Crystal Field Theory (CFT)

Crystal Field Theory (CFT)

1. Crystal Field Theory
•ThistheorywasproposedbyHansBretheandVenVleck.
•Thistheorywasoriginallyappliedmainlytoioniccrystals.
•ThereforeitisknownasCrystalfieldTheory.
•Itwasnotuntil1952thatOrgelpopularizeditsuseforInorganic
Chemists.
•Asecondapproachtothebondingincomplexesofthed-block
metalsiscrystalfieldtheory.
•Thisisanelectrostaticmodelandsimplyusestheligandelectrons
tocreateanelectricfieldaroundthemetalcentre.
•Ligandsareconsideredaspointchargesandtherearenometal–
ligandcovalentinteractions.
•Aswehavejustseen,theclassicvalence-bondapproachwas
unabletoexplainmanyoftheaspectsoftransitionmetal
complexes.
•Inparticular,VBTdidnotsatisfactorilyexplainthedifferent
numbersofunpairedelectronsthatwefindamongthetransition
metalions.

2. •Forexample,thehexaaquairon(II)ion,[Fe(OH
2
)
6
]
2+
,hasfour
unpairedelectrons,whereasthehexacyanoferrate(II)ion,
[Fe(CN)
6
]
4-
,hasnounpairedelectrons.

4. •Despiteitssimplisticnature,crystalfieldtheory(CFT)
hasprovedremarkablyusefulforexplainingthe
propertiesofperiod4(1
st
rowd-block)transitionmetal
complexes.
•Thetheoryassumesthatthetransitionmetalionisfree
andgaseous,thattheligandsbehavelikepointcharges,
andthattherearenointeractionsbetweenmetald
orbitalsandligandorbitals.
•The theory also depends on the probability model of the
d orbitals, that there are two d orbitals whose lobes are
oriented along the Cartesian axes (axial) d
x
2
-y
2
and d
z
2
(following figure)
Period 4 (1
st
row d-block)

5. andthreedorbitalswhoselobesareorientedbetweenthe
Cartesianaxes(interaxial)d
xy
,d
xz
,andd
yz
(following
figure).
Figure: Representations
of the shapes of the 3d
x
2
-y
2
and 3d
z
2
orbitals.
Figure: Representations of the shapes of the 3d
xy
, 3d
xz
, and
3d
yz
orbitals.

6. OrientedalongtheCartesianaxes
•Thed
z
2
andd
x
2
-y
2
orbitalslieonthesameaxesas
negativecharges.
•Therefore,thereisalarge,unfavorableinteraction
betweenligand(-)orbitals.
•Theseorbitalsformthedegeneratehighenergypairof
energylevels.
OrientedbetweentheCartesianaxes
•Thed
xy
,d
yx
andd
xz
orbitalsbisect(betweentheaxes)the
negativecharges.
•Therefore,thereisasmallerrepulsionbetweenligand
andmetalfortheseorbitals.
•Theseorbitalsformthedegeneratelowenergysetof
energylevels.

7. The energy gap is
referred to as Δ
0
(10 Dq),
the crystal field splitting
energy.
d-orbitals (d
x
2
-y
2
and d
z
2
) pointing directly
at axis are affected most by electrostatic
interaction
d-orbitals (d
xy
, d
yx
and d
xz
) not pointing
directly at axis are least affected
(stabilized) by electrostatic interaction
Ligandsapproach metal
Inter-axial, t
2g
Axial, e
g

8. ImportantFeaturesofCFT
•Thecentralmetalcationissurroundedbyligandswhich
containoneormorelonepairsofelectrons.
•Theionicligands(e.g.,F
-
,Cl
-
,CN
-
etc.)areregardedas
negativepointcharges(alsocalledpointcharges)andthe
neutralligands(e.g.,H
2
O,NH
3
etc.)areregardedas
pointdipolesorsimplydipoles.
–Iftheligandisneutral,thenegativeendofthisligand
dipoleisorientedtowardsmetalcation.
•TheCFTdoesnotprovideforelectronstoenterthe
metalorbitals.
–Thusthemetalionandtheligandsdonotmixtheir
orbitalsorshareelectrons,i.e.,itdoesnotconsider
anyorbitaloverlap.

9. •AccordingtoCFT,thebondingbetweenmetalcationandligandis
notcovalentbutitisregardedaspurelyelectrostaticorcoulombic
attractionbetweenpositivelycharged(i.e.,cations)andnegatively
charged(i.e.,anionsordipolemoleculeswhichactasligands)
species.
–Complexesarethuspresumedtoformwhencentrallysituated
cationselectricallyattractligandswhichmaybeeitheranionsor
dipolemolecules.
–Theattractionbetweenthecationsandtheligandsisbecause
thecationsarepositivelychargedandtheanionsarenegatively
chargedandthedipolemolecules,aswell,canoffertheir
negativelyincrementedendsforsuchelectrostaticattractions.
" t " → Triply degenerate set of orbitals
" e " → Doubly degenerate of orbitals
Ionic ligands → Negative point charges
Neutral ligands → Point dipoles or simply dipoles

10. Salientfeaturesofcrystalfieldtheory
•Focusesonthed-orbitalsofthemetal.
•Thecentralmetalcationissurroundedbyligandswhichcontain
oneormorelonepairsofelectrons.
•Theionicligands(e.g.,F
-
,Cl
-
,CN
-
etc.)areregardedas:
–Negativepointcharges(alsocalledpointcharges)
andtheneutralligands(e.g.,H
2
O,NH
3
etc.)areregardedas:
–Pointdipolesorsimplydipoles,i.e.,accordingtothistheory
neutralligandaredipolar.
•Iftheligandisneutral,thenegativeendofthisliganddipoleis
orientedtowardsthemetalcation.
•Theinteractionbetweenthemetalcationandtheligandsis
regardedaspurelyelectrostatic,i.e.themetal—ligandbondis
consideredtobe100%ionic.
Ionic ligands → Negative point charges
Neutral ligands → Point dipoles or simply dipoles

11. •Electrostaticinteractionsinacomplexbetween+vemetal
ionand–vechargesofligand-treatsligandsaspoint
(negative)charges.
–Iftheligandisnegativelycharged
•Ion-ioninteraction
–Iftheligandisneutral
•Ion-dipoleinteraction
•Providesstabilityandholdscomplextogether.
•Repulsionbetweenthelonepairofelectronsontheligand
andtheelectronsinthed-orbitalofthemetalion.
•Thisinfluencesthed-orbitalenergies

12. Why we consider ligand as a point charge in crystal
field theory?
•CFTassumesthatthemetalatomandtheligandsare
linkedbyelectrostaticforcesofattraction.
•Thusligandsareconsideredasnegativechargeswhereas
forneutralligandsthemostelectronegativeatompoints
towardstheatom.

13. GroupingofFived-Orbitals
into
t
2g
ande
g
setsofOrbitals
•Onthebasisoforientationofthelobesofthefived-orbitalswith
respecttocoordinatesthesehavebeengroupedintofollowingtwo
sets.
e
g
setsoforbitals(d
z
2
andd
x
2
–y
2
orbitals)
•Thissetconsistsoftwoorbitalswhichhavetheirlobesalongthe
axesandarecalledaxialorbitals.
•Theseared
z
2
andd
x
2
–y
2
orbitals.
•Thistheorycallstheseorbitalse
g
orbitalsinwhicherefersto
doublydegenerateset.
t
2g
setsoforbitals(d
xy
,d
yz
andd
zx
orbitals)
•Thissetincludethreeorbitalswhoselobesliebetweentheaxes
andarecallednon-axialorbitals.
•Theseared
xy
,d
yz
andd
zx
orbitals.
•Thistheorycallstheseorbitalst
2g
orbitalsinwhichtrefersto
triplydegenerateset.

14. Splitting of d-orbital energies in octahedral fields
Valencebondtheoryapproach
•Thereareseveralcharacteristicsofcoordinationcompounds
thatarenotsatisfactorilyexplainedbyasimplevalencebond
descriptionofthebonding.
•Forexample,themagneticmomentof[CoF
6
]
3-
indicatesthat
therearefourunpairedelectronsinthecomplex,whereas
thatof[Co(NH
3
)
6
]
3-
indicatesthatthiscomplexhasno
unpairedelectrons,althoughineachcaseCo
3+
isad
6
ion.
•Inthesecomplexesasinvolvingsp
3
d
2
([CoF
6
]
3-
)andd
2
sp
3
([Co(NH
3
)
6
]
3-
)hybridorbitals,respectively,butthatdoesnot
provideanexplanationastowhythetwocasesaredifferent.
•Anotherareathatisinadequatelyexplainedbyasimple
valence-bondapproachisthenumberofabsorptionbands
seeninthespectraofcomplexes.

