A Simplified Molecular Orbital Model for Octahedral MetalCarbonyl CompoundsBY WAYNE P. ANDERSON* AND THEODORE L. BROWN?Noyes Chemical Laboratory, University of Illinois, Urbana 61 801, U.S.A.Received 2nd January, 1969A simple model for the x-electron interaction between metal and CO groups in octahedral metalcarbonyl systems has been developed. The basis set employed includes metal dorbitals of x symmetrywith respect to the M-CO bond axes, and two orbitals of x symmetry on each CO, correspondingto the vacant x* orbitals of the CO groups. Each CO is assumed to donate 0.5 electrons to themetal via the cr bond. In compounds of the form M (CO)e-nLn, the ligands L are characterizedby a certain degree of cr donor ability, and by two acceptor orbitals of x symmetry and variableenergy.The model is sufficiently simple to permit exploration of a wide variety of ligandcharacteristics.With the aid of assumptions relating the charge distribution to bond orders, relative CO stretchingforce constants and C0,CO stretching interaction force constants can be calculated as a function ofvariable ligand characteristics. The results support the adequacy of the simple force field commonlyemployed in determining relative force constants in substituted octahedral metal carbonyl systems.Molecular orbital calculations for octahedral metal carbonyl compounds haveshown lm3 a number of important features of the ground state electron distributions.(i) Carbon-oxygen CT bonding in the CO moieties is essentially unaffected by bondingof CO to the metal.(ii) The metal p orbitals, which are the only metal valenceorbitals capable of interacting with both the CT and n orbital sets of the CO groups,are in fact involved almost exclusively in CT bonding. To a first approximationthey may be ignored in considering the 7~ bonding. (iii) the chromium atom inCr(CO)6 carries only a small net charge, which is, however, the result of large chargetransfers between metal and CO in both the CT and 17t bonding systems.There has been a substantial interest in the chemistry of metal carbonyl com-pounds, and in their derivatives with various Lewis bases.4* Physical studies ofthese compounds, and particularly infra-red spectral studies of the CO stretchingmodes in the 2000 cm-' have been employed to assess the natureof the ligand-metal interaction, and to evaluate the effects of substituents.It isnot practicable to carry out detailed molecular orbital calculations on substitutedmetal carbonyls in the same degree of complexity as employed in treating the parent,unsubstituted compound. Accordingly, we have developed a much simpler, moreempirical model for the octahedral systems in which only the essential elements ofthe n electronic network are treated explicitly. With the aid of this model it hasbeen possible to consider the effects of substituents on the bonding between metaland CO, and to develop various comparisons between calculated and observedquantities.DESCRIPTION OF THE MODELThe basis set employed in the calculations consists of a set of three metal orbitals,representing the d orbitals of tZg symmetry in the octahedral point groups, and two* National Science Foundation Trainee, 1965-1968. Present Address, Dept.of Chemistry,University of Delaware, Newark, 1971 1.i to whom inquiries should be addressed.338 MOLECULAR ORBITAL MODEL FOR CARBONYLSorbitals for each CO group or ligand L, fig. 1. Each CO group orbital respresentsone of the two n* orbitals of the CO. Similarly, each ligand L may possess twoorthogonal vacant orbitals of appropriate symmetry as shown in fig. 1. Thus, thereare at most 15 orbitals in the basis set x from which the molecular orbitals areconstructed :4 k = &jCj,* (1)iIn the group 6 carbonyls there is a total of six electrons to be distributed in the mole-cular orbitals formed from this basis set.The bonding 7-c orbitals of the CO groupsare not included in this model at all. They are assumed to form part of the " core "which determines the energies of the six electrons which are being explicitly considered.The justification for this simplification is that the energies of the CO n: orbitals liefar below that of the metal d, orbitals, which are much more closely matched tothe CO n* energies.FIG. 1 .