Crystal Field Stabilization Energy - Chemistry LibreTexts

The Crystal Field Stabilization Energy is defined as the energy of the electron configuration in the ligand field minus the energy of the ... Skiptomaincontent OctahedralPreferenceApplicationsContributorsandAttributions AconsequenceofCrystalFieldTheoryisthatthedistributionofelectronsinthedorbitalsmayleadtonetstabilization(decreaseinenergy)ofsomecomplexesdependingonthespecificligandfieldgeometryandmetald-electronconfigurations.Itisasimplemattertocalculatethisstabilizationsinceallthatisneededistheelectronconfigurationandknowledgeofthesplittingpatterns. Definition:CrystalFieldStabilizationEnergy TheCrystalFieldStabilizationEnergyisdefinedastheenergyoftheelectronconfigurationintheligandfieldminustheenergyoftheelectronicconfigurationintheisotropicfield. \[CFSE=\Delta{E}=E_{\text{ligandfield}}-E_{\text{isotropicfield}}\label{1}\] TheCSFEwilldependonmultiplefactorsincluding: Geometry(whichchangesthed-orbitalsplittingpatterns) Numberofd-electrons SpinPairingEnergy Ligandcharacter(viaSpectrochemicalSeries) Foranoctahedralcomplex,anelectroninthemorestable\(t_{2g}\)subsetistreatedascontributing\(-2/5\Delta_o\)whereasanelectroninthehigherenergy\(e_g\)subsetcontributestoadestabilizationof\(+3/5\Delta_o\).Thefinalansweristhenexpressedasamultipleofthecrystalfieldsplittingparameter\(\Delta_o\).Ifanyelectronsarepairedwithinasingleorbital,thentheterm\(P\)isusedtorepresentthespinpairingenergy. Example\(\PageIndex{1}\):CFSEforahighSpin\(d^7\)complex WhatistheCrystalFieldStabilizationEnergyforahighspin\(d^7\)octahedralcomplex? Solution Thesplittingpatternandelectronconfigurationforbothisotropicandoctahedralligandfieldsarecomparedbelow. Theenergyoftheisotropicfield\((E_{\text{isotropicfield}}\))is \[E_{\text{isotropicfield}}=7\times0+2P=2P\nonumber\] Theenergyoftheoctahedralligandfield\(E_{\text{ligandfield}}\)is \[E_{\text{ligandfield}}=(5\times-2/5\Delta_o)+(2\times3/5\Delta_o)+2P=-4/5\Delta_o+2P\nonumber\] SoviaEquation\ref{1},theCFSEis \[\begin{align}CFSE&=E_{\text{ligandfield}}-E_{\text{isotropicfield}}\nonumber\\[4pt]&=(-4/5\Delta_o+2P)-2P\nonumber\\[4pt]&=-4/5\Delta_o\nonumber\end{align}\nonumber\] NoticethattheSpinpairingEnergyfallsoutinthiscase(andwillwhencalculatingtheCFSEofhighspincomplexes)sincethenumberofpairedelectronsintheligandfieldisthesameasthatinisotropicfieldofthefreemetalion. Example\(\PageIndex{2}\):CFSEforaLowSpin\(d^7\)complex WhatistheCrystalFieldStabilizationEnergyforalowspin\(d^7\)octahedralcomplex? Solution Thesplittingpatternandelectronconfigurationforbothisotropicandoctahedralligandfieldsarecomparedbelow. TheenergyoftheisotropicfieldisthesameascalculatedforthehighspinconfigurationinExample1: \[E_{\text{isotropicfield}}=7\times0+2P=2P\nonumber\] Theenergyoftheoctahedralligand\)field\(E_{\text{ligandfield}}\)is \[\begin{align}E_{\text{ligandfield}}&=(6\times-2/5\Delta_o)+(1\times3/5\Delta_o)+3P\nonumber\\[4pt]&=-9/5\Delta_o+3P\nonumber\end{align}\nonumber\] SoviaEquation\ref{1},theCFSEis \[\begin{align}CFSE&=E_{\text{ligandfield}}-E_{\text{isotropicfield}}\nonumber\\[4pt]&=(-9/5\Delta_o+3P)-2P\nonumber\\[4pt]&=-9/5\Delta_o+P\nonumber\end{align}\nonumber\] Addinginthepairingenergysinceitwillrequireextraenergytopairuponeextragroupofelectrons.Thisappearsmoreamorestableconfigurationthanthehighspin\(d^7\)configurationinExample\(\PageIndex{1}\),butwehavethentotakeintoconsiderationthePairingenergy\(P\)toknowdefinitely,whichvariesbetween\(200-400\;kJ\;mol^{-1}\)dependingonthemetal. Table\(\PageIndex{1}\):CrystalFieldStabilizationEnergies(CFSE)forhighandlowspinoctahedralcomplexes Totald-electrons IsotropicField OctahedralComplex CrystalFieldStabilizationEnergy HighSpin LowSpin \(E_{\text{isotropicfield}}\) Configuration \(E_{\text{ligandfield}}\) Configuration \(E_{\text{ligandfield}}\) HighSpin LowSpin d0 0 \(t_{2g}\)0\(e_g\)0 0 \(t_{2g}\)0\(e_g\)0 0 0 0 d1 0 \(t_{2g}\)1\(e_g\)0 -2/5\(\Delta_o\) \(t_{2g}\)1\(e_g\)0 -2/5\(\Delta_o\) -2/5\(\Delta_o\) -2/5\(\Delta_o\) d2 0 \(t_{2g}\)2\(e_g\)0 -4/5\(\Delta_o\) \(t_{2g}\)2\(e_g\)0 -4/5\(\Delta_o\) -4/5\(\Delta_o\) -4/5\(\Delta_o\) d3 0 \(t_{2g}\)3\(e_g\)0 -6/5\(\Delta_o\) \(t_{2g}\)3\(e_g\)0 -6/5\(\Delta_o\) -6/5\(\Delta_o\) -6/5\(\Delta_o\) d4 0 \(t_{2g}\)3\(e_g\)1 -3/5\(\Delta_o\) \(t_{2g}\)4\(e_g\)0 -8/5\(\Delta_o\)+P -3/5\(\Delta_o\) -8/5\(\Delta_o\)+P d5 0 \(t_{2g}\)3\(e_g\)2 0\(\Delta_o\) \(t_{2g}\)5\(e_g\)0 -10/5\(\Delta_o\)+2P 0\(\Delta_o\) -10/5\(\Delta_o\)+2P d6 P \(t_{2g}\)4\(e_g\)2 -2/5\(\Delta_o\)+P \(t_{2g}\)6\(e_g\)0 -12/5\(\Delta_o\)+3P -2/5\(\Delta_o\) -12/5\(\Delta_o\)+P d7 2P \(t_{2g}\)5\(e_g\)2 -4/5\(\Delta_o\)+2P \(t_{2g}\)6\(e_g\)1 -9/5\(\Delta_o\)+3P -4/5\(\Delta_o\) -9/5\(\Delta_o\)+P d8 3P \(t_{2g}\)6\(e_g\)2 -6/5\(\Delta_o\)+3P \(t_{2g}\)6\(e_g\)2 -6/5\(\Delta_o\)+3P -6/5\(\Delta_o\) -6/5\(\Delta_o\) d9 4P \(t_{2g}\)6\(e_g\)3 -3/5\(\Delta_o\)+4P \(t_{2g}\)6\(e_g\)3 -3/5\(\Delta_o\)+4P -3/5\(\Delta_o\) -3/5\(\Delta_o\) d10 5P \(t_{2g}\)6\(e_g\)4 0\(\Delta_o\)+5P \(t_{2g}\)6\(e_g\)4 0\(\Delta_o\)+5P 0 0 \(P\)isthespinpairingenergyandrepresentstheenergyrequiredtopairupelectronswithinthesameorbital.ForagivenmetalionP(pairingenergy)isconstant,butitdoesnotvarywithligandandoxidationstateofthemetalion). OctahedralPreference SimilarCFSEvaluescanbeconstructedfornon-octahedralligandfieldgeometriesoncetheknowledgeofthed-orbitalsplittingisknownandtheelectronconfigurationwithinthoseorbitalsknown,e.g.,thetetrahedralcomplexesinTable\(\PageIndex{2}\).TheseenergiesgeoemtriescanthenbecontrastedtotheoctahedralCFSEtocalculateathermodynamicpreference(Enthalpy-wise)forametal-ligandcombinationtofavortheoctahedralgeometry.ThisisquantifiedviaaOctahedralSitePreferenceEnergydefinedbelow. Definition:OctahedralSitePreferenceEnergies TheOctahedralSitePreferenceEnergy(OSPE)isdefinedasthedifferenceofCFSEenergiesforanon-octahedralcomplexandtheoctahedralcomplex.Forcomparingthepreferenceofforminganoctahedralligandfieldvs.atetrahedralligandfield,theOSPEisthus: \[OSPE=CFSE_{(oct)}-CFSE_{(tet)}\label{2}\] TheOSPEquantifiesthepreferenceofacomplextoexhibitanoctahedralgeometryvs.atetrahedralgeometry. Note:theconversionbetween\(\Delta_o\)and\(\Delta_t\)usedforthesecalculationsis: \[\Delta_t\approx\dfrac{4}{9}\Delta_o\label{3}\] whichisapplicableforcomparingoctahedralandtetrahedralcomplexesthatinvolvesameligandsonly. Table\(\PageIndex{2}\):OctahedralSitePreferenceEnergies(OSPE) Totald-electrons CFSE(Octahedral) CFSE(Tetrahedral) OSPE(forhighspincomplexes)** HighSpin LowSpin Configuration AlwaysHighSpin* d0 0\(\Delta_o\) 0\(\Delta_o\) e0 0\(\Delta_t\) 0\(\Delta_o\) d1 -2/5\(\Delta_o\) -2/5\(\Delta_o\) e1 -3/5\(\Delta_t\) -6/45\(\Delta_o\) d2 -4/5\(\Delta_o\) -4/5\(\Delta_o\) e2 -6/5\(\Delta_t\) -12/45\(\Delta_o\) d3 -6/5\(\Delta_o\) -6/5\(\Delta_o\) e2t21 -4/5\(\Delta_t\) -38/45\(\Delta_o\) d4 -3/5\(\Delta_o\) -8/5\(\Delta_o\)+P e2t22 -2/5\(\Delta_t\) -19/45\(\Delta_o\) d5 0\(\Delta_o\) -10/5\(\Delta_o\)+2P e2t23 0\(\Delta_t\) 0\(\Delta_o\) d6 -2/5\(\Delta_o\) -12/5\(\Delta_o\)+P e3t23 -3/5\(\Delta_t\) -6/45\(\Delta_o\) d7 -4/5\(\Delta_o\) -9/5\(\Delta_o\)+P e4t23 -6/5\(\Delta_t\) -12/45\(\Delta_o\) d8 -6/5\(\Delta_o\) -6/5\(\Delta_o\) e4t24 -4/5\(\Delta_t\) -38/45\(\Delta_o\) d9 -3/5\(\Delta_o\) -3/5\(\Delta_o\) e4t25 -2/5\(\Delta_t\) -19/45\(\Delta_o\) d10 0 0 e4t26 0\(\Delta_t\) 0\(\Delta_o\) \(P\)isthespinpairingenergyandrepresentstheenergyrequiredtopairupelectronswithinthesameorbital. Tetrahedralcomplexesarealwayshighspinsincethesplittingisappreciablysmallerthan\(P\)(Equation\ref{3}). AfterconversionwithEquation\ref{3}.ThedatainTables\(\PageIndex{1}\)and\(\PageIndex{2}\)arerepresentedgraphicallybythecurvesinFigure\(\PageIndex{1}\)belowforthehighspincomplexesonly.Thelowspincomplexesrequireknowledgeof\(P\)tograph. Figure\(\PageIndex{1}\):CrystalFieldStabilizationEnergiesforbothoctahedralfields(\(CFSE_{oct}\))andtetrahedralfields(\(CFSE_{tet}\)).OctahedralSitePreferenceEnergies(OSPE)areinyellow.Thisisforhighspincomplexes. FromasimpleinspectionofFigure\(\PageIndex{1}\),thefollowingobservationscanbemade: TheOSPEissmallin\(d^1\),\(d^2\),\(d^5\),\(d^6\),\(d^7\)complexesandotherfactorsinfluencethestabilityofthecomplexesincludingstericfactors TheOSPEislargein\(d^3\)and\(d^8\)complexeswhichstronglyfavoroctahedralgeometries Applications The"double-humped"curveinFigure\(\PageIndex{1}\)isfoundforvariouspropertiesofthefirst-rowtransitionmetals,includingHydrationandLatticeenergiesoftheM(II)ions,ionicradiiaswellasthestabilityofM(II)complexes.ThissuggeststhatthesepropertiesaresomehowrelatedtoCrystalFieldeffects. InthecaseofHydrationEnergiesdescribingthecomplexationofwaterligandstoabaremetalion: \[M^{2+}(g)+H_2O\rightarrow[M(OH_2)_6]^{2+}(aq)\] Table\(\PageIndex{3}\)andFigure\(\PageIndex{1}\)showsthistypeofcurve.NotethatinanyseriesofthistypenotallthedataareavailablesinceanumberofionsarenotverystableintheM(II)state. Table\(\PageIndex{3}\):Hydrationenergiesof\(M^{2+}\)ions M ΔH°/kJmol-1 M ΔH°/kJmol-1 Ca -2469 Fe -2840 Sc nostable2+ion Co -2910 Ti -2729 Ni -2993 >V -2777 Cu -2996 Cr -2792 Zn -2928 Mn -2733 GraphicallythedatainTable2canberepresentedby: Figure\(\PageIndex{2}\):hydrationenergiesof\(M^{2+}\)ions ContributorsandAttributions Prof.RobertJ.Lancashire(TheDepartmentofChemistry,UniversityoftheWestIndies)