Molecular Orbital Theory for Octahedral and Tetrahedral Metal ComplexesHarold Basch, Arlen Viste, and Harry B. Gray Citation: J. Chem. Phys. 44, 10 (1966); doi: 10.1063/1.1726431 View online: http://dx.doi.org/10.1063/1.1726431 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v44/i1 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsTHEJOURNALOFCHEMtcALPHYSICSVOLUME44,NUMBER11JANUARY1966 MolecularOrbital Theory forOctahedral andTetrahedral MetalComplexes IlAROLDBASCH,ARLENVISTE, ANDHARRY B. GRAY TheDepartment of Chemistry,ColumbiaUniversity,NewYork,NewYork (Received 4 May 1965) Self-consistentchargeandconfiguration(SCCC)molecularorbitalcalculationsarereportedfor32 selectedoctahedralandtetrahedralfirst-rowtransition-metalcomplexescontaininghalideandchalco-genide ligands. It isfoundthat forthe range of metal oxidation states II through IV,F., chosen to fitthe experimental.1.,isafunctionofonlythemetalatomicnumberforconstantF".Intherangeofformal metal oxidation numbers V through VII, F. is also a function of oxidation number. Calculatedandobservedtrendsincovalency,.1.values,andfirstL->Mcharge-transferenergiesare compared. The conclusion isdrawnthat themolecular orbital method,in its present formulation,givesa reasonableaccount of'the:ground states and lowexcited states in simplemetal complexes. INTRODUCTION THEsemiempiricalmolecularorbitaltheoryinthe Wolfsberg-Helmholzframework1 hasbeenrevived in recent calculations on a wide variety of molecules.2-18 Suchdiversemolecularpropertiesasgeometricconfig-urations,4,o,9electric-dipolemoments/atransitionmo-ments/,3,llelectronicspectra/-8,10-13,15-18chargedistri-butions,and ionization potentials havebeen calculated withvaryingdegreesofsuccess.Inparticular,this reasonablysimpleMOapproachhasbeenofgreat valueininterpretingvariouselectronicstructural properties oftransition-metal complexes.Althoughthe initial resultsareencouraging,there have beentoo few * Presentaddress:AugustanaCollege,SiouxFalls,South Dakota. 1 M.lWolfsbergandL.Helmholz,J.Chern.Phys.20,837 (1952). 2 (a)R.Hoffmanand;W.N.Lipscomb,J.Chern.Phys.36, 2179,3489;37,520(1962);(b)R.Hoffman,ibid.39,1397 (1963); 41,2474,2480,2745(1964). 3C. J. Ballhausen and H. B. Gray, Inorg. Chern.1, 111(1962). L.L.Lohr,Jr.,andW.N.Lipscomb,J.Chern.Phys.38, 1607(1963) ( J:~ Chern.Soc.85,240(1963);Inorg.Chem. 2, 911(1963); ~ b i d 3, 22(1964). 6T. Jordan, H. W.Smith, L. L. Lohr, Jr., and W.N. Lipscomb, J. Am.Chern.Soc. 85,846(1963). 6H.Bedon,S.M.Horner,andS.Y.Tyree,Jr.,Inorg.Chern. 3,647(1964). 7A.VisteandH.B.Gray,Inorg.Chern.3,1113(1964). 8S.1.Shupack,E.Billig,R.J.H.Clark,R.Williams,and H. B. Gray, J. Am.Chern.Soc. 86, 4594(1964). 8E. A.Boudreaux, Inorg. Chern. 3, 506(1964); J. Chern.Phys. 40,246(1964). 10H.A.Pohl,R.Rein,andK.Appel,J.Chern.Phys.41, 3385(1964). 11R.F.FenskeandC.C.Sweeney,Inorg.Chern.3,1105 (1964). 12R.F. Fenske,Inorg.Chern.4,33(1965). 13F.A.Cotton and T.E. Haas,Inorg.Chern.3,1004(1964). 14F.P.Boer,M.D.Newton,andW.N.Lipscomb,Proc. Nat. Acad.Sci.(U.S.)52,889(1964). 16A.Latham,V.C.Hascall,andH.B.Gray,Inorg.Chern. 4,788(1965). 16P.T.ManoharanandH.B.Gray,J.Am.Chern.Soc.87, 3340(1965). 17W.E.Hatfield,H.D.Bedon,andS.M.Horner,Inorg. Chern.4,1181(1965). 18J. Halper,W.D.Closson,andH.B.Gray,Theoret.Chirn. Acta(tobepublished). 