Crystal Field Theory

This theory tried to describe the effect of the electrical field of neighboring ions on the energies of the valence orbitals of an ion in a crystal. CrystalFieldTheory NahklehGroup RobinsonGroup WeaverGroup BodnerGroup TransitionMetals TransitonMetals CoordinationComplexesandLigands NomenclatureofComplexes Isomers Bonding ValenceBondTheory CrystalFieldTheory LigandFieldTheory Crystal FieldTheory Octahedral CrystalFields Tetrahedral CrystalFields Square PlanarComplexes TheSpectrochemical Series High-Spin VersusLow-SpinOctahedralComplexes Atalmostexactlythesametimethatchemistsweredeveloping thevalence-bondmodelforcoordinationcomplexes,physicists suchasHansBethe,JohnVanVleck,andLeslieOrgelwere developinganalternativeknownascrystalfieldtheory. Thistheorytriedtodescribetheeffectoftheelectricalfield ofneighboringionsontheenergiesofthevalenceorbitalsofan ioninacrystal.Crystalfieldtheorywasdevelopedby consideringtwocompounds:manganese(II)oxide,MnO,and copper(I)chloride,CuCl. OctahedralCrystalFields EachMn2+ioninmanganese(II)oxideissurrounded bysixO2-ionsarrangedtowardthecornersofan octahedron,asshowninthefigurebelow.MnOisthereforea modelforanoctahedralcomplexinwhicha transition-metalioniscoordinatedtosixligands. Whathappenstotheenergiesofthe4sand4p orbitalsonanMn2+ionwhenthisionisburiedinan MnOcrystal?Repulsionbetweenelectronsthatmightbeaddedto theseorbitalsandtheelectronsonthesixO2-ions thatsurroundthemetalioninMnOincreasetheenergiesofthese orbitals.Thethree4porbitalsarestilldegenerate, however.Theseorbitalsstillhavethesameenergybecauseeach4p orbitalpointstowardtwoO2-ionsatthecornersof theoctahedron. RepulsionbetweenelectronsontheO2-ionsand electronsinthe3dorbitalsonthemetalioninMnOalso increasestheenergyoftheseorbitals.Butthefive3d orbitalsontheMn2+ionarenolongerdegenerate. Let'sassumethatthesixO2-ionsthatsurroundeach Mn2+iondefineanXYZcoordinatesystem.Two ofthe3dorbitals(3dx2-y2 and3dz2)ontheMn2+ion pointdirectlytowardthesixO2-ions,asshownin thefigurebelow.Theotherthreeorbitals(3dxy, 3dxz,and3dyz)liebetween theO2-ions. Theenergyofthefive3dorbitalsincreaseswhenthe sixO2-ionsarebroughtclosetotheMn2+ ion.However,theenergyoftwooftheseorbitals(3dx2-y2 and3dz2)increasesmuchmorethan theenergyoftheotherthree(3dxy,3dxz, and3dyz),asshowninthefigurebelow.The crystalfieldofthesixO2-ionsinMnOtherefore splitsthedegeneracyofthefive3dorbitals.Threeof theseorbitalsarenowlowerinenergythantheothertwo. Byconvention,thedxy,dxz, anddyzorbitalsinanoctahedralcomplexare calledthet2gorbitals.Thedx2-y2 anddz2orbitals,ontheotherhand, arecalledtheegorbitals. Theeasiestwaytorememberthisconventionistonotethat therearethreeorbitalsinthet2gset. t2g:   dxy,dxz,anddyz   eg:   dx2-y2 anddz2 Thedifferencebetweentheenergiesofthet2g andegorbitalsinanoctahedralcomplex isrepresentedbythesymbolo.Thissplitting oftheenergyofthedorbitalsisnottrivial;o fortheTi(H2O)63+ion,for example,is242kJ/mol. Themagnitudeofthesplittingofthet2g andegorbitalschangesfromone octahedralcomplextoanother.Itdependsontheidentityofthe metalion,thechargeonthision,andthenatureoftheligands coordinatedtothemetalion. TetrahedralCrystalFields EachCu+ionincopper(I)chlorideissurroundedby fourCl-ionsarrangedtowardthecornersofa tetrahedron,asshowninthefigurebelow.CuClisthereforea modelforatetrahedralcomplexinwhicha transition-metalioniscoordinatedtofourligands. Onceagain,thenegativeionsinthecrystalsplittheenergy ofthedatomicorbitalsonthetransition-metalion.The tetrahedralcrystalfieldsplitstheseorbitalsintothesamet2g andegsetsoforbitalsasdoesthe octahedralcrystalfield. t2g:   dxy,dxz,anddyz   eg:   dx2-y2 anddz2 Butthetwoorbitalsintheegset arenowlowerinenergythanthethreeorbitalsinthet2g set,asshowninthefigurebelow. Tounderstandthesplittingofdorbitalsina tetrahedralcrystalfield,imaginefourligandslyingat alternatingcornersofacubetoformatetrahedralgeometry,as showninthefigurebelow.Thedx2-y2 anddz2orbitalsonthemetalionat thecenterofthecubeliebetweentheligands,andthedxy, dxz,anddyzorbitalspoint towardtheligands.Asaresult,thesplittingobservedina tetrahedralcrystalfieldistheoppositeofthesplittinginan octahedralcomplex. Becauseatetrahedralcomplexhasfewerligands,themagnitude