-Schematic representations of basis set employed in x-electron approximation.We employ a Huckel formalism; the secular equations to be solved areC(HiJ(eff)- ekSij)Cjk = 0.jThe diagonal Hamiltonian matrix elements Hi, are assumed to be of the form H,, =Hg-kq, where q represents the net charge on the atom on which orbital i is centred.We employ a value of 2 eV per unit charge for k9-l The off-diagonal matrix ele-ments Hi, are evaluated using the Wolfsberg-Helmholtz approximation :Hij = FSij(Hii + Hjj)/2.(3)The scaling constant F i s given the value 1-75,Although the Q electronic system is not treated explicitly in the calculations, it isnecessary to account in some way for the effect of changes in Q donor ability of theligands on the n energy levels of the metal and the ligands. Therefore, a donorcharacter ot, corresponding to a certain fractional electronic charge transfer to themetal, is assigned to each ligand, L or CO, at the beginning of the calculation. Thisparameter is held fixed throughout all iterative cycles of the calculation.Thus WAYNE P. ANDERSON AND THEODOREqi = Qi + bi,Ni = 1q M = QM- Caiwhere q1 and qM represent the net total electronic chargesrespectively, and Ql and QM represent the correspondingL. BROWN 39(4)on ligand i and the metal,n electronic charges. TheQ value chosen for all CO groups in this work is 0.5 e-, based on the value of 0.47 e-obtained in the more complete molecular orbital ca1culation.l Values of cf forother ligands are varied from 0.25 to 0.75 e- to simulate varying degrees of Q donorability .The diagonal matrix elements for the metal and ligands are given byHM = -4*35-2qM,Hco = - 6.0 -2qcO, (6)HL = ~ , - - 2 q L .The value -4.35 for zero-charge metal is based on the VSIE for an assumed d6configuration on chromium.12 The value of -6.0 for the energy of the vacantx* orbital of the CO is much lower in energy than the virtual 2~ orbital of C0.13In keeping with the usual practice in semi-empirical procedures it is chosen tocorrespond roughly to the difference in energy of the occupied 50 level and theenergy of the (1x45a12n1) singlet configuration l4 in CO.Both values are some-what arbitrary? as is always the case in a calculation in which inter-electronic repul-sions are not explicitly considered. The available data, especially the infra-redCO stretching frequencies? indicate that the CO groups in Cr(C0)6, Mo(CO)~ andW(C0) are similarly bonded. 5a A similar conclusion applies to the mono-substitutedcompounds, e.g., (C6H&P M(C0)5, where M = Cr, Mo, W.lSb It m a y thereforebe assumed that the present model is equally applicable to compounds of thesethree metals.In order to treat other octahedral species, e.g., Mn(CO),X, or V(CO);,it would be necessary only to adjust the HMO appropriately.The overlaps between metal orbitals and the carbon and oxygen 2pn orbitals,S(d, Czpn) and S(d, 02pn) where taken from Schreiner’s results for Cr(C0) 6. l6 Valuesof the d-n* overlaps were obtained from the expression(7)The coefficients preceding the two overlap terms correspond to the coefficients ofthe carbon and oxygen 2pn orbitds in the x* orbital of CO, as given by Ran~i1.l~ Theresults obtained for the relevant overlaps are given in table 1.S(d, n*) = 0.9313 S(d7 C2,,)-0*696 S(d, 02,,)TABLE 1 .-METAL-CARBONYL AND CARBONYL-CARBONYL OVERLAPS IN Cr(CO),s(dJ*); 0.0806S(n:,n*)cis (z,z) 0*0208S(n*,n)Zis(x,y) 0-0591s ( ~ * 7~ *)trans 0.0018a This value refers to the overlap of a single metal orbital with a single CO group.b The overlap of two x* orbitals in which the constituent 2px atomic orbitals are aligned alongC The constituent atomic orbitals are in a common plane, but those of one CO group are normalparallel axes.to those of the other.Gross n-electron populations on the metal and ligands are calculated usingMulliken’s formalism40 MOLECULAR ORBITAL MODEL FOR CARBONYLSwhere the summation i is over all orbitals on centre A, and j i s over all other orbitals.The n charge Q A on A is given by Q A = ZA-PA, where ZA is the number of nelectrons on the neutral centre A (6 for the metal, zero for CO or other ligands).A set of charges Qi are estimated and used as input.The secular equation (2)is solved and a new set of charges QF obtained, using eqn. (8). If I Q:+l- QA I <0401 for all A, the self-consistency criterion is assumed to be met. Otherwise, anew set of input charges, QF2 = 0.9 QA+O.l Qi+l, is used as input, and the cal-culation is repeated. The relatively low weighting of QYi is required to avoidnon-convergency difficulties.RESULTS AND DISCUSSION(i) M(CO)5L COMPOUNDSCharge