ChemicaI Physics 58 (1981) 385-393 North-Holland Publishing Company

SPONTANEOUS DESORPTION OF VIRRATIONALLY EXCITED MOLECULES PHYSPCAECY ADSORBED ON SURFACES”

Donald LUCAS$ and George E. EWING Depnrzment of Chemistry, Indiana Unir;ersity, Bbomingron, IN 474M. USA

Received 12 December 1980

The energy within 2 vibrationally excited phy-sisorbed molecu!e often exceeds that needed to break its bond to the surface. Energy transfer from the vibrating chemical bond. to the surface bond causes the surface bond to ruptore and the vibrationdly relaxed adsorbate is released from the surface. We present a theoretical model which allows an estimation of the residence time of a vibrationally excited adsorbate on a surface. Because of uncertainties in the nature of the surface bond. the lifetimes obtained from the analytical expressions presented have only qualitative significance. The results are interpreted in terms of Franck-Condon overlaps between the wavefunctions which describe the adsorbate-

su’bstrate complex and the released adsorbate. Lifetimes are calculated for hydrogen isotopes adsorbed on sapphire surfaces. Guide-lines are given for estimating lifetimes of other systems in terms of a few easily calculated parameters.

1. Inrroduction

A physically adsorbed molecule may be driven off a surface in a variety of ways. If the system (adsorbate and substrate) is heated the surface bond wiU eventually break in the process called thermal desorption [l-3]. A more specific release of the adsorbate occurs if light

from a laser source drives the vibration of the adsorbate against its surface bond until rupture occurs [4]. In thii paper we will discuss a third type of desorption. Here a chemical bond within the adsorbate is vibrationally excited. The energy in the vibrating chemical bond usually exceeds that needed to break a van der Waals surface bond. After a time, energy transfer from the excited chemical bond to the surface bond causes the surface bond to rupture and the adsorbed molecule is flung off_ This is then an

* Contribution No. 3549 from the Chemical Laboratories of Indiana University. Supported by the National Science Foundation.

i Present address: Energy and Environment Division, Lawrence Berkeley Laboratory, University of California at EerkeIey, Berkeley. CA 94120, USA.

example of vibrational prediisociation of an adsorbed mo!ecule.

We may describe this spontaneous vibrational predissodation process by a simple equation:

A-D* . . . SL_4-D+S+AE_ (I)

The adsorbed molecule is called A-D* and the asterisk tells us it is vibrationally excited. The substrate, S, holds the excited molecule by a van der Waals bond represented by the dots.. After time r the surface bond breaks and the adsorbate, A-D, now vibrationally relaxed, flies away with translational kinetic energy AE. It is our task in this paper to offer a theoretical model which aUows an estimation of the resi- dence time 7 of the vibrationally excited adsorbate.

There are at least two ways in which au adsorbed molecule can become vibrationaily excited. The adsorbate may be the product of a chemical reaction on the surface which has left the adsorbate in a vibrational@ excited state. A few surface reactions have been studied where the vibrational state of the product has been speciiied. One example [S] is the nitrogen atom

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386 D. Lucas, GE. Ewing / Desorprion of aibrationally excited mo!ecules

recombination on iron, wit!? the subsequent release of vibrationally excited Nz_ Another example is the recombination of hydrogen atoms on surfaces prepared in the laboratory [6] or on grains in interstellar space [7]. The product, H$ -. - S, could be released by a process such as that in eq. (1).

Alternatively, the adsorbate may absorb an infrared photon to become vlbrationally excited. This IR induced release of an adsoibed mole- cule is an example of photodesorption. Radia- tion, frequency tuned to match vibrational levels of specific adsorbates, could be used to induce the selective release of different chemical spe- cies or even different isotopes. Because of its potential for separating molecules this applica- tion of the photodesorption process has been named photochromatography by Suslick [8]. He has performed preliminary experiments for separating hydrogen isotopes adsorbed on AlzOj by photochromatography and has written a patent [S] which describes the practical aspects of the process. Others have also consi- dered the feasibility of isotopic separation by IR induced photodesorption [9, lo].

