

bols used.

rflttivt «ttoeity

1.0-

ae-i1

06-i

3 04-

- 68 -

M.CI;Fig. 9. The Cl fractions of the

total negative ion yield in H-C1.

collisions as a function of rela-

tive velocity. For the symbols

used see Fig. 4.

02-

reiative velocity m/s

10'

0.6 H

06 A

co

02A

M . Br,

10*relative velocity m/s

Fig. !0. The Br fractions of the

total negative ion yield in M-Br,

collisions as a function of rela-

tive velocity. The dashed curves

are the calculations of Section

4.3.3.

For the symbols used see Fig. 4.

1.0-1

0.8 ̂

o

2 04-

02-

M . I,

relative velocity m/s

Fig. ]1. The I fractions of the

total negative ion yield in M-I,

collisions as a function of rela-

tive velocity.

For the symbols used see Fig. 4.

" f-i

co

- 69 -

co

10

08

0 6 -

~ 0.4 H

02-

M.TCI

10 H

aa-

0.6-

02-

10'relative velocity tn/s

M. IBr

10* 10S

relative velocity ml%

Fig. 12. The Cl" fractions of the

total negative ion yield in M-IC1

collisions as a function of rela-

tive velocity. For the symbols used

see Fig. A.

.Fig. 13. The Br~ fractions of the

total negative ion yield in M-IBr

collisions as a function of relative

velocity. For the symbols used see

Fig. A.

O.KH

0.08-1

0.06-

004-,

002-

oo

• Na.ICIA K . I do Cs*ia+ K «ÏBr

o*relative velocity

K>5

Fig. 14. The I~ fractions of the to-tal negative ion yield in M-IX col-lisions as a function of relativevelocity.

- 70

in contrast to the other two cases where it remains about constant. Only

in closer observation the fractions behave differently for the three alkali

atoms. For Na it remains constant, whereas for K and Cs a slight increase

at higher velocities is observed. In the case of the heteronuclear halo-

gens IC1 and IBr two different atomic ions are formed, I and respectively

Cl and Br . For velocities up to 2x10 m/s the Cl and Br fractions are

practically constant for all alkalis. In the case of Cs+ICl a small in-

crease in the fraction at 4x10 m/s is observed. This behaviour of IC1

(and IBr) is in striking contrast with the behaviour of the homonuclear

halogens in this velocity region. For higher velocities an increase in the

fraction is observed in case of IC1 for all alkali atoms, whereas the frac-

tion of IBr is similar to that of Br_. The behaviour of the I fraction

for IC1 and IBr differs completely from that of all other fractions. Here

a rapid decrease at 7x10 m/s is observed for K and Cs. For Na the low

velocity part has not been measured, but here no I signal is expected at

all [9]. At higher velocities the fraction remains about constant, at

roughly the noise level caused by the correction procedure to subtract the

I signal due to I„ impurities.

The results presented in this paper are in gocd agreement with those of

Tang et al. [15] concerning the ion ratio X /X in Cs+X9 collisions at

velocities up to 2x10 m/s. For the high energy region only the data of

Bukhteev et aL [14] are available, which do not agree with the present

data.

4. DISCUSSION j

The results presented in the previous section will be discussed in terms

of a two state model, in which the transition between the initial covalent

state and the final ionic state is described by the wellknown Landau- ;

Zener formula. In the M-XY systems the crossing radius R is so large, \

that the interaction potential of the ionic state around R can be re- j

presented by a Coulomb potential, while the covalent potential is equal to

zero. In this case the following approximations are valid

Rc - 1/AES H n = i/R + AE and H 2 2 » 0.*)

) Throughout this paper atomic units are used unless stated otherwise.

- 71 -

This leads to the expression for the diabatic transition probability p,

at impact parameter b

pb = exp(-2TTH,2Rc2/vb) (O

where HlO is the coupling matrix element and v, the radial velocity atI £• D

the crossing point. In the case of atom-atom scattering R and H ] 2 are

the same for the incoming and the outgoing crossing and therefore the

total inelastic cross section Q can be evaluated analytically

R

f C 2Q = 4ir Pb(l-Pb)bdb = 4TTRC F(K/V)

o

where F(K/v) is a wellknown function of reduced velocity [2]. If one

introduces an effective impact parameter b _,. = R IJl as indicated in Fig.

15, the same result for Q is obtained within a few percent

Q = R 2F,(v/v ).x c P cr'

2 2 ,H e r e v i s t h e c r i t i c a l v e l o c i t y , v = 4 T T H . 2 R /*2. I n F i g . 17 F i s

given as a function of the reduced velocity.

For atom-molecule scattering the situation is much more complicated,

because of the extra degrees of freedom introduced. Instead of one

molecular coordinate, three internuclear distances have to be considered.

Calculations have to be performed on crossing potential surfaces, in-

stead of crossing potential curves. If one does not describe chemical

reactions or threshold phenomena but processes, that occur at higher ve-

locities, an important simplification can be introduced. We then are

allowed to consider the motion of the alkali atom relative to the centre

of mass of the halogen molecule and the relative motion of the two atoms

in the molecule, as being completely independent. This means that at the

crossing point the transition probability can be calculated using the

Landau-Zener formula, while some molecular aspects are taken into account.

These are the dependence of the coupling matrix element H.» on the

orientation of the molecule, the vibrational motion of the molecule and

the excited states of the molecular ion involved. The most important

- 72 -

trajectory

crossing radius

Fig. 15. The orientation of the axis (a) of

the halogen molecule with respect to the ef-

fective trajectory of the alkali atom.

-2-

-3

Br<2P»<j).Br('P>'2)

2 3 * 5 6 7

(Br-Br) int»rnucl»*r disUnc* (A)

Fig. 16. The potential energy curves of the ground

state of Br. and the lowest states of Br2> The dashed

lines represent the projection of the centre of the

zero vibrational wave function and of the classical

turning points. The insert gives the distribution

P(EA) over the electron affinities.

- 73 -

molecular aspect is that the electron affinity EA strongly depends on the

internuclear XY distance. This is a consequence of the fact, that for

all halogens the equilibrium distance of XY is larger than that of XY

(see Fig. 16). This means, that if a molecular ion is formed via a ver-

tical Franck-Condon transition, it is formed on the repulsive slope of the

potential and the bond will stretch during the collision. Since both R

and H ] 2 are a function of EA, the collision time is a crucial parameter in

describing the process: it determines whether the internal motion of the

molecular ion has to be taken into account. If this is the case, EA, R

and H 1 2 will be different for the first and second crossing; bondstretching

in the halogen molecular ion will dominate the cross section. On the

other hand, if the collision time is short with respect to the vibrational

and lotational time of the molecular ion, the internal motion in the

molecule can be considered to be frozen. The EA and R are constantc

during the collision and H J 2 is now only a function of the orientation

of the molecule. In this case the total cross section can be calculated

analytically. The treatment shows strong resemblance to that of atom-atom

scattering.

In the following we will at first introduce our model more explicitly.

Thereafter the low velocity part of the measurements will be discussed,

paying attention to bondstretching. From the high velocity measurements,

the vertical electron affinity and, if possible, H „ will be deduced.

At last it will be shown that the results of calculations for the high

velocity range, taking into account the vibrational motion of the target

molecule and the precise relation between H.» and R , can explain the

behaviour of the fraction of atomic ions as a function of velocity.

4.1 Collision model

The essential assumption in the model is, that the internal motion of

the molecule or the molecular ion during the collision and the motion of

the alkali atom or ion relative to the centre of mass of the molecule are

completely independent. We treat the atom-molecule system like an atom-

atom system, where internal changes in the target atom can occur during

the collision. The molecular features of the system can be introduced by

considering the potential curves of the halogen molecule and the corres-

ponding molecular ions. According to our assumption the potential curves

- 74 -

are not disturbed, when an alkali atom or ion is in the neighbourhood. In

Fig. 16 the potential curves for the Br„ system are presented. The curves

have been constructed following the method of Person [183 making use of

the presently available data [29]. This picture is representative for the

other halogens; as for the heteronuclear halogens, the E ground state aod

the excited \l ._ state are not degenerate at large internuclear distance [9].

In the model the total cross section for ion pair formation will be

calculated using the formula

R

Q = 2*j (Pb2d-Pbl) + d-pb3)Pbl)bdb (2)o

where p, , is the diabatic transition probability at the first crossing,b 1

p, „ is the probability at the second crossing when the first crossing has

been passed adiabatically, while p, » is the probability at the second

crossing when the first crossing has been gassed diabatically. Always p, .

is evaluated according to Eq.(I) and actual R and H-» values at the mo-

ment of crossing are used. In atom-atom scattering the relation Pj.i™Pv2*Pb

holds and the integral can be evaluated analytically. For atom-molecule

scattering the equality does not hold anymore and consequently the total

cross section is influenced by the molecular behaviour of the target.

The electron affinity of the molecular ion depends on the collision time

and will increase during the collision and with it R . Because of the ex-

ponential relation between H ] 2 and R , H.~ will drop very quickly as the

bond length increases. Only p, ̂ will be influenced by this effect. There-

fore at low velocities p, „ tends to unity.

The covalent (M+X,) and ionic (M +X~) potential energy surfaces cross

along R =R (^„,0). Balint-Kurti [6] has shown that R depends strongly

on Ry_Y> t n e internuclear X-X separ?tion, and only weakly on 0, the

orientation of the X„ molecular axi& with respect to the alkali M. There-

fore only the radial component of AF.v in the transition probability p,

needs to be considered when calculating p by the two dimensional extension

of the Landau-Zener theory by Nikitin [5] for a fixed Ry_v (AF is the

difference of the derivatives of the diabatic surfaces at the crossing).

In this way the transition is adequately described by the one dimensional

Landau-Zener theory.

The coupling matrix element between the lowest covalent and ionic states

has been shown to vary as a cosine [30,313. The splitting is maximal for

- 75 -

collinear approach and vanishes for broadside approach. This results in

H.„(R ,0)=H° (R )f(0) with f(0) = cos01 z c 1 2 c

for the interaction of the groundstates. Gislason and Sachs [32] also give

the angular dependencies of H ] 2 for some excited Gtate configurations of

(M+X») and (M +X^). The interaction between the covalent groundstate and the+ 1 - 2excited ionic state (M ( S )+X2( II . ,_)) gives rise to a sin20 dependence,

while the interaction involving the n ,/9 state vanishes for all orien-2 + gtations. It is assumed that only the E groundstate and the excited

II . ,„ state are involved in the interaction.

