Crystal Field Theory (CFT) - Detailed Explanation ... - BYJU'S

Crystal field theory was proposed which described the metal-ligand bond as an ionic bond arising purely from the electrostatic interactions between the metal ... ChemistryTheSolidStateCrystalFieldTheory CrystalFieldTheory(CFT) Whatis CrystalFieldTheory? Crystalfieldtheorydescribes thenetchangeincrystalenergyresultingfromtheorientationofdorbitalsofatransitionmetalcationinsideacoordinatinggroupofanionsalsocalledligands. Amajorfeatureoftransitionmetalsistheirtendencytoformcomplexes.Acomplexmaybeconsideredasconsistingofacentralmetalatomorionsurroundedbyanumberofligands.Theinteractionbetweentheseligandswiththecentralmetalatomorionissubjecttocrystalfieldtheory. Crystalfieldtheorywasestablishedin1929treatstheinteractionofmetalionandligandasapurelyelectrostaticphenomenonwheretheligandsareconsideredaspointchargesinthevicinityoftheatomicorbitalsofthecentralatom.Developmentandextensionofcrystalfieldtheorytakenintoaccountthepartlycovalentnatureofbondsbetweentheligandandmetalatommainlythroughtheapplicationofmolecularorbitaltheory.Crystalfieldtheoryoftentermedasligandfieldtheory. Overviewof CrystalFieldTheory Inordertounderstandclearlythecrystalfieldinteractionsintransitionmetalcomplexes,itisnecessarytohaveknowledgeofthegeometricalorspatialdispositionofdorbitals.Thed-orbitalsarefivefolddegenerateinafreegaseousmetalion.Ifasphericallysymmetricfieldofnegativeligandfiledchargeisimposedonacentralmetalion,thed-orbitalswillremaindegeneratebutfollowedbysomechangesintheenergyoffreeion. Asummaryoftheinteractionsisgivenbelow. CrystalFieldSplitting Crystalfieldtheorywasproposedwhichdescribedthemetal-ligandbondasanionicbondarisingpurelyfromtheelectrostaticinteractionsbetweenthemetalionsandligands.Crystalfieldtheoryconsidersanionsaspointchargesandneutralmoleculesasdipoles. Whentransitionmetalsarenotbondedtoanyligand,theirdorbitalsaredegeneratethatistheyhavethesameenergy.Whentheystartbondingwithotherligands,duetodifferentsymmetriesofthedorbitalsandtheinductiveeffectoftheligandsontheelectrons,thedorbitalssplitapartandbecomenon-degenerate. HighSpinandLowSpin Thecomplexionwiththegreaternumberofunpairedelectronsisknownasthehighspincomplex,thelowspincomplexcontainsthelessernumberofunpairedelectrons.Highspincomplexesareexpectedwithweakfieldligandswhereasthecrystalfieldsplittingenergyissmall Δ.Theoppositeappliestothelowspincomplexesinwhichstrongfieldligandscausemaximumpairingofelectronsinthesetofthreet2atomicorbitalsduetolarge Δo. Highspin–Maximumnumberofunpairedelectrons. Lowspin–Minimumnumberofunpairedelectrons. Example:[Co(CN)6]3-&[CoF6]3- HighSpinandLowSpinComplex [Co(CN)6]3- –Lowspincomplex [CoF6]3- –Highspincomplex RecommendedVideos Thepatternofthesplittingofdorbitalsdependsonthenatureofthecrystalfield.Thesplittinginvariouscrystalfieldsisdiscussedbelow: CrystalFieldSplittingin OctahedralComplex  Inthecaseofanoctahedralcoordinationcompoundhavingsixligandssurroundingthemetalatom/ion,weobserverepulsionbetweentheelectronsindorbitalsandligandelectrons. Thisrepulsionisexperiencedmoreinthecaseofdx2-y2anddz2orbitalsastheypointtowardstheaxesalongthedirectionoftheligand. Hence,theyhavehigherenergythanaverageenergyinthesphericalcrystalfield. Ontheotherhand,dxy,dyz,anddxzorbitalsexperiencelowerrepulsionsastheyaredirectedbetweentheaxes. Hence,thesethreeorbitalshavelessenergythantheaverageenergyinthesphericalcrystalfield. Thus,therepulsionsinoctahedralcoordinationcompoundyieldtwoenergylevels: