Dependence of Stability Bond Strength and Electronic Structure of Dimetal Units upon Atomic Number Oxidation Number and Chemical Environment BY BRUCEE. BURSTEN COTTON AND F. ALBERT Department of Chemistry Texas A & M University College Station Texas 77843 U.S.A. Received 6th August 1979 The electronic structures of the Cr and Mo units in the form of neutral diatomic molecules charged diatomic molecules and coordinated by ligands have been investigated by SCF-Xa-SW calculations supplemented by projection of the Xa MOs in atomic orbital basis sets (the PXa pro-cedure). The results are compared with the experimental data on Cr, Mod and the many CP2L and Mo1',L, complexes. This paper addresses the similarities and differences between the " naked " diatomic metal clusters as they are known in the gas phase or in inert-gas matrices and the " clothed " ones that is those in stable chemical compounds where they form bonds to ligand atoms.The naked ones have the advantages of relative simplicity but are more difficult to study because of the low concentrations and the inconvenience of applying standard physical techniques. The clothed ones can be made and studied more conveniently in a range of formal oxidation states but the presence of other atoms and bonds creates some complications. Taking the dimolybdenum unit as an example we have for Mo,(g) a secure value1 of @,,(406 20 kJ mol-l) some disparate estimates2y3 (315 cm-l and 477 crn-l) for vMo-Mo; earlier MO computations3 have suggested a bond order as high as six with YM~-M~z 2.1 A and Dho-Moz 326 kJ mol-I.The most recent spectroscopic data4 on Mo,(g) have been analysed to give rMo-Mo = 1.929 A DMo-Mo = 397 60 kJ mo1-l and vMo-Mo = 477 crn-l. Compounds containing Mo-Mo triple and quadruple bonds have bond lengths ranging from a low of 2.037(3) A in Mo2[(C5H4N) NC(0)CH3]45 to 2.457(1) 8 in Mo,[(F,P)~NCH,]~C~~ which contains a twisted triple bond.6 vM0-Mo values range from ~300 to 426 cm-I and a wealth of information both experimental and theoretical is available on the electronic structures of these bonds. The Cr,(g) molecule is said to have rCrdCr= 1.685 A,4 which is difficult to reconcile with the reported @98 of only z 150 kJ m~l-',~ and distances of 1.83-2.54A ~-~~ found in Cr24+ compounds.8 This short value of Y~ will be correct only if the assumption that the spectrum from which it is derived9 is due to Cr rather than CCrC or OCrO is correct.* While it has been recognized from the startg that this point * If the observed spectrum is due to CCrC or OCrO the C-Cr or 0-Cr distances would have to be x1.78 or % 1.54 A respectively.We emphatically disagree with the statement that these are so implausible as to allow an ips0 facfo rejection of these species. CCrC is not a less likely product of photolysis of Cr(C0)6 than Cr and since Cr-C is 1.91 A in Cr(C0)6 where there are six Cr-C bonds and each C atom also forms a multiple bond to oxygen a Cr-C distance of "1.78 A in CCrC is not a priori unreasonable. B. E. BURSTEN AND F.A. COTTON can be checked conclusively by repeating the measurements with isotopic labelling such an experiment (which would not be difficult) has not yet been done. We shall describe here calculations performed on MO,~+and Cr24+ species with q varying from 0 to 4. The objectives are (1) to compare corresponding molybdenum and chromium species and (2) for each one to investigate the dependence of the bond- ing on the internuclear distance and the charge. COMPUTATIONAL METHODS All calculations were performed using the SCF-Xa-SW method of Slater and Johnson.".'l Starting parameters were chosen as in earlier Xa calculations l2 on Mo and Mo;+. The overlapping atomic-sphere radii used were chosen to be 25 % greater than tangential-sphere radii and the outer-sphere radii were chosen to touch the atomic spheres.This choice of sphere radii results in consistently good virial ratios.13 The calculations were iterated until the largest change in the molecular potential was <0.0005 a.u. The converged calculations were projected onto a Slater atomic orbital (STO) basis using the projected Xa (PXa) method.14 To avoid biasing the PXa