16. Crystalfieldtheoryapproach
(CrystalFieldSplittingofd-OrbitalsinOctahedralComplexes)
•Oneofthemostsuccessfulapproachestoexplainingthese
characteristicsisknownascrystalorligandfieldtheory.
•Whenametalionissurroundedbyanionsinacrystal,thereisan
electrostaticfieldproducedbytheanionsthatalterstheenergiesof
thedorbitalsofthemetalion.
•Thefieldgeneratedinthiswayisknownasacrystalfieldandit
explainthespectralcharacteristicsofmetalionsincrystals.
•Itsoonbecameobviousthatanionssurroundingametalinacrystal
gaveasituationthatisverysimilartotheligands(manyofwhich
arealsoanions)surroundingametalioninacoordination
compound.
•Incaseswheretheligandsarenotanions,theymaybepolarmolecules,
andthenegativeendsofthedipolesaredirectedtowardthemetalion
generatinganelectrostaticfield.
•Strictlyspeaking,thecrystalfieldapproachisapurelyelectrostaticone
basedontheinteractionsbetweenpointcharges,whichisneverexactlythe
caseforcomplexesoftransitionmetalions.

17. •Inviewofthefactthatcoordinatebondsresultfromelectronpair
donationandhavesomecovalency,thetermligandfieldisusedto
describetheeffectsofthefieldproducedbytheligandsina
complex.
•Inthe1930s,J.H.VanVleckdevelopedligandfieldtheoryby
adaptingthecrystalfieldapproachtoincludesomecovalentnature
oftheinteractionsbetweenthemetalionandtheligands.
•Beforewecanshowtheeffectsofthefieldaroundametalion
producedbytheligands,itisessentialtohaveaclearpictureof
theorientationofthedorbitalsofthemetalion.
•Followingfigureshowsasetoffivedorbitals,andforagaseous
ion,thefiveorbitalsaredegenerate.

18. Figure. The spatial orientations of the set of five d orbitals for
a transition metal.

19. Explanation
•Incaseoffreemetalionallthefived-orbitalsaredegeneratei.e.,these
havethesameenergy.
•Nowletusconsideranoctahedralcomplex[ML
6
]
n+
inwhichcentral
metalcation,M
n+
isplacedatthecentreofoctahedronandis
surroundedbysixligandswhichresideatthecornersofthe
octahedronasshowninthefigure.
Figure:Position of
central metal cation,
M
n+
and six ligands in
an octahedral complex
[ML
6
]
n+
•Thethreeaxes,viz.x-,y-,andz-axeswhich
pointalongthecornershavealsobeenshown.
•Nowsupposeboththeligandsoneachofthe
threeaxesareallowedtoapproachtowardsthe
metalcation,M
n+
fromboththeendsofthe
axes.
•Inthisprocesstheelectronsind-orbitalsofthe
metalcationarerepelledbynegativepoint
chargeorbythenegativeendofthedipoleof
theligands.

20. •Thisrepulsionwillraisetheenergyofallthefived-orbitals.
•Ifalltheligandsapproachingthecentralcationareatanequal
distancefromeachofthed-orbitals(i.e.,theligandfieldis
sphericallysymmetrical),theenergyofeachoffived-orbitalwill
raisebythesameamount,i.e.,allthed-orbitalswillstillremain
degenerate,althoughtheywillhavenowhigherenergythanbefore.
•Thisisonlyahypotheticalsituation.
•Sincethelobesofthetwoe
g
orbitalsliedirectlyinthepathofthe
approachingligands,theelectronsintheseorbitalsexperiencegreater
forceofrepulsionthanthoseinthreet
2g
orbitalswhoselobesare
directedinspacebetweenthepathoftheapproachingligands.
•So,energyofe
g
orbitalsisincreasedwhilethatoft
2g
isdecreased.
•Remember:Greatertherepulsion,greateristheincreaseinenergy.
•Thuswefindthatundertheinfluenceofapproachingligands,the
fived-orbitalswhichwereoriginallydegenerateinthefreemetallic
cationarenowsplit(orresolved)intotwolevelsviz.,t
2g
levelwhich
istriplydegenerateandisoflowerenergyande
g
levelwhichis
doublydegenerateandisofhigherenergy.

21. Figure. Splitting of the d orbitals in a crystal field of
octahedral symmetry.
Five degenerate d-orbitals
on the central metal cation
which are free from any
ligandfield
Hypothetical
degenerate d-orbitalsat
a higher energy level
Splitting of d-orbitals
under the influence of
six ligandsin octahedral
complex
----------------------
No splitting state
+0.6Δ
o
= +6Dq = (3/5) Δ
o
-0.4Δ
o
= -4Dq = (2/5) Δ
o

22. •Inotherwordsthedegeneracyofthefived-orbitalsisremoved
undertheinfluenceoftheligands.
•Theseparationoffived-orbitalsofthemetalionintotwosets
havingdifferentenergiesiscalledcrystalfieldsplittingorenergy
levelsplitting.
•ThisconceptofcrystalfieldsplittingmakesthebasisofCFT.

23. •Asshowninfollowingfigure,anoctahedralcomplex
canbeconsideredasametalionsurroundedbysix
ligandsthatarelocatedontheaxes.
Figure. An octahedral complex with the six ligands lying
on the x, y, and z axes.

24. •Whensixligandssurroundthemetalion,thedegeneracy
ofthedorbitalsisremovedbecausethreeoftheorbitals,
thed
xy
,d
yz
,andd
xz
orbitals,aredirectedbetweenthe
axeswhiletheothers,thed
x
2
-y
2
andthed
z
2
,aredirected
alongtheaxespointingattheligands.
•Therefore,thereisgreaterrepulsionbetweenthe
electronsinorbitalsontheligandsandthed
x
2
-y
2
andd
z
2
orbitalsthanthereistowardthed
xy
,d
yz
,andd
xz
orbitals.
•Becauseoftheelectrostaticfieldgeneratedbythe
ligands,allofthedorbitalsareraisedinenergy,buttwo
ofthemareraisedmorethantheotherthree.
•Asaresult,thedorbitalshaveenergiesthatcanbe
representedasshowninfollowingfigure.

25. Figure. Splitting of the d orbitals in a crystal field of
octahedral symmetry.
Five degenerate d-orbitals
on the central metal cation
which are free from any
ligandfield
Hypothetical
degenerate d-orbitalsat
a higher energy level
Splitting of d-orbitals
under the influence of
six ligandsin octahedral
complex
----------------------
No splitting state
+0.6Δ
o
= +6Dq = (3/5) Δ
o
-0.4Δ
o
= -4Dq = (2/5) Δ
o

26. •Thetwoorbitalsofhigherenergyaredesignatedasthee
g
orbitals,
andthethreeorbitalsoflowerenergymakeupthet
2g
orbitals.
•Thesedesignationswillbedescribedingreaterdetaillater,butthe
“g”subscriptreferstobeingsymmetricalwithrespecttoacenter
ofsymmetrythatispresentinastructurethathasO
h
symmetry.
•The"t"referstoatriplydegeneratesetoforbitals,whereas"e"
referstoasetthatisdoublydegenerate.
•Theenergyseparatingthetwogroupsoforbitalsiscalledthe
crystalorligandfieldsplitting,Δ
o
.
•Splittingoftheenergiesofthedorbitalsasindicatedinabove
figureoccursinsuchawaythattheoverallenergyremains
unchangedandthe“centerofenergy(Barycentre)”ismaintained.
" t " → Triply degenerate set of orbitals
" e " → Doubly degenerate of orbitals

27. •Thee
g
orbitalsareraised1.5timesasmuchasthet
2g
orbitalsare
loweredfromthecenterofenergy.
•Althoughthesplittingofthedorbitalsinanoctahedralfieldis
representedasΔ
o
,itisalsosometimesdesignatedas10Dq,whereDq
isanenergyunitforaparticularcomplex.
(1Δ
o
=10Dq)
•Thetwoorbitalsmakingupthee
g
pairareraisedby3/5Δ
o
(+0.6Δ
o
or
+6Dq)whilethet
2g
orbitalsareloweredby2/5Δ
o
(-0.4Δ
o
or-4Dq)
relativetothecenterofenergy.
•IntermsofDqunits,thee
g
orbitalsareraisedby6Dq
whilethethreet
2g
orbitalsare
4Dqlowerthanthecenterof
energy.
Crystal field splitting of d-orbitals
in octahedral complex.
3/5 Δ
o
2/5 Δ
o

28. Hypotheticalstepsforcomplexformation
Wecanconsidercomplexformationasaseriesofevents:
Step1
•Theinitialapproachoftheligandelectronsformsasphericalshell
aroundthemetalion.
•Repulsionbetweentheligandelectronsandthemetalionelectrons
willcauseanincreaseinenergyofthemetaliondorbitals.
Step2
•Theligandelectronsrearrangesothattheyaredistributedinpairs
alongtheactualbondingdirections(suchasoctahedralor
tetrahedral).
•Themeanmetaldorbitalenergieswillstaythesame,butthe
orbitalsorientedalongthebondingdirectionswillincreasein
energy,andthosebetweenthebondingdirectionswilldecreasein
energy.
•Thislossindorbitaldegeneracywillbethefocusofthecrystal
fieldtheorydiscussion(thatiscrucialfortheexplanationofthe
colorandmagneticpropertiesoftransitionmetalcomplexes).

