Jonathan Tennyson and John N. Murell- A Non-empirical Appraisal of the Angular-overlap Model for...

8/3/2019 Jonathan Tennyson and John N. Murell- A Non-empirical Appraisal of the Angular-overlap Model for Transition-metal

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1980 2395

A Non-empirical Appraisal of the Angular-overlap Model for Transition-metal ComplexesBy Jonathan Tennyson an d John N. Murell,' Sc hoo l of Molecu lar Sciences, University of Sussex, Brighton

Non-empirical SCF molecular-orbital calculations of the d-orbital energies in the complexes [MnF,-,CI,]*-( i = 1-6) and distor ted [M nF Gl k- (k = 2 or 4) have been made with in a valence-electron approximat ion. Theseenergies have been shown to be accurate ly model led by a one-electron angular-over lap Hamil tonian. Theangular-over lap parameters for CI and F have a re lat ionship wh ich is s imi lar to th at determined f rom exper iment forsome chromium 111) complexes.

BN 1 9QJ

DESPITEhe success of ligand-field theory in correlatingthe properties, particularly spectroscopic, of transi tion-metal complexes the theory has largely been confined tohigh-symmetry structures : octahetlral, tctraliedral, andto a smaller extent tetragonal and square planar.Notwithstanding the importance of these structuresthey often have less interesting physical properties,particularly magnetic, tha n those of lower symmetry.Ligand-field theory itself is not well suited for exten-sion to low-symmetry complexes. The nunibcr of para-meters required to express the full spherical harmoniccomponents of the ligand field is greater than tlienumber of determinable energy differences amongst thed orbitals. For example, C,, symmetry requires nineparameters to represent those components of t l i c . ligantl

such calculations cannot generally be done within thecurrent limits of computer time with sufficient accuracyto reproduce experimental results.A n advantage of ab in i t io calculations is that struc-tures arc: not restricted by experimental availability.Illorcover, the resulting energies obtained from suchcalculations may always be completely assigned on thebasis of tlieir orbital wavefunctions and not guessedfrom tlie nature of spectral appearance or correlationwithin fainilies. This suggests an alternative way toevaluate the a.0.m. which is with a series of ah initiocalculations, some but not all of which could be comparedwith cxperiment. This procedure is summarised in theSclienic.Although we can a t present makc only crude ah in i t io

Compar isonof s t r u c t u r e sexper imen t a l l y

Angular Ful l compar isonof a completeoverlap G

modeln SCHEMEfield which have non-zero d-d matrix elements, whereasthere are only five d-orbital energies to nicasure.

An alternative approach is to identify tlie perturbingpotential with individual ligaiids rather than as com-ponents of the collective potential of the whole ligandstructure. Although this approach might appear torequire more parameters it has the advantage that thesemay be transferred between complexes within restrictedclasses, thus increasing the data from which they inay beevaluated . This is essentially the approach introducedfirst by Yamatera l p 2 and McClure wliicli has evolvedinto the so-called angular-overlap model (a.0.m.). Tlicmethod has been frequently reviewed4Unfortunately, the analysis of low-symmetry struc-tures is still difficult in the a.0.m. because one generallyhas insuf'ficient da ta for full parameterisation. Thisinsufficiency arises, for example, from the imperfectresolution of electronic spectra and the failure to syn-thesise and isolate key complexes.A h in i t io calculations provide, in principle, a b;isis fordeciding that a spectral observation is consistent withan assumed structure but give little i n t h e way ofphysical explanation of spectral pat terns. I n practice

calculations on transition-metal complexes compared towhat is currently possible on light-atom Inolecules, it isnot unreasonable to assume tha t if crude ab initiocalculations confirm the general principles of the a.0.m.then accurate ab in i t io calculations would do likewise.The precise values of the angular-overlap parametersdeduced by such comparisons would of course depend ontlie quali ty of the calculations.In this paper we compare angular-overlap and abin i t io calculations on two series of complexes. Thefirst is the series [Mn17&Jk- (K = 2 or 4, i = 1-6).The complexes are assumed to have octahedrally directedbonds (are ortlioaxial). The second is the series [MnFJk-( k = 2 or 4) , in which the metal-ligand bond directionsare displaced from octahedral.C A L C U L A T I O N S O N O R T H O A X I A L C O M P L E X E S