results a very flexible even-te~pered'~ valence STO basis was used for all calculations. For Cr atoms the basis consisted of five uncontracted 3d STOs ([ = 0.5 1.0 2.0 4.0 and 8.0) three uncontracted 4s STOs (c = 1.0 2.0 and 4.0) and three uncontracted 4p STOs ([ = 1.0 2.0 and 4.0). For Mo atoms the same exponents were used for the 44 5s and 5p STOs. In all cases the use of these basis sets resulted in an overlap of >0.99 between the LCAO MOs and the corresponding Xa MOs.RESULTS AND DISCUSSION NEUTRAL DIMERS We begin with Mo for which Norman et al. have already reported12 an Xa-SW calculation that led them to propose an Mo-Mo bond order of six. This calculation was done with Mo-Mo distances greater than the 1.929 A now reported from experi- ~ent.~ This short distance implies that the bond order is greater than four. We have reinvestigated the electronic structure at the experimental distance. The orbital energies and the Mulliken percent characters l6 of the valence orbitals of Mo (dMo-Mo1.929 A) obtained from the PXa treatment are given in table 1. = TABLE1.-ORBITAL ENERGIES AND PXa MULLIKEN PERCENT CHARACTERS OF THE VALENCE ORBITALS OF MO orbital efeV %4d %5s %5P 1% -0.53 131 -31 1OU -1.38 24 125 -49 16 -2.49 100 -2oga -3.58 9 112 -21 16 -4.51 100 1ZU -6.24 98 -2 1U -7.00 84 0 16 a Highest occupied orbital.STABILITY OF DIMETAL UNITS B. E. BURSTEN AND F. A. COTTON FIG.1.-Contour plots of the 10 (a),1nu(b),16 (c) and 20 (d) orbitals of Mo2at 1.929 A. Interior contours close to the atomic centres have been omitted for clarity. All plots are in the xz plane. The contour values are kl f2 f3 k4 rt5 = k0.015 10.030 10.060 10.120 10.240 respectively. STABILITY OF DIMETAL UNITS For a singlet ground state the twelve valence electrons should form a closed shell (10,)~ (lnJ4 (20,)' configuration corresponding to two a two n and two 6 bonds between the Mo atoms as previously found by Norman et al.at the longer Mo-Mo bond distances. Before presenting a detailed analysis of the six metal- metal bonds however some comment on the seemingly anomalous Mulliken percent characters (i.e. >lo0 or <0) of the 2a, la and ln orbitals is in order since such intuitively displeasing results tend to indicate deficiencies in the STO basis used for the LCAO projection. However it was precisely to avoid this difficulty that a very flexible basie set was used. The 2ag la and In orbitals are very diffuse containing respectively only 23 20 and 50% of their charge density within the atomic spheres. Mulliken population analysis however assumes that orbitals largely retain atomic character thus allowing the charge density to be equitably divided among the contri- buting AOs.l6 Unfortunately this approximation breaks down for very diffuse orbitals not only in the present case but in semi-empirical and ab initiu LCAO-MO calculations on transition metal systems as well7 Contour plots of the la, In, 16 and 20 orbitals are presented in fig.1. The la orbital as expected," is dominated by the metal 4dz2 AOs. There is appreciable (16%) mixing of Mo 5p character as well however. Although not obvious from the contour plot the A0 coefficients of the projected 1a orbitals indicate that this mixing results in 4d2*-5p bonding interactions via the 442 doughnut a result which will be discussed in more detail later. The In, and 16 orbitals clearly represent bonding interactions between the 4dx,,y and 4dx2-y2,xyAOs respectively.The 20 orbital is dominated by 5s-5s bonding interactions accounting for its resemblance to a diffuse Rydberg orbital but the 4dz2 AOs also participate with coefficients opposite in sign to the 5s AOs. This causes a polarization of the density in a direction perpendicular to the Mo-Mo bond (cf. the oblate contour at the centre of the plot). The 5p orbitals also mix in to give a 5s-5p2 bonding interaction strengthening the overall bonding in the orbital. Although it is clear that there are six bonding interactions in Mo2,it is important to make a distinction between the number of metal-metal interactions and the strengths of these interactions/ Whereas the number controls the magnetic properties of the molecule it