29. Step3
•Uptothispoint,complexformationwouldnotbe
favored,becausetherehasbeenanetincreaseinenergy
asaresultoftheligandelectron–metalelectronrepulsion
(step1).
•Furthermore,thedecreaseinthenumberoffreespecies
meansthatcomplexformationwillgenerallyresultina
decreaseinentropy.
•However,therewillbeanattractionbetweentheligand
electronsandthepositivelychargedmetalionthatwill
resultinanetdecreaseinenergy.Itisthisthirdstepthat
providesthedrivingforceforcomplexformation.
•Thesethreehypotheticalstepsaresummarizedin
followingfigure.

30. Figure. The hypothetical steps in complex ion formation according
to crystal field theory.

31. High-and Low-Spin States
•Theparamagnetismisacharacteristicofsomed-block
metalcompounds.
•Letussimplystatethatmagneticdataallowusto
determinethenumberofunpairedelectrons.
•Inanisolatedfirstrowd-blockmetalion,the3dorbitals
aredegenerate(ofthesameenergy)andtheelectrons
occupythemaccordingtoHund’srules:
–e.g.,followingdiagramshowsthearrangementofsix
electrons.

32. •However,magneticdataforarangeofoctahedrald
6
complexesshowthattheyfallintotwocategories:
–Paramagnetic
–Diamagnetic
•Theformer(paramagnetic)arecalledhigh-spin
complexesandcorrespondtothoseinwhich,despitethe
dorbitalsbeingsplit,therearestillfourunpaired
electrons.
•Thediamagneticd
6
complexesaretermedlow-spinand
correspondtothoseinwhichelectronsaredoubly
occupyingthreeorbitals,leavingtwounoccupied.
Diamagnetic = Low-spin = Covalent complex (3d) = Inner orbital
complex
Paramagnetic = High-spin = Ionic complex (4d) = Outer orbital
complex

33. Crystal field theory (CFT) splitting diagram
Example of influence of ligand electronic properties on d orbital
splitting. This shows the comparison of low-spin versushigh-
spin electrons.
First-row transition metals = 3d or 4d
d
2
sp
3
= Diamagnetic = Low-spin = Covalent complex (3d) = Inner
orbital complex
sp
3
d
2
= Paramagnetic = High-spin = Ionic complex (4d) = Outer orbital
complex

35. Explanation
•Thecobaltatominthegroundstatehastheouterelectron
configuration:
•The2+and3+ionshavethefollowingouterelectron
configuration:
and

36. Weakligand→F
-
•Withweakligands,suchasF
-
,bothions(Co
2+
and
Co
3+
)formoctahedralcomplexesinwhichtheligand
electronsareaccommodatedinsp
3
d
2
hybridorbitals.
•Inotherwords,thepartiallyfilledinnerd-orbitals
arenotused.
•Thistypeofcomplexisknownasanouterd-orbital
complex.

37. Strongligand→
-
CN
•Withstrongligands,suchas
-
CNions,spin-pairingof
theinnerd-electrons,occursandbothions(Co
2+
and
Co
3+
)formoctahedralcomplexesinwhichtheligand
electronsareaccommodatedind
2
sp
3
hybrids.
•Inotherwordsthepartiallyfilledd-orbitalsareused,
andthistypeofcomplexisknownasaninnerd-orbital
complex.

38. Energetics
Electrostatic between metal ion and donor atom (ligand)
•Step i: Separate metal and ligandhigh energy
•Step ii: Coordinated metal -ligandstabilized
•Step iii:Destabilization due to ligand-d electron
repulsion
•Step iv: Splitting
due to octahedral
field.

39. Whathappenstotheenergiesofelectronsinthed-
orbitalsassixligandsapproachthebaremetalion?
•Whensixligandsapproachthebaremetalion:
•Ifwecomparethed
xy
andthed
x
2
-y
2
,wecanseethatthere
isasignificantdifferenceintherepulsionenergyasligand
lonepairsapproachd-orbitalscontainingelectrons.
Electronsinthed
xy
orbitalare
concentratedinthe
spacebetweenthe
incomingligands.
Electronsinthed
x
2
-y
2
orbitalpointstraightat
theincomingligands.

40. •Now,d
xz
andd
yz
behavethesameasd
xy
inanoctahedralfield,and
d
z
2
behavesthesameasd
x
2
-y
2
.
•Thismeansthatthed-orbitalsdivideintotwogroups,onelower
energythantheother,asshowninthefollowingdiagram.
•Thed
xy
,d
xz
,andd
yz
orbitalsarecollectivelycalledthet
2g
orbitals,
whereasthed
z
2
andd
x
2
-y
2
orbitalsarecalledthee
g
orbitals.
•Theoctahedralsplittingenergyistheenergydifferencebetweenthe
t
2g
ande
g
orbitals.
•Inanoctahedralfield,thet
2g
orbitalsarestabilizedby2/5Δ
o
,and
thee
g
orbitalsaredestabilizedby3/5Δ
o
.

41. Absorptionspectrumof[Ti(H
2
O)
6
]
3+
•Theeffectofcrystalfieldsplittingiseasilyseenbystudyingthe
absorptionspectrumof[Ti(H
2
O)
6
]
3+
becausetheTi
3+
ionhasasingle
electroninthe3dorbitals.
•Intheoctahedralfieldproducedbythesixwatermolecules,the3d
orbitalsaresplitinenergyasshowninthefollowingfigure.
•Theonlytransitionpossibleispromotionoftheelectronfromanorbital
inthet
2g
settooneinthee
g
set.
Crystal field splitting of d-orbitalsin
octahedral complex.
3/5 Δ
o
2/5 Δ
o
•Thistransitiongivesrisetoasingle
absorptionband,themaximumof
whichcorrespondsdirectlytothe
energyrepresentedasΔ
o
.
•Asexpected,thespectrumshowsa
single,broadbandthatiscenteredat
20,300cm
-1
,whichcorresponds
directlytoΔ
o
(followingfigure).

42. Figure.The electronic spectrum of
[Ti(H
2
O)
6
]
3+
in aqueous solution.
e
-
jumps to
higher level
Absorbed λ
Transmitted λ Incoming
λ
t
2g
t
2g
e
g
e
g
Light of
510nm
λ
max
= 20,300 cm
-1
↓
Whentheionabsorbslight,
electronscanmovefromthe
lowert
2g
,energyleveltothe
highere
g
level.
Thedifferenceinenergy
betweenthelevels(Δ)
determinesthewavelengths
oflightabsorbed.
Thevisiblecolorisgivenby
thecombinationofthe
wavelengthstransmitted.
Ground state
Excited state

43. •Theenergyassociatedwiththisbandiscalculatedas
follows:
•WecanconvertthisenergypermoleculeintokJmol
-1
by
thefollowingconversion.
•Thisenergy(243kJmol
-1
)islargeenoughtogiveriseto
othereffectswhenametalionissurroundedbysix
ligands.
•However,onlyforad
1
ionistheinterpretationofthe
spectrumthissimple.
•Whenmorethanoneelectronispresentinthedorbitals,
theelectronsinteractbyspin-orbitcoupling.

44. •Anytransitionofanelectronfromthet
2g
tothee
g
orbitalsis
accompanied(
هارمہ انوہ
)bychangesinthecouplingscheme
whenmorethanoneelectronispresent.
•Theinterpretationofspectratodeterminetheligandfield
splittinginsuchcasesisconsiderablymorecomplicatedthat
inthed
1
case.
•Theorderingoftheenergylevelsforametalioninan
octahedralfieldmakesiteasytovisualizehowhigh-and
low-spincomplexesarisewhendifferentligandsarepresent.
•Iftherearethreeorfewerelectronsinthe3dorbitalsofthe
metalion,theycanoccupythet
2g
orbitalswithoneelectron
ineachorbital.
•Ifthemetalionhasad
4
configuration(e.g.,Mn
3+
),the
electronscanoccupythet
2g
orbitalsonlyifpairingoccurs,
whichrequiresthatΔ
o
belargerinmagnitudethantheenergy
necessarytoforceelectronpairing,P.

45. •Theresultisalow-spincomplexinwhichtherearetwo
unpairedelectrons.
•IfΔ
o
issmallerthanthepairingenergy,thefourthelectron
will
beinoneofthee
g
orbitals,whichresultsinahigh-
spincomplexhavingfourunpairedelectrons.
•Thesecasesareillustratedinfollowingfigure.
Figure.Crystalfield
splittingenergycompared
totheelectronpairing
energy.
> = Greater than
< = Less than

46. Meanpairingenergy(P)
“Mean pairing energy (P) is the energy which is
required to pair two electrons against electron-electron
repulsion in the same orbital.”
Representationandunit
•Pisgenerallyexpressedincm
-1
.
Characteristics
•Pisthepairingenergyforoneelectronpair.
•Pairingenergydependsontheprincipalenergylevel(n)
ofd-electrons.
Calculationoftotalpairingenergyofd
x
ion
•Ifmisthetotalnumberofpairedelectronsint
2g
ande
g
orbitalsind
x
ionandPisthepairingenergyforone
electron,then
•Totalpairingenergyformelectronpairs=mPcm
-1
.