10 attempts at a critical evaluation ofthe method.A good start in evaluationofthe generality ofthesimpleMO methodhasbeenmadebyCottonandHaas,13who studiedthevariationoftheso-calledFfactorin exactlyfittingthe..:lvaluesinaseriesofoctahedral ammine complexes.Also,Fenske and Sweeneyll,12have studiedMn04- andTiF63- indetail.Recently,Boer, Newton,andLipscomb14 havecalculatedtheoretical F factors fortheB2and BH molecules. It isclearthatthesteadydevelopmentofasatis-factoryMOtheoryfortransition-metalcomplexes dependsuponmakingdetailedstudiesandimprove-ments in the existing approximateschemes.In particu-lar,thereistheobviousneedforastandardand consistentmethodofchoosingtheparametersofthe calculationthatcanbetransferredfromonemolecule to another. For this purpose we have ch.osen to calculate 32octahedralandtetrahedralcomplexescontaining first-rowtransitionmetalsandone-atomligands.The complexeswereselectedto explorethe possibility that, usingessentiallythesamesetofinitialassumptions, thevariation of..:land ligand to-metal(L-7M)charge transferwith(1)geometry,(2)ligand,(3)metal oxidationnumber,and(4)metalatomicnumber couldbemadethefunctionofasingleparameter, theF factor. METHOD Themethodasusedinthisinvestigationissimilar tothat applied inthecalculation ofMn04-.7 Asusual, the secular equation to be dealt with isofthe form, (1) Thematrixelementsarebetweenproperlynormalized (with ligand-ligand overlap)symmetry basis functions, x,,,a.Thex,Jla'sincludeatomicorbitalsofthemetal and linear combinations of ligand atomic(or molecular) orbitals; Gij isthe group overlap matrix, G"=(xJla!xv{J)=G .."o~ {J "3... J'3JA,.Uot, (2) Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsMOLECULARORBITALTHEORYFORMETALCOMPLEXES11 Histhe Hamiltonian matrix, withJCastheone-electronHamiltonianoperator.19 The superscripts aand J.I. labelthe rowandirreducible representation,respectively,to whichthe x/a's belong. The0 functionshowsthat thereare nononzeromatrix elements between basis functionsbelongingto different representations,ordifferent rowsofthe same represen-tation. (a)H;;.The diagonal-Hamiltonianmatrix elements H;; areapproximatedasthe negative valuesofvalence orbitalionizationpotentials(VOIP's).TheVOIPfor the transition correspondingtothe ioniza-tionofanelectronfromconfigurationMatoform configurationMb,iscomputedfromthe formula, VOIP(q)=I(q)+E(Mb)-E(Ma),(4) whereq isthechargeontheatom,l(q)istheground-stateionizationpotentialofM a q(notnecessarily resultinginMbq+I);E(Mb)andE(Ma)aretheEAv's ofthe twoconfigurations,Mband Ma, whereaparticu-larEAv istheweightedmeanoftheenergiesofallthe multiplettermsarisingfromagivenconfiguration relativetothegroundstateoftheatomorionin question.Theweightingfactorisequaltothetotal degeneracy(spinXorbital)oftheterm.Afteraverag-ingovertheJcomponents,wehave,forexample, The evaluation of EAv'sforthe pertinent configurations, wheremissingterms prevent adirectaveragingcan be donestraightforwardlybyusingtheequationsof Slater20 relating the energies of the individual multiplets toEAv intermsoftheSlater-Condonparameters.For example, 1 E(3P)+3F2(pp) EAv(p2)=E(1D) - 3F2(pp). E(1S) -12F2(pp) (6) InthesecasesonecanderiveanEAv foreachRussell-Saunderstermwhichtheoreticallyshouldbeidentical forallthetermswithinonegivenconfiguration.How-ever,theEAv'sactually differ in someconfigurations by afewthousandcm-I.InallsuchinstancestheEAv's derivedfromthedifferenttermswereaveraged.Term energiesandionizationpotentialsweretakenfrom 19C.C.J. Roothaan,Rev.Mod.Phys. 23,69(1951). 20J.C.Slater,QuantumTheoryof AtomicStructure(McGraw-HillBookCompany,Inc.,NewYork,1960),Vol.1,Chap.14 and Appendix12a; Vol.2,Appendix22. Moore.21 Slater-Condonparametersweretakenfrom theliterature22,23orobtainedbyaleast-squaresfitof the relevant spectral data. Forthemetal,threedifferentorbitalH;;'sare required:3d,4s,and4p.TheVOIPforagivenmetal orbitalisconsideredasalinearcombinationofthree different configurations in order to adequately represent fractionalpopulations.Forinstance,for4sthethree configurationsaretakentobedn-ls,dn-2S2,and dn-2sp. Alltheconfigurationsarecalculatedasfunctionsof chargeandfromtheresultingnineVOIPcurves,the metal 3d,4s,and 4pH;.'s can easily beevaluated.7 