[MnXJ2- is a d 3 system and in an octahedral field theground state is 4A 2g. Excited doublet s tates are sufficientlyhigh in energy that t he ground sta te is also a quartet in alllower-symnietry structures tha t we examined. [MnXGI4is t P and in a weak octahedral field the ground state is614 'I'he ground states of both [MnFGI4-and [MnCI,]*-ar e 1;nown to have this designation and i t is reasonable to


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J.C.S. Daltonassume that all systems we considered of lower symmetryare sextet states.To make the calculation cornpu tation ally inexpensivewe have chosen a non-empirical valence-electron modelrather tha n full ab initio calculation s. Tlie niodel has beenfully described in previous papers and used for predictivepurpose^.*^^ Because all the complexes have the samenumbe r of valence orbi tals the convergence of t he SC Fprocedure for the whole series can be started froni theconverged vectors of a high-sy mmet ry member of th eseries, and this gave a significant saving in com puter tim e.Metal-halogen bond lengths were taken from th e experi-mental values of [M nFJ2- an d [MnCl,J- in K,[MnX,] :Mn-F 1 . 7 4 , Mn-C1 2.28 A . They were assumed constantfor all compounds including the d 5complexes; this assump-tion enabled us t o use a common set of int egrals for @ ant1d5 calculations.To further limit the computational requirements wcrestricted the orbital basis to a iiiiriimal description of thehalogen ligands. It is not too expensive to take a largerbasis for the metal, for example, choosing d orbitals at thedouble-zeta level, but such an unbalanced basis set maylead to a charge distribution which is far froin tlie correctvalue. Preliminary calculations showed that with adouble-zeta d basis th e diffuse comp onent of t he 3d orbitalwas compensating for a relatively poor description of theligands. We arehe basis used is described in Table 1 .

TABLESumm ary of t he basis *

Atom ty pe Core orbital s Valence orbita lsMI^ IS, 2s, 2 p STO-3G 3s, 31, STO-3G3d 6G4s, 4p 1G

2P 4GF 1s STO-3G 2s STO-3Gc1 IS , Bs, 2 p STO-3G 3 ~ ,p STO-3G* STO-3G using exponents of E. Clementi and D. L.Raimondi, J . Chem. Phys., 1963, 38, 2686; 5G, compact partof the double-zeta basis of P. J . Hay, J . C h e m . Phys., 1977,66 , 4377; lG, single Gaussian with exponent 0.32 after J .Demuynck, A . Veillard, an d V. Waulgren, J . A m e r . Chcnz.SOC.,1973, 95,5563, 4G, four-Gaussian fit to the Hartree-Fock 2 p atomic orbital ( R . F. Stewart, J . Chenz. Pliys., 1969,50, 2485.

making no claim that this is optimal for its size for thesystems studied but we believe it has a reasonable corn-promise between balanc e and accuracy for our purposes.

Examination of the orbital wavefunctions showed thatthe singly occupied orbitals for d5 systems were 95o/bcomposed of d functions and th e same was true of the singlyoccupied orbitals and two lowest virtual orbitals in the d3systems.Figurc 1 shows the orbital energies calculated for theseries [MnF,-iCli]k- in a way that brings out the orbitalcorrelations in th c series. The occupied-virtual splittingin the d :$ ons is much larger than thc corresponding splittingi l l (I5 and this is a property of t he SCF Hatniltonian. Toobtain ;L t,,--e,, splitting for tlie & j case that can be directlyc - o m p r e t l to esperiinent i t would be necessary to make a

