摘要:

1980Theoretical CN DO Molecular-orbital Analysis of Metal-Ligand Bondingas a Function of Ligand Basicity in Some Purely -Bonding SystemsBy S. P. Bhattacharyya. Theory Group, Department of Physical Chemistry, Indian Association for the Cultiva-tion of Science, Calcutta-700032, IndiaA theoretical molecular-orbital (m.0.) analysis of the correlation of metal-ligand bond strength with the basicityof the ligands in a number of purely a-bonding systems has been made at the CNDO lwei of approximation. Anenergy partitioning analysis consistent with the unrestricted Hartree-Fock (UHF) model at this level reveals theexistence of linear correlations of the various energy contributions to metal-ligand interactions with ligand basicity.The diatomic ’ shared electron density ’ and exchange interaction energy (EZAB) are the most suitable parametersfor assigning a covalency index to various metal-ligand bonds.An apparently irregular behaviour of the covalentinteraction energy component (€‘AB) computed a t the CNDO level is critically examined.THE factors that affect the strength or the stability of theco-ordinate bond formed between a donor (the ligand)and an acceptor (the metal ion) moieties are of consider-able interest. Although a number of electrostaticmodels 1-4 exist for the theoretical treatment of co-ordination compounds, these are not suitable for appli-cation to strongly covalent complexes. In such cases,the best resort is to molecular-orbital (m.0.) theory.This paper concerns a theoretical CNDO m.0.in-vestigation on the variations in the energetics of metal-ligand bonds in a series of nickel( II)-amine complexeswith changes in the basicity of the ligands. Its purposeis two-fold: (i) to provide a rationale for the observedvariations of the strength of an M-L bond with increasingligand basicity; (ii) to attempt to generate a 111.0.parameter which can be used as a covalency index in thecontext of semiempirical orbital theories. However, thepicture which has emerged out of an analysis made withthe help of semiempirical orbital theories may not have aone to one correspondence with the actual molecularphenomena. Thus the results presented should beregarded as preliminary results to be refined laterthrough more rigorous studies.To isolate the effect of a single ligand variable amodel system of ligands has been chosen in which (a) theco-ordination occurs through the same type of atom, (b)the state of hybridisation of the donor orbitals remainsidentical, (c) the chemical environment around the donoratom in the ligand moiety is constrained to remain thesame, and (d) the only factor that changes from onedonor to the other is the ionisation energy of the donororbital.It is hoped that the trends observed in this some-what idealised system will provide some insight into thebehaviour of real systems.The specific group of ligands chosen is NH,, NMeH,,NMe,H, NMe,, and NEt,, in all of which the co-ordin-ation is assumed to occur through the a (sp3 hybrid)lone pair of electrons on the nitrogen atom.Thecalculation proceeds in the following steps. (i) For eachligand, a perfect octahedral co-ordination is assumed andthe bptimum metal-ligand bond length is calculated byusing LCAO-MO-SCF theory at the CND05-‘ level ofapproximation using UHF methodology. The para-metrisation scheme adopted is the one recently developedby our group.8-10 (ii) The total UHF energy of eachsystem is partitioned into a number of components, e.g.coulombic interaction , exchange interaction, covalentinteraction energies, etc. following which the variationsof these quantities are analysed as functions of ligandbasicity.THEORETICALPartioning of the UHF-LCAO-MO-SCF Energy in CNDOApproximation.-Ehrensen and Seltzer l1 first invoked anenergy-partitioning analysis in connection with CNDO-MOtheory and applied i t to develop a ‘ bond-strength index ’ inclosed-shell molecules.In the present case we are dealingwith open-shell systems and hence the partitioning shouldrefer to the unrestricted Hartree-Fock (HF) operator or toany other open-shell HF type of operator and wavefunction(~,Ppefi Sllell). Thus equation (1) is applicable, and with the+ c Ecore-core AB (2)A > Busual definitions of G:, GE,,,, and lz””’” we can write (2).The definitions l1 of other terms are given for one-centreinteractions in equations (3)-(5) and for two-centreG = 2 P E P + p!P,u;, (3)PEAPEA WCA(4)( 5 )interactions in equation (6). EiB represents the so-calleddiatomic covalent interaction energy, a quantity arisingentirely from the diatomic shared density.The occ(0r) andocc(p) values correspond to the number of occupied orbitalshaving cc and p spin respectively346 J.C.S. DaltonA simple explanation of the origin of the EzB term isas follows. If the atoms A and B are bonded through theorbitals p (on A) and v (on B), the probability of simul-taneously finding an electron in the orbital p having, say,a spin and an electron on v having similar spin is not simplyPi;(.) . PF:(a). The Fermi correlation forces some of theelectron density, viz. (PFv) , into the bonding region, therebyreducing coulomb interaction between the electron pair byan amount equal to ( ~ v j 2 g ~ B . The probability is thus givenby Pi:(.) . P;,?