Most of the mathematical machinery for dis- cussing spontaneous desorption of vibrationally excited mo!ecules has recently beenset down in a slightly disguised form. The systems that have been discussed are vibrationally excited van der WaaIs molecules such as HCl* - - - O(CHJz, r?j . . . He, or Hz - - - Hz, and their vibrational predissociation lifetimes have been theoreticaIIy described [11-13-J. The vibrational prediisocia- tion in these excited van der WaaIs molecules is formally similar to spontaneous desorption of -4-V -. . S. For this reason we will be drawing freely on the theory of relaxation of excited van der Waals moIecules in setting up our theoreti- cal model for vibrational predissociation of molecules on surfaces. A series of papers 1143 on rhe thermal desorption of atoms on surfaces wri?ten over 40 years ago and largely ignored by -ihose working on van der -Waals molecules also contains essentially the same mathematical methods.

In section 2, to follow next, the theoretical model will be presented. A numerical example

for calculation of desorption rates of HT - - - A1203 will be given in section 3. A general guide to desorption rates of other systems will be offered in section 4 which we hope will be useful to those designing experi- ments. Finaily a summary is gathered in section 5.

2. The theoretical model

2.1. The golden rule

An energy level diagram for the desorption process of eq. (1) may be viewed in fig. 1. We begin, on the left, with the vibrationally excited system A-D* . . . S in one of the discrete levels labeled by the u, quantum number. These levels represent the stretching vibration of the adsor- bed molecule against the van der Waals bond which holds it to the surface. Isoenergetic with A-D* - - - S is the continuum of A-D (now vibrationally relaxed) as it fries away with trans- lational energy AE and velocity urn from the surface S. This picture, which represents energy transfer from a discrete level into a continuum, invites application of the golden rule or its equivalent [15]:

(2)

In order to obtain r-l we need to specify the final and initial state wavefunctions, qgt and Yf’ and give a coupling term V,,.

2.2. The wauefunchxzs

We will take the initial state wavefunction to be

WP’ = r-‘R,(r)&(x),

which describes the state of A-D* . - - S. The geometry for the problem is shown in fig.

2. The distance between the center of mass.of A-D and the surface is given by r. We can provide R,(r), which describes the vibration bf the adsorbate against the surface, only after the surface bond potential function is specified. We

D_ Lucas, G.E. Ewing / Desorpfion of vibrationally excited tmfecules 387

Fig. 1. Spontanwus desorption of a vibrationally excited moiecule adsorbed on a surface. The scale for the energy is that for Hz .__ ALO3 considered in the text.

2- IA OA

A-D---S

will use the Morse function for this potentid,

V(r)=D,{exp[-2a(r-rc)]-2 exp[-a(r-r,)l), (4)

with D, the depth at the bottom of the well at separation r,. The steepness of this potential energy function is given by the range parameter a. The analytical form of the Morse oscillator wavefunctions R,(r) for the discrete v, levels is given elsewhere [13,14]. An harmonic oscillator wavefunction &(x) describes the internal vibration of A-D with x the v&rational dis- placement coordinate and u the quantum level. The adsorbate may be generalized to a poly- atomic molecule in which case A represents other atoms in the molecule. In this paper, however, we will imagine A-D as a diatomic moIecule with atom D directed toward the sur- face. The initial state for the harmonic oscillator is &I(X).

The final state wavefunction,

P, = r-l&(r) &(X) m , (3

defines A-D + S; The molecule A-D which has

been released from the surface is now vibra- tionally relaxed and &(x) describes this condi- tion. As A-D flies far away from the surface with translational kinetic energy LIE its wave- function resembles a plane wave. Near the sur- face the translational motion of A-D is moderated by its interaction with the surface. The wavefunction R,(r) describing the continuum behavior of A-D under the influence of a Morse potential is given elsewhere [13]. FortunateIy, we will not need the involved analytical forms of either R,(r) or R,(r) for this paper.

2.3. The coupling term

The coupling term V,, must connect the coordinates of the vibrating chemical bond of A-D” with the surface bond of A-D’ .- - S. We

will make a simple assumption to connect the x and r coordinates. We imagine that motion of the chemical bond of A-D moduiates the sur- face potential energy only because the distance between D and S changes. This coupling term

388 D. Lucas, G.E. Ewing j Desorption of uibrationally excited molecules

proposed many years ago for vibrational relax- ation processes and discussed elsewhere [13, 16) is given by

Vmn(x, r) = -2asaDCx{exp [-Za(r -I-,)]

-exp C-a (r - rC)]L (61

where the fraction of displacement of D toward S is

u = nlAliiI&D, (7)

with mA the mass of A and m~-o the adsorbate mass. The component of the vibrational dis- placement of A-D toward the surface is given by

s =cos 8, (8)

where 13 is defined in fig. 2.