distributions for a number of hypothetical compounds of the type M(C0)5Lare given in table 2. For M(CO)6 the net charge on the metal is close to that obtainedin previous work from this laboratory for Cr(C0)6.1 When a CO is replaced by aligand which has a much lower n acceptor capacity than CO the charge on the metalbecomes more negative, although a large part of the increased negative charge isdeposited on the remaining CO groups.Thus, for a ligand with no n bonding ability,and a cr donor capacity of 0.5 e-, the charge on the metal decreases from +0-762for M(C0)6 to 3-0.645, a change of 0.117 e-. The total charge change on the fiveremaining CO groups, however, is 0.511 e-. The change in metal charge is inter-mediate between that experienced by the axial CO, 0.183 e-, and each radial CO,0*082e-. The effect on the axial CO is approximately twice that for the radial.For a ligand of given cr donor ability, the presence of n-acceptor orbitals on L doesnot appear to affect seriously the n-electron distribution for a, energy levels aboveabout -2 eV.In this connection, az represents an approximation to the n energylevel of the zero charge ligand rather than of the ligand in the complex. The latterquantity is given by HL, eqn. (6) after convergence.The manner in which the amount of n charge transferred to L varies with the crdonor character of L is revealed by noting the n electron distribution in the fourcases for which a, is - 4-5 and oL is varied from 0.25 to 0.65. The n-charge transferredto L increases by 0.166 in this series, whereas the total for the five CO groups is only0.148. This effect is due to the net charge dependencies of the Hii. The resultindicates the strong synergistic relationship between the Q donor and n acceptorcharacteristics of the ligand.(ii> MULTIPLY SUBSTITUTED COMPOUNDS, M(CO),L6-,The effect of successive replacements of CO groups by non n-acceptor ligandsis a rapidly decreasing positive charge on the metal and increasing negative chargeon the CO groups, as shown by the data in table 3 for ligands of no n-acceptorcharacter and oL = 0.50.The decrease in net charge qM at the metal and theincreased negative charges on the CO groups, are non-linear functions of the numberof added ligands. The results are consistent with the observation that successivereplacements of CO groups, especially by non n-acceptor ligands, are increasinglydifficult to effect.(G) FORCE CONSTANTSCoulson and Longuet-Higgins l8 used simple Huckel theory in arriving at relation-ships between C-C stretching and stretch-stretch interaction force constants iTABLE 2.AHARGE DISTRIBUTIONS AND DIAGONAL AND INTERACTION FORCE CONSTANTS FORM(CO)&SUBSTITUENT PARAMETERSa, =L QL-6.0' 0.50 a - 0.627030000- 2.5- 4 5- 4.5- 4.5- 4.5- 5.0- 5.0- 5.5- 5.5- 5.50.250.500.650.650.250.410.550-650.500.6500.250.65000- 0.047-0.142-0.197- 0.260- 0.308- 0.350-0.438- 0.205- 0.325- 0.58 14M QEO QEO F200.762 - 0.627 - 0.627 16.490.727 - 0.674 - 0.770 16.340.645 - 0.709 - 0.810 16.220.603 - 0.730 - 0.83 1 16.140.610 - 0.725 -0.815 16.170.742 - 0.657 - 0.7230.706 - 0.67 1 - 0.7330.676 - 0.683 - 0.7340.656 - 0.691 - 0.7350.708 - 0.664 - 0.7030.680 - 0.673 - 0.7006.396-356-3 16.286.376.340.829 - 0.614 - 0.666 16.540.778 - 0.633 - 0.670 16.470.707 - 0.653 - 0,662 16-41a These parameters correspond to those for CO42 MOLECULAR ORBITAL MODEL FOR CARBONYLSunsaturated hydrocarbons and quantities derived from the theory.In the simplestapproximation, the stretching force constant is assumed to vary linearly with mobilebond order.lg An expression of the formFco = 6*8P:O+C (9)where F', represents the stretching force constant, P,"" is the total CO x bond order,and C is a constant, was used by Cotton in relating the CO force constants inoctahedral metal carbonyls to bond order. Since charge transferred to CO inour model occupies a n* orbital, thenP,"" = 2- I QcJ2 1.(10)TABLE 3.