In calculations of the total cross section the orientational effects

are averaged out by integrating over all orientations of the molecular axis

with respect to the incoming alkali atom.Eq.(2) becomes

TT 2TTR -n 2-n

Q-f f j (P b 2 ( l -P b l ) + (1-Pb3)pbl)sin9ded<|>bdb/J J sin9ded<f> (3)

o o o o owhere p.. is explicitly a function of the orientation,

bi

Pbi=exp(-2TrH°22Rc

2cos20i/vbi) with H ^ O t ^ e ^ H ^ C R j c o s e j .

The calculation has been performed for the effective impact parameter al-

ready defined. In this case a simple relation exists for the angle between

v. and the molecular axis at the first and the second crossing

cos6„ =cos<f>sin6. (the indices belong to p. „ o ) . The situation is drawnZ,O 1 DZ,J

in Fig. 15. Two limiting cases will be considered.

In the high velocity limit we assume the molecular vibration and

rotation to be frozen during the collision, i.e. R and H]2(R ) arethe same for both crossings, and the integration can be performed analy-

2tically. In the integration over the azimuthal angle <j>, cos <j> is replaced

by its average value £. The resulting expression for Q, which is the

orientation averaged cross section for atom-molecule scattering in the

high velocity limit is then given by

/

Q=(TrRc2/a)[(/;/2)erf(a)+/2exp(-a2/2)j exp(x2)dx-/2Ïexp(a2/2)erf(a//ÏF)] :

o

=Rc2F2(v/vcr) (4) \

x ' Iwith a2=4ïïH°2

2Rc2/(*^v)=vcr/v and erf(x)=(2/v^)|exp(-t

2)dt. I

o

- 76 -

3 5-

Fig. 17. Reduced total cross sections calculated using an effective trajectory.

The curve F. represents the atom-atom case, curve F, the atom-molecule case

without bondstretching and curve F, the atom-molecule case with a completely

stretched bond of the molecular ion.

- 77 -

F„ is shown in Fig. 17 as a function of reduced velocity. We note that the

maximum of F„(v/v ) has been shifted with respect to that of F,(v/v ) ,2 cr 1 cr

the atom-atom reduced cross section, by a factor 4.35 towards lower reduced

velocity. This shift has also been observed by Anderson, who performed the

calculations in a plane, averaging over both orientation and impact para-

meter [30]. Our results are in good agreement with numerical calculations,

which will be presented in a forthcoming paper [33].

In the low velocity limit we assume complete stretching of the XY bond

in the molecular ion formed; p, „ is then taken to be equal to unity. The

molecular rotation is considered to be frozen. The calculation of the

total cros? section is analogous to the derivation of Eq. (4). As a result

one obtains

Q=Rc2[Tr-(ir3/2/a/2)exp(-a2/2)erf(a/v/2)]=Rc

2F,(v/vcr). (5)

F» is shown in Fig. 17 as a function of reduced velocity. The enormous

increase of F„ at low velocities is due to bondstretching. The value of

F» in its maximum is about 60% of the maximal value of F„. At high vt o-

cities F and F_ converge to the same limiting curve.

Another molecular aspect of the target is its vibrational motion and

therefore one has to do with a distribution over electron affinities. This

distribution over electron affinities P(EA) is completely determined by

the Franck-Condon overlap factors and will be assumed to be normalized by

P(EA)dEA=l. As the critical velocity depends on EA, the total cross

section Q has to be evaluated for each electron affinity, i.e. Q=Q(v,EA).

It has been shourn. [34,35,2] that for the hyperthermal energy region the

probability of the formation of a molecular ion XY in a vibrational

state v' is proportional to the Franck-Condon overlap factor q^i» where v

is the vibrational state of the parent molecule. Hencr the EA averaged

total cross section can be obtained by integrating the product of P(EA) and

the specific cross section for each EA,

+*> •

Q(v)= I P(EA)Q(v,EA)dEA . (6)

Then the fraction of dissociated molecular ions F(v) is obtained by

EAd

F(v)= [I/Q(v)]j P(EA)Q(v,EA)dEA.

- 78 -

In the high velocity region Eq. (4) is given in a more explicit form by

Q(v,EA)=Rc2(EA)F2(v/vcr(EA)). (8)

By substitution of Eq. (8) into Eqs. (6) and (7) it follows that

and

Q(v)=j P(EA)Rc2(EA)F2(v/vcr(EA))dEA (9)

EAr d o

F(v)=[l/Q(v)] P(EA)Rc (EA)F2(v/vcr(EA))dEA. (10)

« 00

2Since v =v (EA)a-(H (EA) „ R (EA)) , the relation between H „ and R is

cr cr i £. c i £ c

a very fundamental one in Eqs. (9) and (10). It determines the trend in

the fraction as a function of the relative velocity.

4.2 Low veloeity vegion

The low velocity region is the region, where the cross section is

strongly influenced by the vibrational motion of the molecule and the mo-

lecular ion. The most important feature is the change in electron affini-

ty of the molecular ion during the collision due to bondstretching. Other

features are the rotation of the molecule or the molecular ion, the orien-

tation of the molecule at the moment of the first crossing and the energy

transfer from the alkali to the halogen. Threshold and post-threshold

phenomena have been discussed in previous papers [8,9]. The present re-

suits will be interpreted in terms of the collision model. In Ref. [9]

it has been demonstrated, that in the low velocity region the excited2II. ,_ state plays a part in the collision due to bondstretching. As the

rotational times are at least a factor of ten longer than the vibrational

time even for high J states, the molecule can be considered to be non-

rotating during the collision [29].

For a proper interpretation of the results, it is very important toi

give an upper limit of this velocity region to permit a quantitative I

analysis of the high velocity results. This limit will be calculated and

afterwards it will be shown, that the calculated value is consistent with

the experimental results. The method is to calculate the stretch-time,

needed for a significant increase of R at the second crossing. As the

' -I

- 79 -

2 +potential curve of the I state of the molecular ion can be estimated

[18], one can perform a classical calculation of the XY internuclear dis-

tance as a function of time, by solving numerically the differential

equation of motion on this potential curvo. These calculations, which will

be discussed in a forthcoming paper [33], show that 4x10 m/s is an upper

limit for the bondstretching region for all systems. This means that the

collision time has to be shorter than one tenth of the vibrational time

of the molecular ion to exclude the influence of bondstretching. For in-4 -14

stance in the system Cs+Br_ the collision time at v=4xlO m/s is 2x10 s-t 3

and the vibrational time ot Br_ is 2.2x10 s. From the potential curvesit is evident, that the change in R due to bondstretching is less for

2 2 + C

the ^i/2 state than for the Z groundstate. Therefore the upper limit

for the groundstate is higher than the one to be expected for the excited

state. Its value is confirmed by an analysis of the experimental total

cross sections. With this aim we focus our attention on Fig. 17. It is

observed, that if bondstretching does not level off, i.e. p,„ in Eq. (2)

remains equal to unity, F„ converges to F_ in the high velocity limit,

completely concealing the maximum in F_. If one observes in the total

cross section a second maximum at high velocity, this is only possible

when bondstretching has ended, i.e. p, „ deviates from unity. The velocity

of the minimum before the second maximum then can be considered as an

upper limit for the low velocity range. As is clear from the results, this

upper limit is about 4x10 m/s. Since the collision process can almost

completely be described by taking into account the groundstate of the

molecular ion, as will be shown in the following, the critical velocities

for F„ and F, are the same and indeed F2 and F„ will converge to the same

limiting curve at high velocities. Additional evidence for the argument

is obtained by the experimental observation, that the ratio of the value

of the first and the second maximum is in agreement with the ratio 0.6 of

the maxima of F_ and F, within experimental error.

We now focus our attention on the behaviour of the fraction in this

velocity region. At first the case of the heteronuclear halogens will be

considered, as excited states of the molecular ion formed in the collision

can be separately measured by observing the I formation, whereas the

groundstate leads to formation of X and IX . The fractions of Cl and

Br from IC1 and IBr are almost constant. The rise in the fractions at

- 80 -

velocities of 2x10 m/s is due to effects, that will be discussed in the

next section. Since the Cl and Br fractions are constant, we can con-

clude that bondstretching does not influence the fraction of atomic ions

dissociating from the groundstate. This is consistent with our picture,

that the XY potential is not disturbed by the presence of the alkali ion

during the collision. Observing the I fraction from IX, we see that at

low velocities about 10% of the total cross section is due to I for-

mation. The I fraction does fall off rapidly at higher velocities,

disappearing at all at about 1.2x10 m/s, which is in agreement with our

estimate of the upper limit. We note, that no I is formed at all in the

case of Na [9].

The potential curves for the homonuclear halogens strongly resemble the

curves for the heteronuclear ones. Therefore we expect the same general2 2 +

trend. However, in this case the II .,» excited state and the Z ground-

state of the molecular ion are degenerate in the dissociation limit. The

fractions in the case of the homonuclear halogens behave almost like the

sum of the I and the X fractions for the IX case. Therefore the decrease

in the fractions at velocities of about 8x10 m/s observed for all homo-

nuclear halogens except for the Na fractions, may be attributed to the

leveling off of the bondstretching which is responsible for the ion for-

mation from the excited «• tte. The distinct behaviour of Na, namely no I

formation in Na+IX and a constant X fraction in Na+X„, has to do with the

fact, that the increase of R due to bondstretching is too small to effect

p,n (Eq. (2)) strongly [9].

In the model the influence of energy transfer from the alkali atom to the

halogen molecule on the behaviour of the fraction is neglected, as the

internal motion of the molecule has been decoupled from the motion of the

alkali atom. The energy transfer is only effective at the lowest relative

velocities. The result will be an enhancement of the fraction. The small

peak in the Cl fraction in the case of Cs+ICl at about 4x10 m/s might

be attributed to this effect. In their measurements of the systems Cs+X_

Tang et al. [15] explained the decrease in the ratio X /X» at about 25 eV

(lab) in terms of energy transfer. From our results concerning the Cs+ICl

system it seems more probable, that the decrease in the fractions for2

Cs+X» at low velocities is mainly due to the excited II ,_ state of themolecular ion.

- 81 -

; 4.3 High velocity regionÏ'

j The high velocity region is defined by considering the vibrational and

rotational motion as frozen during the collision. Bondstretching does

1 not occur and the molecular aspects which have to be taken into account are

the orientation, the Franck-Condon overlap between the two states of the

•: molecule and eventually the excited states. Calculations on the total cross

section and the fraction of dissociated molecular ions only can be per-

formed on a quantitative basis if excited states of the molecular ion do

: not contribute to the cross section. This will be examined first.