47. Example
•Calculatethetotalpairingenergyofd
7
ioninhighspin
aswellasinlowspinoctahedralcomplexes.
Solution
•Weknowthattheconfigurationofdioninhighspin
stateist
2g
5
e
g
2
whichshowsthatm=2+0=2.
•Totalpairingenergyfor2pairedelectrons=2xP=2P
•Theconfigurationofd
7
ioninlowspinstateist
2g
6
e
g
1
whichgivesm=3+0=3.
•Totalpairingenergyfor3pairedelectrons=3xP=3P

48. Example
•Calculatethetotalpairingenergyfor[Cr(H
2
O)
6
]
2+
ionin
highspinandlowspinstate.Giventhatmeanpairing
energy=23,500cm
-1
.
Solution
•In[Cr(H
2
O)
6
]
2+
ion,CrispresentasCr
2+
whichisad
4
ion.
•Thustheconfigurationofd
4
ioninhighspinstateist
2g
3
e
g
1
whichgivesm=0andhence:
•Totalpairingenergyof[Cr(H
2
O)
6
]
2+
ioninhighspin
state=0xP=0
•Theconfigurationofd
4
ioninlowspinstateist
2g
4
e
g
0
whichgivesm=1andhence
•Totalpairingenergyof[Cr(H
2
O)
6
]
2+
ioninlowspin
state=1xP=1x23,500cm
-1
=23,500cm
-1

55. Theeffectofligandsandsplittingenergyonorbital
occupancy
•s-electronsarelostfirst.
–Ti
3+
isad
1
–V
3+
isd
2
–Cr
3+
isd
3
Hundsrule
•Firstthreeelectronsareinseparated-orbitalswiththeirspins
parallel.
•Fourthe
-
haschoice
Electronwillgoto:
–Higherorbital→ifΔ
0
issmall:Highspin
–Lowerorbital→ifΔ
0
islarge:Lowspin
•Weakfieldligands
–SmallΔ
0
,highspincomplex→leadtoasmallersplitting
energy
•Strongfieldligands
–LargeΔ
0
,lowspincomplex→leadtoalargersplittingenergy
Assignment
Q:Whatistheeffectofligandsand
splittingenergyonorbitaloccupancy?

56. No field
Maximum number
of unpaired electrons
Free Mn
2+
ion
t
2g
t
2g
e
g
e
g
[Mn(H
2
O)
6
]
2+
[Mn(CN)
6
]
4-
Weak-field ligand
High-spin complex
P > Δ
0
Strong-field ligand
Low-spin complex
P < Δ
0
small large
large
[Cr(H
2
O)
6
]
2+
[Cr(CN)
6
]
4-
t
2g
t
2g
e
g
e
g
small
P > Δ
0
P < Δ
0
> = Greater than
< = Less than
[Δ
0
< P]
[Δ
0
< P]
[Δ
0
> P]
[Δ
0
> P]

57. Weak-field ligand
Strong-field ligand
•Thepossibleelectronicconfigurationsforoctahedrald
n
(d
1
tod
10
,n=1–10)transition-metalcomplexes[M(H
2
O)
6
]
n+
.
•Onlythed
4
throughd
7
caseshavebothhigh-spinandlow-
spinconfigurations.
P > Δ
0
[Δ
0
< P]
P < Δ
0
[Δ
0
> P]

58. The various electronic configurations for low spin
octahedral complexes

59. The various electronic configurations for high spin
octahedral complexes

60. Factors for the magnitude of the ligand field
splitting
•Ofcourse,wehavenotyetfullyaddressedthefactorsthat
areresponsibleforthemagnitudeoftheligandfield
splitting.
•Thesplittingofthedorbitalsbytheligandsdependson:
–Thenatureofthemetalionandtheligands
–Theextentofbackdonation
–πbondingtotheligands
Assignment
Q:Writenoteon:
a)Theeffectofligandsandsplitting
energyonorbitaloccupancy?

61. Covalency
•Covalencyisthenumberofelectronpairsanatomcan
sharewithotheratoms.
•Thetotalnumberoforbitalsavailableinthevalence
shellisknownascovalency,whethertheorbitalsare
completelyfilledorempty.

62. Chemical and theoretical background
A reminder about symmetry labels
•Thetwosetsofdorbitalsinanoctahedralfieldare
labellede
g
andt
2g
(followingfigure).
Figure.Splitting of the d orbitals in an octahedral crystal field, with
the energy changes measured with respect to the barycentre.

63. •Inatetrahedralfield(followingfigure),thelabelsbecomee
andt
2
.
•Thesymbolstanderefertothedegeneracyofthelevel:
–atriplydegeneratelevelislabelled→t
–adoublydegeneratelevelislabelled→e
•Thesubscriptgmeansgeradeandthesubscriptumeans
ungerade.
•TheGermanwordsgerade(even)andungerade(odd)
designatethebehaviourofthewavefunctionunderthe
operationofinversion,anddenotetheparity تاواسُم ہلدابُم ۔
یربارب - تاواسُم ۔ ےسيج رادقِم ، ہبتُر ںيم (evenorodd)ofan
orbital.
•Theuandglabelsareapplicableonlyifthesystempossesses
acentreofsymmetry(centreofinversion)andthusareused
fortheoctahedralfield,butnotforthetetrahedralone.

64. Figure.Crystal field splitting diagrams for octahedral (left-hand side)
and tetrahedral (right-hand side) fields. The splittingsare referred to a
common barycentre.

65. Figure.The changes in the energies of the electrons occupying the
d orbitals of an M
n+
ion when the latter is in an octahedral crystal
field. The energy changes are shown in terms of the orbital energies.

66. Energy difference between the two sets of d-orbitals
•Theenergydifferencebetweenthetwosetsofdorbitals
intheoctahedralfieldisgiventhesymbol∆
oct
.
•Thesumoftheorbitalenergiesequalsthedegenerate
energy(sometimescalledthebarycenter).
•Thus,theenergyofthetwohigher-energyorbitals(d
x
2
-
y
2
andd
z
2
)is+3/5∆
oct
(+0.6∆
oct
),andtheenergyofthe
threelower-energyorbitals(d
xy
,d
xz
,andd
yz
)is-2/5∆
oct
(-0.4∆
oct
)belowthemean.
(+0.6∆
oct
)
(-0.4∆
oct
)
(1∆
oct
)

67. Barycenter
•Thebarycenter(orbarycentre)isthecenterofmassoftwoormore
bodiesthatareorbitingeachother,orthepointaroundwhichthey
bothorbit.
•Itisanimportantconceptinfieldssuchasastronomyand
astrophysics.
•Thepointatthecentreofasystem;anaveragepoint,weighted
accordingtomassorotherattribute.
•Ican'tfigureoutwhatthatbarycentrepartofthediagrammeans.
•Thefirstsectionofthediagramrepresentstheenergyofthed
orbitalsbeforetheligandscomeintothepictureandthe3
rd
section
representstheenergyofthedorbitalsafterthe6ligandshave
arrangedinanoctahedralstructure.
•Whatdoesthe2
nd
sectionofthegraphrepresent?
•OnoneexplanationofCFSEtheysaythis:
–Ifyouputanelectronintothet
2g
,likethatforTi
3+
,thenyoustabilize
thebarycenterofthedorbitalsby0.4Δ
o
.butIhavenoideawhatthis
means.
•Whatisthebarycentre?

68. •Barycenterliterallymeanscenterofmass.
•Inthiscase,itisjustrepresentingtheideathat,sinceenergymust
beconserved,andyousplittwostatesup(doublydegeneratee
g
level)andthreestatesdown(triplydegeneratet
2g
level),the
barycenterisjusttheplacewherethefive-folddegenerateenergy
levelwouldhavebeenintheabsenceofthesplitting,butincluding
theaverageeffectofthecrystalfieldinteraction,distributedover5
orbitals.

69. •TheonlyexplanationofbarycentreIcouldfindwereones
relatingtoastronomy.
•Asforthisconcept,I'vesettledfortheideathatthemiddlepart
ofthegraphrepresentsthesituationinwhichtheligandsforma
theoreticalsphericalchargearoundtheatomasopposedtotheir
chargesarrangedinanoctahedral(ortetrahedral,squareplanar
etc.)structure.
•Inthisimaginarysphericaldistributionofchargeeachdorbital
feelsthesameamountofrepulsionsotheyremaindegenerate.