Fortheligands,withvalenceorbitalssandp,the sameprocedurecanbefollowed,requiringfourVOIP curves.However,wehaveconsideredonlytheconfigu-rations2pn;i.e.,fractionalpopulationwasconsidered onlyintheplevel.Theadditionalconstraintwas imposed that n be equal to the occupancy ofthe p level inthe ground-state configurationoftheneutral ligand, asinonecalculationofMn04-.7 Richardsonand Rundle24 also found that the ligand Hio'Swere relatively insensitive functionsofcharge. Valencestateionizationenergiesofpotentials (VSIE'sorVSIP's)havebeencomputedby Skinner, Pritchard,andPilcher,2>-27andHinzeandJaffe.28 These methods assumeahybridizedstate oftheatom, implyingaparticularspatialorientationoftheorbital favorableforbondformation.Suchaconceptisnot necessaryinMOtheory.It isforthisreasonthatwe suggestthenamevalence-orbitalionizationpotentials fortheenergiescalculatedfromEAv values.29 Inaddi-tion,the VOIP's can be derived as naturally continuous functionsofchargeontheatomand,usingMulliken's prescription for summing populations,30 the Hu's canbe adjustedforvariationsofchargeonthemetalatom. Thus,themajoradvantageoftheVOIP'sisperhaps theirsimplicity.Finally,aclearrelationshipbetween Hi/s, VOIP's,andtheconcept ofelectronegativity has recently been established.31,32 21C.E.Moore,"AtomicEnergyLevels,"Natl.Bur.Std. Circ.No. 467(1958),Vols.1,2, and 3. 22J.HinzeandH.H.Jaffe,J.Chern.Phys.38,1834(1963). FkandGktaken fromHinzeand Jaffedifferbyamultipli-catIveconstantfromtheFkandGkusedbySlater(Ref.20). 23J. S. Griffith,TheTheory of Transition Metal Ions(Cambridge University Press,Cambridge,1961). 24J.W.RichardsonandR.E.Rundle,U.S.AtomicEnergy Commission,ISC-830,1956. 2. H.A.SkinnerandH.O.Pritchard,Trans.FaradaySoc. 49,1254(1953). 26H.O.PritchardandH.A.Skinner,Chern.Rev.55,745 (1955). 27G.PilcherandH.A.Skinner,J.Inorg.Nucl.Chern.24, 937(1962). 28J. Hinze and H.H. Jaffe,J. Am.Chern.Soc.84, 540(1962); Can. J.Chern.41,1315(1963); J. Phys.Chern.67,1501(1963). 29H.Basch,A.VisteandH.B.Gray,Theoret.Chim,Acta (to be published). 30R.S.Mulliken,J.Chern.Phys. 23,1833(1955). 31c. K. Jrgensen,Orbitalin Atoms and Molecules(Academic Press Ltd., London,1962),Chap.7. 32G.Klopman,J.Am.Chern.Soc.86,1463,4550(1964). Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions12BASCH,VISTE,ANDGRAY TABLEI.Averageenergiesofconfigurationsb (in1000em-I). Metaln a" an-Isa,,-Ip a"-2s2 a,,-2span-2p2 Sc338.316.336.10.020.246.1 Ti440.718.139.45.827.455.3 V540.320.946.012.240.576.4 Cr655.336.559.230.856.1 Mn758.242.971.339.369.3104.3 Fe840.425.150.827.150.8 Co927.913.142.219.346.8 Ni1014.71.430.210.441.5 Cu110.030.712.046.5 Zn120.036.180.6 aRelativeto ground-state multiplet. b For neutral atom first-rowtransition metals. (b)Hij.Theoff-diagonalHamiltonianmatrixele-ments areapproximated usingEq.(7), H;j=-!FmGiXVOIP.+VOIPiJ,(7) whichcontainsanadjustableparameterFm,calledthe F factor.The subscript m is used to differentiate among U,11',"', etc.- type interactions.In most applications ofthemethodtodate,it hasbeennecessarytouse Fmgreaterthanoneandalsotouseseparatevalues forF" andF ..inorderto achievereasonableresults. (c)Implicit in the previous discussionisthe neglect ofallnonvalenceatomicorbitals.Thedesignation, "valence"inthiscontextisnecessarilyarbitrary.For example,themetal3porbitalhasafinite,albeit small,overlapwiththeligandfunctionsand,if includedinthecalculation,wouldprobably have some effect,particularlyontheantibondingMOlevels. Omitting the nonvalence atomic orbitals may be unduly optimistic,14butneverthelessseemsnecessaryifsim-plicity istobepreserved.The valenceorbitals used in thesecalculationsare,therefore,3d,4s,and 4p forthe metal,and ns and np onthe ligand. (d)Thetreatmentofgroupoverlapintegrals, normalizations,andcorrectionfactorsrelatingthe