'• The influence of excited states on the total cross section can be ob-

"- served experimentally for the heteronuclear halogens. In this case the

; excited states of the molecular ion are formed via a Franck-Condon

transition in a repulsive state, which will dissociate into I and X. By

measuring the I partial cross section the importance of these excited

states can be revealed. From Fig. 14 it is clear, that no I is formed at

high velocities for both heteronuclear halogen systems studied and there-

fore it is inferred, that excited states do not play any role in this

case. From both the measurements of the total cross sections and of the

fractions it is clear, that there is a close resemblance between IBr and

Br„ and to a lesser extent between all halogens. It follows that also in

f the case of the homonuclear halogens excited states are most likely not in-

volved. This is confirmed by the smooth behiviour of the fraction, suggesting

that no extra channel opens in this velocity region. The exclusion of ex-

"' cited states implies, that our collision model can be used to discuss the

;' results.

In this model the distribution over electron affinities P(EA) takes ac-

; count of the effect of the vibrational motion of the molecule before the

collision. This distribution is mainly determined by the wave function of

the vibrational groundstate of the XY molecule as shown by the Franck-Condon

overlap calculations by Kendall and Grice [343 and by Zembekov [31] These

authors applied a delta approximation for the wave functions of the XY

:•' molecular ion for continuum states as well as for the vibrational states

below the dissociation limit. P(EA) is shown to be a gaussian in the case

'J of Br„, the centre of which corresponds to the vertical electron affinity

• EA . The EA is approximately equal to EA,, i.e. the projection of the

equilibrium distance of Br. on the groundstate of Br falls at about the

- 82 -

Na-'-Cl

K +C1 2

Cs+Cl2

Na+Br

K +Br2

Cs+Bi-

Na+I2

K +I 2

Cs+I2

Na+ICl

K +IC1

Cs+ICl

Na+IBr

K +IBr

M +I2

M +I2

W(XY")

-1cm

220

150

115

200

130

140

90

EAdeV

1.138

1.392

1.521

1.463

'.543

1.52J

1.521

o

eV

0.25

0.23

0.21

0.21

0.23

0.25

0. 17

eV

1.02

1.02

1.04

1.47

1.47

1.46

1.72

1.72

1.72

1.47

1.48

1.48

1.62

1.62

1.74

1.69

EAVeV

1.02+0.05

1.47^0.05

1.72+0.05

1.48+0.05

1.62+̂ 0.05

1.74+0.05

1.69+0.05

Rc

&

3.52

4.34

5.06

3.93

5.02 \

5.95

4.22

5.50

6.63 ;

3,94 :

5.04

5.97

4.10

5.30

—

Table I

Values, which are used in the experiment, for the parameters w [18],

EA, [29] and a. The experimental results for the averaged vertical

electron affinity EA of the halogen molecules Cl.,, Br„, I_, IC1 and

IBr together iJith the crossing radii R for the various M-XY systems.

For M+I2 (M=»Cs, K, Na) the effect on EA by changing a>(XY~) is shown

(see text).

- 83 -

level of the dissociation limit of Br„. EA, is the difference between the2 d

electron affinity of the halogen atom and the dissociation energy of the

halogen molecule. For the other halogens also a gaussian distribution for

P(EA) is assumed. The standard width a of the gaussian is deducted from

the vibrational state distribution of XY at room temperature. It is suffi-

cient to take into account vibrational states with v=0,l and 2(at v=3 the

population has decreased to less than 3%). As the vibrational spacing is

only about 0.01 eV, it is a good approximation to introduce an overall

vibrational state distribution being the summation of the distribution

with v=0,l and 2. The result is still a gaussian which is slightly broader

in comparison with the gaussian at 0 K. The width a of P(EA) is determined

by projecting the "classical turning points" of the overall vibrational

distribution of XY on the XY potential curve.

4.3.1 Vertical electron affinities

Rough calculations for the determination of the vertical electron

affinity can be performed by considering in the first instance the criti-

cal velocity as independent of EA. Then Q(v) 2i Q(v,EA ) in Eq.(6) and from

Eq. (7) follows F(v) 3* d P(EA)dEA, which is no function of v, being

valid in first approximation. Using this simplification rather accurate

values of EA can be obtained since the fraction is extremely sensitive to

EA More accurate values are obtained when EA is calculated using Eqs. (='

(9) and (10) together with an appropiate H.„-S relation. Care was t'

taken to fit both the trend in the fractions and the position of the i

Landau-Zener maxima in the total cross sections. The latter are not i;

very critical for the determination of EA (̂ 0.02 eV). The resulting 7j

values for EA^ are given in Table I for all M-XY systems. The accuracy is f;

better than 0.05 eV. The 'herewith used values of the width a of P(EA) are \-t

also given in Tabel I. It is noteworthy that a depends on the shape of the j't

XY potential and thus the value of EA . The shape is only roughly known h

from estimates by Person [lo]. However, in the case of I_ it is demonstra- |

ted that a relatively large error in the vibrational frequency of I_ \,-1 1'

(115 _+ 25 cm ) does not influence drastically the EA (see Table I). f

For comparison no accurate values of EA are available. By the method of |

inversion of orbiting scattering Anderson and Herschbach [30] have j

derived values for EAv from elastic cross section data. However, these j

vary appreciably with tha collision energy. The lowest values, which are I

- 84 -

Na+Cl2

K +C12

Cs+Cl2

Na+Br2

K +Br2

Cs+Br2

Na+I2

K +I2

Cs+I2

Na+ICl

K +IC1

Na+IBr

K +IBr

Vmax

m/s

9.OxlO4

3.6xlO4

2.3xlO4

8.5x104

2.8x104

1.5x104

9. OxlO4

2.4xlO4

1.3x104

9.5x104

3.OxlO4

9.OxlO4

3.3xlO4

H°2(exp)

eV

0.48

0.25

0.17

0.42

0.19

0.12

0.40

0.16

0.10

0.44

0.19

0.41

0.19

Komarov[36]

H°2(theory)

eV

0.81

0.54

0.40

0.53

0.29

0.18

0.40

0.19

0.10

0.53

0.29

0.45

0.23

Olson et al. [37]

H°2(theory)

eV

0.54

0.38

0.28

0.48

0.28

0.18

0.41

0.21

0.12

0.47

0.28

0.4<

0.24

Grice et al. [38]

H°2(theory)

eV

1.28

0.72

0.45

1.16

0.53

0.28

1.04

0.41

0.19

Table II

Experimental results for the positions (v ) of the Landau-Zener maxima in the total

cross sections of M-XY and for H,O(R )•o

For comparison theoretical estimates for H.-O*) are given.

- 85 -

the most reliable ones to the opinion of the authors, agree well with our

results (for K+Cl-, Br~, I» and IC1 these values of EA are respectively

1.2, 1.6, 1.7 and 1.5 eV); The theoretical estimates (_+ 30%) by Person

agree with our experimental values within 25%.

4.3.2 Coupling matrix elements

The velocity dependence of the total cross sections at high velocities

is determined by F_(v/v ) , cf. Eqs. (4), (8) and (9). From a comparison

of F» in Fig. 17 wiih the experimental total cross sections, which ex-

hibit a second maximum, one obtains information on the coupling matrix

element H° (R ). The maximum of F_(v/v ) is found at the velocity\ I c i. cr

0.34v . Consequently the coupling matrix element can be deter-cr

mined from the velocity v , at which the maximum in th° experimentalmax

total cross section is observed

H°2(Rc)=0.58(vmaj£/Rc2)1/2 (11)

Here the crossing radius has to be calculated for an effective electron

affinity. If Q is calculated using Eq. (8) with EA=EA or using Eq. (9)

with an appropiate H]2~R relation and P(EA), the results are almost

identical. This means that for the effective EA the EA can be taken. Eq.

(11) only holds for the homonuclear halogens; a slight difference might

be expected for IX since in this case the relation

Hj2(R »0)=H°2(R )cos© is not exactly true.

In the case of all Na systems, except Na+Cl-, a distinct Landau-

Zener maximum is observed. In the other systems this is more or less con-

cealed by bondstretching, but using our results of the impact parameter

calculations (33) and observing t!.e data more closely, also in the other

systems reasonable estimates for v can be made. The accuracy of v ismax * max

about 10% for the Na systems and better than 50% for the other systems and

Na+Cl2- Using Eq.(ll) H°2(Rc(EAv)) has been determined for all systems.

The values are given in Table II together with those of v .In the same° max

table the theoretical estimates of H J 2 by Komaiov [36], Olson et al. [37]

and Grice and Herschbach [38] have been added using our experimental R

values. It is seen that within its error limits the Olson results show an

- 86 -

excellent resemblance with the experimental data. The Komarov values yield

a good approximation of H-2 only for the systems M-I- and M-IBr. The

results of Crice and Herschbach are all about a factor of three too high.

4.3.3 H-^-B relations14 o

The theoretical methods to determine H . are discussed in a review

article by Janev [39]. In principle these methods only apply to atom-atom

interactions. It is pointed out, that the correct asymptotic behaviour of

the coupling matrix element should be H _ <v exp(-vR ) with v*t^ï~. Using the

Landau-Herring method C40], indeed this result is obtained, whereas the

Heitler-LonJon (LCAO) method predicts H J 2 * exp(-(v+Y)Rc)with y ^ E A .

An exact asymptotic expression for the H,2~R relation has been reported

by Janev [40]. Within the framework of the Landau-Herring method a com-

plicated formula has been derived, which accounts for the long range in-

teraction in the two atom system; its application, however,is in error in

the crossing point itself [41].In the asymptotic region (vR » 1 ) and for

spherically symmetric states the formula is reduced to the expression given

by Komarov [363

Hl2(Rc)*(v/r(l/v))(2v)1/v+1/2Rc

l/v~1exp(-vRc). (!2a)

Application of Eq. (12a) to the case of H+X„ is questionable because of

the above mentioned conditions. Olson, Smith and Bauer [37] suggested the

representation of H.~ in a reduced form

H-2 (R *)*c.R exp(-c2R ) (12b)

where

and R

An essential property of Eq. (12b) is the equivalence of v and y in the

reduction. An analysis of the in 1971 available data by Olson et al. de-

livered the we11known semi-empirical formula

H *(R )»1.0R *exp(-0.86R*). (12c)1 4m C C C

This relationship represents 83% of the data within a factor of three.