70. CrystalFieldSplittingEnergy(∆
0
)
•Theenergygapbetweent
2g
ande
g
setsisdonatedby∆
0
or10Dq
where0in∆
0
indicatesanoctahedralarrangementoftheligands
roundthecentralmetalcation.
•Thisenergydifferencearisesbecauseofthedifferenceinthe
electrostaticfieldexertedbytheligandsont
2g
ande
g
setsoforbitals
ofthecentralmetalcation.
•∆
0
or10Dqiscalledcrystalfieldsplittingenergy.
•Withthehelpofsimplegeometryitcanbeshownthattheenergyof
t
2g
orbitalsis0.4∆
0
(=1Dq)lessthanthatofhypotheticaldegenerate
d-orbitalsandhencethatofe
g
orbitalsis0.6∆
0
(=6Dq)abovethat
ofthehypotheticaldegenerated-orbitals.
•Thus,wefindthatt
2g
setlosesanenergyequalto0.4∆
0
(=4Dq)
whilee
g
setgainsanenergyequalto0.6∆
0
(=6Dq).
•Thelossandgainofenergiesoft
2g
ande
g
orbitalsisexpressedby
negative(-)andpositive(+)signsrespectively(Followingfigure).

72. Assignment
Q:Usecrystalfieldtheorytodrawthemostprobablystructure
ofhexafluorocobaltate(III)[CoF
6
]
3−
(F
-
isaweakfieldligand).
–Co:1s
2
,2s
2
,2p
6
,3s
2
,3p
6
,3d
7
,4s
2
–Co
3+
:1s
2
,2s
2
,2p
6
,3s
2
,3p
6
,3d
6
,4s
0
•AccordingtoCFT,whensixF
-
approachestheCo
3+
,thed-orbitals
splitinthefollowingmanner:
Conclusion
•Δ
o
→ smaller
•Complex → high spin
•Geometry → octahedral
•Magnetic nature → paramagnetic
← Electronic configuration

73. Crystal field stabilization energy:
high-and low-spin octahedral complexes
•Wenowconsidertheeffectsofdifferentnumbersofelectrons
occupyingthedorbitalsinanoctahedralcrystalfield,the
electronswillallfitintothelower-energyset.
•Thisnetenergydecreaseisknownasthecrystalfield
stabilizationenergy(CFSE).
•Forad
1
system,thegroundstatecorrespondstothe
configurationt
2g
1
.
Figure. The d-orbital filling for the d
1
, d
2
, and d
3
configurations.

74. •Withrespecttothebarycentre,thereisastabilization
energyof-0.4∆
oct
;thisistheso-calledcrystalfield
stabilizationenergy,CFSE.
Figure.Splitting of the d orbitals in an octahedral crystal field,
with the energy changes measured with respect to the barycentre.

75. •Forad
2
ion,thegroundstateconfigurationist
2g
2
andthe
CFSE=-0.8∆
oct
;
ad
3
ion(t
2g
3
)hasaCFSE=-1.2∆
oct
.
•Forad
4
ion,twoarrangementsareavailable:
–Thefourelectronsmayoccupythet
2g
setwiththe
configurationt
2g
4
,or
–Maysinglyoccupyfourdorbitals,t
2g
3
e
g
1
,
dependingon
whichsituationismoreenergeticallyfavorable.
•Iftheoctahedralcrystalfieldsplitting,∆
oct
,issmallerthan
thepairingenergy,thenthefourthelectronwilloccupythe
higherorbital.
•Ifthepairingenergyislessthanthecrystalfieldsplitting,
thenitisenergeticallypreferredforthefourthelectronto
occupythelowerorbital.

76. •Thetwosituationsareshowninfollowingfigure.
•Theresulthavingthegreaternumberofunpaired
electronsiscalledthehigh-spin(orweakfield)situation,
andthathavingthelessernumberofunpairedelectrons
iscalledthelow-spin(orstrongfield)situation.
•Configurationt
2g
4
correspondstoalow-spin
arrangement,andt
2g
3
e
g
1
toahigh-spincase.
Low-spin
High-spin
Figure. The two possible spin situations for the d
4
configuration.
d
4

77. •Thepreferredconfigurationisthatwiththelowerenergy
anddependsonwhetheritisenergeticallypreferableto
pairthefourthelectronorpromoteittothee
g
level.
•Twotermscontributetotheelectron-pairingenergy,P,
whichistheenergyrequiredtotransformtwoelectrons
withparallelspinindifferentdegenerateorbitalsinto
spin-pairedelectronsinthesameorbital:
–Thelossintheexchangeenergywhichoccursupon
pairingtheelectrons
–Thecoulombicrepulsionbetweenthespin-paired
electrons
•Foragivend
n
configuration,theCFSEisthedifference
inenergybetweenthedelectronsinanoctahedralcrystal
fieldandthedelectronsinasphericalcrystalfield
(followingfigure).

78. Figure.The changes in the energies of the electrons occupying the
d orbitals of an M
n+
ion when the latter is in an octahedral crystal
field. The energy changes are shown in terms of the orbital energies.

79. •Toexemplifythis,considerad
4
configuration.
•Inasphericalcrystalfield,thedorbitalsaredegenerate
andeachoffourorbitalsissinglyoccupied.
•Inanoctahedralcrystalfield,followingequationshows
howtheCFSEisdeterminedforahigh-spind
4
configuration.
•Foralow-spind
4
configuration,theCFSEconsistsof
twoterms:thefourelectronsinthet
2g
orbitalsgiverise
toa-1.6∆
oct
term(4x-0.4=-1.6∆
oct
),andapairing
energy,P,mustbeincludedtoaccountforthespin-
pairingoftwoelectrons(-1.6+P).
•Nowconsiderad
6
ion.
•Inasphericalcrystalfield,onedorbitalcontainsspin-
pairedelectrons,andeachoffourorbitalsissingly
occupied.

80. •Ongoingtothehigh-spind
6
configurationinthe
octahedralfield(t
2g
4
e
g
2
),nochangeoccurstothenumber
ofspin-pairedelectronsandtheCFSEisgivenby
followingequation.
•Foralow-spind
6
configuration(t
2g
6
e
g
0
)thesixelectrons
inthet
2g
orbitalsgiverisetoa-2.4∆
oct
term(6x-0.4=-
2.4∆
oct
).
•Addedtothisisapairingenergytermof2Pwhich
accountsforthespinpairingassociatedwiththetwo
pairsofelectronsinexcessoftheoneinthehigh-spin
configuration.
•FollowingtablelistsvaluesoftheCFSEforalld
n
configurationsinanoctahedralcrystalfield.
Important
↓ ↓

81. Table.Octahedral crystal field stabilization energies (CFSE) for d
n
configurations;
pairing energy, P, terms are included where appropriate. High-and low-spin
octahedral complexes are shown only where the distinction is appropriate.

82. •Twopossiblespinconditionsexistforeachofthed
4
,
d
5
,d
6
,andd
7
electronconfigurationsinanoctahedral
environment.
•Thenumberofpossibleunpairedelectrons
correspondingtoeachdelectronconfigurationis
showninfollowingtable,whereh.s.andl.s.indicate
highspinandlowspin,respectively.

83. Table.The d electron configurations and corresponding
number of unpaired electrons for an octahedral
stereochemistry

84. •Followinginequalitiesshowtherequirementsforhigh-
orlow-spinconfigurations.
•Firstinequalityholdswhenthecrystalfieldisweak,
whereassecondexpressionistrueforastrongcrystal
field.
•Followingfiguresummarizesthepreferencesforlow-
andhigh-spind
5
octahedralcomplexes.
Assignment
Q:WhatisthevalueofCFSEforhigh-andlow-spin
octahedralcomplexesincaseofd
4
tod
7
system.Also
calculatethenumberofunpairedelectronsind
9
systemby
consideringCu
2+
ion.
> = Greater than
< = Less than

85. Figure.The occupation of the 3d orbitals in weak and strong field Fe
3+
(d
5
) complexes. Splitting of five d-orbitalsin presence of strong(er) and
weak(er) ligandsin an octahecralcomplex. (a) Five d orbitalsin the free
metal ion (b) Splitting of d-orbitalsin presence of weak(er) ligands(c)
Splitting of d-orbitalsin presence of strong(er) ligands.
xyyzzxx
2
x
2
-y
2
x
2
x
2
-y
2
xyyzzx
xyyzzx
x
2
x
2
-y
2Small
↓
Large
↓
(a)
(b) (c)
High spin
Low spin

86. •Wecannowrelatetypesofligandwithapreferencefor
high-orlow-spincomplexes.
•Strongfieldligandssuchas[CN]
-
favourtheformation
oflow-spincomplexes,whileweakfieldligandssuchas
halidestendtofavourhigh-spincomplexes.
•However,wecannotpredictwhetherhigh-orlow-spin
complexeswillbeformedunlesswehaveaccurate
valuesof∆
oct
andP.
•Ontheotherhand,withsomeexperimentalknowledgein
hand,wecanmakesomecomparativepredictions:
–Ifweknowfrommagneticdatathat[Co(H
2
O)
6
]
3+
is
low-spin,thenfromthespectrochemicalserieswecan
saythat[Co(ox)
3
]
3-
and[Co(CN)
6
]
3-
willbelow-spin.
•Theonlycommonhigh-spincobalt(III)complexis
[CoF
6
]
3-
.