2.4. Desorptior: rates

Fortunately the matrix element (T~‘\V,,\Yr(no’) of the golden rule using our expressions for the wavefunctions and the coupling term has a simple analytical result. The

* %

-“, ‘1, i \ : .D ,

;: r .

l3 r :- . : :

Fig. 2. The coordinates for a physically a&orbed molecule on a surface.

algebra given elsewhere [13] yields

X { n$l ecn -w+q2_1]

x{[(d0-~~-~~~iq2m1/2d0~*exp (-~q~). (9)

Several terms need defining in this rate expression. The harmonic oscilIator matrix element for the chemical bond of the adsorbate is [l6]

(10)

CL = m+_mJm+_-D, (11)

is the reduced mass of A-D. The vibrational energy WA_,, is the difference between the o = 1 and o = 0 states of the adsorbate.

The adsorbate trapped by the Morse potential [eq. (4)] can be represented by the dimension- less parameter

d = (2mA_DD,)“‘/aii. (12)

The vibrational energy levels of the adsorbate against its surface bond are

W ,=-[ah(2d -1-2r~Jj’/8m~_~+D,, (13)

given relative to the bottom of the Morse potentia1 well. Since the Morse parameters for the surface bond are not well known we Iose little useful information by rounding off d to an integer and calling it do. This parameter which appears in the rate expression of eq. (9) may be interpreted as the number of bound states of A-D .a. S contained in the Morse potential well.

The final translational energyhE of A-D now released from the surface is incorporated in the dimensionless term

qm = (2mA-&E)“‘/a h = p/a tr, (14)

which is a reduced momentum scaled by the range parameter a. Since A = h/p the q,,, parameter is related to the de Broglie wavelength of A-D flying away from the surface

D. Lucas, G.E. Ewing f Desorption of L’ibmtima~ly excited m&cute+ 389

by the expression

A = 2sr/aq,. (1%

The parameter q,,, appears in the rate expres- sion of eq. (9). We obtain ti by finding the energy remaining after the adsorbate bond from the vv level has been broken,

AE= WA-D-D,+ W,. (16)

We now have all the expressions needed to perform numerical calculations of 7:: by vibra- tional predissociation of the adsorbate on a surface.

However, thermal desorption is a competitive mechanism for releasing molecules from a sur- face. In this case the adsorbate and substrate are in equilibrium at temperature T. The energy needed to dissociate the adsorbate (in its u,. = 0 level) from the substrate is Do = D,- W,. The probability of the adsorbate site on the surface having this energy is exp (-D,/kl). The adsorbate can pick up this energy at its collision frequency, v = We/h, with the surface so the resulting thermal desorption rate is

(ro’)rr’ = Y exp (-Do/kT). (17)

This crude estimate of the thermal desorption rate, Frenkel’s formula, has been known for decades Cl] and has been recast by others in more sophisticated forms [14, 171.

3. A numerical example

One of the most thoroughly studied examples of physical adsorption is HZ on AlaOS. The properties of AlaO, for chromatographic separation of ortho- and para-Ha and its iso- topes have been discussed [lS]. Moreover, the Hz a.. AIZOa system was selected for photo- chromatographic experiments [8]. It is particu- larly useful for our purposes that the surface bond for Hz - - - AlJ& has been described [19]. It is for these reasons that we select this system for our sample numerical calculation of desorp- tion.

King and Benson [19] view HZ polarized by the electric field from A13+ and O*- ions near

the A1203 surface. The resulting induced dipole of HZ orients the molecule so that it is held perpendicular to the surface from which the electric field emanates. {It is this induced dipole which enables HZ. to absorb infrared radiation easily [20] and becomes vibrationally excited in the photochromatographic experiments.) They offer a variety of potential functions for the adsorbate-surface bond. The one they prefer is HZ located over a vacancy on the surface and is of the form

V(r) = &P(rJr)9 -9(relr151 with D, = 1.0 x lo-l3 erg and r, = 2.40 A.

(18)

An ambiguity results in trying to fit the range parameter of the Morse potential of eq. (4) to the 9-5 King and Benson potential of eq. (18). The 9-5 potential energy goes to zero at r = u = 2.07 A and somewhat arbitrarily we adjust the Morse potential so that it goes to zero at this separation as well. The result is a = 2.09 X 10’ cm-‘.