- 87 -

Most of these data were obtained using wavefunctions without the proper

asymptotic form. Apart from the electron affinity of the acceptor atom and

the ionization potential of the donor atom the relation (12c) does not in-

volve specific features of the atoms. Applying the LCAO method Grice and

Herschbach [38] did perform calculations on H ] 2 for the M-X interaction,

which also take into account the atomic radius of the acceptor atom. In a

preliminary way the same treatment has been applied to the case of M-X9

interactions. The results are characterized by a pre-exponential and an

exponential factor, which are specific for the halogen molecule involved.

In the case of Cl2, Br_ and I» special H „-R relations are reported to cal-

culate the coupling matrix element for the various alkalis. The H._ values

obtained by applying these relations are about a factor of three larger

than those evaluated using the Olson relation (12c). The authors consider

the exponential factor as rather well defined.

In Fig. 18 our experimental data for the coupling matrix element using

the reduced HJ?-R semilog plot of Olson et al. are summarized. For com-

parison the curve of Olson (Eq. (I2c)) is sh>wn. From the arrangement of

the experimental points in this figure we conclude, that in a good approxi-

mation two sets of straight lines with quite different slope c? can be

drawn to these points, namely the XY lines - connecting the alkali points

for each halogen molecule - and the M lines - connecting the halogen

points for each alkali atom. As shown in the figure a straight Na line

with c2*0.65^0.07 is fitted to the halogen points. In the same way K and

Cs lines can be drawn, having a slightly steeper slope c,»0.75+0.07. It is

seen, that the Cl2 points show a positive deviation with respect to these

lines. The relations of Grice and Herschbach can also be given on the re-

duced scale of Eq. (12b). A good agreement with our data is obtained when

multiplying the Grice relations by respectively 0.38, 0.36 and 0.38 for

C ^ , Br_ and I». These scaling factors have been determined by the positions

of the Landau-Zener maxima for Na. The resulting XY curves are also given

in Fig. 18. It is noteworthy, that the Grice relations account in the right

way for variations of H-2 with the ionization potential (v) for a fixed

electron affinity (y). The slopes (c2) of these lines are about 1.3. From

the different behaviour of the M lines and the XY lines it £s clear, that

variations of v and y are not equivalent in this reduced plot.

- 88 -

I01

theory. Olson el al (1971)

---M.a,]M.Br, theory Gnce et al 0974)M.I, J

present resultso - NO.XYA . K .XVo - Cs.XV

No. XV best fit

25 ~" 30 35Re*

Fig. 18. Correlation of the reduced coupling matrix element H._ &i , led

by the reduced crossing distance R with the reduced crossing distance.

The reduction scheme is defined in Eq. (12b), as proposed by Olson,

Smith and Bauer [37].

The curves of Grice and Kerschbach ( 38.1 have been scaled in the experimen-

tal points for Ka+Cl,, Br_ and I, by resp. 0.38, 0.36 and 0.38.

25-

06 08

Hectran attintty (sV)

Fig. 19. OiljVRc'~ ^ v c r a s ;i function of the dec trot: affinity. The solid

curves show the results for Na and Cs using the relation of Olson et al.

(Eq. (12c)); the dashed Na curve shows Che results using the Komarov for-

mula (Eq. (12a)). The curves (a), (b) and (c) follow from the calculations;

these lines give a best fit to the observed trend in the fractions for

M+XY (except Cl^) (see ssction 4.3.3). The points are the experimental

results derived from v and EA. . The arrows indicate EA (XY).

The insert represents the distribution P(EA) of elsctron affinities of Br?.

- 89 -

Another approach to obtain information about the H „-R relations is

to consider the velocity dependence of the fractions. From Eq. (10) it is

evident that, if the fraction is dependent on the velocity, v has to be

a function of the electron affinity. If the v vs. EA curve has a nega-

tive slope over the electron affinities of the distribution P(EA), the

fraction does increase with velocity. This holds for velocities of the

order of v ; at very high velocities the fraction becomes constant, be-er 2

cause of the asymptotic 1/v behaviour of F„. In Fig. 19 (H.9.R ) -w is

plotted as a function of EA for the H.2~R relations of Komarov (Eq. (12a))

and Olson (Eq. (12c)). A striking difference between the two relations is,

that the Olson curves exhibit a maximum as a function of EA. This is due

to the special reduction introduced by Olson (Eq. (J2b)), namely the pre-

exponential factor (vy) of H.2- Therefore all reduced relations of the

type of Eq. (12b) exhibit a maximum as a function of EA, the position of

which is fixed by the coefficient c~. As a consequence c» determines the

trend in the fraction as a function of velocity. By substitution of Eq.

(12b) into Eq. (10) a best value for c_ is obtained, when fitting the

theoretical fraction to the experimental one. These calculations, which

were performed numerically, also provide the total cross section using Eq.

(9). The coefficient c, is determined by fitting the maximum of Q to the

experimentally observed value. In this way a set of c. and c9 values is

deduced for all systems studied. The values turn out to be only depending

on the alkali atom involved, i.e. variations in EA within the distribution

P(EA) have the same effect on v for all halogens. The resulting

values are c.=0.44 and c2=0.65 for Na, c.=0.43 and c,=0.75 for K and c =

0.41 and c2=0.75 for Cs. The error in c2 is about 10%. Only in the case of

M+C12 a much higher exponential factor has to be used in order to obtain a

good agreement with the fractions (c„=1.3). The results of the calculations

are shown for Br_, resp. the fractions for M+Br9 in Fig. 10 and the total

cross section for Na+Br„ in Fig. 5. The (H.-.R ) vs. EA relations which

are used are shown in Fig. 19.

From the trend in the fractions, H,o-R relations have been establishedI z c

which account for a variation in EA in the right way. The same type of re-

lations also has been derived from the analysis of the maxima in the total

cross sections and H.„ (see Fig. 18). The, in those two ways independently

- 90 -

Fig. 20. Correlation of the reduced coupling matrix element H., divided

by the reduced crossing distance Rc with the

The reduction scheme is defined in Eq. (12d).

by the reduced crossing distance Rc with the reduced crossing distance.

- 91 -

derived values for the coefficient c~» are identical confirming the col-

lision model and especially the assumptions leading to Eq. (6). From Fig.

18 it is clear, that the role of v and y in Eq. (12b) is different, as two sets

of lines could be drawn. Therefore the XY lines and the relations given by

Grice cannot be used for a calculation of the trend in the fraction.

The fact, that two different sets of lines could be drawn suggests, that

a different reduction for R might provide a relation which accounts, with

fixed coefficients, for both variations in v and y. In stead of a reduction

of the type R. = ( V + Y ) K /2, R =(c_v+(1-C_)Y)K has been examined. The choice

of c =1.0 results in better fits to the experimental H values. This in-

troduces a new type of relations,

H12* = cl C exp("c2 Rc*>

** <with H . = 2 H.,/(VY) and R - VR .

\ I 11 c c

The best fit to all H° 9 values using Eq. (12d) was obtained by taking

c =1.73 and c_=0.875. In Fig. 20 the experimental H values are shown on

this reduced scale together with the best fit line. The deviation of the

data from this line is less than 10%. The exponential part of the relation

(12d) behaves like exp(-vRc) as predicted by Komarov [36] and

Janev [39]. When fitting the trend in the fraction with Eq. (12d), no im-

provement with respect to the relations of the type of Eq. (12b) was

obtained.

5. CONCLUSIONS

This experimental study on the ion pair formation in alkali atom-halogen

molecule collisions covers a wide velocity range. The low velocity part has

been the subject of several studies. In these studies, which are based on a

two particle Landau-Zener model, the influence of the internal motion of

the target molecular ion has not been taken into account properly. Accor-

dingly the maximum in the total cross section just above threshold is errone-

ously indicated as the Landau-Zener maximum and the values derived for H°„

are incorrect [2,13].

- 92 -

In the high velocity part, in which the vibrational time of the molecular

ion is much larger than the collisional time, the process can be described

in terms of a two particle interaction. The results can be interpreted in

a quantitative way, especially since excited states of the XY molecular

ion do not participate at high velocities. The measurements have led to a

precise determination of the vertical electron affinity of the halogen

molecules. From the positions of the Landau-Zener maxima, values for the

coupling matrix element have been derived. From the observed trend in the

fractions a relation between H ^ and EA could be established. It is

remarkable, that in order to estimate H°» for a three particle system the

relation of Olson et al. gives very good results. However, this relation is

too simple to predict in s right way the dependence of H° on the ionization

potential (v) of the donor atom and on the electron affinity (y) of the

acceptor molecule.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the critical comments on the manuscript

by Professor J. Kiste...aker and Dr. A.E. de Vries. They enjoyed very much the

stimulating discussions with J. Aten.

They wish to thank A. Mayers for his technical assistance.

This work is part of the research program of F.O.M. and was made possible

by financial support from Z.W.O..

- 93 -

REFERENCES

[1] J. Los, in: The Physics of Electronic and Atomic Collisions3

VIII ICPEAC, Inv. Lect., eds. B.C. Cobic and M.V. Kurepa

(Beograd, 1973), p. 621.

[2] A.P.M. Baede, Advan. Chem. Phys., Vol. XXX (1975), p. 463.

[3] S. Wexler, Ber. Bunsenges. 77 (1973) 606.

[4] J.P. Toennies, Phys. Chem., vol. VI A (1974), p. 228.

[5] E.E- Nikitin, in: Chemische Elementarprozesse, ed. H. Hartmann, (1968)

p. 43.

[6] G.G. Balint-Kurti, Mol. Phys. 25 (1973) 393.

[7] C. Nyeland and J. Ross, J. Chem. Phys. 54 (1971) 1665.

[8] A.P.M. Baede, D.J. Auerbach and J. Los, Physica 64 (1973) 134.

[9] D.J. Auerbach, M.M. Hubers, A.P.M. Baede and J. Los, Chem. Phys. 2 (1973) 107.

[10] A.M.C. Moutinho, Ph.D. Thesis (1971), University of Leyden.

[11] M.M. Hubers and J. Los, Chem. Phys. 10 (1975) 235.

[12] R.K.B. Helbing and E.W. Rothe, J. Chem. Phys. 51 (1969) J607.

[13] S.J. Nalley, R.N. Compton, H.C. Schweinler and V.E. Anderson, J. Chem.

Phys. 59 (1973) 4125;

R.N. Compton and C D . Cooper, J. Chem. Phys. 59 (1973) 4140.

[14] A.M. Bukhteev, Yu. F. Bydin and V.M. Dukel'skii, Sov. Phys.-Techn. Phys.