is the strengths that determine the bond length and bond energy.The complexity of the contour plots of the orbitals precludes their use in estimating the relative strengths of the a ;rc and 6 interactions but the projected LCAO orbitals produce an informative representation of the bonds. It is generally assumed that the extent of bonding between two atoms in an orbital is related to the amount of shared charge in the inter-atomic region. This is the under- lying assumption in the use of Mulliken overlap population^^^ to estimate relative bonding strengths. However the breakdown in the conventional Mulliken analysis for the diffuse 20 orbital leads us to employ the following modification. For a molecular orbital v consisting of AOs on atoms A and B we write The charge density distribution in the orbital given by the square of v,,(r),will consist of one-centre terms involving only AOs on either atom A or atom B and the two- centre cross terms which we will call the overlap distribution OD@) B.E. BURSTEN AND F. A. COTTON Multiplying OD(r) by the occupation of the orbital and integrating overall space gives the Mulliken overlap population (MOP) MOP = n I OD(r) dr = 2 2 cp cy Sij ly where Sljis the overlap integral’’ between xf and xy. However the use of Sljis the source of difficulty for diffuse orbitals,17 so we prefer to display OD(r) directly thus focusing on the distribution between the atoms. Fig. 2 and 3 present surface plots of OD(r) for the four occupied MOs of Mo,.The la overlap distribution not surprisingly is indicative of a large charge concentra- FIG.2.-Overlap distribution function for the la (a)and 1 n,,(6) orbitals of Mo at 1.929A. The xz plane has been plotted with z increasing from the bottom corner to the right corner of the plot. The position of one of the atoms is indicated by the dot on the lower plot. STABILITY OF DIMETAL UNITS FIG.3.-Overlap distribution function for the 16 (a) and 20 (b) orbitals of Mo at 1.929 A. The positions of the atoms are indicated by the dots on the upper plot. tion between the atoms. The smaller peaks on either side of the Mo atoms result from the complex nodal structure of the Mo 4d 5s and 5p AOs and are not of im-portance in this discussion.The large “ wells ” off the end of each Mo atom result from overlap of the diffuse 5pz orbital on one Mo with 4dz2 orbital on the other MO. Since as noted earlier the 5pz orbitals mix into the la MO to produce bonding between the atoms via the 4dz2 “ doughnut,” the 5pz-4dz2 overlap off the ends of the molecule must be negative. It is important to note that Mulliken analysis of this orbital would consider these “ wells ” as antibonding contributions to the MO an assumption which seems unsatisfying. The ln overlap distribution consists of two large peaks on either side of the nodal plane of the orbital and small features around the atoms due again to the nodal B. E. BURSTEN AND IF. A. COTTON structure of the 4d AOs. From a comparison of the la and lnuoverlap distributions it would appear that the a bond is probably stronger than one rc bond but less strong than the sum of both rc bonds and reminds one of the relative a and n bond strengths in hydrocarbons.The 16 overlap distribution is distinguished by its flatness suggesting an insensi- tivity of the 6 interaction to the metal-metal bond length and presumably also the converse i.e. that the metal-metal bond length is relatively insensitive to the amount of 6 interaction." Thus it seems doubtful that the extremely short bond length of Mo relative to Mo"L species owes much to the addition of another 6 bond. On the other hand the 20 overlap distribution indicates a fairly substantial buildup of density along a ridge running through the centre of the Mo-Mo bond and we con- clude that this second a bond may actually be stronger than the 6 bonds even though it lies at higher energy.The existence of this second CT bond in conjunction with the absence of ligand effects may largely account for the very short bond in Mo,. For Cr we have performed calculations at internuclear distances of 1.685 and 1.80 A. The orbital energies of the two Cr calculations are compared with those of Mo in fig. 4. At both distances a bond order of six is obtained in complete analogy 0 -9 In 1 a ............