Using D, = 1.0 x lo-l3 erg and a = 2.09 x 10’ cm-’ together with rn*-n = rnsl = 3.32 x lo-” g we obtain d = 3.71 (da =4) by eq. (12). The zero point vibration of HZ against the surface is W, = 2.53 x 10-r” erg (128 cm-‘) from eq. (13). With the vibrational frequency of Hz, WA-u = W,, = 8.26~ lo-” erg (4130 cm-‘) [20], we obtain AE = 7.51 x 10-r’ erg (3795 cm-l) by eq. (16). We then find q,,, = 10.2 by eq. (14), which corresponds to a de Broglie wavelength of A =0.29 A by eq. (15). Finally, use of eqs. (10) and (11) gives (w) = 8.96 x lo-” cm. Application of eq. (9) reveals r, = 6.0 x lo-’ s as the lifetime of Hz - - - AlzOs from the v,=O level.

The error limits that may be placed on this lifetime are large. An uncertainty in the range parameter of only LO% introduces a variation in -ru, by an order of magnitude. Variations in the range parameter by more than 20% result from different choices of potentials ofIered by King and Benson [19]. Reasonable values of a fall between 2 x 10’ cm-’ and 3 x 10’ cm-‘. We can then safely say only that the desorption lifetime is better described by a nanosecond time scale rather than microseconds or picoseconds.

390 D. Lucas, G.E. Ewing / Desorptiqn of cibrationally excited molecules

In setting up experiments to detect molecules released from a surface by vibrational predisso- ciation the thermal desorption channel must be considered. We will use eq. (17) for H; on Al& and our original set of parameters. We find v = We/h = 3.8 x IO” s-l and DO = Y&T W0 = 7.5 x lo-” erg and consequently 70 = 3 x IO-to s at 77 I< and 7;“’ =0.2 s at 20 K. Thus the thermal and vibrational desorp- tion rates may be competitive at 77 K but vibrational desorption clearly dominates at 20 K.

A large isotope effect is predicted for op - - - AlzOs vibrational predissociation. Work- ing through the same type of arithmetic as before with WA_,, = W,, = 5.92 x lo-r3 erg (2990 cm-‘) we find qm = 11.8 and r,= 1.2 x lo-’ s from the u,. = 0 level.

4. Other systems, other channels

Rather than provide more detailed numerical calculations of other systems we will examine the form of ihe rate expression of eq. (9) to learn what factors are primarily responsible for the efficiency (or ineEiciency) of the desorption process.

Two Franck-Condon factors appear in eq. (9). The first deals with changes in the vibra- tional wavefunctions when A-D* is relaxed to A-D. The overlap of the dr(x) and &(x) wavefunctions through the coupling term yields the vibrational Franck-Condon factor a’~~a’(x)~. The energy scale for the coupling term is D,, the we:1 depth of the surface bond. This accounts for all the system parameters to the Ieft of the bracket of eq. (9).

The desorption lifetime follows a simple exponentiai dependence for qrn > do_ There is a simple physical explanation for this behavior. The departing molecule is approximately described by a plane wave of de Broglie wavelength A = 27r/aq,. The adsorbed molecule in its u, = 0 level is (almost) an harmonic oscil- lator against the surface and its wavefunction resembles a gaussian. It is the overlap of the near plane wave and the gaussian functions within the matrix element of the golden rule which determines the efficiency of the desorp- tion process. The magnitude of this overlap is dominated by the de Broglie wavelength of the -4-D molecule flying away from the surface. Algebraically the exponential dependence on the de Broglie wavelength appears in the final term, exp (-mQ, of eq. (9). We have referred io the logarithmic lifetime dependence of the sort shown in fig. 3 as the momentum gap cor- relation [Zl]. The momentum gap can serve as a useful guide in estimating the lifetiie of the vibrational desorption process. Because q,,, = (2rn+,_oE)“*/a~ we see that three system parameters are involved: a, AE, and mA_D.

The remaining terms reflect the Franck- A linear change in a results in an exponential Condon factor involving changes in the motions change in r,,_ Thus the uncertainty in this of the adsorbate while on the surface and after parameter because of the poorly defined surface it is released. The wavefunctions R,(r) and bond potential energy makes quantitative R,(r) through the ccupling term of eq. (6) yield theoretical calculations unreliable. The energy this translational Franck-Condon factor. The gap AE is seen from eq. (16) to depend on result involves only the reduced parameters do three terms. An adsorbate which has both a low and qm. While the vibrational Franck-Condon vibrational frequency and a strong surface bond factor contains on!y quadratic terms whose favors a small AE and a short vibrational pre- numerical range is rather limited, the trans- dissociation. time. Adsorbates in excited vibra-

lational Franck-Condon factor contains a product expression, a factorial term and an exponential. It is the translational Franck- Condon factor then which really dominates the outcome of the desorption rate.

