Crystal Field Theory - Chemistry LibreTexts

Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to the presence of ligands. Skiptomaincontent BasicConceptElectronsinOrbitalsDescriptionofd-OrbitalsOctahedralComplexesTetrahedralComplexesSquarePlanarComplexesProblemsAnswersContributorsandAttributions Crystalfieldtheory(CFT)describesthebreakingoforbitaldegeneracyintransitionmetalcomplexesduetothepresenceofligands.CFTqualitativelydescribesthestrengthofthemetal-ligandbonds.Basedonthestrengthofthemetal-ligandbonds,theenergyofthesystemisaltered.Thismayleadtoachangeinmagneticpropertiesaswellascolor.ThistheorywasdevelopedbyHansBetheandJohnHasbrouckvanVleck. BasicConcept InCrystalFieldTheory,itisassumedthattheionsaresimplepointcharges(asimplification).Whenappliedtoalkalimetalionscontainingasymmetricsphereofcharge,calculationsofbondenergiesaregenerallyquitesuccessful.Theapproachtakenusesclassicalpotentialenergyequationsthattakeintoaccounttheattractiveandrepulsiveinteractionsbetweenchargedparticles(thatis,Coulomb'sLawinteractions). \[E\propto\dfrac{q_1q_2}{r}\] with \(E\)thebondenergybetweenthechargesand \(q_1\)and\(q_2\)arethechargesoftheinteractingionsand \(r\)isthedistanceseparatingthem. Thisapproachleadstothecorrectpredictionthatlargecationsoflowcharge,suchas\(K^+\)and\(Na^+\),shouldformfewcoordinationcompounds.FortransitionmetalcationsthatcontainvaryingnumbersofdelectronsinorbitalsthatareNOTsphericallysymmetric,however,thesituationisquitedifferent.Theshapesandoccupationsofthesed-orbitalsthenbecome importantinbuildinganaccuratedescriptionofthebondenergyandpropertiesofthetransitionmetalcompound. Whenexaminingasingletransitionmetalion,thefived-orbitalshavethesameenergy(Figure\(\PageIndex{1}\)).Whenligandsapproachthemetalion,someexperiencemoreoppositionfromthed-orbitalelectronsthanothersbasedonthegeometricstructureofthemolecule.Sinceligandsapproachfromdifferentdirections,notalld-orbitalsinteractdirectly.Theseinteractions,however,createasplittingduetotheelectrostaticenvironment. Figure\(\PageIndex{1}\): Distributingachargeof−6uniformlyoverasphericalsurfacesurroundingametalioncausestheenergyofallfivedorbitalstoincreaseduetoelectrostaticrepulsions,butthefivedorbitalsremaindegenerate.Placingachargeof−1ateachvertexofanoctahedroncausesthedorbitalstosplitintotwogroupswithdifferentenergies:thedx2−y2anddz2orbitalsincreaseinenergy,whilethe,dxy,dxz,anddyzorbitalsdecreaseinenergy.Theaverageenergyofthefivedorbitalsisthesameasforasphericaldistributionofa−6charge,however.Attractiveelectrostaticinteractionsbetweenthenegativelychargedligandsandthepositivelychargedmetalion(farright)causeallfivedorbitalstodecreaseinenergybutdoesnotaffectthesplittingsoftheorbitals. Thetwoegorbitalspointdirectlyatthesixnegativelychargedligands,whichincreasestheirenergycomparedwithasphericaldistributionofnegativecharge.Incontrast,thethreet2gorbitalspointbetweenthenegativelychargedligands,whichdecreasestheirenergycomparedwithasphericaldistributionofcharge. Forexample,consideramoleculewithoctahedralgeometry.Ligandsapproachthemetalionalongthe\(x\),\(y\),and\(z\)axes.Therefore,theelectronsinthe\(d_{z^2}\)and\(d_{x^2-y^2}\)orbitals(whichliealongtheseaxes)experiencegreaterrepulsion.Itrequiresmoreenergytohaveanelectronintheseorbitalsthanitwouldtoputanelectroninoneoftheotherorbitals.Thiscausesasplittingintheenergylevelsofthed-orbitals.Thisisknownascrystalfieldsplitting.Foroctahedralcomplexes,crystalfieldsplittingisdenotedby\(\Delta_o\)(or\(\Delta_{oct}\)).Theenergiesofthe\(d_{z^2}\)and\(d_{x^2-y^2}\)orbitalsincreaseduetogreaterinteractionswiththeligands.The\(d_{xy}\),\(d_{xz}\),and\(d_{yz}\)orbitalsdecreasewithrespecttothisnormalenergylevelandbecomemorestable. ElectronsinOrbitals AccordingtotheAufbauprinciple,electronsarefilledfromlowertohigherenergyorbitals(Figure\(\PageIndex{1}\)).Fortheoctahedralcaseabove,thiscorrespondstothedxy,dxz,anddyzorbitals.FollowingHund'srule,electronsarefilledinordertohavethehighestnumberofunpairedelectrons.Forexample,ifonehadad3complex,therewouldbethreeunpairedelectrons.Ifoneweretoaddanelectron,however,ithastheabilitytofillahigherenergyorbital(dz²ordx²-y²)orpairwithanelectronresidinginthedxy,dxz,ordyzorbitals.Thispairingoftheelectronsrequiresenergy(spinpairingenergy).Ifthepairingenergyislessthanthecrystalfieldsplittingenergy,∆₀,thenthenextelectronwillgointothedxy,dxz,ordyzorbitalsduetostability.Thissituationallowsfortheleastamountofunpairedelectrons,andisknownaslowspin.Ifthepairingenergyisgreaterthan∆₀,thenthenextelectronwillgointothedz²ordx²-y²orbitalsasanunpairedelectron.Thissituationallowsforthemostnumberofunpairedelectrons,andisknownashighspin.Ligandsthatcauseatransitionmetaltohaveasmallcrystalfieldsplitting,whichleadstohighspin,arecalledweak-fieldligands.Ligandsthatproducealargecrystalfieldsplitting,whichleadstolowspin,arecalledstrongfieldligands. Figure\(\PageIndex{2}\):LowSpin,StrongField(∆o˃P)HighSpin,WeakField(∆o˂P)Splittingfora\(d^4\)complexunderastrongfield(left)andaweakfield(right).Thestrongfieldisalowspincomplex,whiletheweakfieldisahighspincomplex. Asmentionedabove,CFTisbasedprimarilyonsymmetryofligandsaroundacentralmetal/ionandhowthisanisotropic(propertiesdependingondirection)ligandfieldaffectsthemetal'satomicorbitals;theenergiesofwhichmayincrease,decreaseornotbeaffectedatall.Oncetheligands'electronsinteractwiththeelectronsofthed-orbitals,theelectrostaticinteractionscausetheenergylevelsofthed-orbitaltofluctuatedependingontheorientationandthenatureoftheligands.Forexample,theoxidationstateandthestrengthoftheligandsdeterminesplitting;thehighertheoxidationstateorthestrongertheligand,thelargerthesplitting.Ligandsareclassifiedasstrongorweakbasedonthespectrochemicalseries: I-