(a) - Pi:(.).ElB is, therefore, directlyassociated with the occurrence of orbital overlap andchemical-bonding effects. Accordingly, it should be animportant parameter for assessing the covalent characteror strength of a given M-L bond. The analysis shows thatthis is indeed true. The residual two-centre interactionsstill present in Egkb (CNDO) are all of coulombic type.Thus, we can write expressions (7)-(9).E:B = - z B d B ( p i A + P f A > f ZA&B(GB + %3)Ek4 = (PZbpBQB + P!BPfA + e A P g B f P6sAPB“B)giB(7)(8)Errcore = Z A Z B d B ( 9)RESULTS AND DISCUSSIONIn Figure 1 total binding energies of the complex ionshave been plotted against ionisation energies of theligand,12 the index of ligand basicity in the model. Theplot clearly demonstrates the linear increase in M-Lbond energies with increasing basicity of the ligand.Y I \.P 1 U9 10 11Ligand ionisation energy (eV)FIGURE 1 Net binding energy of a series of nickel(I1)-aminecomplex ions shown as a function of ligand ionisation energyThe usual notion of a stronger metal-ligand bond withligands of higher basicity is thus theoretically sub-stantiated.Obviously, it would be of interest to isolatethe specific two-centre interactions controlling this trend.Figure 2(d) presents a plot of unpaired electron densityon a 3d orbital of NiII against ligand basicity. The plotclearly demonstrates that unpaired electron density inthe metal 3da orbitals decreases linearly with increasingligand basicity implying that a higher degree of L+Mtransfer of electron density occurs through the M-Lcharge-transfer interactions with ligands of higherbasicity.An examination of Table 1 reveals that the totalA R ‘ diatomic overlap population ’ PaB(= 2 Pi:) be-P Vtween the metal and a ligand atom, conventionally calledtotal bond order, increases with increasing ligandbasicity. Thus, increased basicity of the ligand triggersa higher degree of charge localisation in the bondingregion.It is interesting to note that while the 3d,L, and4p,L, ‘ shared densities ’ increase with increasing ligandbasicity, the 4s,L, terms shows an opposite trend.However, the 4s orbital on the metal seems to play arelatively unimportant role in determining the generaltrends.In Figure 2 ( 4 , (b), and (c) plots are shown of theTABLE 1Variation of M-L overlap populations with ligand basicityin octahedral six-co-ordinate metal complexes of NiIIOverlap population (0.p.)a = b = c = Total = ’0.p. per bondLigand 3&L, 4s,L, 4p,L, a + b + c (PAB)NMeH, 0.6454 0.9986 2.6550 4.2990 0.7165NMe,H 0.667 4 0.9962 2.6820 4.3456 0.7242NMe, 0.6684 0.9942 2.7006 4.359 6 0.7266NEt, 0.6740 0.991 6 2.721 6 4.3866 0.731 1NH, 0.623 6 0.999 8 2.6070 4.230 7.0.705 13d,L,, 4s,L,, and 4fi,L, components of the metal-ligandcovalent interaction energies (EiB) against ligandbasicity index. It is surprising that these energyquantities decrease with increasing basicity. The3d,L, and the other exchange interactions contributingto EiB, however, increase with increasing ligand basicity(Figure 3).One may recall that the diatomic exchangerepulsion energy is directly proportional to the total‘ shared density ’ in the bond region; thus an increase inElB is expected if P A B increases with increasing ligandbasicity. The concomitant decrease in EiB which alsois a linear function of P A B , however, needs explanation.It is a sum of the product of three terms, viz. 2 2 P;y” .p;ty”. Si:. An increase in the ligand basicity leads to anenhancement of the ‘ diatomic shared density ’ 2 2 Pi:but in turn pi: decreases. This is not peculiar to thepresent CNDO model. Correlation of conventionalCNDO bonding parameters (pi) with atomic electro-negativity l3 shows the generality of this behaviour.In the present case this decrease in PA: more than offsetsthe effect of an increase of electron density in the bondingregion.Thus, the use of EiB as an index of covalencyin the CNDO model may give misleading conclusionsfor a series of closely related species. It is thereforeA BP VA BP VA B A Bshould be used to assess the degree of covalency in agiven chemical bond, particularly when a CNDO type ofmodel is employed in computing the