We have plotted the desorption lifetime from the u, = 0 level given by eq. (9) as a function of q,,, for several values of & in fig. 3. The vibra- tional Franck-Condon overlap has been given a typical value (r2~2u2{.x)2 = 2 x 10m3 and the adsorbate weI1 depth is taken to be 2 x lo-r3 erg, a representative value for physisorp- tion [2].

D. Lucas, GE. Ewing I DesorpTion of uibracionnlly excited molecules 391

9,,,=(2n1~_~ AE) “2,(1x

Fig. 3. The lifetime of a vibrationally excited mo!ecule adsorbed on a surface.

tional energy states (IJ,= 1,2 . ..) against the surface with the energy W, will be released with a smaller energy gap and tend to have shorter residence times. Isotopic changes affect both m&u and dE (through WA-, and W,) and may result in either an increase or decrease in TO.

In regions where do> qm, the released adsor- bate has relatively low translational momentum and its effective de Broglie wavelength near the surface is dominated by the shape of the adsorbate-substrate potential well. The lifetime for desorption then depends exponentially on do with milder variations with q,,,.

As an application of fig. 3 [or eq. (9)] let us estimate the lifetime of CH8 ... AlzOa. We take the molecular excitation to be [22] w&u = P& = 6 x lo-r3 erg (3010 cm-‘) and 0, = 2 x lo-” erg (1000 cm-l). We find do= 12 with Q ~2.5 X IO* cm-’ and appioximate CHZ by CH3-H* and take & before ~2s2~2(~)2 = 2 X lo-‘. Ignoring the zero point vibration against the surface we find AE = WA-D-D== 4 X 1013 erg (2000 cm-‘) which gives qm = 18. Fig. 3 then reveals r. = lo-’ s.

The model we have presented leading to eq. (9) or fig. 3 contains critical limitations which

we now explore. We have ignored energy flow channels which may leave either the released adsorbate or the surface excited.

We have treated the substrate, S, as a homo- geneous mass. This bulk mass absorbs the momentum needed to balance that of the departing adsorbate but accepts negligible energy. However, let us now imagine S to be an atom or ion (or several atoms or ions) at the surface bound directly to A-D. This portion of the surface is in turn coupled to the rest of the lattice. The disposition of the energy and momenta now changes significantly. We can take care of this in the simplest way by replac- ing rnA_D [in eqs. (12)-(14) and the abscissa of fig. 33 by the reduced mass of A-D and S,

&A-D5 = mA-_DmS/(mA-D+ mS.), (19)

where ms is the effective mass of the surface beneath the adsorbate. The picture that emerges is that of A-D flying away from the surface and the rebounding vibrationally excited S* colliding with its neighbors which take up its translational ener-v and distribute it to the remainder of the solid. The substrate will retain energy WS into the localized vibrational modes of the surface which supports the adsorbate. This process is

A-D* ..-S+A-D+S*+AEv-s (20) with

AEv_s= W..-D-D,+ W,- WS.

We call this the V-S channel.

(21)

Again referring to the CHZ -0 - Alr03 exam- ple, the substrate has fundamental vibrations up to 870 cm-’ [231 and strong optical absorption to ~1600 cm-’ [24]. The en:rgy gap may then be AEv-s = 400 to 1100 cm . If we imagine methane bound directly to A13+ then the effective reduced mass wil1 be J.Jc~.~ = 1.7 x 10eZ3 g. Using o = 2.3 x 10’ cm-l we have do = 10 and a resulting qEs = 6.3 to 10.4.

Desorption leading to a vibrationally excited released adsorbate may be represented as

A-D* . ..S-+A+-D+S+~E~X.. (22)

The energy gap now is

AEvv = W-j,_,-, - DC + W, - WA*_* (23)

392 D. iiicar, G.E. Ewing / Desorpticn of oibrationally excited molecules

and has been reduced from eq. (16) by the energy WArD in the vibration of A*-D. This process is anaIogous to V-V transfer in gas phase relaxation [16].