-cALCULATED CHARGE DISTRIBUTIONS IN MULTIPLY SUBSTITUTED CARBONYLDERIVATIVEScr, "L 9M QL QkO QEOcis-M(CO)4L2co 0.50 0.502 - - 0.827 - 0.92500 0-75 0.367 - - 0.91 5 - 1.013cis-M(CO),L3m 0.25co 0.5000 0.65-4.5 0-4.5 0.25-4.5 0.50-4.5 0.54-4.5 0.65-5.5 0.25-5.5 0.50-5.5 0.650.5400.2950.1510-8560-6620.51 10.4890.4300.7970.6720-597-- 0.079-0.165- 0.305-0.331- 0.408- 0.332-0.515- 0.633- 0.930- 1.098- 1.200- 0.707- 0.806- 0.865- 0.872- 0.885- 0.684- 0.709-0.716Jones 2o has derived expressions for the interaction force constants in metalcarbonyl compounds based on molecular orbital considerations.Assuming thatthe interaction force constants are small (-3 %) in comparison with the diagonalterms, and that x bonding is the major mode of interaction, the CO-CO interactionconstants klk, may be written as ktk = - F i ( & ) k . The quantity (SJk representsthe displacement in co-ordinate ri resulting from unit displacement in r,. Sincetransfer of charge to a CO group results in a change in CO bond order,(sCO,)k = ~'(AQco,)~,k i k = -FiC'(AQc&* (11)The quantity (AQc0Jk is the change in 7c charge on the ith CO resulting from a unitincrease in bond length in the kth CO.We define a unit stretch of COk as one which lowers the n* level of c o k by 1 eV.The required quantities are evaluated by carrying out the molecular orbital calculationfor a series of values of the x* energy level of a given CO, and then assessing theslope of the relationship between the various Qcoi and aco for the kth CO.(AQCOi)khas been found by direct calculation to be linear in the magnitude of variation inthe energy of another CO in this manner. The proportionality constant C' is chosento give a fit with some chosen reference set of dataWAYNE P . ANDERSON AND THEODORE L. BROWN 43Thus, eqn. (9) and (11) provide the basis for evaluating substituent effects onstretching force constants and C0,CO stretching interaction force constants, oncethe disposable parameters have been chosen. The procedure used has been tocompare the calculated force constants with those obtained from a simplified forcefield analysis as described by Cotton and Kraihan~el,'~ and employed in variousdegrees of elaboration by others.21* 22 In this model the M-C stretching forceconstants are ignored, and only Fco and kco,co stretch interaction constants areincluded.The resulting values for the force constants are expected to differ fromthose based on a more complete force field analysis, but the manner in which theyvary with changes in substituents might be expected to follow closely the variationwhich would emerge from more complete calculations. Accordingly, values forC and C' of 5.03 mD/A and -0.317, respectively, have been chosen to give fits forFco and kcis for Cr(CO),. Using these values, the force constants for substitutedcarbonyls listed in table 2 were computed.Graham 24 has presented a simple rule, based upon Cotton's earlier considerations,for determining Q and n parameters for each ligand X or L in Mn(CO),X or Mo(CO),Lcompounds.Mn(CO),CH, is chosen as reference in the manganese series ; changesin diagonal CO force constants in Mn(CO)5X compounds are related to Q and nparameters as follows :AFa = a+2n,AF' = ~ + n .0.5 -jl0.2 5-0000O O00 0000. I 0-3nnnI 1 IFdo - 430FIG. 2.RadiaI-axial CO force stretching constant difference in M(CO)5L compounds as a functionof x-electronic charge transferred to L.The model incorporates the notion that variations in charge at the metal dueto varying Q donor character of the ligand are relayed isotropically to all remainingCO groups.The n acceptor character of X, on the other hand, is experienced totwice the degree by the axial CO as compared with the radial CO. Graham's rulespredict that the difference in axial and radial CO force constants should be a functiononly of the n acceptor character of X. Fig. 2 depicts a graph of the calculated Fdo-Fz0 against QL, the calculated n electronic charge transferred to the ligand. Assumingthat the n parameter is a linear function of the n charge transferred to L. the relation-ship should be linear, and independent of the amount of CT charge transferred. Thisis roughly the case ; for example, for QL = 0, F& - F&-, changes by only 0.02 ou44 MOLECULAR ORBITAL MODEL FOR CARBONYLSof a 0-34 total, when aL is varied from 0.25 to 0.65 e-, a change which represents alarge variation in 0 donor character. The assumption that CJ effects from the ligandsare distributed isotropically to the remaining CO groups thus appears satisfactoryon the basis of the model.We now examine the effects of not providing for a differential degree of n: bondingfor the two kinds of CO in M(C0)5L.Assuming that there is a greater degree of n:bonding to the axial CO, one might expect that this would occasion a slightly greaterdegree of cr bonding from this CO to the metal. This in turn would have the effectof lowering the n* orbital energies on that CO, increasing still