--.. _.l._.............--- -0. -.%.*. . ........-(.*- -2 Ib -.-- .........---.*.* ......-.. -3 Mo,(1.929 ,&I Cr2(1.685 A1 Cr2(1.800AJ FIG.4.-Molecular orbital energies of Mo2 at 1.929 A and Cr2at 1.685 and 1.800 A.with Mo,. The slight upward shifts of the lo, In and 16 levels in Cr relative to Mo probably result from both a slight increase in the metal d orbital energy and slightly weaker bonding. The la orbital rises by nearly 1 eV indicating that the main a bond in Cr is probably weaker than that in Mo,. This is consistent with predictions from extended Huckel calculations2' of the M bond energies2 for M0 (79 kcal mol-l) and Cr (61 kcal mol-l) although the predicted value for Mo is so much lower than the experimental value (97 & 5 kcal mol-l) that the results of such extended Huckel calculations are of dubious value. It is also notable that the drop in STABILITY OF DIMETAL UNITS energy of the 20 orbital of Cr relative to that of Mo, a change which is consistent with the observation that the atomic ionization potential of Cr 4s electrons is greater than that of Mo 5s electrons,22 appears to agree with the shifts in the electronic spectra of matrix isolated Mo and Cr2.The first allowed excitation presumably the 20 -+ la (52 t'Z;) transition is blue-shifted from 19530 cm-l in Mo to 21 930 cm-I in Cr . With the exception of the 20 orbital lengthening the Cr-Cr bond from 1.685 to 1.80 A results in the expected changes uiz. the bonding orbitals rise in energy while the antibonding levels drop. The 20 orbital behaves curiously showing a slight decrease in energy upon bond lengthening as might be expected for an antibonding orbital. The reason is that the increase in bond length greatly changes the character of the 20 orbital; nearly all of its 3dz2 character is lost at 1.80A resulting in an essen- tially nonbonding 4s-4s MO with slight mixing in of 4p character very similar to the onorbital proposed for multiply bonded compounds.18 That the orbital remains at very nearly the same energy would seem to indicate that the second o bond in Cr2 even at 1.685 A is not as strong as that in Mo, but this is inconsistent with the extremely short Cr-Cr bond and supports our view that the reported distance should be checked.QUADRUPLY CHARGED DIMERS Theoretical study of charged M2units is important because they form the basis ofa myriad of M"L quadruply bonded corn pound^^^^^^ in which the effects of the ligands upon the molecular and electronic structures are still incompletely understood.Thus depending upon the number geometry basicity and n-bonding capabilities of the ligands the formally quadruply bonded dichromium(r1) complexes span a remarkably wide range of CrCr bond lengths from 1.83 to 2.54 A.8 In this section we will first examine the electronic structure of the base M;+ units comparing them to the neutral dimers and investigating the effects on the molecular orbitals of changing M-M bond length. The valence molecular orbital energies of Mo;+ are shown next to those of Mo in fig. 5. The bond length of 1.929 A has been retained to facilitate the comparison even though the shortest known Mo-Mo quadruple bond5 is more than 0.1 A longer than this. The calculation on Moi+ employed Dlth rather than Dmh symmetry allowing us to selectively occupy the two different components of both the 6 and 6 representations.Thus the 6 representation of Dmh splits into b, + b, under symmetry in which the former uses dX2+2 orbitals as a basis and the latter uses dx,,orbitals. This breaking of symmetry will be helpful in our simulation of ligand donation effects in the next section. It should be noted that the spherical averaging of the XCC-SWmethod guarantees that the (b,, bZg)and (bl, bZu)set of orbitals will remain degenerate as they should. There are a number of interesting features in fig. 5. The ground configuration of Moi+ which we have constrained to correspond to a 'A, ground state is alg2e:b2s2 (or equivalently alg2e,4b,,2)corresponding to one O two n and one 6 bond for a total