In the CHT *.- Al103 system just considered the released adsorbate may be excited in the u2 vibration at 1525 cm-’ [22]. The energy gap originally A.E=2000 cm-’ is now lowered to &XE,-475 cm-’ and the reduced momentum becomes q,” - 8.6.

While either the V-S or V-V channels lower the momentum gap they also introduce an additional Franck-Condon factor involving the excitation of a vibrational mode of the substrate or the adsorbate. As we saw a typical value for this Franck-Condon factor in a rate expression is =10e3 (or lo3 in a residence time). Thus whiie values of q,, ~6.3 to 10.4 for the V-S channel of CHZ -a- Al203 applied to fig. 3 would suggest times from rO= lo-’ to lo-’ s, the vibrational Franck-Condon factors to excite the substrate modes increase these times to To== 10e6 to lo-” s. Likewise qm 28.6 expected for the V-V channel when the v1 mode of the released methane is excited yield r0 2 lo-’ s rather than ro= 10e8 s read from fig. 3. In any event all these channels are more efficient than the process in which the released CH, deposited no energy into either itself or the substrate_

A final relaxation channel may leave the released adsorbate rotationally excited

A-D* --.S+A-D’+S-i&5,,_~.,

with the ener,7 gap

(24)

&v-X.,, = w,, -D, + w,- W&D?. (25)

The energy partitioned into the tumbling motion of the released adsorbate is given by WA-D+. In the case of CHZ k-. Alz03 we might expect to find the released methane in a high J state.

It should be noted that there are channels in which the adsorbate is not released from the surface. Transfer of vibrational ener-9 from one adsorbed molecule to another adsorbed mole- cule nearby is possible through long-range

.

coupling terms. Another possibility is that the surface modes are in resonance with the excited adsorbate, resulting in energy transfer to the substrate with no energy remaining to break the surface-adsorbate bond. Brus [25] has treated this relaxation channel. He considers the energy transfer of a vibrationally excited molecule to the surface of a dielectric solid as a classical electromagnetic phenomenon. When there is a match in their vibrational frequencies and their oscillator strengths are large, the vibrating elec- tric dipole of the adsorbate couples strongly with surface polarons. The lifetime associated with this channel of resonance energy transfer from the adsorbate to the substrate is 7” 10-l' s. However, the energy transfer rate drops rapidly when the adsorbate vibrational frequency is even slightly off resonance from the characteristic surface polaron frequency. If these frequencies are mismatched by only 10% the lifetime increases two orders of magnitude to t = 10M1’s. If the mismatch widens, the surface mode adsorption coetiicient at the frequency of the vibrating adsorbate vanishes and this chan- nel for energy transfer is closed. For the mole- cules we have been considering at VA_*-3000 to 4000 cm-’ on typical dielectric solids with 3;, L- 1000 cm-‘, we expect therefore that this non-desorptive channel will be closed.

We have been talking about desorption from dielectric solids. What about metals? Here the free electrons are able to take up energy in a variety of ways. The surface plasmons can be driven over a wide frequency range by a vibra- tionally excited adsorbate as Brus shows {25,26]. With such an efiicient channel for vibrational relaxation without breaking the sur- face absorbate bond, metals may be poor sub- sirates for the desorption experiments we have been discussing. Calculations for such systems have, however, been performed [27J

Exploration of the various V-V and V-T,R channels has been initiated for vibrationally excited van dar Waals molecules [i3,28-311. Further theoretica investigation of the V-S channel should probably await the first experi- mental results of vibratitinally induced desorp- tion.

D. Lucas, G.E. Ewing / Desorption of vibrationally excited molecules 393

5. SMlmary

Let us summarize this guide to spontaneous desorption of physically adsorbed vibrationally excited molecuies. The most efficient desorption processes will occur for adsorbates with a small number of bound states (do small) and when released the adsorbate has small translational momentum (small qm). This momentum gap correlation is most succinctly revealed by fig. 3. Smaller translational momentum will be achieved if the adsorbate can take up energy into its internal motions. Absorption of energy into lattice modes of the substrate will also serve to reduce the translational momentum and provide for more e9icient desorption. However, if the vibrational frequency of the adsorbate is in near resonance with surface polarons or plasmons of the substrate, energy transfer to the solid will be so efficient that desorption will be quenched.

A test of these possible relaxation channels awaits the first experimental measurements of desorption of vibrationally exdited molecules.

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