Crystal field theory - Wikipedia

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Crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field ... Crystalfieldtheory FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Crystalfieldtheory(CFT)describesthebreakingofdegeneraciesofelectronorbitalstates,usuallydorforbitals,duetoastaticelectricfieldproducedbyasurroundingchargedistribution(anionneighbors).Thistheoryhasbeenusedtodescribevariousspectroscopiesoftransitionmetalcoordinationcomplexes,inparticularopticalspectra(colors).CFTsuccessfullyaccountsforsomemagneticproperties,colors,hydrationenthalpies,andspinelstructuresoftransitionmetalcomplexes,butitdoesnotattempttodescribebonding.CFTwasdevelopedbyphysicistsHansBethe[1]andJohnHasbrouckvanVleck[2]inthe1930s.CFTwassubsequentlycombinedwithmolecularorbitaltheorytoformthemorerealisticandcomplexligandfieldtheory(LFT),whichdeliversinsightintotheprocessofchemicalbondingintransitionmetalcomplexes. Contents 1Overviewofcrystalfieldtheory 1.1High-spinandlow-spin 2Crystalfieldstabilizationenergy 2.1Opticalproperties 3Geometriesandcrystalfieldsplittingdiagrams 4Seealso 5References 6Furtherreading 7Externallinks Overviewofcrystalfieldtheory[edit] Accordingtocrystalfieldtheory,theinteractionbetweenatransitionmetalandligandsarisesfromtheattractionbetweenthepositivelychargedmetalcationandthenegativechargeonthenon-bondingelectronsoftheligand.Thetheoryisdevelopedbyconsideringenergychangesofthefivedegenerated-orbitalsuponbeingsurroundedbyanarrayofpointchargesconsistingoftheligands.Asaligandapproachesthemetalion,theelectronsfromtheligandwillbeclosertosomeofthed-orbitalsandfartherawayfromothers,causingalossofdegeneracy.Theelectronsinthed-orbitalsandthoseintheligandrepeleachotherduetorepulsionbetweenlikecharges.Thusthed-electronsclosertotheligandswillhaveahigherenergythanthosefurtherawaywhichresultsinthed-orbitalssplittinginenergy.Thissplittingisaffectedbythefollowingfactors: thenatureofthemetalion. themetal'soxidationstate.Ahigheroxidationstateleadstoalargersplittingrelativetothesphericalfield. thearrangementoftheligandsaroundthemetalion. thecoordinationnumberofthemetal(i.e.tetrahedral,octahedral...) thenatureoftheligandssurroundingthemetalion.Thestrongertheeffectoftheligandsthenthegreaterthedifferencebetweenthehighandlowenergydgroups. Themostcommontypeofcomplexisoctahedral,inwhichsixligandsformtheverticesofanoctahedronaroundthemetalion.Inoctahedralsymmetrythed-orbitalssplitintotwosetswithanenergydifference,Δoct(thecrystal-fieldsplittingparameter,alsocommonlydenotedby10Dqfortentimesthe"differentialofquanta"[3][4])wherethedxy,dxzanddyzorbitalswillbelowerinenergythanthedz2anddx2-y2,whichwillhavehigherenergy,becausetheformergroupisfartherfromtheligandsthanthelatterandthereforeexperienceslessrepulsion.Thethreelower-energyorbitalsarecollectivelyreferredtoast2g,andthetwohigher-energyorbitalsaseg.Theselabelsarebasedonthetheoryofmolecularsymmetry:theyarethenamesofirreduciblerepresentationsoftheoctahedralpointgroup,Oh.(seetheOhcharactertable)TypicalorbitalenergydiagramsaregivenbelowinthesectionHigh-spinandlow-spin. Tetrahedralcomplexesarethesecondmostcommontype;herefourligandsformatetrahedronaroundthemetalion.Inatetrahedralcrystalfieldsplitting,thed-orbitalsagainsplitintotwogroups,withanenergydifferenceofΔtet.Thelowerenergyorbitalswillbedz2anddx2-y2,andthehigherenergyorbitalswillbedxy,dxzanddyz-oppositetotheoctahedralcase.Furthermore,sincetheligandelectronsintetrahedralsymmetryarenotorienteddirectlytowardsthed-orbitals,theenergysplittingwillbelowerthanintheoctahedralcase.SquareplanarandothercomplexgeometriescanalsobedescribedbyCFT. ThesizeofthegapΔbetweenthetwoormoresetsoforbitalsdependsonseveralfactors,includingtheligandsandgeometryofthecomplex.SomeligandsalwaysproduceasmallvalueofΔ,whileothersalwaysgivealargesplitting.Thereasonsbehindthiscanbeexplainedbyligandfieldtheory.Thespectrochemicalseriesisanempirically-derivedlistofligandsorderedbythesizeofthesplittingΔthattheyproduce(smallΔtolargeΔ;seealsothistable): I−



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