bond order of 4.This is the expected result. What is surprising however are the orbital shifts upon the removal of four electrons from Mo,. The most prominent feature is the large upward shift of the 2al orbital of Moi+ relative to the 20 orbital of Mo,. This shift has been attributed by Norman et all3 to greater stabilization of the Mo 4dAOs relative to the Mo 5s AOs. The lalgand la, MOs of Mo~+ exhibit large stabilization and destabilization respectively relative to their counterparts in Mo,. This strongly suggests that the main component of the Mo-Mo o bond is B. E. BURSTEN AND F. A. COTTON 5 4 3 2 1 eV 0 -1 -2 -3 -4 -5 M02 FIG.5.-Molecular orbital energies of MoZ and Moi+ at 1.929 A.The zero of energy has been as-signed to the average of the 6 and 6" orbital energies. strengthened upon the removal of electrons from the diatomic unit most probably because of a contraction of the Mo 4d22 orbitals in the charged species. In Mo they are diffuse enough to allow significant overlap of the positive lobe on one Mo 442 with the negative torus on the other one but contraction induced by making the atoms positive increases the positive overlap and results in more effective 4d22-4dz2 inter-action. The leu and leg MOs of MO;+ exhibit analogous downward and upward shifts albeit not as great as those of the la, and la, levels and a similar explanation is applicable. That the 4dx,,, AOs in Mo are too large for optimal interaction is apparent in fig.2(b),OD@)for the ln MO. There are clearly valleys off the ends of the molecule indicative of the over-extension of the 4dX,,, AOs on one atom to the far side of the other atom an effect which will be Iessened by contraction of the 4d orbitals. The 6 and 6" MOs of Mo;+ shift very slightly upward and downward relative to those of Mo, evidence for a very slightly weaker 6 interaction in the charged species. This shift is again consistent with a contraction of the Mo 4d orbitals since the geometry of dxy,x*-y2 orbitals dictates that their overlap will montoni-cally decrease with increasing compactness of the orbitals. The very small magnitude of the shift shows the insensitivity of the 6 interaction to changes in atomic charge as well as changes in bond length.To investigate the energetics of the orbitals of M;+ as a function of metal-metal bond lengths we have performed calculations on Cr;+ at 1.85 2.00 and 2.15 A. The orbital energies for the three calculations are shown in fig. 6. Increasing the metal- metal distance results in smooth nearly linear upward shifts of the bonding orbitals and downward shifts of the antibonding orbitals with slopes in the order cr E TC >6. STABILITY OF DIMETAL UNITS 1.85 A 2.00 A 2.15 A FIG.6.-Molecular orbital energies of Cr$+at 1.85 2.00 and 2.15 A. The zero of energy has been assigned to the average of the lbzgand lbl orbital energies. The Ib2 orbital is the highest occupied orbital in all three calculations. PRESENCE OF LIGANDS If we assume an electronic configuration for M;+ of (a1,)2(e,)4(b2g)2, i.e.the metal d,2 d,, dyzand dxyAOs are half-filled (neglecting for now the higher lying s and p AOs) the interaction of ligands with the Mi+ unit can occur in three different ways. (1) The ligands can donate charge to the empty dxz-y2,s orp orbitals. (2) The ligands can donate charge into the antibonding blu,e or aZUorbitals. (3) The ligands can accept charge from the occupied metal levels. The effect of the first of these will be to reduce the effective positive charge on the metal atoms without significantly affecting the bond order. The second and third interactions will each reduce the bond order of the metal-metal bond besides causing a reduction or increase respectively in the positive charge on the metal atoms.The geometry of the ligands and their electronic requirements will dictate the relative importance of these three types of interaction . We have chosen to demonstrate the effect of ligands on the dimeric unit by performing a PXa calculation on [MO~CI~]~-, in which only the first two effects will be possible Calculational details are given el~ewhere.