~~

F I G u m 1 Calculated orbital energies for the series [hZnT~, iCl , ]k-trmisformed according to cquation (1 ) : k -:(a ,b) or 4 (c, d )E(6 )- S (0 ) - 0.0067 (fz), -0.0352 (b), -0.1875 ( r ) , or-0.2037 El , ( d ) . Thc lines whicli pass through or close toc;tlculatcd points have been inserted to bring out more clearlythe pattern between the calculated orbital energies

0 6 0

0 58

0 6

0 155

ILu0 150

1.14

1 1 2

1.00

0 98

0 1 2 3 4 5 6i


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separate calculation on a configuration with th e e, orbitaloccupied.We shall separately consider the behaviour of th e e, an dt,, sets of bo th ion types. A t,, set is defined as the orb italsth at originate as t,, in octahedral symmetry and which aresplit in lower symmetries. Within each set we make alinear transformation such that the orbital energies of th etwo octahedral ions are equal. This can be achieved bydefining an energy E' as in equation (1 ) where E( i ) is an

E'(i)= E ( i )+ [(3- ) / 6 ) [ E ( 6 )- E ( O ) ] (1 )orbital energy of a coinplex with i chlorine ligands. Therewill be one such transform ation for each of th e four sets.Energy differences for isotners within a set are unaffectedby the transformation. The calculated values of E ' ( i ) areshown in Figure 1 .The symmetry appar ent in Figure 1 leads one to expectth at the orbital energies can be represented by an empiricalHamiltonian of simp1: form, possibly a one-electronHamiltonian. Points to be noted are: (a) the symmetrycentre shown by each t,, an d e , orbital set at the degenerate( e ) orbi tal for t1iefac-[MnF3Cl.Jk- struc tur e; (b) he existenceof near degeneracies such as those in the t,, orbital setbetween b , and b , orbitals for cis-[MnX,Y,lk-, and a Lan dey orbitals of cis- an d trans-[MnX,Y2Ik-; (c ) the splittingsof both the t Z p nd e , are twice ats large for i~an s- [M nX ~Y ,] ~-as for [MnX,YIk'-; ( d ) that the t, , orbital set forms xparallelogram grid [shown particularly in Figure I ( d ) ];an d (e ) the mirror planes in the horizontal ancl vertical axesthrough th e symmetry centre of t he eg sets.M O D E L HA M I L T ON I A N S

Before turning to the angularly distorted structures, weestablish ;I niodel one-electron Hamiltonian whose eigen-.# = C:=lAk (2 )

(3 )(4 )

A: = (dz~]A1]dZ~>e,4 2 < 4 & q d , ) = c7-

values simulate th e calculated orbital energies of th e lastsection and which is consistent with the basic tenets of theangular-overlap model. We assume th at the Hami1toiiia.n

Taking M-X1 to define the z direction, the matrix ofA1isdiagonal with elements (3)-(7).* The matrix Ak willtherefore be obtained from A 1 by the matrix transforination(8) where F ( ( I ) is the orthogonal matrix known as theangular-overlap matrix [equation (9)]. For example, for aligand on the x axis [ligand 2 with polar co-ordinates(7c/2, O ) ] , application of (9 )gives ( l o ) ,and for ligand 3 on they axis we obtain (11 ) . As the d-orbital basis is of even

i (e , + 3es) 0 0 0 - ( 3 / 4 ) ( ~ ,- 41 (10)] ( 1 1 )[ (3!/4)(c,- 6) 0 0 0 ~ ( 3 e u C 6 )0 es 0 0 00 0 en 0 00 0 0 c, 0-(3?/i)(c, - s) 0 0 0 I(Re, 1- C6 )

i(e, + 3es) 0 0 0 (3h/4)(eD - vb)c, en 0 0 00 0 er9 0 00 0 0 C 0

A2 -=

AS =

inversion sy innietry , eleiiients of A h are the same for ligantlsalong the positive ant1 negative directions o f ;L Cartesianaxis.If the inatrix I 1 is constructed for a n octalwt1r;il coinplex

!i(t2(J= 4e, t 2es ( '2)E ( e s ) = 3 e , -+ 3es (13)from the ,4x matrices defined above, then its eigenvaluesare as in (12 ) antl ( 1 3 ) . The splitting between tlie two levelsis as in (14 ) .

