The Geometries of and Bonding in Certain TransitionMetal ComplexesBY R. MCWEENY, R. MASON AND A. D. C. TOWLDept. of Chemistry, University of SheffieldReceived 23rd January, 1969Two topics in structural transition metal chemistry are discussed. First the Chatt-Dewar theoryfor the bonding between metals and unsaturated ligands such as carbon disulphide, oxygen andacetylene is developed ; it is shown that the molecular orbital wave function contains wave functionsbelonging to the excited states of the individual fragments and the theory is then correlated withsome recent structural results. Secondly, the trans-influence of a number of ligands in severalplatinum(II) complexes is described and related to their electronegativities and ligand-metal p(a)overlaps.The Chatt-Dewar model for the bonding between transition metals andunsaturated ligands has been qualitatively successful for many discussions of theproperties of organometallic molecules ; during the last few years, semi-empiricaltheories of varying sophistication and reliability have developed this largely symmetry-based model to predictions of molecular energy levels and related matters.We nowexamine the implications of a simple molecular orbital theory on recent observationsof the geometries of unsaturated ligands co-ordinated to metals in low oxidation states.The model for the bonding between the metal and ligand is based, as in the Chatt-Dewar model, on the highest occupied orbitals of the metal M and ligand L beingrespectively 7r and a symmetry, the lowest empty orbitals being of opposite symmetry.The molecular orbitals are constructed, as usual, by a linear combination of orbitalsof the component systems.The a orbitals lie close together and interact quitestrongly to give the bonding and antibonding orbitals, aML and The 71 orbitals,initially filled on the metal and unfilled on the ligand, in general interact more weaklyto give the xML and orbitals. If we disregard mixture of all other orbitals, weconsider only the electron configurations ML[x2a2], M[&] and L[G~] which allcorrespond to spin singlet ground states (the complexes of interest are all diamagnetic).If we neglect overlap, the molecular orbitals ML have the normalized form,a = oM sin O+ oL cos 8,O* = aM cos 0-0, sin 8,n* = nM sin 4+n, cos 4,7~ = nM cos # + nL sin #,with the ground state of the complex being represented by the wave functionY = + I aanz!.(2)a and 5, for example, represent spin-orbitals with a and B spin factors respectively ;d and 4 are defined by the equations6, = 2 sin2 0 (a charge donated by the ligand),6, = 2 sin2 4 (n charge back-donated by metal).2R . MCWEENY, R . MASON AND A. D. C. TOWL 21Inserting (1) into (2) and expanding, we obtain the following terms in the wavefunction :sin2 8 cos2 4 I o M ~ M ~ M E M 1 + cos2 8 sin2 4 I o L o j n l ? t L I + cos 8 sin 6 cos 4 sin 4 x(- I OMZMZLEL I + [ OMEMOLE, I + i ~ M ~ M z L ~ L I - I 1 )+sin2 8 sin2 4 1 ~ M ~ M ~ L E L I + cos2 8 cos2 4 I QLcTLzM~M 1 +sin2 e cos 4 sin { I oMcM~MzL 1 - I o M ~ , i i L n M i +ax2 # sin 8 cos e( I o,nM?t:,aL 1 - I CMZMEMOL I ] +cos e2 cos 4 sin 4{ 1 O L ~ L ~ M E L I - I oLzLEL~M I 1 +sin2 4 sin e cos 6( 1 C T L ~ L Z L ~ M I - 1 ~ , ~ L z L ~ M 1 >.(3)The various terms are identifiable as antisymmetrised products of wave functionsrepresenting the states of the separate systems M and L. For example,4 [ o L ~ L ~ M E M i = A . 1/42 I o L ~ L 1 I/ J2 I ZMEM Iwith A antisymmetrizing the product of two normalized wave functions representingthe singlet ground states of [7&] and [o?], performing all possible electron inter-changes and summing with appropriate signs.The first two terms in eqn. (3) arise from the ionic wavefunctions M2-• L2+ andM2+ L2- while the last four terms describe singlet states belonging to the singlyionized functions, M- L+ and M+ L- respectively-they are, therefore, relativelyunimportant.That is to say, if the coefficients of the various wave functions in(3) were regarded as variational parameters, those of the " ionic states " woulddecrease in magnitude on optimizing the wave function. (A similar situation occursin the molecular orbital treatment of the hydrogen molecule where complete neglectof the " ionic states " yields the Heitler-London wave