~~~~~ The PXa total Mulliken orbital populations are given in table 2 referred to the coordinate system in fig. 7. These are compared to "idealized " Mo;+ wherein 5s and 5p contributions to the filled levels are ignored resulting in a (~~)~(xz)~(yz>~(xy)~ configuration on each Mo atom. The main component of Mo-CI boHding is donation from the C1 3px orbitals to Mo 4d,~-~zand 5s orbitals the bonding B.E. BURSTEN AND F. A. COTTON TABLE 2.-BONDING AND ANTIBONDING CONTRIBUTIONS TO THE ATOMIC ORBITAL POPULATIONS OF [IVf02c&]4-bonding antibonding total Mo24-t a 0.99 0.09 1.08 1.o 0.36 0.31 0.67 0.0 1.oo 0.09 1.09 1.o 1.oo 0.09 1.09 1.o 1.oo 0.09 1.09 1.o 0.15 0.12 0.27 0.0 total 4.50 0.79 5.29 4.0 C1:b 3s 1.96 3Px 1.78 3PY 3Pz 1.98 1.96 total 7.68 a See text. See fig. 7 for the reference coordinate system. x FIG.7.-Coordinate system of [Mo2Cl8I4-. C1" is the chlorine atom used for the population analysis in table 2. (big or a,,) contribution being slightly greater than the antibonding (b2uor a2u). There are smaller C1 to Mo donations from the 3s 3py and 3p orbitals the effect of which is to make the 4dzz 4dxy,4dxzand 44 A0 populations greater than one.Any charge in these AOs in excess of the half-filled configuration must result from MOs which are metal-metal antibonding as indicated in tabie 2. The net result of all the bonding and antibonding effects is a reduction of the Mulliken bond order from 4.0 (1.0 0,2.0 n,1.0 S) in Mo:+ to 3.71 (0.93 0 1.82 TI,0.96 S) and a reduction of the charge on the Mo atom from +2.0 to +0.71. The chloride ions have donated 0.94 e per Mo atom via mode (1) and 0.35 e per Mo by mode (2). Another way to study the first mode of ligand-metal bonding i.e. ligand 0 donation without metal-metal bond order reduction has been accomplished by investigating the energetics of Crh+ and MoZ+ (q = 4 3 2 1 0) at 1.850and 1.929 A respectively.Charge is reduced from 4-4 by introduction of equal amounts of elec-tron density to the b, and b2uorbitals resulting in no change in the metal-metal bond order and simulating the effect of idealized simple donation to the metal dXz-,,z STABILITY OF DIMETAL UNITS orbitals. The calculated differences in the o and o*,7t and n*,and 6 and 6* orbital energies are summarized in table 3. Several interesting trends are evident. The TABLE3.-vARIATION OF THE O-O* 71-71* AND 6-6" ORBITAL ENERGY DIFFERENCES (ev) FOR QUADRUPLY BONDED M%+ 4 Crg+ 0-0* 71-71 * 6-6 " o-o* Moj+ n-n* 6-6 * 4.0 5.73 3.39 0.69 8.94 6.50 1.54 3.O 5.35 3.70 0.88 8.01 6.51 1.75 2.0 4.82 3.91 1.10 6.96 6.38 1.94 1.o 3.95 3.92 1.33 5.73 5.94 2.11 0.0 2.46 3.74 1.21 4.37" 4.74" 2.21" a This value is from a calculation which was ill-behaved and is not fully converged.o-o* energy separation in both species decreases monotically with decreasing positive charge corroborating the proposal in the previous section that the dz2 orbitals of the neutral atoms are too extended for optimal bonding at short distances. In contrast the n-n* separations in both molecules are not a monotonic function of the charge. Rather the n-n* separation maximizes at a particular degree of simulated donation indicating that the 7t-bonding can be optimized. The 6-6* separation is monotically increasing with increasing donation except for the Cr;+ (q = 0) calculation. This is surprising in that the 6-6" interaction should increase with increasing diffuseness of the Cr 3d orbitals.A possible explanation of this anomaly is a dominance of the 6 and 6* orbital energies by the charge residing in the dX2-,,2 orbitals for it must be remembered that the quadruple bond has been preserved ; the electron configuration (als)2(eJ4 (b2s)2(bJ2 (b2u)2 formally corresponds to one o bond two 7t bonds two 6 bonds and one 6 antibond. Upon comparing the Cr;+ calculations to those of Mo$+,it is seen that both the o-o* and n-n* energy separations span a wider range for Moj+ and that the n-n* separation in Mo;+ maximizes at a greater positive charge. All of these trends indi- cate that the Mo 4d orbitals in Mo;' are less contracted than the Cr 3d orbitals in Cr$+ at the chosen bond distances.Although a more judicious choice of Mo-Mo bond length would have been 2.00 to 2.05 A the orbital separations are expected to decrease only slightly and we expect the compact character of the Cr 3d orbitals to be general. These simulations of the effects of simple o donation by ligands although ad- mittedly simplistic can be used to explain several puzzling trends in the structural chemistry of quadruply bonded compounds. For example the replacement of the chloride ions in [M02C&l4- by methyl groups which are stronger charge donors results in a lengthening of the metal-metal bond from 2.139 A in K4M02C18. 