further the amountof n: bonding. The effect is not likely to be great, however ; it seems best to ignorethis second-order effect, since other factors, such as polarization of the 0 bond systemcould be responsible for equally large effects of indeterminate direction.The variations in diagonal force constants calculated from the model are too smallas compared with the " observed " variation in these quantities.For example,F& - F& in MO(CO)~NH~C~H~ is about 0.74 whereas the correspondingcalculated quantity for a cr bonding only ligand is about 0.33. Similarly, the" observed " change in Fe0 from the parent carbonyl in this case is about 1.4 mD/&whereas the calculated decrease is 0.62 mD/A. Some of the relatively low responseto ligand change in the theoretical model probably results from using a low value of2eVlunit charge for the charge corrections to the H i .A part of the apparentvariation in force constants calculated from the observed spectra is due to variationsin the M-C a bond strength. Thus, if the net charge on the metal is considerablymore negative after replacement of CO by an amine, for example, the metal-carbonylQ bonds may be weakened. This would result in a lowering of the CO stretchingfrequencies independently of changes in the ?t bonding to CO. As argument againstthe importance of this hypothesis, 0 bonding effects should be isotropic, and thusnot affect the F& - F'o difference. Finally, the assumed relationship between Qcoand stretching force constant, eqn. (9), may be in error. To reproduce properlythe variations in Fco calculated from the observed spectra using the simplified forcefield, the force constant dependence on bond order should be about 2.2 times largerthan provided for in eqn.(9) and (11). With this scaling, variations in both Goand Fto are well reproduced.It is of interest to examine the effect of variation in Fc, with variable cr donorcharacter, for a given value of a,. Fig. 3 and 4 shows graphs of F& and F60 againsta, for three different a,. Also,the dependence of the force constant on Q donor character of L depends on then-acceptor level in L. Angelici and Malone 2 5 have noted that in a series of W(CO),Lcompounds, graphs of F;o and Fto against pK, for the ligands have the same slopesfor amines and phosphines. If pK, can be taken as a measure of 0 donor character,these graphs have the same character as those in fig.3 and 4. The vertical separationbetween the plots for the amines and phosphines 2 5 is substantial for Fzo, and smallfor F&. This fact suggests that there is some n acceptor character operative inthe phosphines, but the similarity in slopes noted by Angelici and Malone poses aproblem if the n-acceptor character of the ligands is thought of in terms of a,. Themore meaningful quantity to consider may be QL, the amount of charge on the ligandin the complex. If points of equal QL are connected together, lines such as thedotted lines shown in fig. 3 and 4 (for Q = 0.205) result. These lines have essentiallythe same slope as the line for the a-only ligand. It appears, therefore, that theexplanation for Angelici and Malone's result is that the quantity of 7t charge residenton the phosphines in the complexes is roughly constant, and not that the phosphinesare incapable of 7c-acceptor character.26The two behave differently as a function of a,WAYNE P.ANDERSON AND THEODORE L . BROWN 45For the interaction force constants the calculations support the rough adequacyof the assumptions frequently made, that the trans interaction force constant istwice the cis value. When L differs drastical!y from CO, e.g., a, not included,0.25 0 . 5 0 0.75mFIG.. 3.Variation in F& with cs donor stength of ligand L in M(CO),L, for different x-acceptorlevels of L.I 1 0!750.25 0 - 5 0OLFIG. 4.