t2g–setofthreeorbitals(dxy,dyzanddxz)withlowerenergy eg–setoftwoorbitals(dx2-y2anddz2)withhigherenergy CrystalFieldSplittingin OctahedralComplex Thissplittingofdegeneratelevelinthepresenceofligandisknownascrystalfieldsplitting.Thedifferencebetweentheenergyoft2gandeglevelisdenotedby“Δo”(subscriptostandsforoctahedral).Someligandstendtoproducestrongfieldstherebycausinglargecrystalfieldsplittingwhereassomeligandstendtoproduceweakfieldstherebycausingsmallcrystalfieldsplitting. CrystalFieldSplittingin TetrahedralComplex  ThesplittingoffivefolddegeneratedorbitalsofthemetalionintotwolevelsinatetrahedralcrystalfieldistherepresentationoftwosetsoforbitalsasTd.Theelectronsindx2-y2anddz2orbitalsarelessrepelledbytheligandsthantheelectronspresentindxy,dyz,anddxzorbitals.Asaresult,theenergyofdxy,dyz,anddxzorbitalsetareraisedwhilethatosthedx2-y2anddz2orbitalsarelowered. ThereareonlyfourligandsinTdcomplexesandthereforethetotalnegativechargeoffourligandsandhencetheligandfieldislessthanthatofsixligands. Thedirectionoftheorbitalsdoesnotcoincidewiththedirectionsoftheligandsapproachtothemetalion. CrystalFieldSplittingin TetrahedralComplex Thus,therepulsionsintetrahedralcoordinationcompoundyieldtwoenergylevels: t2–setofthreeorbitals(dxy,dyzanddxz)withhigherenergy e –setoftwoorbitals(dx2-y2anddz2)withlowerenergy Thecrystalfieldsplittinginatetrahedralcomplexisintrinsicallysmallerinanoctahedralfiledbecausethereareonlytwothirdsasmanyligandsandtheyhavealessdirecteffectofthedorbitals.Therelativestabilizingeffectofesetwillbe-6Dqandthedestabilizingeffectoft2setwillbe+4Dq CrystalFieldStabilizationEnergy Inachemicalenvironment,theenergylevelsgenerallysplitasdirectedbythesymmetryofthelocalfieldsurroundingthemetalion.Theenergydifferencebetweentheegandt2glevelsisgivenasor10Dq.Itstatesthateachelectronthatgoesintothelowert2glevelstabilizesthesystembyanamountof-4Dqandtheelectronthatgoesintoegleveldestabilizesthesystemby+6Dq.Thatisthet2gisloweredby4Dqandtheeglevelisraisedby+6Dq. Forexample,thenetchangeinenergyford5andd10systemswillbezeroasshownbelow. d5:-3(-4Dq)+2(+6Dq)=-12Dq+12Dq=0 d10:-6(-4Dq)+4(+6Dq)=-24Dq+24Dq=0 Thedecreaseinenergycausedbythesplittingoftheenergylevelsiscalledthe“LigandFieldStabilizationEnergy(LFSE)”.  CrystalFieldStabilizationEnergyTable Thecrystalfieldstabilizationenergiesforsomeoctahedralandtetrahedralcomplexesof3dmetalionsaretabulatedbelow. ElectronicConfiguration  OctahedralComplex TetrahedralComplex WeakField(-Dq) StrongField(-Dq) WeakField(-Dq) StrongField(-Dq) d0 0 0 0 0 d1 4 4 6 6 d2 8 8 12 12 d3 12 12 8 (18)* d4 6 16 4 (24)* d5 0 20 0 (20)* d6 4 24 6 (16)* d7 8 18 12 12 d8 12 12 8 8 d9 6 6 4 4 d10 0 0 0 0 Thus,thecrystalfieldsplittingdependsonthefieldproducedbytheligandandthechargeonthemetalion.Anexperimentallydeterminedseriesbasedontheabsorptionoflightbycoordinationcompoundwithdifferentligandsknownasspectrochemicalserieshasbeenproposed.Spectrochemicalseriesarrangesligandsinorderoftheirfieldstrengthas: I– 
P–Electronentersinthet2glevelgivingaconfigurationoft2g4eg0.Ligandsproducingthisconfigurationareknownasstrongfieldligandsandformlowspincomplexes. Δo