H;;'stothe H'ds has been givenin detail in a previous paper.7 RESULTS VOIP's forthe 3d,4s,and 4p valenceorbitals ofthe metals ScthroughZnhavebeendetermined fromthe averageenergiesofthepertinentconfigurations.29 The data havebeensmoothedby aleast-squaresquadratic fitacrossthetransitionseries.Formoreefficient computerprogrammingtheresultingVOIP'sare represented quadra tically, VOIP(q) = Aq2+Bq+C,(8) whereqisthecharge.TheA,B,andCparameters, togetherwithsomeneutralatomEAv's,arepresented inTablesIandII.Fortheligands,onlytheconfigu-rationS2pnoftheneutralatomwasusedandthese VOIP'sarelistedinTableIII.Inallcalculationsthe ligandp"wasassumedmorestable(by10000cm-I) thanP.. ,andthelatterwassetequaltothevalue foundinTableIII.Thisadjustmentisderivedfrom inspectionoftheoreticallycalculatedH'ii,14.aa.M-36and fromcharge-transfer spectra.37 .38 TheligandsinvestigatedwereF,Cl,Br,S,andO. Interatomic bonddistances wereeithertaken fromthe TABLEII.VOIPcurves forfirst-rowtransitionmetals' (in 1000 em-I). VOIP curveb TiVCrMnFeCoNi A17.1515.814.7514.113.813.8514.2 218.4514.09.755.513.813.8514.2 318.4514.09.755.513.813.8514.2 49.38.558.057.67.357.257.35 59.38.558.057.67.357.257.35 69.38.558.057.67.357.257.35 77.87.457.257.27.37.557.95 87.87.457.257.27.37.557.95 97.87.457.257.27.37.557.95 B160.8568.074.7580.886.291.1595.5 277.8587.095.95105.0101.5106.25110.7 376.7587.396.95106.0101.9105.55108.2 450.454.1557.5560.963.8566.6569.05 558.562.9566.8570.373.0575.2577.05 655.057.5560.4563.867.3571.3575.65 735.645.4547.5549.350.851.9552.85 848.950.8552.8555.257.860.6563.75 948.950.8552.8555.257.860.6563.75 C127.431.435.138.641.944.847.6 244.651.457.964.170.075.680.9 355.461.467.774.381.288.495.9 448.651.053.255.357.359.160.8 557.260.463.365.968.370.572.3 666.070.674.778.381.484.086.0 726.927.728.429.229.930.731.4 835.936.837.838.839.740.741.6 934.436.438.139.440.340.840.9 "FromRef.29. bThetypeofelectronbeingionized,andtheconfigura tions,areasfollows forthe nine VOIP curves. 1: d, d". 2: d, an-Is. 3: a, an-Ip. 4: s, an-I s. 5: $, an-2s.2 6:s,dn-2sp.7:p,d.... lp. 8: p, dn-fpS.9:p,an-2sp.Successive points on a curve differonly inthe number ofa electrons. 83S.SuganoandR.G.Shulman,Phys.Rev.130,506,512, 517(1963). 34R.E.WatsonandA.J.Freeman,Phys.Rev.134,A1526 (1964) . aliH. Basch and H. B. Gray, unpublished calculations on MnOr. 86K.D.CarlsonandR.K.Nesbet,J.Chern.Phys.41,1051 (1964). 17C.K.J91rgensen,AbsorptionSpectraandChemicalBonding inComplexes(Addison-WesleyPublishing Company,Inc.,Read-ing,Massachusetts,1962). 88C.J.BallhausenandH.B.Gray,MolecularOrbitalTheory (W. A.Benjamin,Inc.,NewYork,1964)Appendix 8. Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsMOLECULARORBITALTHEORYFORMETALCOMPLEXES13 literature39-49 orestimated.5O51 Dayandindependently estimated the bond distance.s in COBr42-(2.43A),MnCI.2- (2.40A),andFeC142- (2.30A) whichdifferfromours(TablesIVandV)by+0.05, +0.07,and+0.03A,respectively.Thisgivesagood indication ofthe accuracy ofestimated bond distances. TheparameterF"wasconsistentlytakentobe2.10 forallHi;andF"wasvariedinordertofittheob-served53-68 exactly.Allligand-ligandcorrection factors38 were calculated usingF m = 2.00 forboth (J"- and 7r-typeinteractions.Wavefunctionsfortheligands (neutral atom)weretaken fromClementi69 or(forBr) Watsonetal.,7andforthemetalsfromRichardson etaJ.7172 Neutral-atomfunctionswerechosenfor4s and4p,whilethe3dfunctionwastakenfromthedn configurationforM+.Theeffectofchoiceofwave-39A.F.Wells,Struct1IYalInorganicChemistry(OxfordUni-versity Press, London,1962),Chap.8. 40V.W.H. Baur,Acta Cryst.ll, 488(1958). 41C.K.Jprgensen,ActaChem.Scand.12,1539(1958). 42H.W.SmithandM.Y.Colby,Z.Krist.103,90(1940). 41B.N.Figgis,M.Gerlock,andR.Mason,ActaCryst.17, 506(1964). 