87. Figure.Distribution of d
6
electrons of Co
3+
ion in the
weak-field complex, [CoF
6
]
3-
and strong field
complex, [Co(NH
3
)
6
]
3+
.

88. Coulomb’sLaw
•Energyofinteractionbetweentwochargesq
1
q
2
is
proportionaltotheproductofchargesdividedbythe
distancebetweentherecentres.

89. Assignment
Justifythefollowingstatement:
•However,wecannotpredictwhetherhigh-orlow-spincomplexes
willbeformedunlesswehaveaccuratevaluesof∆
oct
andP.
Ans:
•Supposed
5
system.
•Ifwehavethedataofμ=5.9BM
•Itsmeanthereare5unpairedelectronswhichisonlypossibleifΔ
0
willbesmall.
•Sowecansaythatthegivensystemishigh-spin.
•Ifwehavethedataofμ=1.8BM
•Itsmeanthereisonly1unpairedelectronwhichisonlypossibleif
Δ
0
willbelarge.
•Sowecansaythatthegivensystemislow-spin.

91. How to predict the spin state of a given octahedral
complex ion?
•BycomparingthevaluesofΔ
0
andPofagivenmetallic
ion,thespinstateoftheoctahedralcomplexionformed
bythatmetallicioncanbepredicted.
•Δ
0
tendstoforceasmanyelectronstooccupyt
2g
orbitals
whilePtendstopreventtheelectronstopairint
2g
orbitals.
•Thisdiscussionshowthat:
–WhenΔ
0
<P,theelectronstendtoremainunpaired
andhencehighspin(weak-fieldorspinfree)
octahedralcomplexionsareobtained.
–WhenΔ
0
>P,theelectronstendtopairandhencelow
spin(strong-fieldorspinpaired)octahedralcomplex
ionsareobtained.

92. •ExamplesofsomeHS-andLS-octahedralcomplexesaregivenin
followingtable.
•InthistablethevalueofP(incm
-1
)ofthecentralmetalionofthe
correspondingcomplexdeterminedfromspectroscopicdataand
thatofΔ
0
(incm
-1
)forthecomplexesarealsolisted.
•Fromthistableitmaybeseenthatthespin-stateofthecomplexes
predictedbyCFTisthesameasthatobservedexperimentally.
Conclusion
•IneverycasewhereΔ
0
<P:
–HS-complexisformed
•IneverycasewhereΔ
0
>P:
–LS-complexisformed
> = Greater than
< = Less than

93. Table. Examples of some LS-and HS-octahedral
complexes.

94. Assignment
Q:Inthefollowingconfiguration:
–d
5
–d
6
•For[Mn(H
2
O)
6
]
2+
and[Co(NH
3
)
6
]
3+
predictsthevalueofP(cm
-1
)
andΔ
0
(cm
-1
).
•Determinetheirspin-state,eitherthevalueofspin-stateobserved
experimentallymatchwithpredictedbyCFT.
Ans:
d
5
•[Mn(H
2
O)
6
]
2+
→P(cm
-1
)=25500
→Δ
0
(cm
-1
)=7800
•Spin-state→Observedexperimentally=HS
→PredictedbyCFT=HS
d
6
•[Co(NH
3
)
6
]
3+
→P(cm
-1
)=21000
→Δ
0
(cm
-1
)=23000
•Spin-state→Observedexperimentally=LS
→PredictedbyCFT=LS
Δ
0
> P
Δ
0
< P

95. Splitting of d orbital energies in fields of other
symmetry
Thetetrahedralcrystalfield
•Althoughtheeffectonthed-orbitalsproducedbyafield
ofoctahedralsymmetryhasbeendescribed,wemust
rememberthatnotallcomplexesareoctahedraloreven
havesixligandsbondedtothemetalion.
•Forexample,manycomplexeshavetetrahedral
symmetry,soweneedtodeterminetheeffectofa
tetrahedralfieldonthed-orbitals.
•Followingfigureshowsatetrahedralcomplexthatis
circumscribed(دودحم انرک)inacubewherealternative
cornersarevacant.
•Alsoshownarelobesofthed
z
2
orbitalandtwolobes
(thoselyingalongthex-axis)ofthed
x
2
-y
2
orbital.

96. Figure. A tetrahedral complex
shown with the coordinate
system. Two lobes of the d
z
2
orbital are shown along the z-axis
and two lobes of the d
x
2
-y
2
orbital
are shown along the y-axis.
Figure. Tetrahedral
arrangement of four ligands
(L) around the metal ion
(M
n+
) in tetrahedral complex
ion, [ML
4
]
n+
.

97. •Notethatinthiscasenoneofthed-orbitalswillpointdirectlyatthe
ligands.
•However,theorbitalsthathavelobeslyingalongtheaxes(d
x
2
-y
2
and
d
z
2
)aredirectedtowardapointthatismidwayalongadiagonalofa
faceofthecube.
•Thatpointliesat(2
½
/2)lfromeachoftheligands.
•Theorbitalsthathavelobesprojectingbetweentheaxes(d
xy
,d
yz
,
andd
xz
)aredirectedtowardthemidpointofanedgethatisonlyl/2
fromsitesoccupiedbyligands.
•Theresultisthatthed
xy
,d
yz
,andd
xz
orbitalsarehigherinenergy
thanarethed
x
2
-y
2
andd
z
2
orbitalsbecauseofthedifferenceinhow
closetheyaretotheligands.
•Inotherwords,thesplittingpatternproducedbyanoctahedralfield
isinvertedinatetrahedralfield.
•Themagnitudeofthesplittinginatetrahedralfieldisdesignatedas
Δ
t
,andtheenergyrelationshipsfortheorbitalsareshownin
followingfigure.

98. Summary
•Thedistanceofd
x
2
-y
2
andd
z
2
fromligands=(2.5/2)l
•Thedistanceofd
xy
,d
yz
,andd
xz
fromligands=(l/2)
•Itsmeanthelobesd
x
2
-y
2
andd
z
2
areawayfromligandssohaveless
energywhilethelobesd
xy
,d
yz
,andd
xz
arecomparativelycloseto
ligandssohavegreaterenergy.
•Duetothisfacttheorbitalsareinvertedascomparedtooctahedral
geometry.
d
x
2
-y
2
and d
z
2
orbitals→ less in energy
d
xy
, d
yz
and d
xz
orbitals→ higher in energy

99. Differences between the splitting in octahedral and tetrahedral
fields
•Thereareseveraldifferencesbetweenthesplittinginoctahedraland
tetrahedralfields.
1.Notonlyarethetwosetsoforbitalsinvertedinenergy,butalsothe
splittinginthetetrahedralfieldismuchsmallerthanthatproduced
byanoctahedralfield.
Figure. The orbital splitting pattern in a tetrahedral field that is
produced by four ligands.

101. 2.First,thereareonlyfourligandsproducingthefieldrather
thanthesixligandspresentintheoctahedralcomplex.
3.Second,noneofthed-orbitalspointdirectlyattheligands
inthetetrahedralfield.
•Inanoctahedralcomplex,twooftheorbitalspointdirectly
towardtheligandsandthreepointbetweenthem.
•Asaresult,thereisamaximumenergysplittingeffecton
thed-orbitalsinanoctahedralfield.
•Infact,itcanbeshownthatifidenticalligandsarepresent
inthecomplexesandthemetal-to-liganddistancesare
identical,Δ
t
=(4/9)Δ
o
[Δ
t
=0.45Δ
o
].
•Theresultisthattherearenolow-spintetrahedral
complexesbecausethesplittingofthed-orbitalsisnot
largeenoughtoforceelectronpairing.

102. 4.Third,becausethereareonlyfourligandssurroundingthe
metalioninatetrahedralfield,theenergyofallofthed
orbitalsisraisedlessthantheyareinanoctahedralcomplex.
•Thesubscripts"g"donotappearonthesubsetsoforbitals
becausethereisnocenterofsymmetryinatetrahedral
structure.
Formationoftetragonalfield
•Elongation:Supposewestartwithanoctahedralcomplex
andplacetheligandslyingonthez-axisfartherawayfrom
themetalion.
•Asaresult,thed
z
2
orbitalwillexperiencelessrepulsion,and
itsenergywilldecrease.
•However,notonlydothefived-orbitalsobeya“centerof
energy"rulefortheset,butalsoeachsubsethasacenterof
energythatwouldcorrespondtosphericalsymmetryforthat
subset
.
g is used in O
h
symmetry
mean in octahedral structure

103. •Conservationofenergy:Therefore,ifthed
z
2
orbitalis
reducedinenergy,thed
x
2
-y
2
orbitalmustincreasein
energytocorrespondtoanoverallenergychangeofzero
forthee
g
subset.
•Thed
xz
andd
yz
orbitalshaveaz-componenttotheir
direction.
•Theyprojectbetweentheaxesinsuchawaythatmoving
ligandsonthez-axisfartherfromthemetalionreduces
repulsionoftheseorbitals.
•Asaresult,thed
xz
andd
yz
orbitalshavelowerenergy,
whichmeansthatthed
xy
orbitalhashigherenergyinorder
topreservethecenterofenergy(2)forthet
2g
orbitals.
•Theresultisasetofd-orbitalsthatarearrangedasshown
infollowingfigure.