A,,(.t= 3e, - e, + e6 (14)Fo r a niised -ligan tl coin ples [ILSnF,-iCIJX'- he eigen values

can be espressed i n ternis of eh for C1 and 1; ligards or thedifference between them if any tw o members of th e seriesare compared. We thus define a set of parameters (15) infA = e,(Cl) - A(F)where A = 0, , or 6 (15)

term s of which we can rep resent all such differences. Ifhowever wc scale our energies according to tlie same formulaas ( I ) then the eigenvalues of H' [equation ( I t ; ) ] can h a

ti'(i)= N( i ) $- [ (3 - )/C,][H(G) l ( O ) ] ( 1 6 )espressecl in term s oi two paraineters: f', = f, - s for theeq set antl f', = f, - s for the t,, set. The splittirigsespressed in these units are relative to mean values ofi (2fm4- s) and (3i/2)(fU+ fs ) for the tZ qand ey orbital setsrespectively ancl are given in Table 2 .

($'Ii ( 1 + 3cos20) 0 - 31 21sin20 0 (31/4)(1- ~ 0 ~ 2 0 )(31 2) infpsin20 cosfpcoso sin4cos29 -cosqkinO - sin+sin20(3*/2)cos$sin20 -sinfpcos0 cosfpcos20 sin+sintl - cos+sin20(3t 4)sin24( - os28) cos2t$sin0 isin24sin20 cos2+cos0 .+sin2$(3 + cos23)( 3k / i \ co s2~$( 1- os20) - in2qkinO icos2fpsinf0 - in2&osfj :-cosB+(R + c0 ;dU)

(d ) =

is the sum of separate operators Ak for each ligand ( k )[equation (2)3 and that Ak is invariant to rotation about th eM-Xk bond (we only consider linearly ligating ligands)Thus the 5 x 5 d orbital matrix of any Ak can be diagonal-ised to u, x ( 2 ) ,and 6(2) compon ents. This allows th e effectof an individual ligand to be parameterised by three matrixelements.* To conform with convention these are given the synibol e,which we trust will not be confused with the group-theory

We note that as we have tlie absolute values for theorbital energies i t is possible to determine all threc f,+parameters whereas only information about tlie splittingsis required to get the two f' A parameters. E.rperiinentallyit is usually only possible to obtain information about thesplittings and not th e absolute energies. 'I'hus elh para-meters [equation (17)1 ar e generally deduced from experi-n'ent.

symbol. e',+= eh - ea where A = 0 or x (17)


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J.C.S. DaltonP A R A M E T E R F I T T I N G

Tn contrast to t he usual experimental situation, fromcalculation we have more data tllan parameters : 38distinct orbital energies for each [h'lnFfi-?Cli]i- eries to fitthree f,+ parameters. We can thus adopt a least-squares

TABLECoefficients of th e f'h parameters for all complescs con-

sidered: h = for the eg se t and A = x fo r the I,, set.The eigenvalues have been identified by the d-orbitalCartesian equivalent, although for cis antl T ~ Ycomplexes there is mixing of thesei 0 1 2 2 3 3 4 4 B GTsomcr cis t r a n s f a c ~ P Y is t rans- 2 0 g - g 1 0 (3412) 2 - 1 - 4 00XYY -fi t using suitable differences between members of th eseries. Since th e equations relating ptram eter s ant l energiesitre linear t l i i 5 fitting can be accoinplislied azn;tlyticnlIy.From the transformed energies ( 1 1 ) optimum values o ff ant1 f', are c:ilcnlntetl an d c;ic.h of t h c iile:ins prolyides n

X Z

0 6 0

't)