44M.ListerandL.E.Sutton,Trans.FaradaySoc.37,393 (1941) . 46W.N.LipscombandA.G.Whittaker,J.Am.Chem.Soc. 67,2019(1945). 46B.Zaslowand R.E.Rundle,J. Phys.Chem. 61,490(1957). 47P.Pauling,Ph.D.thesis,UniversityCollege,London,1960; quotedbyA.B.BlakeandF.A.Cotton,Inorg.Chem.3,5 (1964). 48Tables of Interatomic Distances and Configurations in Molecules and Ions,Special Publication No.11(Chemical Society, London, 1958). 49R.W.G.Wyckoff,CrystalStructures,IntersciencePub-lishers,Inc.,NewYork,1951),Vol.1. 60M.J.Sienko andR.A.Plane,PhysicalInorganicChemistry (W.A.Benjamin,Inc.,NewYork,1963),p.68. uN.S.HushandM.H.L.Pryce,J.Chem.Phys.26,143 (1957) . 62P.Day andC.K.Jrbrgensen,J.Chem.Soc.Suppl.2,1964, 6226. 63C.J.BallhausenandF.Winther,ActaChem.Scand.13, 1729(1959). 64V.O.Schmitz-DuMont,H.Brokopf,andK.Burkhardt, Z.Anorg.Chem.295,7(1958). 66C.K.Jprgensen,Advan.Chem.Phys.5,62,85(1962). 63Reference37,pp.110-111andpp.284-289. 67Reference 37,p.113. 58R.Englman,Mol.Phys. 3, 48(1960). 69W.Low,Phys.Rev.109,247,256(1959). 60S.Siegel,Acta Cryst. 9,684(1956). 61R. J. H. Clark,J. Chem.Soc. 1964, 417. 62N.S.GillandR.S.Nyholm,J.Chem.Soc.1959,3997. 63C.J.Ballhausen,IntroductiontoLigandFieldTheory (McGraw-HillBookCompany,Inc.,NewYork,1962),Chaps. 4,5, and7. 6( Reference 63,p.228. 66F.A.Cotton,D.M.L.Goodgame,andM.Goodgame,J. Am.Chem.Soc.84,167(1962). 66C.Furlani,E.Cervone,andV.Valenti,J.Inorg.Nuc1. Chem.25,159(1963). 67G.P.Smith,C.H.Liu,andT.R.Griffiths,J.Am.Chem. Soc.86,4796(1964). 68N.K.Hamer,Mol.Phys. 6,257(1963). 68E. Clementi, J.Chem.Phys. 40,1944(1964);IBM Research Paper RJ-256. 70R.E.WatsonandA.J.Freeman,Phys.Rev.124,1117 (1961) . 71J. W.Richardson,W.C.Nieupoort, R.R. Powell,andW.F. Edgell,J. Chem. Phys. 36,1057(1962). 72J.W.Richardson,R.R.Powell,andW.C.Nieupoort,J. Chem. Phys. 38,796(1963). TABLEIII.LigandVOIPsa.b(in 1000cm-I). Ligand a From Ref.29. o F CI Br S b For configuration s'p". s 2608 323.6 203.8 193.8 166.7 p 1274 150.4 110.4 99.6 93.4 functionsonthecalculationwasnotinvestigated,but it isexpectedthatthetrendsunderconsiderationhere arenotalteredforanyconsistentchoice.Also,it has recently been claimed that the one-electron LCAO-MO model isrelatively insensitive to such changes.73 Oncetheelements ofthe secular equations had been calculatedasinput,thesecularequationsweresolved foreigenvaluesandeigenvectors,andaMulliken populationanalysis31 wascarriedout.Theoutput metalcharge(q),s,andp characterwerecompared withtheinput q,s,andp (the latter mayberegarded as the independent variables of charge and configuration intheinput).Theinputq,s,andp populationswere thenadjustedbyaniterativeprocedureuntilinput andoutputq,s,andp agreedto0.005at whichpoint thecalculationwasconsideredself-consistent.The wholeprocesswasprogrammedinFORTRANtoiterate automatically,andrunonanIBM7094computer. Inputconsistsessentiallyofthetotalnumberof electrons,metaloxidationstate,metalandligand VOIP's,groupoverlapmatrix,F-factormatrix,and initialguessvaluesforq,s,andp;theprogramthen iteratestoaself-consistentchargeandconfiguration (SCCC). Overlap integrals are evaluated by a separate machine program. Theresultsofthecalculationson16octahedral and16tetrahedralone-atom-ligandtransition-metal complexesare presented in Tables IV and V.TableVI summarizesthecompositionoftherelevantsecular determinantsforbothoctahedralandtetrahedral geometries. DISCUSSION Themolecularorbitalenergy-leveldiagramswhich representthesecalculationsoftetrahedralandoctahe-dral complexes are shown schematically in Figs.1 and 2. TheMO'sareconnectedtotheatomicorbitalsfrom whichtheyaremainlyderivedandtheMOschemes aremosteasilyunderstoodintermsoftheorderingof theatomicenergylevels.Thebracketsencloselevels ofcomparableenergiesderivedfromessentiallythe sameatomicorbitals;insomecasesthereisacon-sistentorderingwithinabracketedset(shownexpli-citly inthe figures),in others not. 78R.G.Shulman,Bell TelephoneLaboratories, forFile,Case 38140-13. Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions14BASCH,VISTE,ANDGRAY TABLEIV.Results of SCCC calculations of various octahedral complexes(all energies in 1000 cm-I). Complexes TiF6:t- TiCls:t- TiBrs:t- VFss- VCls:t- VF64- CrFs:t- CrCl,3-Bonddistances,A1.97- 2.45b 2.56"1.94d 2.39"2.150 1.930 2.380 3dVOIP-120.3-88.6-84.0-127.3-94.5-116.7-134.1-99.2 4s VOIP-100.6-78.9-76.9-101.6-80.4-95.3-103.7-81.4 4pVOIP-55.7-44.0-41.2-70.7-50.6-65.3-70.4-49.4 Metal charge+1.12+0.66+0.68+1.02+0.59+0.93+0.97+0.53 3dpopulation2.812.953.143.773.953.884.764.95 4s population0.000.150.000.010.100.050.060.16 4ppopulation0.070.240.180.200.360.140.210.36 t,,, eigenvalue-149.4-108.4-96.0-149.2-107.9-149.8-149.2-108.9 2t,. eigenvalue-90.4-71.4-70.2-100.8-80.2-104.8-110.3-87.1 3e. eigenvalue-73.1-58.0-57.1-84.8-66.5-92.7-94.7-73.5 2t,. occupation11122333 3e. occupation00000000 Ll17.5"13.8b 13.00 15.9f 13.9b 12.00."15.2h13.8h First allowedL->M chargetransfer: calculated orbital energyi59.037.025.848.427.745.038.921.8 Observedband>500 ;(;380,1400.;;(;40,140,1>371>370.1 F.(0.005)1.531.601.511.551.571.591.601.61 CrBrs:t- CrOs!/- MnF.r- MnF64- FeFs3- CoFss- COOSIII- NiFr Bond distances,A2.532.000 1.741'2.12d1.92d 1.89d 2.101 2.00m 3d VOIP-92.6-114.7-150.9-129.6-145.2-153.4-122.8-153.4 4sVOIP-79.0-91.6-112.4-99.9-108.2-112.3-93.5-112.1 4pVOIP-50.1-59.3-75.1-65.0-69.0-69.7-54.6-67.4 Metal charge+0.64+0.75+1.00+0.85+0.87+0.84+0.56+0.78 3dpopulation5.264.915.655.896.767.727.968.79 4spopulation0.100.080.060.100.140.170.220.20 4ppopUlation On 0.260.290.160.240.260.260.23 t,,,eigenvalue-95.8-125.5-147.9-149.7-149.1-148.9-126.1-149.4 2t,. eigenvalue-83.0-93.6-111.0-120.1-125.6-132.0-112.5-139.1 3e.eigenvalue-69.7-77.5-89.1-111.7-111.9-118.9-103.0-131.8 2t,. occupation33333456 3e. occupation00022222 Ll13.20 16.2"'"21.8"8.4"14.0&13.1"' 9.6",& 7.3" First allowed L->M charge transfer: calculated orbital energyi12.831.936.929.623.516.913.617.6 Observed energy 2e intetrahedral,and 3eg> 2t2g in octahedral. Thesignificancethat canbeattachedtothewave-functionsandenergiescalculatedbythesimpleMO method has beenthe subject of considerable debate.ll,12 100 60 20 0 -20 1 -60 u ...

.,j -100 -140 -180 -220 J 30, J 512 'I 'I " " 'I ,'1 II 4p ,I I I I 412

J 2. metal [I, J2p" -_:..:2pg 20,+1.+ 1t225 ==J-- - ligand FIG.1.Molecularorbitalenergy-leveldiagramfortetrahedral complexes.Drawn to scale forFeCJ.2-. Earlyinvestigators1,8placedgreatemphasisonthe transition moments computed using the derived ground-statewavefunctions.Inonecase,l however,although the results compared satisfactorily with experimentally determinedintensities,thebandassignmentssubse-quently have been shownto require revision.7 Direct experimentalevidenceofcovalency intransi-tion-metal complexes has come from magnetic resonance experimentswhich,under favorableconditions,canbe interpretedtoyieldvalues forcovalent mixingparam-eters.6aInparticular,onesuchwork33 reportedthe coefficients forthe ligand2sand2psymmetry orbitals 100 50 o -50 ..-100