function). The remainingterms may now be written in the form,= aA(@Lg@Mg) + bA(@Le@Me) +C(AC3@L,03@M,0- 3@L,- 13@M,+ 1- 3@L,+ 13@M,- l]+A(l@L1@M)]-mLS and mMO are the ground states of L and M while QLemMe are excited singletstates produced by double excitations into the lowest empty orbitals.The secondterm must be expected to have lower weight than the first which represents the" no-bond " situation. We note that in the limit of very small overlap, our functionwill correspond to the well-known Mulliken charge transfer wave functions. Thesingly excited wave functions appear only when overlap is large and the molecularorbital method more appropriate. We infer from (3) that the coefficients a and care defined byc/a = tan 6 tan 4showing that the importance of the interaction terms, and hence the excited statecomponents of the wave function, increases with increasing charge transfer from themetal to ligand and vice versa.The appearance of triplet states in the term describing the interaction is of mostinterest to us. 3@L,m, for example, is the spin-triplet state of the ligand arising froma single excitation into the empty n orbital, with spins coupled to unity and with " z "component rn = 0, & 1.The functions in the square brackets arises by vectorcoupling the triplet states of the fragments to a resultant spin S = 0. The ter22 BONDING IN TRANSITION METAL COMPLEXESA(lmLIQM) arises from the same single excitations but with spins coupled to give asinglet state of each fragment. Since each term is individually normalized, thetriplet terms occur with three times the weight of the singlet term. A variationalcalculation would allow the ratio of these coefficients to vary but the general picturewill remain unchanged.In the complex the charge density is a weighted sum of densities associated withfragments in their various individual states. The terms in which the fragments arein their first excited triplet states appear with large weighting and all lead to a ligandcharge distribution virtually identical with that possessed by an isolated ligandmolecule in its first excited triplet state.The geometry of a ligand will thereforespontaneously change on co-ordination, the forces acting on the nuclei being morenearly those of the triplet state rather than those of the ground state.Recent X-ray structural analyses show that (i) the carbon disulphide ligand in(Ph,P),PtCS, has a geometry remarkably similar to that of its ,A2 excited state.,’(ii) The electron distribution in z-bonded oxygen complexes approximates that ofthe 3Z; excited state in a way which varies according to the electronic nature of theremaining ligands in the cornple~.~~ The state is, in valence bond terms,predominantly 0f-O- and the reactivity of (Ph,P),PtO, towards carbon dioxide,sulphur dioxide, aldehydes and ketones may be rationalized along these lines.’(iii) The geometries of acetylene, ethylene and butadiene co-ordinated to metals inlow valence states often approaches that of their excited states.6 For acetylene,Blizzard and Santry have recently discussed its co-ordinated geometry.8 Substitutedacetylenes are cis-bent on co-ordination in contrast to the excited state of the un-co-ordinated molecule which is trans-bent. It is obvious qualitatively that non-bonded interactions of the substituent groups with the metal will stabilize the cis-bentligand on co-ordination. However, Blizzard and Santry * point out that the cis-bentstructure can be explained solely in terms of the symmetry of the various orbitals ofthe metal and ligand-it is largely a question of the contribution of the carbon 2sorbitals to the various metal-ligand molecular orbitals.CNDO-MO calculationsindicate that the observed angles of bonding in co-ordinated acetylene can beaccounted for by the transfer of approximately 0-5 electron from the ligand nu orbitalsto its z* counterpart; this estimate is not inconsistent with other estimates of theextent of charge transfer in metal to ligand interaction^.