030V

cL

separate fitting to fs . In fact the separate fittings givealmost the Same value for f s (0.0034EIlan d 0.003 6Eh foth e dinegative ions and -0.020 OEh an d -0.025 8Eh for thetetranegative ions). We have therefore used an averagein each case; th e optiniuni f h parameters are given in Table3. A coinparison of the calculated and model orb ital energiesis shown i n Figure 2. Tlie poorest fitting is for the t,, set of

TABLEOptimised f,+ parameters (in Ell)* for the series[MnF,-iCIJk- (i = 1-6)

fU fw fsk - ; 2 - .0156 - .0001 0.0035k - 4 - .0425 -0.0339 -0.0259* Thoughout this paper: lE h= 2 G26 kJ mol-1.the clinegative complexes [Figure 2 ( h ) ] and this is to beexpected from Figure 1 ( h ) which ha s a less perfect symme trythan the othe rs; however, we note th e greatly expandedenergy scale of Figure 2 ( h ) compared to th e others.

ITro in Table 3 , f u is iiiuch larger than f, an d fs as iscxpectetl. T t must be reineniberecl tha t these parametersrepresent t l i c b tliffrrencc Iwt\\ecn C1 an d IT ligancls a n t l we a r c

0 16

U0Y0V

r--

0 56 Fitted 0 601.20

T3

1-10

l b l

/0000

0.15 Fitted

00

___t_0 16

E'IGIJKE 2 Comparison of the calculated ( a h i u r it t o) an d model w-bitd energies ( in El))obtained f r o m optiniisetl parameters (Table 3) :k =I '2 ( a , b ) or 4 c, d ) . The lines at 4.5" ar e to ernphahize where poiilts of ail t.uact tit s h ou ld lie


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1980 2399led to conclude th at there is a larger difference in 0 nietal-ligand interaction between these ligands than there isbetween x an d 6 interaction. Whether the term iiitcr-action can be replaced by bonding is arguab le. Sincethere are no d orbitals on the ligands there is no 6 bonding inthe normal sense, but a. 6 electrostatic efTect is present.TH E EFFECT OF ANGULAR DISTOKTIONS

70 examine tlie predictions of th e angul;Lr-ovt:rlap niodelfor bo nd-angle dis tort ion we have s tudi ed tlie c.1i;~nge inorbital energies of [MnFJk - ( h = 2 or 4) when tlie two 2-axis ligands are displaced to polar angles ( O , $ ) an d (x - . 4)respective ly. A11 Mn-I.; bond lengtl ls were kept con sta nt.The lowest symm etry of the distorted complex is C,,.Calculations were niade for 0 = 5 and 1 0 with rjb = 0,15 , 3 0 , aiid 45 (values of 6)outsidc this range are related hysymmetry).

For all values of 6) he orbital energies in th e eBantl f2? setswere found to vary as sinW over the range of 0 esatiiined.\Ve tlierefore sliow i n Table 4 the energies relative to tlic

TABLECalculated orbital-energy differenccs (in El,) bctwcen

distorted (with 0 = 10) and undistorted [h11iI;,]~ .Th e eigenvalues are th e Cartesian conipoiients of thedominant d orbital; for rjb = 45 the t,, compoiientsare yz -- xz , xy, and y : + xz respectively$ I0 0 15 30 45

( a ) k = 2 2 -0.0042 -0.0042 -0.0041 -0.0041x2 - 2 0.0052 0.0051 0.0050 0.0049( b ) k = 2 .yz 0.0032 0.0031 0.0028 0.0027XY 0.0050 0.0049 0.0049 0.0049X 9 0.0119 0.0120 0.0122 0.0123

(G ) k = 4 z2 - .0080 - .0080 - .0080 - .0080( d ) k = 4 YZ -0.0012 -0.0013 -0.0014 -0.0015,y2 - 2 0.0005 0.0003 0.0002 0.0002

XY 0.0003 0.0003 0.000:~ 0.000:3X 2 0.0045 0.0046 0.0047 0.0048

undistorted structure for 0 = 10 only. The most strikingfeatur e of th ese results is tliat tlie dependence on 4 is veryweak.