"'0 ...-150 -200 -250 -300 l.g 25 -350metalligand FIG.2.Molecularorbitalenergy-leveldiagramforoctahedral complexes.Drawn to scaleforFeF.a-. in3ell as0.116and 0.337,respectively,inKNiF3This canbecomparedwith0.007and 0.386calculatedhere forNiFe4-.Unfortunately,thecomparisonisnot quantitatively validsincethe"experimentally"deter-mined coefficientsareactually derived from19Fhyper-fineinteractionsusingF- 2sand2p,atomicwave-functionswhichdifferfromtheneutralatomF wavefunctions used in this investigation. Ofgreateruseandreliabilityarethecalculated chargedistributionspartitioningtheelectronsinthe MO'sintolocalizedcontributionsoftheparticipating atoms.Although arbitrarily defined,these gross atomic popUlationsandresultantbondordersandbond polaritieshavelongbeenusedsuccessfullytopredict andconfirmtheexistenceofchemicallyreactivesites Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsMOL EC U LA R0RBI TALTHE 0RYFO:RMET A LCOM PLEX ES17 in complex organic molecules.75 In addition, an examina-tion ofthe dominatingorbital contributionstoagiven calculated chargedistribution has helpedelucidatethe factorsgoverningtheformationandpropertiesof molecules.Ofparticular interest inthe realm oftransi-tion-metalcomplexesaretherelativemagnitudesand trendsinthederivedchargedistributionsindicating degreeand kind ofcovalency. In the calculations reported here(Tables IV and V) thecomputedchargeonthemetaldecreasesandthe occupationofthemetal4sand4porbitalsincreases withincreasingatomicnumber(Z).Thisincreased participationof4sand4pinthebondingreflectsthe increasedstability oftheseorbitals ingoingacrossthe transitionseries.Theloweringofchargeisindicative ofincreasedcovalency(foragivenligand)with increasingZandisinqualitativeagreementwiththe orbitalelectronegativitiescalculatedforthesemetals by Hinzeand Jaffe.28 Additionalevidenceissuppliedbyanexamina-tionofthetransition-metalradialwaveunctionsof Richardsonetal.71 orClementiandRaimondi.16 They showthat theradiiofmaximumradialchargedensity ofthefreeatomandionwaveunctionsshrinkby approximately0.04A onincreasingZbyoneunit. However,the computed ionicradiiand observed bond distancesincomplexes(foragivenoxidationstate, ligand,andgeometry)varybyavaluesomewhere betweenzeroand0.03A.Thiscanbeinterpretedby assumingthat thereducedchargeonthe metal dueto increasedcovalencycompensatesformostofthe naturalcontractionofthe3dradialfunctionwith increasingZ,yieldingaslownetdecreaseintheob-servedbonddistance.Thecalculationsalsoreveal that,foragivenligand,theself-consistentcharge changesslowlywithincreasingformaloxidationstate. This isinqualitativeagreementwithasimilarexperi-mentalobservationmadebyShulmanandSugano77 forcyanide complexes,althoughtheir explanation may not be directly applicablehere. The variation of charge with ligand fora given metal isseentofollowF> 0> CI> Br> S,asisexpected fromtheknowntrendsinmetalbindingbythese atoms.Asoutlinedpreviously,transition-metalcom-plexes are known to have substantial covalent character andthissuggeststhattheligandnp(n=2,3,4)H',; areinthestabilityrangeofthemetal3dH' iiThe actualchoiceofH' ,wavefunctions,andFfactors determinesthedegreeofcovalencyforanisolated complex,and allthreechoicesare somewhat arbitrary; althoughonesetmaybesuperiortoanother.The simpleMOmethod,however,offersnounambiguous way of findingthis set in an absolute sense.In addition, 71C.A.Coulson,Valence(OxfordUniversityPress,London, 1961),Chap. 9. 78E.ClementiandD.L.Raimondi,J.Chern.Phys.38,2686 (1963). 77R. G.Shulman and S.Sugano,J. Chern.Phys. 42, 39(1965). sincethenumbersofinteresttoushere(electronic spectra)areofthesameorderofmagnitudeasthe inherenterrorinthetheory upon whichthecomputa-tionsarebased,significancecanbeattachedonlyto consistent behavior within a group of molecules. Inbothtetrahedralandoctahedralgeometries,~measuresthesplittingofthedr-d"(i.e.,11" and(1', respectively,withregardtointeractionswithligand orbitals)metal orbitals.For agiven set ofVOIP's and wavefunctions,~ iscompletelydeterminedbythe choiceofF"andFr[Eq.(7)J.SinceFrprincipally determinesthepositionofthefirstL-+Mcharge-transferband,Frwasfixedat2.10toapproximately fittheL-+MbandinthedOandd1 cases,wherethe electronic repulsioncorrectionstothe simple difference oftheone-electronenergylevelscanbeestimated [seelater,Eq.