2H2027 to 2.147 A in Li,Mo,(CH& 4THF." It might appear then that chloride ion is a better ligand for the formation of quadruple bonds than is the methide ion.However the situation is very different for chromium for which the complex [Cr2(CH&j4- exists28 but the analogous octachloro compound does not. It is very likely if not entirely certain that this is the result of thermodynamic factors and an attractive explanation is in the electronic differences between Cr and Mo in quadruply bonded complexes. Increased donation by the methyl groups decreases the charge on the Mo atoms beyond the optimal point resulting in orbitals which are too diffuse and causing the Mo atoms to move further apart to compensate. The Cr atoms on the other hand require greater donation than Mo atoms and chloride ions may be in- B. E. BURSTEN AND F. A. COTTEN capable of delivering enough density to the Cr atoms to stabilize a quadruple bond.This argument has of course neglected completely the second mode of ligand-metal interaction which we discussed earlier. It is apparent that modes (2) and (3) of ligand interaction with Mi+ units can also be easily simulated by calculations with varying degrees and distributions of added electron density. Such calculations will be made in the future to develop a compre- hensive description of the electronic effects of ligands on multiple metal-metal bonds. This work has been supported by the National Science Foundation through a research grant and a National Needs Postdoctoral Fellowship to B. E. B. S. K. Gupta R. M. Atkins and K. A. Gingerich Znorg. Chem. 1978 17 321 I. W. Klotzbucher and G.A. Ozin Inorg. Chem. 1977 16 984. W. Klotzbucher G. A. Ozin J. G. Norman Jr and H. J. Kolari Inorg. Chem. 1977 16 2871. Yu. M. Efremov A. N. Samoilova V. B. Kozhukhovsky and L. V. Gurvich J. Mol. Spectr. 1978,73,430. * F. A. Cotton W. H. Ilsley and W. Kaim Inorg. Chem. 1979,18 2717. F. A. Cotton W. H. Ilsley and W. Kaim J. Amer. Chem. Soc. 1980 102 1918. 'A. Kant and B. Strauss J. Chem. Phys. 1966 45 3161. A. Bino F. A. Cotton and W. Kaim J. Amer. Chern. Soc. 1979 101 2506 and references therein. Yu. M. Efremov A. N. Samoilova and L. V. Gurvich Optics and Spectroscopy 1974 36 654. lo J. C. Slater The Selfconsistent Field for Molecules and Solids Quantum Theory of Molecules and Solids (McGraw-Hill New York 1974) vol. 4. l1 K.H. Johnson Ann. Rev. Phys. Chem. 1975 26 39. l2 J. G. Norman Jr H. J. Kolari H. B. Gray and W. C. Trogler Znorg. Chem. 1977,16,987. l3J. G. Norman Jr J. Chem. Phys. 1974 61,4630. l4 B. E. Bursten and R. F. Fenske J. Chem. Phys. 1977,67 3138. K. Ruedenberg R. C. Raffenetti and R. D. Bardo Energy Structure und Reactivity Proceed- ings of the 1972 Boulder Seminar Research Conference on Theoretical Chemistry ed. D. W. Smith (Wiley New York 1973) p. 164. l6 R. S. Mulliken J. Chem. Phys. 1955 23 1833. l7 J. H. Ammeter H.-B. Burgi J. C. Thibeault and R. Hoffmann J. Arner. Chem. Soc. 1978 100,3686. l8 F. A. Cotton Znorg. Chem. 1965 4 334. l9 R. S. Mulliken J. Chem. Phys. 1955 23 1841. 2o F. A. Cotton J. M. Troup T. R. Webb D. H. Williamson and G. Wilkinson J.Amer. Chem. Soc. 1974 96 3824. 21 R. Hoffmann J. Chem. Phys. 1963 39 1397. 22 C. E. Moore Atomic Energy Levels (Nat. Bur. Stand. Circ. 467 vol. I1 and 111 1952 1958). 23 F. A. Cotton Chem. SOC.Rev. 1975 4 27. 24 F. A. Cotton Accounts Chem. Res. 1978 11 225. 25 5. G. Norman Jr and H. J. Kolari J. Amer. Chem. Soc. 1975 97 33. 26 B. E. Bursten Ph.D. Thesis (University of Wisconsin Madison Wisconsin 1978). 27 J. V. Brencic and F. A. Cotton Inorg. Chem. 1969 8 7. 28 J. Krausse G. Marx and G. Schodl J. Organometul. Chem. 1970 21 159.