6 (1961) 496.

[15] S.Y. Tang, C.B. Leffert, E.W. Rothe and G.P. Reck, J. Chem. Phys.

62 (1975) 132.

[16] N. Kashihira, F. Schmidt-Bleek and S. Datz, J. Chem. Phys. 61 (1974) 160.

[17] A.A. Zembekov, Chem. Phys. Lett. 11 (1971) 415.

[18] W.B. Person, J. Chem. Phys. 38 (1963) 109.

[19] J.A. Aten and J. Los, J. Phys. E: Sci. Instr. 8 (1975) 408.

[20] J. Perel and A.Y. Yahiku„ in: The Physics of Electronic and Atomic Collisions3

V ICPEAC, Abstr. of Pap., ed. i.P. Flaks (Leningrad, 1967),

p. 400.

[21] R.R. Herm and D.R. Herschbach, Report UCRL-10526, Univ. of Cal. (1962);

A.P.M. Baede, W.F. Jungmann and J. Los, Physica 54 (1971) 459.

[22] A. Hurkmans, E.G. Overbosch and J. Los, to be published

(Surface Sci.);

A. Hurkmans, E.G. Overbosch, K. Kodera and J. Los,

Nucl. Instr. & Meth. 132 (1976). 'i

- 94 -

[23] M. Kaminsky, Atomic and Ionic Impact Phenomena on Metal Surfaces,

Springer Verlag (1965), Ch. 11;

J. Bdttinger and J.A. Davies, Rad. Effects II (1971) 61.

[24] C. Brunnëe, Z. Physik 147 (1957) 161.

[25] M. Hollstein and H. Pauly, Z. Physik 196 (1966) 353.

[26] E. Hulpke and Ch. Schlier, Z. Physik 207 (1967) 294.

[27] A. Hurkraans, private communication.

[28] J.W. Gadzuk, Surface Sci. 6 (1967) 133.

[29] R.S. Berry and C.W. Reimann, J. Chem. Phys. 38 (1963) 1540;

G. Herzberg, Molecular Spectra and Molecular Structure I, Van No^trand

Reinhold Company (1950).

[30] R.W. Anderson and D.R. Herschbach, J. Chem. Phys. 62 (1975) 2666;

R.W. Anderson, Ph.D. Thesis (1968), Harvard University.

[31] A.A. Zembekov, Teor. i. Eksper. Khimiya, 9 (1973) 366 (in Russian).

[32] E.A. Gislason and J.G. Sachs, J. Chem. Phys. 62 (3975) 2678.

[33] J.A. Aten, M.M. Hubers, A.W. Kleyn and J. Los, to be published»

(Chem. Phys.) (this thesis, Chapter IV).

[34] G.M. Kendall and R. Grice, Mol. Phys. 24 (1972) 1373.

[35] M.S. Child, Theoretical Chemistry Vol. IV (Molecular Collision theory)3

Academic Press, London and New York (1974).

[36] I.V. Komarov, in: The Physics of Electronic and Atomic Collisions,

VI ICPEAC, Abstr. of Pap. (Cambridge, U.S.A., 1969),

p. 1015.

[37] R.E. Olson, F.T. Smith and E. Bauer, Appl. Optics 10 (1971) 1848.

[38] R. Grice and D.R. Herschbach, Mol. Phys. 27 (1974) 159.

[39] R.K. Janev, to be published (1976).

[40] R.K. Janev and A. Salin, J. Phys. B: Atom. Molec. Phys. 5 (1972) 177.

[41] E.A. Andreev, Theoret. Chim. Acta 34 (197'0 73.

- 95 -

C H A P T E R IV

SIMPLE TRAJECTORY CALCULATIONS ON ION PAIR FORMATION

IN ALKALI ATOM-HALOGEN MOLECULE COLLISIONS*

J.A. Aten, M.M. Hubers, A.W. Kleyn and J. Los

ABSTRACT

Impact parameter calculations are reported on ion pair formation in alkali

atom-halogen molecule collisions. Assuming straight line trajectories for the

alkalis, the transition probability is calculated using the Landau-Zener

formula. Both diabatia and adiabatic potential surfaces are used. The re-3 5

suits are given for a. large velocity range, from 5x20 m/s to 2x10 m/s3Brs3 I~). Total crossfor some selected systems M+X~ (M=Na3 K3 Cs and X2=C1

sections for negative ion formation and fractions of dissociated ions are

reported and are discussed with respect to the experimental results of a

preceding papsr.

1. INTRODUCTION

In a preceding paper [I], henceforth referred to as I, measurements

are reported on ion pair formation in collisions between alkali atoms and

halogen molecules. The measurerents concerned the determination of total

cross sections as a function of the velocity of the fast alkali beam, in

the range from threshold up to 2x10 m/s (.2* 5000 eV). By means of a mass

spectrometer the fraction of atomic ions of the total ion yield has been

measured.

It is inferred in I, that these collisions could be treated as two parti-

cle interactions, provided that some molecular aspects are taken into ac-

count. In describing the behaviour of the total cross section as a function

of velocity, it is assumed that during the collision the rotation of the

") Submitted for publication to Chemical Physics.

- 96 -

molecule can be neglected. Secondly tie trajectory of the alkali atom is

approximated by a straight line. As a consequence the angle between the

molecular axis and the vector connecting the alkali atom and the cm. of

the halogen molecule at the second passing of the crossing radius is uniquely

correlated with the angle at the first crossing. This made it possible to

include the angular dependence of the coupling matrix element H „ in the

calculation of the total cross section in an analytical way. In fact an

effective impact parameter has been chosen, which gives the same result

for the calculated total cross section as when integrating over all impact

parameters.

The second molecular aspect taken into account in paper I is bondstretch- j

ing of the negative molecular ion during the collision. When at the first j

crossing a transition takes place from the covalent to the ionic configu- |

ration, the molecular ion is formed on the steep repulsive part of the

groundstate potential, which leads to bondstretching. With increasing inter-

nuclear separation in the molecular ion the electron affinity is sharply j

enhanced, and the radius at which the second crossing takes place is moved ;

outwards. Simultaneously H _ decreases exponentially. In paper I bond-

stretching is treated only in a qualitative way. Two regimes are distinguished.

In the lower velocity region bondstretching is assumed to be complete and

the diabatic transition probability at the second crossing is put equal to

unity. In the high velocity region the collisional time is short with re-

spect to the vibrational time of the molecular ion and here no bondstretch-

ing will occur.

This treatment is adequate for a semi-quantitative description. It indi-

cates that a maximum in the total cross section either is due to bondstretch-

ing or can be identified with the wellknown Landau-Zener maximum. For those

experimental curves where these two maxima are separated, a value for H _

could be deduced from the measurements.

In this paper the results of simple trajectory calculations on two dimen-

sional potential surfaces are presented. The model, that will be introduced,

can be considered as an extension of the collision model of paper I, as here

the integration over impact parameters is carried out and the effect of

bondstretching is included quantitatively. The same model will be used in a

forthcoming paper on differential cross sections for ion pair formation in

alkali-halogen collisions. Three dimensional trajectory calculations for ion

pair formation have been performed only in the near threshold region [2].

2. THEORETICAL METHOD j

Trajectory calculations are performed on two dimensional potential sur-

faces, which represent the groundstate configurations of (M+X„) and M +X„)•

In the diabatic representation of the potential surfaces the internal motion

in the halogen molecule is completely decoupled from the motion of the al-

kali atom; in the adiabatic representation a coupling is introduced. Both re-

presentations have been used in the calculations. The dynamics of the

collision have been simplified by assuming straight line trajectories for

the alkali, which is quite a good assumption in the velocity region consi- •.',

dered [3J. The transition probability for going from one surface to the

other is calculated at the crossing of the diabatic surfaces using the

Landau-Zener formula.

The potential surfaces are defined as a function of r and r„, where r^

is the internuclear distance in the halogen molecule or molecular ion and r„

is the distance between the alkali atom and the center of mass of the halo-

gen molecule. The covalent potential is given by

Vcov<V r2> = V X 2( r l > 0 )

where V is the Morse potential of the neutral halogen molecule. The re-2pulsive part of the potential surface for small distances r9 has been

omitted in accordance with the assumption of straight line trajectories.

The ionic potential surface is given by

V (r r 1 = -l/r +V -(r,)+D -D. -EA +1 (2)ionv 1' 2' 2 X- 1 cov ion at K*>

where: V - is the Morse potential of the halogen molecular ion I2 •

D is the dissociation energy of the halogen molecule :

D. is the dissociation energy of the halogen molecular ion j

EA is the electron affinity of the halogen atom >

I is the ionization potential of the alkali atom. j

Eq. (2) represents the. superposition of the Coulomb interaction of the alka- •

li ion with the centre of mass of the halogen molecular ion, the Morse po- j;

tential of the molecular ion, and additional constants. The repulsive core ff'

is neglected as in the case of the covalent potential. ?The crossing distance |R | is given by the intersection of the two diabatic |

potential surfaces given in Eqs. (1) and (2). It is clear that the set of II) Throughout this paper atomic units are used unless stated otherwise. I

- 98 -

-33 4 5 6

r, (Br.Br) internuctear distance (A)

Fig. 1. Potential curves of the electronic

groundstates of the Br molecule and the Br_

molecular ion. The internuclear distance dis-

tribution for Br at 300 K and the correspon-

ding distribution of vibrational states in Br„

after electron transfer are also shown. EA. is

the electron affinity corresponding to a

transition at the dissociation limit of Br.,;

EA is the vertical electron affinity corres-

ponding to the equilibrium distance of Br,.

35-

30-

25-

s

Ia l5"

10-

5-

r.(Br,) r(Br2-)

2 3 4 5 6 7r, (Br-Br) htemuclear distance (A)

Fig. 2. Crossing radii for the systems Na, K

and Cs + Br2 as a function of the internuclear

distance r^ of the halogen molecule. The

arrows indicate the equilibrium distances of

the Br, molecule and the Br, molecular ion.

- 99 -

vectors R in fact is a curve in the (r.,ro) plane, but only the componentc I i.along the r„ axis, R „, is used here. Its value is given by

R c 2 = ^ ^ m o l ^ c l » ' ( 3 )

where the electron affinity of the halogen molecule is given by

EA ,(r,) = Vv (r.)-V -(r.)-D +D. +EA .molv r X- 1 X„ 1 cov ion at

In the following R _ will be denoted by R .