104. •Withthemetal-to-ligandbondlengthsbeinggreaterinthez-
direction,thefieldisnowknownasatetragonalfieldwith
z-elongation.
•Compression:Iftheligandsonthez-axisareforcedcloser
tothemetaliontoproduceatetragonalfieldwithz-
compression,thetwosetsoforbitalsshownaboveare
inverted.
•Followingfigureshowsthed-orbitalsinthistypeoffield.
Figure. The arrangement of the d
orbitalsaccording to energy in a
field with elongation by moving the
ligandson the z-axis farther from
the metal ion in an octahedral
complex.

105. Figure. The arrangement of d
orbitalsin a field with
compression of the ligands
along the z-axis.

106. Figure.Crystal field splitting diagrams for octahedral (left-hand
side) and tetrahedral (right-hand side) fields. The splittingsare
referred to a common barycentre.
•Followingfigurecomparescrystalfieldsplittingforoctahedral
andtetrahedralfields;remember,thesubscriptginthesymmetry
labelsisnotneededinthetetrahedralcase.

107. •Since∆
tet
issignificantlysmallerthan∆
oct
,tetrahedral
complexesarehigh-spin.
•Also,sincesmalleramountsofenergyareneededforant
2
←
etransition(tetrahedral)thanforane
g
←t
2g
transition
(octahedral),correspondingoctahedralandtetrahedral
complexesoftenhavedifferentcolours.
Chemical and theoretical background
Notation for electronic transitions
•Forelectronictransitionscausedbytheabsorptionand
emissionofenergy,thefollowingnotationisused:
–Emission:(highenergylevel)→(lowenergylevel)
–Absorption:(highenergylevel)←(lowenergylevel)
•Forexample,todenoteanelectronictransitionfromtheetot
2
levelinatetrahedralcomplex,thenotationshouldbet
2
←e.
Tetrahedralcomplexes→onlyhigh-spin

108. ExplainΔ
t
=(4/9)Δ
o
•Incaseofacubicsymmetry,theligandsdonotapproach
anyofthed-orbitalsalongtheorbitalaxis(following
figure).
•Theyjustinteractmorewiththet
2
orbitalslyingmidway
betweencoordinateaxes,directedalongtheedgesofthe
cubethanwitheorbitalspointingtowardsthefaceofthe
cube.
•Hencethet
2
levelsareraised(by4D
q
)whereasthee
levelsarelowered(by6D
q
)tomaintainthebarycentre.
•Itcanbeshownthattheeightligandsinacubic
symmetrywillproduceafieldnearly8/9timesasstrong
asthecorrespondingoctahedralfield,sothat:
(10D
q
)cubic ≈ 8/9(10D
q
)octahedral

109. •Iffourligandsarenowremovedfromthealternative
cornersofthecube,theremainingfourligandsforma
tetrahedralarrangementaroundthecentralatom.
•Thoughtheenergylevelsremainsimilar,thecrystalfield
splittingisreducedtohalf,sothat
(10D
q
)
tet
= 1/2 (10D
q
)cubic ≈ 4/9(10D
q
)
oct
Figure. A cubic and
tetrahedral arrangement of
four ligands(L) around the
metal ion (M
n+
) in tetrahedral
complex ion, [ML
4
]
n+
.
Assignment
Q: Explain Δ
t
= (4/9)Δ
o

110. Formation of square planar complex from octahedral
complex
•Asquareplanararrangementofligandscanbeformallyderived
fromanoctahedralarraybyremovaloftwo trans-ligands
(followingfigure).
Figure.A square planar complex can be derived from an
octahedral complex by the removal of two ligands, e.g. those on
the z-axis; the intermediate stage is a Jahn–Teller distorted
(elongated) octahedral complex.

112. •Ifweremovetheligandslyingalongthez-axis,thenthe
d
z
2
orbitalisgreatlystabilized;theenergiesofthed
yz
and
d
xz
orbitalsarealsolowered,althoughtoasmaller
extent.
•Theresultantorderingofthemetald-orbitalsisshownat
theleft-handsideoffollowingfigure.
Assignment
Q: What will be the splitting of d-orbitalsabout the barycentrein
trigonalbipyramidal?

113. Figure.Crystal field splitting diagrams for some common fields referred
to a common barycentre; splittingsare given with respect to ∆
oct
.
Barycentre

114. Thesquareplanarcrystalfield
[Crystal field splitting of d-orbitalsin tetragonal
(elongated distorted octahedral) and square planar
complexes]
•Beforeconsideringthesplittingofd-orbitalsofthecentral
metalcationinthesecomplexes,weshouldunderstandhow
tetragonallydistortedoctahedralandsquareplanar
geometriesareobtainedfromregularoctahedralgeometry.
a)Regularoctahedralgeometry
•Consideraregular(symmetrical)octahedralcomplex,
[M(L
b
)
4
(L
a
)
2
]inwhichMisthecentralmetalliccation,L
a
aretwotrans-ligands(i.e.,L
a
aretheligandslyingalong
thez-axis)andL
b
arethebasalequotorialligandslyingin
xyplane.
•Inthiscomplexallthesixbonddistances(fourM-L
b
and
twoM-L
a
distances)areequal[followingfigure(a)].

115. Figure.To get tetragonal and square planar geometries from octahedral
geometry.

116. b)Elongateddistortedoctahedral(tetragonal)shape
•NowiftwoL
a
ligandsaremovedslightlylongerfromthe
centralmetalcation,MsothateachofthetwoM-L
a
distancesbecomesslightlylongerthaneachofthefourco-
planarM-L
b
distances,thesymmetricalshapeof
octahedralcomplexgetsdistortedandbecomesdistorted
octahedralshape[abovefigure(b)].
•Inthisshape,sincethetwotrans-ligandhaveelongated,
thedistortedoctahedralshapeisalsocalledelongated
distortedoctahedralshape.
•Obviouslytheelongationoftwotrans-ligandstakesplace
along+zand-zaxes.
•Elangateddistortedoctahedralgemoetryisalsocalled
tetragonallydistortedoctahedralshapeorsimply
tetragonalshape.

117. c)Squareplanargeometry
•NowifthetwoL
a
ligandsarecompletelyremovedaway
fromthez-axis,thetetragonallydistortedoctahedralshape
becomessquareplanarwhichisafour-coordinated
complex[abovefigure(c)].
Splittingofd-orbitalsfromregularoctahedralgeometry
tosquareplanargeometry
•Nowinordertoconsiderthesplittingofd-orbitalsin
elongateddistortedoctahedralandsquareplanar
complexes,westartwiththesplittingofd-orbitalsin
octahedralcomplexes.
•Wehavealreadyseenthatinoctahedralcomplexes,the
energyofd
xy
,d
yz
,andd
zx
orbitals(t
2g
orbitals)isdecreased
whilethatofd
z
2
andd
x
2
-y
2
orbitals(e
g
orbitals)isincreased
[followingfigure(b)].

119. •Nowinelongateddistortedoctahedralcomplex,sincethe
distanceofthetrans-ligands(L
a
ligands)isincreasedfrom
thecentralmetalionbyremovingthemawayalongthez-
axis,d-orbitalsalongthez-axis(i.e.,d
z
2
orbital),d-orbital
inyzplane(i.e.d
yz
orbital)andd-orbitalinzxplane(i.e.
d
zx
orbital)experiencelessrepulsionfromtheligandsthan
theydointheoctahedralcomplexwhilethed-orbitalsin
xyplane(i.e.,d
xy
andd
x
2
-y
2
orbitals)experiencemore
repulsionthantheydointheoctahedralcomplex.
•Consequentlytheenergyofd
z
2
,d
yz
andd
zx
orbitals
decreasewhilethatofd
x
2
-y
2
andd
xy
orbitalsincrease
[abovefigure(c)].
•Notethatd
yz
,andd
zx
orbitalsstillremaindegenerateas
theyareintheoctahedralcomplex.