Looking a t the results in the spirit of t he a.0.m. describedin Model Hamiltonians, the perturbation Hamiltonian( i . e . the difference between H for the distorted and un-distorted structur es) for the displaced structure is, from (8),given by equation (18). Froin (9 ) the matrix H ( 0 ,4) anbe shown to have the non-zero elements (19)-(24) whichW ( 0 ,4) = 3 9 0 , 4)AF((0, 4 ) +

R d ) ( x- , $ ) A lF({l)(x- , 4) 2A (18)(1:))

(34/2)sin220e,, ( 2 0 )Htza= -%in20 e, (21 )

(23)Hf44= 2sin20 e, (23)

(24)

I f f l l = -5 + 3cos20)(1 - ~ 0 ~ 2 0 ) ~ ~- sin220 enHlj = H31= (3&/8)(l- ~ 0 ~ 2 0 ) ( 1- ~ 0 ~ 2 0 )

1fjs3 = $sin220 e, - sinW e,

H ~ ~# ( I - ~ 0 ~ 2 0 ) ~, + ;sin220 e,c lepnd on the e,+ para mete rs defined by ( 1 7 ) . The onlynon-zero off-diagonal element is H T l 5= (z21Hlxz -- yz}which is at first sight surprising because for a general angle4 the matrix should be syninietry factorised into 3 x 3(symmetry A) and 2 x 2 (A) blocks. T he angular-overlap Ham iltonian (for linearly ligating ligands) therefore

hits a liiglier syiiimetry within a d-orbital basis than the f u l lHamiltonian.

(i) The elemen tshave no dependence on 4. (ii) The orbital energies canbe shown to have a sin% dependence for small values of 0.The tliiLgonal t,, block o f H depends on sn 20 or sin220( wl i i c l i is approxiiiiately 4sinW for siiiall 0 ) . For the e ,bluck the trace of the 2 x 2 matrix is as in equation (25);ind tlie deterininatit is a s in ( 2 6 ) . I t follows that theeigenvalucs which obey equatio n (27) will depend on sin.

We note th e following propertie s of If.

(25)D = - 3sin4F)(e,)S ( 2 6 )

-. ( c ~ e ~ $e,)sin,20

A2 - TA + 1) = 0 (2i)( i i i ) Hie trace olti (the average encrgy of tlie d orbitds) isindepeiident 01 (0 , 4).Points (i ) antl (ii) are consistent with the calculatedresults sliown in Table 4 , but point (iii) is not. The netshift of the orbital energies is not predicted by the a.0.m.and we deduce tha t i t arises from a charge redistribution ontlie coniplexcs as they are distortctl. A Mulliken popul-ation analysis of tlie orbitals confirms this and shows anelectron shift from the ligands to the rnctal which is pro-portional to sin20.

In ordcr to fit tlic changes i n calculated orbital energies11it11 angular-overlap parameters it is tlierefore necessaryto introduce ;L furth er parani cter -qsin20 to dccoiiiiiiodateth e shift in the su m of o rbital energies discussed abo ve.This transfornis [~f.11))-(24)] as in equation (28). Fitting

Kr i j= H 13. + 6,, -qsin20 (28)can tlieii be achieved using the cliagorial t,, block of K andchecked agaiiist tlie eg block. Table 5 gives the values for

TAULEeh (F ) an d q parameters (in El,) as fitted for thc t,, orbitalsc t of distorted [MnI;,lk--, and coin parison between

calculated and fitted levels for the eg orbital set usingthese values; A, an d A, ar e the roots of expression (27)

e , e, rlh = ; 0.066:l 0.0158 0.1380k = 4 0.0408 0.0141 -0.0279( -A,&)

-7ph____--1, -1

-A_--_ 7 FittedJ< = 2 -0.0060 -0.0054 0.0028 0.0026IZ = 4 -0.00 75 -0.0073 0.0026 0.0034eu, efn, antl q .orbital set in a satisfactory manner.

C A C . Fittcd CdC.