ofthesplittingissmaller.Thedifferencebetweentheenergies ofthet2gandeg orbitalsinatetrahedralcomplex(t)isslightlyless thanhalfaslargeasthesplittinginanalogousoctahedral complexes(o). t=4/9o Square-PlanarComplexes Thecrystalfieldtheorycanbeextendedtosquare-planar complexes,suchasPt(NH3)2Cl2. Thesplittingofthedorbitalsinthesecompoundsis showninthefigurebelow. TheSpectrochemical Series Thesplittingofdorbitalsinthecrystalfieldmodel notonlydependsonthegeometryofthecomplex,italsodepends onthenatureofthemetalion,thechargeonthision,andthe ligandsthatsurroundthemetal.Whenthegeometryandthe ligandsareheldconstant,thissplittingdecreasesinthe followingorder. Pt4+ > Ir3+ > Rh3+ > Co3+ > Cr3+ > Fe3+ > Fe2+ > Co2+ > Ni2+ > Mn2+   strong-fieldligands                       weak-fieldligands Metalionsatoneendofthiscontinuumarecalledstrong-field ions,becausethesplittingduetothecrystalfieldis unusuallystrong.Ionsattheotherendareknownasweak-field ions. Whenthegeometryandthemetalareheldconstant,the splittingofthedorbitalsdecreasesinthefollowing order. CO CN- > NO2- > NH3 > -NCS- > H2O > OH-   F-   -SCN- Cl- > Br-   strong-fieldligands                           weak-fieldligands Ligandsthatgiverisetolargedifferencesbetweenthe energiesofthet2gandeg orbitalsarecalledstrong-fieldligands.Thoseatthe oppositeextremeareknownasweak-fieldligands. Becausetheyresultfromstudiesoftheabsorptionspectraof transition-metalcomplexes,thesegeneralizationsareknownas thespectrochemicalseries.Therangeofvaluesoffor agivengeometryisremarkablylarge.Thevalueofo is100kJ/molintheNi(H2O)62+ ion,forexample,and520kJ/molintheRh(CN)63- ion. High-SpinVersusLow-Spin OctahedralComplexes Onceweknowtherelativeenergiesofthedorbitalsin atransition-metalcomplex,wehavetoworryabouthowthese orbitalsarefilled.Degenerateorbitalsarefilledaccordingto Hund'srules. Oneelectronisaddedtoeachofthedegenerateorbitals inasubshellbeforeasecondelectronisaddedtoany orbitalinthesubshell. Electronsareaddedtoasubshellwiththesamevalueof thespinquantumnumberuntileachorbitalinthe subshellhasatleastoneelectron. Octahedraltransition-metalionswithd1,d2, ord3configurationscanthereforebedescribed bythefollowingdiagrams. Whenwetrytoaddafourthelectron,wearefacedwitha problem.Thiselectroncouldbeusedtopaironeoftheelectrons inthelowerenergy(t2g)setof orbitalsoritcouldbeplacedinoneofthehigherenergy(eg) orbitals.Oneoftheseconfigurationsiscalledhigh-spin becauseitcontainsfourunpairedelectronswiththesamespin. Theotheriscalledlow-spinbecauseitcontainsonlytwo unpairedelectrons.Thesameproblemoccurswithoctahedrald5, d6,andd7complexes. Foroctahedrald8,d9,and d10complexes,thereisonlyonewaytowrite satisfactoryconfigurations. Asaresult,wehavetoworryabouthigh-spinversuslow-spin octahedralcomplexesonlywhentherearefour,five,six,or sevenelectronsinthedorbitals. Thechoicebetweenhigh-spinandlow-spinconfigurationsfor octahedrald4,d5,d6, ord7complexesiseasy.Allwehavetodois comparetheenergyittakestopairelectronswiththeenergyit takestoexciteanelectrontothehigherenergy(eg) orbitals.Ifittakeslessenergytopairtheelectrons,the complexislow-spin.Ifittakeslessenergytoexcitethe electron,thecomplexishigh-spin. Theamountofenergyrequiredtopairelectronsinthet2g orbitalsofanoctahedralcomplexismoreorlessconstant.The amountofenergyneededtoexciteanelectronintothehigher energy(eg)orbitals,however,depends onthevalueofoforthecomplex.Asaresult, weexpecttofindlow-spincomplexesamongmetalionsandligands thatlietowardthehigh-fieldendofthespectrochemicalseries. High-spincomplexesareexpectedamongmetalionsandligands thatlietowardthelow-fieldendoftheseseries. Compoundsinwhichalloftheelectrons arepairedarediamagneticthey arerepelledbybothpolesofamagnet.Compoundsthatcontain oneormoreunpairedelectronsareparamagneticthey areattractedtothepolesofamagnet.Theforceofattraction betweenparamagneticcomplexesandamagneticfieldis proportionaltothenumberofunpairedelectronsinthecomplex. Wecanthereforedeterminewhetheracomplexishigh-spinor low-spinbymeasuringthestrengthoftheinteractionbetweenthe complexandamagneticfield. PracticeProblem5:Explain whytheCo(NH3)63+ion isadiamagnetic,low-spincomplex,whereastheCoF63- ionisaparamagnetic,high-spincomplex. Click heretocheckyouranswertoPracticeProblem5