one-electrondensity matrix.Since EhL, the so-called covalent (also called re-sonance) interaction-energy component of the ML bond,decreases in magnitude as the basicity of ‘ L ’ increases,coulombic components must dominate the trends1980 347TABLE 2Coulombic components (eV) of metal-ligand bond energy in a series of octahedral amine complexes of nickel(I1)Interaction energiesElectron Metal Metal Ligand Net electrostaticrepulsion 3d-ligand 4s, 4p-ligand electron-metal stabilisation ofLigand between M and L core core core M-L bond83.774 7 - 86.556 0 -24.003 7 - 77.399 4 - 2.623 NMeH,NMe, 83.414 5 -86.593 2 -25.283 1 - 76.016 3 -2.51 1NEt, 83.207 8 -86.625 8 -25.912 8 -75.391 5 - 2.75583.994 0 - 86.356 9 -23.640 7 -75.963 6 - 1.650 NH3NMe,H 83.540 6 -86.362 1 - 24.790 6 - 76.507 2 - 2.2981 eV z 1.60 x J.The metal-ligand core-core repulsion energy is 101.967 2 eV in each case.5.15 r9 )E 0.890)rIni- .-5C0L c4 0.870,2 - 3 1 1 I I I I I I5 8 11 1 4 6 9 12Ligand i o n i s a t i o n energy (eV)FIGURE 2 Different properties of a series of nickel(11) hexamine complex ions correlated with ligand basicity: (a) correlation of 3 d , L ~covalent interaction energy of metal-ligand bond ; (b) 4s,L, covalent interaction energy of M-L bond ; (c) 4buL, component as in( b ) ; (d) net unpaired electron density in a 3d, metal orbital, L, is a ligand orbital (0 type) with the same symmetry as that of theinteracting metal orbital.Ligands: (0). NMe,; (@), NEt,; (a), NMeH,; (A), NMe,H; (W), NH348 J.C.S. DaltonFrom Table 2, one can see how the different two-centrecoulombic energy components vary with ligand basicity.The balance of different coulombic interaction energieshas been plotted against ligand basicity in Figure 4. Anon-linear correlation emerges. It may be pointed outthat in Mulliken's l4 valence-bond theory of charge-transfer (c.t.) complexes also, the stability of the c.t.c% Y 0.20cc 0AIn=Ec>r.-F z" 0-19cc000aJcQ,0r V XQ,.- .wLc .-0.18C- -bJ& m uN0.169Ligand ionisat ion energy ( e V )ligand bond shown as a function of ligand basicity.FIGURE 3 3d0Lb Exchange interaction energy of the nietal-Ligands:(O), NMe3; (e), NEt.3; (01, NMeHa; (A), NMe2H; (m), NH3complexes shows a similar non-linear correlation with theionisation energy of the donor.In the present case, thequantity plotted in Figure 4 is essentially the c.t.stabilisation of the M-L bond defined in the context ofm.0. theory. However, the result that the trends in thestability of the M-L bonds are not determined by what isusually defined as covalent interactions in the languageof semiempirical m.0.theories needs further analysis.One may point out that the total two-centre coulombicenergy component as defined in CNDO theory incor-porates in it the effects arising from M-L transfers ofelectron density, a phenomenon definitely controlled bycovalent interactions between the donor and acceptororbitals. It is, thus, debatable whether E:, alone can beregarded as the diatomic covalent interaction-energyA I \c 2 1.501 I 1 Ic , 8.00 9.00 10.00 11.00Ligand ionisation energy (eV)FIGURE 4 Net coulombic contribution to the stabilisationof the metal-ligand bond correlated with ligand basicitycomponent. A b initio calculations and parallel analyseswould provide a clearer physical picture.The author thanks the referees for their suggestions andcomments; sincere thanks are also due to Professor MihirChowdhury for discussions, and to the staff of the UniversityCentre of Computer Science, Calcutta, for their co-operation.[8/2135 Received, 11th December, 19781REFERENCESC.K. Jmgensen, S. M. Horner, W. E. Hatfield, and S. Y.Tyres, jun., Internat. J . Quantum, Chem., 1967, 1, 191.P. Daudel and R. Daudel, J . Phys. Radium, 1946, 7 , 14.R. Ferreira, Adv. Chem. Phys., 1967, 13, 55.F. Gallais, D. Voigt, and J. F. Labarre, J . Chim. Phys.,1965, 62, 761; F. Gallais, P. De Loth, and J. F. Labarre, ibid.,1966, 63, 413.J . A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys.,1965, 43, S129.J. A. Pople and G. A. Segal, J . Chem. Phys., 1965, 43, S136. ' J. A. Pople and G. A. Segal, J . Chem. Phys., 1966, 44, 3289.S. P. Bhattacharyya and M. Chowdhury, J . Phys. Chem.,9 S. P. Bhattacharyya and M. Chowdhury, J . Phys. Chem.,lo S . P. Bhattacharyya, Indian J . Chem., in the press.l1 S. Ehrensen and S . Seltzer, Theor. Chim. A d a , 1971, 20, 17;l2 D. H. Aue, H. M. Webb, and M. T. Bowers, J . Amer. Chem.l3 S . P. Bhattacharyya, Indian J . Chem., 1978, A16, 4.l4 R. S. Mulliken, J . Amer. Chem. Soc., 1952, 74, 811.1977, 81, 1593.1977, 81, 1602.M. S. Gordon, J . Amer. Chem. Soc., 1969, 91, 3122.Soc., 1976, 98, 311

ISSN:1477-9226    

DOI:10.1039/DT9800000345

出版商:RSC    

年代:1980

数据来源: RSC