From Fig. 1 it is clear that E A m o l is strongly depending on r , as the

equilibrium distance of the molecular ion is shifted with respect to that of

the molecule. In Fig. 2 R is given as a function of r. for Na, K and

Cs+Br2>

The potential surfaces defined by Eqs. (1) and (2) are the diabatic sur-

faces. If the coupling between these surfaces at the points of intersection

is known, the adiabatic surfaces for this system can be constructed. The

lower adiabatic surface is then given by

V . C W - I :(Vcov+V.on)V(Vcov-Vion)2+4H12

2]. (4)

The coupling matrix element H]2(R ) is calculated using a reduced relation

of the type as given by Olson et al. [4]

H12* = CjVezpC-c-jR,.*) <5)

with H * = H1O//I.EA n and R * = R (i/f+^A ,)//ï. The coefficients12 12 mol c c mol

c. and c„ depend on the actual system studied. For the adiabatic surface the

internal motion of the halogen molecule is no longer decoupled from the mo-

tion of the alkali atom.

The transition probability for diabatic transition from one diav:>atic sur-

face to the other is calculated using the Landau-Zener formula [5]. For the

systems studied here the general form reduces to

p =

where v , is the radial velocity of the alkali atom with respect to the

- 100 -

Fig. 3. The dependence of R on the collision time T . 1 for the systems Na,

K and Cs + Br2 in the case of ionic scattering. For K + Br, two curves are shown.

The oscillating curve corresponds to a transition to a boundstate of the Br"

molecular ion at rj =2.40 8. The dip between the two maxima indicates the tur-

ning point in the B ^ vibiational motion. The dotted part of the curve is not

used in the calculation, see text. The other K + Br2 curve -.-.- gives the Rc

dependence after a transition to a continuum state of the BrZ ion at r, -

2.26 8, The Na + lir, curve is accompagnied by four trajectories with impact

parameter zero. The velocities are: a) 5 x JO m/s; b) 10 m/s; c) 2 x 10 m/s;

d) 4 x 10 m/s. In the case of Cs + Br2 Rc reaches a value of 228 8 in its

maximum. For the transition at r. » 2.40 8 the vibrational period T .. is indi-vib

cated.

- 101 -

centre of mass of the halogen molecule. This means that in our range of im-

pact velocities the dependence of p on the relative velocity of the two ha-

logen atoms has been neglected [6]. In the calculation of p the dependence

of H „ on the orientation of the molecule is taken into account. In the

case of the X„ groundstate the orientational dependence of H.~ is shown to

be [7,8]

H ] 2 = H}2(Rc)cose

where 0 is the angle between the molecular axis and the radial velocity

vector of the alkali atom with respect to the cm. of the halogen molecule.

As p is mainly determined by H.„ and via Eq. (5) by R , it is important to

know the dependence of R on r,, i.e. on the collisional time T .., .c 1 coll

The mechanism of ion pair formation now can be introduced using the

diabatic potential surfaces. When using adiabatic surfaces the treatment is

i = ( 1 / l J ) 9 7 ;

(with u representing the reduced mass of the halogen molecule) and by sub-

sequent substitution of r, in Eq. (3). As is evident from Eq, (2), r. is

only dependent on the V - potential and hence in the diabatic representation2

the motion of the halogen molecule is decoupled from that of the alkali.

The resulting dependence of R on the collisional time x .., shown for the

systems Na, K and Cs with Br„ in Fig. 3, will be discussed in detail in

the next section.

As for each trajectory with an impact parameter b<b i. R the inter-IIlcLX C

section of the potential surfaces is passed twice, there are two interaction

paths leading to ionization [3]. The first interaction path is called cova-

lent scattering; in this case the first crossing is passed diabatically and

the second adiabatically. The transition to the ionic surface takes place at

the second crossing. The second interaction path is called ionic scattering;

here the first crossing is passed adiabatically and the second diabatically.

The transition to the ionic surface takes place at the first crossing. As,

analogous. The change in R during the collision can be calculated applying \

diabatic surfaces by integrating the equation of motion for the two halogen i

atoms on the ionic potential surface V. :v ion

3V. (r.,r ) Ï., . i \ ion \ i.

ri = (" 1 / l )

- 102 -

on the covalent surface, the internuclear distance in the halogen molecule

is kept constant, the crossing radius will not change during the collision;

with ionic scattering, however, bondstretching will start after the first

crossing and at the second crossing r. and hence R will have increased, as

shown in Fig. 3.

If the collision process is described using adiabatic instead of diabatic

surfaces, Eq. (6) will be replaced by

9 V_ (r,,r )

j 1

In contrast to Eq. (6) here the motion of the halogen molecular ion is also

a function of r„ via the square root term in Eq. (4), i.e. it is a function

of the position of the alkali ion. Hence a coupling between the motion of

the halogen molecule and the alkali atom is introduced, as Eq. (7) is deter-

mined by the relative positions of the three particles involved. The

consequence of introducing the adiabatic surfaces is that the gradient of

the potential in the neighbourhood of the crossing is reduced, which in

turn makes bondstretching slower.

The dynamics of the collision is simplified in the present model by

assuming straight line trajectories for the alkali atoms. This assumption

is justified in the velocity region under consideration, as is confirmed by the

work of Delvigne C3], who showed that the differential cross sections for

these processes decrease sharply for values of the reduced scattering angle

beyond T = 200 eV x degree. In the case of K+Br~ the maximal scattering

angle is 20° at a relative velocity of 8x10 m/s (^ 10 eV). The halogen

atoms are supposed to be at rest before the collision. The value of R at

the second crossing is calculated for each impact parameter and velocity by '^

solving Eq. (6) or (7), and substitution in Eq. (3). The actual total cross ;

sections for ion formation were obtained by integrating the trajectories •>.

leading to ionization over all impact parameters, over the sp.icial orien- j

tation of the molecular axis before the collision and over the initial dis~ j

tribution of internuclear distances r. in the halogen molecule. This distri- \

bution was calculated assuming for the neutral halogen molecule harmonic ;j.1

wavefunctions, weighted by Boltzraann factors as in paper I. The total cross j

section consists of two contributions, the ionic and the covalent cross '.;.;

sections, due to scattering along the ionic path and along the covalent path ;:

- 103 -

respectively. The computer program used for the calculations has been written

in ALGOL 60 and was run on a CDC 6600 computer. Per energy point about 10

trajectories were calculated in about 100 sec.

3. RESULTS AND DISCUSSION

In this section the results of the trajectory calculations will be dis-

cussed in relation with the measurements of paper I. The effect of bond-

stretching will be examined for the different systems studied. In the first

place the role of the alkali atom in the bondstretching process is analysed

using the total cross section results concerning M+Br». As a second step

the influence of the halogen molecule is analysed for the system Na+X„.

3.1 Bondstretaking

The main effect of bondstretching is a large enhancement in the total

cross section for ion pair formation. Bondstretching only occurs in the

case of ionic scattering, whereas in our model it does not play a part in

covalent scattering. The effect of bondstretching is maximal at impact ve-

locities around 10 m/s; the velocity at which it disappears is related to

the ratio between the collisional time T -, and the vibrational timecoll

T ., of the negative molecular ion.In Fig. 3 the evolution of R , derived from Eqs. (5) and (6), is given as

a function of T nn for the three alkali atoms colliding with Br„. Thecoli z

shape of these curves depends on the internuclear distance at the moment of

electron transfer. For the system K+Br_ two curves are shown, one starting

at a rather small internuclear distance leading to dissociation and one

starting at an internuclear distance somewhat larger than the equilibrium

distance of the Br» molecule. In this case an oscillating behaviour is

found, which is due to the reflection of the halogen atoms against the outer

slope of the Br„ potential well. This reflection was found to have an. 3

effect in the calculations only in the near threshold region below 3x10

m/s, which is far below the velocity region under consideration; hence

this part of the curve is given as a dotted line.

To give a rough indication of the effect of bondstretching the straight-

line trajectories for impact parameter b=0 are given for four relative ve-

locities in the case of Na+Br,» From Fig. 3 it can be seen, that at 4x10 m/s

•t:

''i

- 104 -

MO-

Br,

relative velocity m/s

Fig. 4. The dependence of the total cross section for negative ion formation

on the relative velocity in M+Br- (M = Na, K, Cs) collisions. The full lines

represent on an absolute scale the calculated total (ionic *covalent) cross

sections; the dotted lines give separately the covalent cross sections. The

open symbols are the experimental results from paper I, the solid symbols are

the experimental points taken from Ref. [10]. The experimental total cross

sections have been scaled to the calculated ones at the position of the

(Landau-Zener) maximum of the corresponding covalent cross section. The various

symbols indicate the alkali atom involved. O # - Na + Br2. A A -

O - Cs+Br . irR corresponds to the vertical electron affinity

(Table I).

- 105 -

the change in R due to bondstretching decreases rapidly and that at even

higher velocities, i.e. x ,, << T ., , bondstretching will no longer be

effective. In the case of K or Cs both R and the change in R due to bcnd-c c

stretching are larger than for Na. This implies, that at the same relative

velocity the collision time will be longer and consequently bondstretching

will be effective up to higher velocities for K and Cs.

When going from !„ via Br» to Cl„ the velocity range where bondstretching

is effective will be extended towards higher relative velocities; with in-

creasing vibrational frequency w the velocity of the strc ching of the

(X-X) bond becomes higher. In the Na+X_ curves it was in fact observed,

that the velocity, at which bondstretcving is no longer effective, is2

roughly proportional to to .

3.2 Total cross sections

In the calculations parameters are used, which have been determined in

paper I by fitting the total cross section and the fraction measurements in

the high velocity region (see Table I). In this section the validity of the

model including the use of the parameter values obtained in paper I will be

examined for the entire velocity range. Therefore it has not been tried to

obtain best fits for all parameters involved. In the calculations use has

been made of both the diabatic and adiabatic surfaces introduced in the pre-

vious section. The results only differ in the low velocity region, where

bondstretching is effective. When using adiabatic surfaces bondstretching is

suppressed somewhat, but this effect is only significant for the systems

Na+X„. The results presented in this section are all calculated using adia-

batic surfaces.

In Figs. 4 and 5 the results of the calculations for the total cross

sections are presented. In the same figures the calculated covalent cross

sections are given. Because in the present model the covalent cross section

is not influenced by bondstretching, the position of the Landau-Zener

maximum can be easily seen here. The experimental results of paper I, which

are also given in Figs. 4 and 5, have been scaled to the calculated total

cross section in the maximum of the corresponding covalent cross section,

i.e. the Landau-Zener maximum^ As the Landau-Zener maximum is located at

rather high collision energies, the experimental points in this region are

considered to be rather accurate and independent of beam monitor effects

[1]. The agreement in the velocity dependence between the calculated total

- 106 -

•4

ï

40-1

30-

20

10-

Na-CI2

50

_ 40-o

30-

20-

10

Na.l ,

K)' O5 2relative velocity m/s .