-Variation in F& with a donor strength of ligand L in M(CO)5L. for diEerent x-acceptorlevels of L46 MOLECULAR ORBITAL MODEL FOR CARBONYLSoL = 0.50, the ratio k,/k,, is about 1-6, significantly less than 2, as assumed in thesimplest model.The ratio R = k,/k,, where k, is an average of the two kinds ofcis interaction force constants, appears to depend on QL, and is given by an expressionof the form(14)To apply this relationship to analysis of observed vibrational data it is necessary toreplace QL by a quantity which can be determined from the data. One might dothis by computing a n parameter for a ligand using Graham's rules, eqn. (12) and(13), and assuming R = 2. Then it might be assumed that Q L = nL/nco x 0.627.From this, R could be determined, a new set of force constants calculated, and theprocedure iterated to convergence.In his considerations of the interaction force constants in unsubstituted metalcarbonyls, Jones 2o made the simplifying assumption that the n-electronic chargeon the metal remains constant during a stretching vibration of a single metal carbonylgroup.This assumption is based on the notion that as one CO is stretched, leadingto transfer of n-electron density to that CO, there is a simultaneous contraction ofthe other CO groups, with a resultant transfer of n charge to the metal, such thatthe metal charge remains constant.the change in metal x-charge due tostretching of thejth CO, and the change in n charge on the ith CO due tostretching of the jth CO, were computed for several substituted metal carbonyls(table 4). Although is indeed small in comparison with the total chargeon the metal, it is actually larger than the corresponding changes occurring on theCO groups cis to the perturbed one.Therefore the assumption of a constant chargeon the metal is not satisfactory. From the results described earlier, the relationshipsbetween the cis and trans CO-CO interaction force constants are consistent withthe qualitative arguments based on the simple n-electronic considerations first putforward by Jones, and do not depend on the assumption of a constant metal x charge.Stone and co-workers 21 have put forth relationships between the interaction forceconstants in the substituted metal carbonyl compounds which appear to dependon the assumption of constancy of metal n charge in the CO stretching process.The results of our calculations support neither the assumptions themselves nor thegeneral character of the force constant results calculated from the observed spectrausing those results. In particular, in the n electron approximation, the stretchingforce constant for the CO trans to the substituent is always less than for the radialCO groups if L is a weaker 7c acceptor group than CO.However, the present ap-proach does not allow for a trans polarizing effect in the 0 system.R = k,/k, = 2-0.5 (0.627- QL).To test this assumption, values ofTABLE 4.-EFFECT OF A " UNIT DISPLACEMENT " OF ONE CARBONYL GROUP ON THE CHARGE ONTHE METAL IN METAL CARBONYLScompounds UL QM (~~263 (AQM)WCO) 6 - 3.762 0.042 0.067Cr(C0)5LCT 0-25 3.468 0.055 0.075(a, = a) 0.65 3.753 0.058 0-074Cr(CQ5L 0.25 3.492 0.05 1 0-073la = - 4 .5 ) 0.65 3-806 0 . 0 4 9 0.068This research was supported by a grant, GP 6396X, from the National ScienceFoundation47 WAYNE P . ANDERSON AND THEODORE L . BROWNA. F. Schreiner and T. L. Brown, J. Amer. Chem. SOC., 1968,90,3366,5947.K . G. Caulton and R. F. Fenske, Inorg. Chem., 1968,7,1273.N . A. Beach and H. B. Gray, J . Amer. Chem. SOC., 1968,90,5713.T . A. Manuel, Adv. Organometal. Chem., 1965, 3, 181.I. Wender and P. Pino, editors, Organic Syntheses via Metal Carbonyls, (Interscience Publishers,New York, N.Y., 1968), vol. 1.F. A. Cotton, Inorg. Chem., 1964, 3,702.D. J. Darensbourg and T. L. Brown, horg. Chem., 1968,7,959.F. A. Cotton, Rev. Pure Appl. Chem., 1966,16,175.lo L. L. Lohr and W. N. Lipscomb, J. Chem. Phys., 1963,38,1607.l 1 P. C. Van Der Voorn and R. S. Drago, J. Amer. Chem. SOC., 1966,88,3255.l2 H. Basch, A. Viste and H. B. Gray, Theor. Chim. Acta, 1965,3,458.l 3 B. J. Ransil, Rev. Mod. Phys., 1960, 32,245.l4 J. D. Simmons and S . G. Tilford. J. Chem. Phys., 1966, 45, 2965.15a G. Bor, Spectrochim. Acta, 1962, 18,817.15b F. A. Cotton and C. S. Kraihanzel, J. Amer. Chem. Soc., 1962, 84,4432.l6 A. F. Schreiner, Ph.D. Thesis, (University of Illinois, 1967).l7 R. S. Mulliken, J. Chem. Phys., 1955, 23, 1841.Is C. A. Coulson and H. C. Longuet-Higgins, Proc. Roy. SOC. A, 1958, 193,456.'O L. H. Jones, J. Mol. Spectr., 1960, 5, 133 ; 1962, 9, 130.21 J. Dalton, I. Paul, J. G. Smith and F. G. A. Stone, J . Chem. SOC. A , 1958, 1195.22 H. D. Kaesz, R. Bau, D. Hendrickson and J. M. Smith, J. Amer. Chem. SOC., 1967, 89,2844.23 F. A. Cotton, Inorg. Chem., 1968, 7, 1683.24 W. A. G. Graham, Inorg. Chem., 1968,7,319.25 R. J. Angelici and M. D. Malone, Inorg. Chem., 1967, 6,1731.26 R. P. Stewart and P. M. Treichel, Inorg. Chem., 1968, 7,1942.' W. D. Horrocks and R. C. Taylor, Inorg. Chem., 1963,2,723.S. Bratoz and S. Besnainou, J. Chern. Phys., 1961, 34,1142