(9) J.TheresultsoffittingF"tore-produce the experimentally determined are tabulated in Tables IV and V. AdetailedexaminationofF"valuesrevealsthe following: (a)TheF,,'sbelongingtothe16octahedral complexes(TableIV)followtheequation,F,,(n) = [0.027n+1.546J0.02,whereforTi,n=O,forV, n= 1,etc.,independentofthemetaloxidation state or combining ligand. (b)Nineofthe16tetrahedralcomplexes(VCI., VCI.-,MnCI.2-,FeCI.-,FeCI.2-,CoCI.2-,COO,6-, COS46-,NiCll-)inTableV followthesameequation with the same average deviation. (c)For the high-oxidation-state(V,VI,VII)tetra-hedralmetaloxyanions(CrO,2-,MnO,-,MnO,2-, MnO,3-)theF,,'sshowadefiniteoxidation-state dependenceandlieoutsidetherangefoundforthe other complexes. Wenowproceedtoacomparisonofthecalculated and observed variations inand L-+M charge transfer. (1)~ with geometry. With the reservations specified above,it appears possible to transfer theF factor from octahedral totetrahedral geometriesquantitatively.It isimportanttonotethatthisstatement islimitedto first-rowtransition metals containing one-atom ligands with a single 11" valence orbital. The inclusion of a second 11" valenceorbital(asforexample11"*indiatomicor complexunsaturated8 ligands)couldconceivablyalter the whole character ofthis analysis.Extension to other geometries must betested separately. ThevariationofF"inthehigh-oxidation-state oxyanionsseemsto beadirectresultoftheunusually large~ forthese complexes.778 (2)~ withmetal-ionoxidationnumber.Formetal complexes,whichdonothaveappreciable1I"-acceptor ability,~ isknowntoincreaseastheformalpositive chargeontheionincreases.Forexample,comparing 78A.CarringtonandC.K.J9lrgensen,Mol.Phys.4,395 (1961). Downloaded 16 Apr 2013 to 141.161.91.14. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions18BASCH,VISTE,ANDGRAY experimental results for V (H20) 62+--N(H20) 63+,.FeC4-,VF64- >CrF63- >MnF62-,and MnF64-> FeF63-. Asaruleofthumb,asimilarmovementofthefirst L-+Mcharge-transferbandtolowerenergywithin-creasingformalpositivechargeisalsoexpectedfor complexesofagivenligandanddifferentoxidation states ofasinglemetal.Here thecomparison isnot an isoelectronic oneand sothe expectation is qualitatively less clearcut.The calculationspredictthat theorbital energy ofthe first L-+M transition is practically insen-sitivetooxidationnumberforsuchcomparisons. However,theelectronicrepulsioncorrectionfactors areexpectedtoincreasedirectlyproportionaltothe numberofelectronsintheupper("d-orbital")MO. ThiscorrespondstoincreasingkinEq.(9)andshifts the calculatedtrend inthe expected direction. (5)Chargetransferwithmetalz.Ithasbeen establishedexperimentallythatthepositionofthe firstL-+Mbandinananalogousseriesofcomplexes shiftstolowerenergy ingoingfromTitoCo.Forthe seriesofoctahedralfluoridesandchloridesandtetra-hedralchlorides,thecalculatedtrendisasexpected. The dominating factor seemsto bethe steady decrease inthemetal3dH' i;withincreasingZ,althoughthe self-consistent chargeonthe metal decreases. Whiletheobservedtrendisgenerallyfollowedby thecalculatedvalues,themagnitudesofthechanges appearatfirstsighttobetoolarge.It isprobable that the VOIP curves exaggerate the increasing stability ofthemetal3dH';;bothwithchargeandwithin-creasingZ.4Thisisnotcertain,however,sincethe interelectronic-repulsioncorrections increaseinaseries fromTi to Co. (6)Chargetransferwithligand.Theenergyofthe firstL-+Mband forametal inagiven oxidation state isexpectedtoparalleltheinstabilitiesofthevarious ligandp levels.In these calculationstheVOIPorder is SS. The inclusion of electronic-repulsion terms in complexes with fewd electrons is expected to reduce the calculated one-electron differences between adjacent ligands since, intermsofthequantitiesdefinedinEq.(9),J(a,a) isexpectedtoincreaseintheorder S