Fig. 5. The dependence of the total cross

section for negative ion formation on the re-

lative velocity in Na + Cl_ and Na + I,

collisions. The full lines represent on an ab-

solute scale the calculated total (ionic +

covalent) cross sections; the dotted lines

separately give the calculated covalent cross

sections. The open symbols are the experimental

results from paper I, the solid symbols are the

experimental points taken from Ref. ClOJ. T P P

experimental total cross sections have been

scaled to the calculated ones in the (Landau-

Zener) maximum of the corresponding covalent2

cross section. uR corresponds to the verti-

cal electron affinity EA (Table I).

1.0-

0B-

06-

0.4-

0.2-

B IP

M.Br,

10'relative velocity rr/s

Fig. 6. The dependence of the Br fraction of

the total negative ion yield on the relative

velocity in M + Br2 (I = Na, K, Cs) collisions.

The full lines represent the calculated frac-

tions; the symbols represent the experimental

points from paper I. The various symbols indi-

cate the alkali atom involved.

O - Na + Br2, A - K + Br2> D - Cs + Br2-

- 107 -

cross sections and the experimental data-e.g. the location of the maxima and

minima-is remarkably good, at least if one takes into account, that the para-

meters used in the calculations were determined from the high velocity data

of paper I. The discrepancies in the low velocity part of the cross sections

may be due to effects, concerning on the one hand electronically excited states

and energy transfer during the collision and on the other hand the fast al-

kali beam monitor.

The results of the calculations will be discussed using the Na+Br„ re-

sults, as all relevant effects can be observed here. The changes which occur

when considering other alkali atoms or halogen molecules will be discussed

afterwards. In the system Na+Br„ two distinct maxima 1. the total cross

section are observed, the one at 1.2x10 m/s being due to bondstretching and

the one at 8.5x10 m/s being the Landau-Zener maximum. At low velocities

the total cress section is determined mainly by bondstretching. This is

evident from the estimates in section 3.1 and from the fact that the covalent

cross section hardly contributes to the total cross section. The rise in the

cross section from threshold to 1.2x10 m/s is due to the fact, that for

Na the increase in R and hence the decrease of H ~ in case of complete

stretching of the (Br-Br) bond is not large enough to make the diabatic

transition probability at the second crossing of the ionic pathway equal to

unity for low velocities. Therefore this transition probability will in-

crease with the velocity. The value of the cross section in its maximum at

4 2

1.2x10 m/s is about equal to ITR , which means that for ionic scattering

the diabatic transition probability at the second crossing has become equal

to unity. The following decrease in the total cross sections to higher ve-

locities is due to the reduction of the effect of bondstretching. In the

minimum at 4.5x10 m/s bondstretching is no longer effective. When calcu-

lating the cross section using diabatic surfaces, the position of thid mini-

mum is shifted towards higher velocities and is almost completely filled up.

This difference is due to the large H.? for the Na systems at tl _ rirst

crossing, which in the case of adiabatic surfaces decreases the slope of

the (Br-Br) repulsive potential and consequently the velocity with which

the two Br atoms separate. At high velocities the Landau-Zener maximum can

be observed, because it is not concealed by bondstretching. This is clear

from the fact, that in this velocity region the covalent and ionic cross

section contribute about equal parts to the total cross section.

- 108 -

ci2

Br2

X2

Na +

Na +

Na +

K +

Cs +

Table

Cl?

Br?

H

Br,

Br,

T

(cm )

220

150

115

cl

3.70

0.51

0.44

0.53

0.50

D.ion(eV)

1

1

1

1

0

0

0

0

.31

.15

.02

C2

.30

.70

.65

.80

.80

(

2

2

3

e

&)

.66

.84

. 19

EAv(X2)

(eV)

1.02

1.47

1.72

Values, which are used in the calculations, •

for the parameters wCxI) [9], D. (X~) [10], \'

re(x") [1], EAv [13, Cj Cl] and c2 Cl], f

Other parameters used are taken from Ref. [11] j

(ionization potentials) and Refs. [12] and [13] j

(spectroscopie data of the halogens). j

- 109 -

In changing in the case of Br„ the alkali atom, from Na to K or Cs, two

effects can be observed.

In the first place the influence of bondstretching is extended to higher ve-2

locities and ac low velocities the cross sections become equal to ITR .

This is due to the larger initial value of R and to the larger increase of

R during the collision (see Eq. (3) and Fig. 3). In the second place the

position of the Landau-Zener maximum is shifted towards lower velocities,

as can be observed in the covalent cross section. Therefore the Landau-Zener

maximum is almost completely concealed by bondstretching and the total

cross section exhibits a monotonous decrease over the entire velocity range,

the decrease being mainly determined by bondstretching.

If in the case of Na the halogen molecule is changed as indicated in Fig.

5, the most important effect is the change in the upper limit of the region

where bondstretching is effective. The position of the Landau-Zener maximum

is hardly affected by choosing different halogens. In the case of I» the

minimum between the two maxima in the total cross section is shifted towards

lower velocities. This means, that the upper limit of the bondstretching

region is reduced with respect to the Br~ situation, the reason being the

smaller value of w and the smaller difference in equilibrium distances of

I» and I„. The value of the cross section in its low velocity maximum at

1.0x10 m/s is less than nR . This indicates, that in case of I„ bond-c 2

stretching is never effective enough to make the diabatic transition at the

end of ionic scattering equal to unity. In case of Cl, the opposite is ob-

served. Here the upper limit of the bondstretching region is so high, that

even for Na the Landau-Zener maximum is concealed by bondstretching. The re-

sulting curve resembles the one observed for K+Br„. Though a very good agree-

ment between calculations and experimental results is observed in the case

of Na+Cl_, the validity of our simpla model is doubtful in the case of Cl»;4

for K+C1„ the experiment shows a maximum at 3.6x10 m/s, which is notreproduced by the calculations.

3.3 Fraations of dissociated ions

The fraction of dissociated molecular ions will be mainly determined by

three effects. In the first place the fraction is determined by the distribu-

tion over electron affinities P(EA) as pointed out in paper I. Secondly the

fraction will be influenced by the contribution from electronically excited

- no -

states of the molecular ion, as these all dissociate. In the third place at

low velocities energy transfer from the alkali ion to the molecular ion and

deformation of the X? potential by the alkali ion will lead to an enhancement

of the fraction. In our model only the first effect is taken into account.

The only difference with the calculations in paper I is, that in the pre-

sent model the fraction can also be calculated in the low velocity region.

As bondstretching does not influence the dissociation mechanism of the mole-

cular ion, a constant fraction in the bo. dstretchin^ region is predicted by

our model.

In Fig. 6 the calculated and experimental results for the fraction of

M+Br„ (M=Na,K,Cs) are shown. In the low velocity region below 2x10 m/s

the calculated fractions are about constant, as expected from the model. The

experimental fractions for K and Cs, however, exhibit a decrease with in-

creasing velocity in this region. As explained in paper I this difference is

attributed partly to the excited »,/2 s t a t e °f t n e Br_ and partly to

energy transfer. In the high velocity region above 2x10 m/s the results of

the calculations are in agreement with the experimental results and almost

identical with those of the calculations of paper I.

From the calculations of the fraction in case of Cl_ it became evident,

that in this case other processes, which are not included in our model,

will be effective. Evidence for this has already been obtained from the

total cross sections for K+C1_. Additional evidence comes from a compari-

son of the measured fractions and from the excitation cross section measure-

ments by Anderson et al. [14] for the system K+C1_. The pronounced in-

crease in the fraction for Cl™ at 2x10 m/s coincides with the onset of the

excitation cross section. Anderson [7] attributed the photon emission to

transition to the excited il, .» state of Cl~.

Concluding we might remark, that simple trajectory calculations as re- !

ported in this paper describe the experimental total cross sections very j

well. These calculations, however, do not explain the low velocity behaviour

of the fractions since these are very sensitive to effects like the in-

fluence of excited states and energy transfer. Complete trajectory calcu- :

lations are needed in order to give a more accurate description of the frac-

tions at low relativ velocities, where the parameters from paper I might

be used.

- Ill -

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the critical comments by Dr. A.E. de

Vries and Professor J. Kistemaker.

This work is part of the research program of F.O.M. and was made possible

by financial support from Z.W.O..

REFERENCES

Hi] M.M. Hubers, A.W. Kleyn and J. Los, to be published (Chem.Phys.)

(this thesis, Chapter III).

[2] R. Duren, J.Phys.B. 6(1973) 1801;

U. Havemann, L. Zülicke, E.E. Nikitin and A.A. Zembekov, Chem.

Phys.Lett. 25 (1974) 487.

[33 G.A.L. Delvigne and J. Los, Physica 59 (1972) 61.

[4] R.E. Olson, F.T. Smith and E. Bauer, Appl.Optics 10 (1971) 1848.

[5] L. Landau, Physik.Z.Sowjetunion 2 (1932) 46;

C. Zener, Proc.Roy.Soc., London A 137 (1932) 696.

[6] E.E. Nikitin, in: Chemische Elementavprozesse3 ed. H. Hartmann,

(1968) p. 43.

C7] R.W. Anderson, Ph.D. Thesis (1968), Harvard University.

[8] R.W. Anderson and D,R. Herschbach, J.Chem.Phys. 62 (1975) 2666;

A.A. Zembekov, Teor.i.Eksper.Khimiya, 9 (1973) 366 (in Russian).

[9] W.B. Person, J.Chem.Phys. 38 (1963) 109.

[10] A.P.M. Baede, D.J. Auerbach and J . Los, Physica 64 (1973) 134.

[11] C.E. Moore, Civa. 46?'3 Nat.Bur.Standards (USA).

[12] R.S. Berry and C.W. Reimann, J.Chem.Phys. 38 (1963) 1540.

[13] B. Rosen, Intern.tables of selected constants. 17. Spectroscopie

data relative to diatomic molecules. (Pergamon Press, New York,

1970).

[14] R.W. Anderson, V. Aquilanti and D.R. Herschbach, Chem.Phys.Lett.

4 (1969) 5.