^THE TRANS-INFLUENCE OF LIGANDSThe classification of ligands according to their “ trans-directing ” properties,i.e., their relative tendency to direct an incoming ligand into a trans-position tothemselves, for substitution reactions in planar platinum (11) complexes, has beenestablished for some time.1° The extension of this classification to a series basedon the effectiveness of a ligand to influence the rate of displacement of trans-ligandswas made by Basolo and Pearson l1 and forms the definition of the trans-effect ”.Two theories have some success in rationalizing the trans-effect in terms ofelectronic effects transmitted by the trans-directing ligand across the metal to theleaving group ; they are based respectively on the inductive and mesomeric effectsof the trans-directing ligand.2* A generalization of the relative importance ofinductive and mesomeric effects is difficult for little is still known of the detailedmechanisms of substitution in d6 and d8 planar complexes while the variations ofreaction rate with solvent, metal oxidation state, incoming group participation andsteric effects are not understood in any general way. These difficulties have led to anincreasing interest in observable ground state effects of a ligand L on a trans-liganR. MCWEENY, R. MASON AND A . D. C . TOWL 23X and infra-red and nuclear magnetic resonance spectroscopy has been used to studythe trans-bond weakening effect of a ligand 14* l5 (differentiating an equilibriumproperty (trans-influence) from the kinetic trans-effect).We prefer to examinebond lengths in this connection since again it is not clear that interpretation of infra-red and nuclear magnetic resonance data is at all straightforward-for example,few data are available for bond force constants in the complexes of interest.Structural data, from X-ray analyses, of some planar platinum(I1) complexes arecollected in table 1.TABLE 1 .-PLATINUM-CHLORINE BONDLENGTHS IN SOME PLATINUM(II) COMPLEXESmolecule trans-ligand Pt-Cl bond length (A)(Pr(acac), C1)- 0 2.28 f0.01 ''trans-(PEt,),PtCl, CI 2.30 50.01 l7(G2H 1 7)2PtzC12 C=C 2.31 &O-01cis-(PMe3),PtC12 P 2-37&0-01 l9trans-(PPh,Et),PtHCl H 2.42f0.01 2otrans-(PPhMe,),(SiPh,Me)PtCl Si 2.45f0.01 21The order of trans-influence is seen to be : Si>H>P>C=C, C b O .Although less data are available, a similar series may be provided for other d8(Ni(l1) and Pd(I1)) planar complexes and for octahedral d6 (Co(III), Rh(III), Ir(III),Grinberg's original discussion l 2 of the trans-effect was based on purely electro-static grounds, relating polarizability to the trans-directing ability of a ligand.Syrkin and Yashkin related polarizability of a ligand to the covalent character ofthe metal-ligand bond and, using valence bond methods, showed that in d8 planarcomplexes an increase in the degree of covdence in the M-L 0 bond decreasedthe covalence of the trans M-X a bond and hence increased the lability of X.23Fig.1 shows that for the data of table 1, the trans-influence of L increases smoothlywith decreasing electronegativity (the effective electronegativity of C = C is that oftrigonal carbon).24 Chatt et reached a similar conclusion from infra-reddata. This result is related to those of Syrkin and Yashkin; if we consider relativeenergies of L, M and X a-bonding orbitals, then if the ligand X is more electronegativethan L, the following qualitative scheme is obvious.P t (I V)) .22t1 EnY-MtAEi ?AE2 > AEI L- ' a'E,-XiThe a-molecular orbital electron density will be principally within the M-Lbond (high covalence) and on the ligand X (high ionic character of M-X).Gray and Langford 26 base a theory of the trans-effect on the magnitude of theM-L and M-X a-overlap integrals.The suggestion here is that if the a-donororbital of the ligand L has a greater overlap with the metal pa orbital than does theligand X a-orbital, then the M-L bond is strengthened at the expense of the M-Xbond. The overlap calculations of Gray and Langford have now been extendedcomprehensively to a number of ligands and metals and are given in table 224 BONDING I N TRANSITION METAL COMPLEXES01.5 I2.2 5 2 - 3 0 2 3 5 2.40 2.4 5Pt-CI distance, AFIG.1.-Variation of the Pt-Cl bond length in L-Pt-Cl as a function of the Pauling electro-negativity, XL, of the trans-ligand L.TABLE 2.