These parameters obey ( 2 7 ) fur the c,

C O MP A R I S O N WITH EXPERIMENTBy adding eA(F) equation (17)] and f^ I -_c),+(Cl)e,+(F)] t is possible to obtain values for e,(Cl) as well ase,+(F) these may be compared with experimental

results where available. Glerup et have determinedthese parameters using tlie spectra of trans-]Cr(amine),-A ( B ) I nt (amine = NH, or pyridine; A , H =F,1-,Br-, OH,, OH-, etc.) complexes. Although our para-meters for manganese complexes are not directly trans-ferable to chromium(rrr) complexes a comparison isnevertheless interesting as one would expect ratios


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J.C.S. Daltonbetween parameters to be similar. Table 6 gives such acomparison. Although our parameters are approxim-ately double those obtained for Crlll the ordering andrelative magn itude are in good agreement.

TABLEiAngulsr-overlap parameters in El, ( l l i i , = 2 .159 x lo5cm-l) froni this work and derived experimentally l2 forCr l I I

Mn" CrllIM n I Ve:,(Cl) 0.0472 0.033 0.0252e,,(CI) 0.0122 0.0061 0.0040e'n (F) 0.0158 0.0141 0.0077e O ( W 0.0663 0.0498 0.0336

Glerup et al.12 also consider a scheme similar to ours foranalysing the experimental spectra of the series [Cr-(OH,)6-1(NH,)i]3+ i = 1-6) because spectral data forten isomers were available. However, they concludedthat their fitting was unreliable as the water ligandappears to change its mode of ligation between membersof the series.C O N C L U S I O N

Contrary to our expectation when sta rting this projectwe have found tha t the d-orbital energies obtained fromnon-empirical SCL;molecular orbital calculations can beniodellcd accurately by the angular-overlap rnodel.Th e only modification tha: wc have found necessary toachieve a fit between th e two sets o f energies was to adda parameter representing charge redistribution for thedis torted [MnF,]" structures.The SCF calculations allow one to make a moredetailed analysis of t he a.0.m. tlian does experiment

because absolute values of the parameters eA(A= 0 , x , or8) can be obtained; from experiment one normally hasonly sufficient information to obtain the differencese', = e, - s and e', = en- s. Our calculations showthat there is no justification in equating eA with e'Ai.e. in neglecting e6. We found that the difference inea between F and C1 is of similar magnitude to the differ-ence in e, values.Finally we recognize that our calculations have pro-vided a test for the a.0.m. only for complexes in whichtheir is litt le metal-ligand covalent bonding. Un-fortunately covalent bonding ligands are computation-ally more demanding because they are necessarilypolyatomic a nd at the present time a series of calculationsof th e type we have made using CN- ligands, say, wouldbe difficult to justify.

R t w i u e d , 31st J a n u a r y , 19801O/ 107

REFERENCES1. Yamatera, Na tu vwis s . , 1957, 44 , 375.H . Yamatera, Bull. C h e m . SOC. a p a n , 1958, 31, 95 .D. S. McClure, ' Advances in the Chemistry of CoordinationComplexes,' ed. S. Kirscher, McMillan, New York, 1961, p. 498.M . Gerloch and K. C. Slade, ' Ligand Field Parameters,'Cambridge University Press, 1973.C . E. Schaiffer, Structure and Bonding, 1973, 14 , 69.I > . W. Smith, Stvuctuve and Bonding, 1978, 35, 87.J . N . Murrell an d I . G. Vincent, J . C . S . F a v a d ay 11, 1975,890.

8 J . N . Murrell and C. E. Scollary, J.C.S . DaZton, 1976, 818.R J . N . Murrell and C . E. Scollary, J . C . S . Dalton, 1977, 1034.

1" P. C. Moews, jun., Inorg . Chenz. , 1966, 5, 5.11 H. Bode and W. Wendt, 2 . anorg. C h e m . , 1952, 269, 165.12 J . Glerup, 0 . Mernstcd, and C . E. Schaffer, Inorg . Chem. ,1976, 15, 1399.

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