- 112 -

S U M M A R Y

This thesis deals with measurements of the total cross section

for ion pair formation in single collisions of alkali atoms with

simple molecules (diatomic halogens and SF,) in the electronvolt

range. The collision process is represented by M + XY -> M +XY

in which M and XY denote the fast alkali atom and the thermal

target (halogen) molecule respectively. An electron jump at a large

distance R due to coupling between the covalent and the ionic

state is responsible for the ion pair formation.

In first approximation the collision process is assumed to be

a two particle interaction, in which some molecular aspects of the

target molecule are included. Important molecular aspects are the

vibrational motion of the molecule and the molecular ion and the

interaction of the alkali ion with the molecular ion during the

collision. As a consequence the internuclear distance in the XY

molecular ion will increase during the collision. This phenomenon

of bondstretching will dominate the behaviour of the total cross

section for ion pair formation at low relative velocities.

In case of atom-molecule interaction the Landau-Zener (L.Z.)

maximum in the total cross section can therefore only be observed if

occurring at very high velocity. In various experiments a maximum

is observed just above threshold energy, which is interpreted up to

now as a L.Z. maximum; however, it is caused by bondstretching. The

position of the L.Z. maximum is of high importance as the coupling

matrix element H „ between the two states involved is derived from it.

Chapter I describes measurements of total cross sections for ion

pair formation in collisions of alkali atoms with the interhalogens

IBr and IC1 at energies from threshold up to 40 eV. It is observed

that in this energy region electronically excited states of XY play

a part, depending on the alkali involved. This is explained in terms

of bondstretching using a modified L.Z. theory.

In Chapter II results are reported on total cross section measure-

ments for M + SF, in the same energy region. The relative importance

of translational energy vs internal energy in promoting ion pair

formation is investigated for the various negative ions formed. It

appears that at threshold only the total (internal + translational)

energy is important in overcoming the threshold fov ion formation.

In other terms it means that due to quenching by the alkali ion

- 113 -

the vibrational energy of SF, is completely transferred into

translational energy at threshold. As a result the electron affinity

EA, derived from the threshold behaviour of the total cross section

in a molecular beam experiment, generally corresponds with the

adiabatic EA of the target molecule. Therefore the electron

affinities determined in chapter I are the adiabatic ones.

Chapter III gives the results of total cross section measurements

for ion pair formation in M-XY (halogen molecule) collisions for

a large velocity region. The L.Z. maximum in the total cross section

appears to occur at very high velocity; the corresponding values

of H J 2 for the various alkali-halogen systems are reported. A

discussion is devoted to the relation between H,„ and. R . From the11 c

fractions of dissociated ions accurate values have been obtained

for the vertical EA of the halogens.

In Chapter IV simple trajectory calculations are reported for

the alkali-halogen (M-X„) interaction. Using thj impact

parameter method total cross sections for ion pair formation

have been calculated for a large velocity region with parameters

from chapter III. There is a good agreement with the measurements

from that chapter in the entire velocity region.

- 114 -

S A M E N V A T T I N G

In dit proefschrift wordt een onderzoek beschreven naar de

totale werkzame doorsnede voor ionenpaar vorming in enkelvoudige

botsingen tussen alkali atomen en eenvoudige molekulen (cwee-

atomige halogenen en SF,)bij boventhermische energ**sën. Het botsings-6 +

proces wordt weergegeven door M + XY-»- M + X Y , waarbij

M het snelle alkali atoom en XY het thermische doelwit (halogeen)

molekuul voorstelt. Aan de ionen vorming ligt ten grondslag een

elektron sprong op grote afstand R als gevolg van de koppeling

tussen de kovalente en ionogene toestand.

Het botsingsproces wordt in eerste benadering opgevat als een

twee-deeltjes wisselwerking, waaraan vervolgens enige molekulaire

eigenschappen van het doelwit molekuul zijn toegevoegd. Belangrijke

molekulaire aspekten zijn de vibratie beweging van het molekuul en

het molekulaire ion en de wisselwerking tussen het alkali ion en het

molekulaire ion tijdens de botsing. Een gevolg is dat tijdens de

botsing de internukleaire afstand in het (X-Y) ion zal toenemen.

Dit verschijnsel, "bondstretching" genoemd, zal het snelheids-

afhankelijk gedrag van de werkzame doorsnede voor ionenpaar vorming

bij lage botsingssnelheden domineren.

Derhalve zal het Landau-Zener (L.Z.) maximum in de totale

botsingsdoorsnede voor atoom-molekuul verstrooiing alleen waarneem-

baar zijn, als het bij zeer hoge relatieve snelheid ligt. Het in vele

gevallen optredend maximum vlakbij de drempelenergie, tot op heden

geïnterpreteerd als een L.Z. maximum, is het gevolg van bondstretching.

De positie van het L.Z . maximum is belangrijk omdat hieruit de grootte

van de wisselwerking H.„ tussen de twee relevante toestanden afgeleid

wordt.

Hoofdstuk I beschrijft metingen van totale werkzame doorsneden voor

ionenpaar vorming in botsingen tussen alkali atomen met IBr en IC1 voor

boventhermische energieën (tot 40 eV). Centraal staat de vondst, dat in

dit energiegebied elektronisch aangeslagen toestanden van XY een rol

kunnen spelen, afhankelijk van het alkali. De verklaring wordt gegeven

in termen van bondstretching m.b.v. een gewijzigde L.Z. theorie.

- 115 -

Hoofdstuk II geeft resultaten voor totale botsingsdoorsneden voor

ionenpaar vorming la M + SF voor eenzelfde energiegebied. De rela-

tieve invloed op de doorsnede van vibratie ën translatie excitatie

is onderzocht voor de verschillende negatieve ionen, die in de

botsing gevormd worden. Het blijkt dat vlakbij de drempel slechts

de totale (interne + translatie) energie van belang is voor de vorming

van een ionenpaar. Anders geformuleerd betekent dit, dat door quenching

o.i.v. het alkali ion de vibratie energie van SF, bij de drempel

volledig omgezet wordt in translatie energie. Een algemeen gevolg

hiervan is dat de elektronen affiniteit EA bepaald uit het drempel-

gedrag van de botsingsdoorsnede in een molekulaire bundel experiment

correspondeert met de adiabatische EA van het doelwit molekuul.

De elektronen affiniteiten bepaald in hoofdstuk I kunnen daarom als

adiabatisch beschouwd worden.

Hoofdstuk III geeft de resultaten weer van metingen van totale

werkzame doorsneden in M - XY (halogeen molekuul) botsingen voor

een zeer groot snelheidsgebied. Het L.Z . maximum blijkt pas bij

zeer hoge snelheid op te treden; hieruit zijn waarden voor H „

afgeleid voor de alkali-halogeen systemen. Een diskussie wordt

gewijd aan het verband tussen H,o en R . Uit de fracties van de11 c

gevormde gedissocieerde ionen zijn nauwkeurige waarden verkregen

voorde vertikale EA van de halogenen.

In hoofdstuk IV worden eenvoudige baanberekeningen beschreven

voor alkali-halogeen botsingen (M - X„) voor een zelfde snelheidsgebied

als in hoofdstuk III. Met behulp van de impact parameter methode

zijn totale werkzame doorsneden voor ionenpaarvorming berekend,

gebruik makend van de hoge snelheidsparameters uit hoofdstuk III. De

overeenstemming met de metingen uit dit hoofdstuk is goed over het

gehele snelheidsinterval.

- 117 -

Het in dit proefschrift beschreven onderzoek is verricht in de groepMolekulaire Bundels van het F.O.M. Instituut voor Atoom- en Molecuul-fysica te Amsterdam. Het is het rasulc<±a.t van een goede samenwerking enenthousiaste werksfeer binnen dit instituut.

Ik ben Professor J. Kistemaker dankbaar voor de mij geboden gelegen-heid in deze omgeving te hebben kunnen werken. Voor de wijze, waarop hijhet instituut organiseert en leiding geeft heb ik grote bewondering.Ik dank hem voor de kritische belangstelling voor mijn werk.

Ik dank mijn promotor Professor J. Los, die de afgelopen vier jaarmijn leermeester is geweest. Joop's bijzondere meesterschap reikte veelverder dan alleen zijn wetenschappelijke en technische steun bij hetonderzoek. Hij leerde me een kritische houdii.g jegens de wetenschap, deprodukten en bedrijvers ervan. Ik dank Joop en Keetie voor hun persoon-lijke belangstelling en hun gastvrijheid.

Dr. Dan Auerbach heeft mij ingewijd in de atoomfysica. Gedurende mijneerste jaar op het F.O.M. Instituut was hij een onmisbare steun en gang-maker .

De samenwerking binnen de groep heb ik zeer op prijs gesteld. De tech-nische steun, die ik tijdens de vele nukkigheden van de molekulairebundel machine heb ondervonden van Andre Mayers, was groot. De totstand-koming van het - in dit proefschrift centraal staande - hoofdstuk IIIis voor een belangrijk deel te danken aan Aart Kleyn. Ik bewonder zijninzet en zijn heldere manier van denken. De vruchtbare discussies metJacob Aten hebben veel bijgedragen tot de interpretatie van de resulta-ten van hoofdstuk III. De samenwerking met Aart Kleyn en Jacob Aten istenslotte geculmineerd in het totstandkomen van hoofdstuk IV.

Ik dank Dr. Dolf de Vries voor zijn altijd aanwezige belangstelling enzijn kritische kommentaren op mijn artikelen.

Voor de hulp bij het rekenwerk voor het SF, artikel dank ik FransVitalis.

Onmisbaar zijn de werkzaamheden geweest van de technische groepen vanhet instituut: voor hun medewerking dank ik Ton Neuteboom en de instru-mentmakers, Evert de Haas en de konstrukteurs, Paul van Deenen en deelektronici, Coen Visser en de automatiseringsgroep en Jan Verhoeven ende vacuumafdeling. In het bijzonder wil ik danken Ruud Boddenberg, PaulJansen, Han Platvoet, Joop van Wel, Ton Haring en Frans Monterie en van-wege hun centrale plaats binnen het instituut Mevr. Wiemer en ToonAkkermans.Tot slot wil ik allen bedanken die de verschijning van dit boekje tech-nisch mogelijk gemaakt hebben. Mevr. Tine Köke-Van der Veer en Mevr.Kitty Wünsche voor de typografische verzorging, Mevr. Maryvonne Turksma-Cabanas en Mevr. Hanna Vanenberg voor het vervaardigen van de tekeningenen Hans Okhuizen voor het offset werk; tenslotte voor de administratievehulp Mevr. Louise Roos, Ria Priester en Josée Wolthers.aan martientje3 aan betty, aan dirk.