-METAL (PO) - LIGAND HYBRID (0) OVERLAP INTEGRALSligand atom andhybridization Co(II1)0.450-470-5 10.400.430.360.380-3 10-340.370.560.510.480.5 10.450.470.500.520-480.500.5 10.54NI(I1)0.490.520.550-450.470.400-430.360-380-410.550.530.500.520.470.490.500-530.480-490-500.56Rh(1II) Pd(I1)0.490.520.550.450.470-400-420.370-3 80.380.510.500.470.470.440.440.440.480.430.440.430.510.480.520.550.450.480.410.420-370.3 80-390.500-490.470.470.430-440.440.480.430.430.430.51Ir(II1)0.480-5 10.540.440-470-400-410-360.370.3 80.490.490.460.460.420.430.430.470-420.420.410.50R(IU0.480.510.540.440.470.410.420.370.380.390.490.490.460.460.430-430.430.460-420.420-410.50Au(l1I)0.480.510.540-450.480-410.420.370-380.390.490.480.450.460-420.430.420.460.410.410.410.50These overlap integrals have been calculated as follows :(i) Atom radii (A) ; C(sp3) 0.77, C(sp2) 0.74, C(sp) 0.71 ; N(sp3) 0.70, N(sp2) 0.63 ;H, 0.27 ; 0, 0.66 ; F, 0.62 ; Si, 1.00 ; P, 1.00 ; S, 1.00; C1, 0.99 ; As, 1.12 ; Br, 1-14;Co(TII), 1.26 ; Ni(Il), 1.24 ; Rh(IV), 1.33 ; Pd(II), 1-31 ; Ir(III), 1-36 ; Pt(II), 1.33 ;Au(TII), 1-31.For the first row transitionmetals they are those of Richardson et aL2’; for the second and third row metalsthey are the functions of Basch and Gray.28(ii) S.C.F.wavefunctions were used for all atomsR. MCWEENY, R . MASON AND A . D . C. TOWL 25(iii) All metal wavefunctions are those of the + I oxidation state.Whilst thisassumption will undoubtedly introduce some error, it will probably be a systematicone and with little variation from metal to metal. Cotton and Harris conclude 29that failure to correct the metal wavefunction for varying metal charge in (PtC1,)2-leads to an error of less than 4 % in the M-L overlap integrals for charge variationsbetween 0 and + 1.(iv) All ligand wavefunctions are those of Clementi 30 for neutral atoms, doublezeta functions being used where available.(v) The calculated values are based on the method of Demuynck and Kaufmann 31and Mulliken's rules.For platinum(II), the a-overlap integrals have the order :Si-H, C, P>Cl>N>O>Fin general qualitative agreement with trends in the bondlengths noted in table 1and confirming, for the trans-influence of ligands, the suggestions of Gray andLangford relating to the trans-effect.We emphasize that the agreement is onlyqualitative-we cannot sensibly deal, for example, with the relative trans-influenceof tri-alkyl and triaryl phosphine ligands.Perturbation theory indicates that bond strength may be related to S2/AE (S theoverlap integral and AE, the energy separation between the orbitals being mixed).The above discussion now shows that both relative ligand a-orbital energies andrelative ligand-metal cr overlap integrals reproduces the trend of the trans-influenceability of a ligand.The bond length data additionally illustrate a mesomeric contribution to thetrans-influence which would, in principle, be exerted in one of two ways,(i) A n-acceptor ligand L is able, through the usual synergic effect, to effectivelyincrease its donor capacity which in turn increases the inductive contribution to thetrans-influence, and(ii) As has been pointed out previously, a n-acceptor ligand will directly competewith the ligand X for excess charge in the metal.The fact that ethylene and carbonmonoxide have little or no trans-influence and that, experimentally, the trans-influence of a a-bonded alkyl is greater than that of a formally a-bonded phosphineclearly indicate that the second process is dominant. In short, therefore, a strongtrans-influence follows from the ligands with large inductive, a-donor and weakn-acceptor properties. (In all of this discussion we assume that the ligand X hasnegligible n-bonding capacity.) By contrast, the large trans-effect of ethylene andcarbon monoxide can be accounted for, as Chatt et al.and Orgel 32 pointed out, interms of the stabilization of transition states and not from any initial ground statelabilization of the trans-ligand.We are grateful to the S.R.C. for support of this work.M. J. S . Dewar, Bull. SOC. Chim. Fr., 1951, 18, C71.J. Chatt, J. Chem. SOC., 1953, 2939.M. Baird, G. Hartwell, R. Mason, A. I. M. Rae and G. Wilkinson, Chem. Comm., 1967, 92.R. Mason and A. I. M. Rae, in preparation.J. A. McGinnety and J. A. Ibers, Chem. Comm., 1968, 235 and references therein.R. Mason, Nature, 1968, 217,543.'I R. Ugo, F. Conti, S . Cenini, R. Mason and G.B. Robertson, Chem. Comm., 1968, 1948.* A. C. Blizzard and D. P. Santry, J . Amer. Chem. 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