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
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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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