120. •Insquareplanargeometrytheenergiesofd
z
2
,d
yz
andd
zx
orbitalsagainfalldownwhilethoseofd
x
2
-y
2
andd
xy
orbitalsriseup[abovefigure(d)].
•Thusthesplittingofd-orbitalsintovariousorbitalsin
squareplanarcomplexestakesplaceasshownat(d)of
abovefigure.
•Therelativeenergyorderbetweenthevarioussplittedd-
orbitalsinsquareplanarcomplexesisuncertainbutthe
ordershowninabovefigure(d)hasbeenestablishedfor
5d
8
configurationfromspectroscopicdata.
•Theextentofsplittingofd-orbitalsinsquareplanar
complexesdependsonthenatureofthecentralmetalatom
andligands.
•Semi-quantitativecalculationsforsquareplanarcomplexesofCo
2+
(3d
7
),Ni
2+
(3d
8
)andCu
2+
(3d
9
)haveshownthat∆
1
=∆
0
,∆
2
=2/3∆
0
(or0.66∆
0
)and∆
3
=1/12∆
0
(or0.08∆
0
)

121. and hence
Figure.Theorbitalsplitting
parametersforasquare-planar
complex.
ForthesquareplanarcomplexesofPd
2+
(4d
8
)andPt
2+
(5d
8
)
spectroscopicresultshaveshownthat:
forcomplexesofthesamemetalandligandswiththesameM-L
bondlengths.

122. Diamagneticpropertyofd
8
ionshavingsquareplanargeometry
•Theenergyleveldiagramforthed-orbitalsinasquareplanarfieldis
showninfollowingfigure.
•Itcanbeshownthattheenergyseparatingthed
xy
andd
x
2
-y
2
orbitalsis
exactlyΔ
o
,thesplittingbetweenthet
2g
ande
g
orbitalsinanoctahedral
field.
•d
8
ions such as Ni
2+
, Pd
2+
, and Pt
2+
form square planar complexes that are
diamagnetic.
•Fromtheorbitalenergydiagramshowninabovefigure,itiseasytosee
why(followingfigure).
Figure.Energiesofdorbitals
inasquareplanarfield
producedbyfourligands.

123. Figure. The d
8
-orbital energy diagram for the square planar
environment, as derived from the octahedral diagram.

124. •Eightelectronscanpairinthefourorbitalsoflowest
energyleavingthed
x
2
-y
2
availabletoformasetofdsp
2hybridorbitals.
•Ifthedifferenceinenergybetweenthed
xy
andthed
x
2
-y
2
is
notsufficienttoforceelectronpairing,allofthed-orbitals
areoccupied,andacomplexhavingfourbondswouldbe
expectedtoutilizesp
3
hybridorbitals,whichwouldresult
inatetrahedralstructure.
•Thefactthatsquareplanard
8
complexessuchas
[Ni(CN)
4
]
2-
arediamagneticisaconsequenceofthe
relativelylargeenergydifferencebetweenthed
xy
andd
x
2
-y
2
orbitals.
•Thefollowingexampleshowsanexperimentalmeans
(otherthansingle-crystalX-raydiffraction)bywhich
squareplanarandtetrahedrald
8
complexescanbe
distinguished.

125. Assignment
Q:Thed
8
complexes[Ni(CN)
4
]
2-
and[NiCl
4
]
2-
aresquareplanar
andtetrahedralrespectively.Willthesecomplexesbe
paramagneticordiamagnetic?
•Considerthesplittingdiagramsshowninfollowingfigures.
Figure.Crystal field splitting diagrams for octahedral (left-hand
side) and tetrahedral (right-hand side) fields. The splittingsare
referred to a common barycentre.

126. Figure. Crystal field splitting diagrams for some common fields
referred to a common barycentre; splittingsare given with respect
to ∆
oct
.

127. •For[Ni(CN)
4
]
2-
and[NiCl
4
]
2-
,theeightelectronsoccupy
thedorbitalsasfollows:
Thus,[NiCl
4
]
2-
is
paramagneticwhile
[Ni(CN)
4
]
2-
is
diamagnetic.
Although[NiCl
4
]
2-
istetrahedraland
paramagnetic,
[PdCl
4
]
2-
and
[PtCl
4
]
2-
aresquare
planar and
diamagnetic.
Thisdifferenceisaconsequenceofthelargercrystalfieldsplitting
observedforsecondandthirdrowmetalionscomparedwiththeir
firstrowcongener;Pd(II)andPt(II)complexesareinvariablysquare
planar.

128. Factorsaffectingthecrystalfieldsplitting(Δ)
•Theenergy-levelsplittingdependsonfourfactors:
1.Chargeonthemetalion(
Natureofmetalcation
)
•Increasingthechargeonametalionhastwoeffects:
–Theradiusofthemetaliondecreases
–Negativelychargedligandsaremorestronglyattractedtoit
(metal)
•Bothfactorsdecreasethemetal–liganddistance,whichinturn
causesthenegativelychargedligandstointeractmorestrongly
withthed-orbitals.
•Consequently,themagnitudeofΔ
o
increasesasthechargeon
themetalionincreases.
•Typically,Δ
o
foratripositiveionisabout50%greaterthanfor
thedipositiveionofthesamemetal;forexample,for
[V(H
2
O)
6
]
2+
,Δ
o
=11,800cm
−1
;for[V(H
2
O)
6
]
3+
,Δ
o
=17,850
cm
−1
.
Radius → decreases
Ligand(-ve) → strongly attracted

129. •Theinfluenceofthisfactorcanalsobestudiedunderthe
followingfourheading:
Differentchargesonthecationofthesamemetal
•Thecationfromtheatomsofthesametransitionseriesand
havingthesameoxidationstatehavealmostthesamevalueof∆
0
butthecationwithahigheroxidationstatehasalargevalueof∆
0
thanwiththeloweroxidationstate,e.g.,
(a)∆
0
for[Fe
+2
(H
2
O)
6
]
+2
=10,400cm
-1
………3d
6
∆
0
for[Fe
+3
(H
2
O)
6
]
+3
=13,700cm
-1
………3d
5
(b)∆
0
for[Co
+2
(H
2
O)
6
]
+2
=9,300cm
-1
………3d
7
∆
0
for[Co
+3
(H
2
O)
6
]
+3
=18,200cm
-1
………3d
6
•Thiseffectisprobablyduetothefactthatthecentralionwith
higheroxidationstatewillpolarizetheligandsmoreeffectively
andthustheligandswouldapproachsuchacationmoreclosely
thantheycandothecationofloweroxidationstate,resultingin
largersplitting.

130. Differentchargesonthecationofdifferentmetals
•Twodifferentcationshavingthesamenumberofd-electronsand
thesamegeometryofthecomplexbutwithdifferentchargecan
alsobecompared.
•Thecationwithahigheroxidationstatehasalargevalueof∆
0
than
withaloweroxidationstate.
•Forexample,thebehaviortowardsthesameligandofV(II)and
Cr(III),whicharebothd
3
ioncanbecompared.
•Itisobservedthatthevalueof∆
0
in[V
+2
(H
2
O)
6
]
+2
islessthanthat
in[Cr
+3
(H
2
O)
6
]
+3
asisshownbelow:
∆
0
For[V
+2
(H
2
O)
6
]
+2
=12,400cm
-1
……3d
3
∆
0
For[Cr
+3
(H
2
O)
6
]
+3
=17,400cm
-1
……3d
3
•Thisfactcanbeexpressedintermsofthechargeonthecation.
•TheCr
+3
ion,whichhaspositivechargethanV
+2
ion,exertsa
greaterattractionforwatermoleculesthandoestheV
+2
.
•HencethewatermoleculesapproachtheV
+2
ionsoexertastronger
crystalfieldeffectonthed-electronsofCr
+3
ion.

131. Samechargesonthecationbutthenumberofd-electronsis
different
•Incaseofthecomplexeshavingthecationwithsamechargesbut
withdifferentnumberofd-electronsinthecentralmetalcationthe
magnitudeof∆
0
decreaseswiththeincreaseofthenumberofd-
electrons,e.g.,
∆
0
for[Co
+2
(H
2
O)
6
]
+2
=9,300cm
-1
…….3d
7
∆
0
for[Ni
+2
(H
2
O)
6
]
+2
=8,500cm
-1
…….3d
8
•Fromthecombinationofmentionedabovefacts,itcanbe
concludedthat:
–Forthecomplexeshavingthesamegeometryandthesame
ligandsbutdifferentnumberofd-electrons,themagnitudeof∆
0
decreaseswiththeincreaseofthenumberofd-electronsinthe
centralmetalcation(No.ofd-electronsisdirectlyproportionalto
1/∆
0
)
–Incaseofcomplexeshavingthesamenumberofd-electronsthe
magnitudeof∆
0
increaseswiththeincreaseofthecharges(i.e.,
oxidationstate)onthecentralmetalcation(oxidationstateis
directlyproportionalto∆
0
).

132. 2.Theidentityofthemetal
•Thecrystalfieldsplitting,∆,isabout50percentgreaterforthe
secondtransitionseriescomparedtothefirst,whereasthethird
seriesisabout25percentgreaterthanthesecond.
•Thereisasmallincreaseinthecrystalfieldsplittingalongeach
series.
[Δ
o
(3d)<Δ
o
(4d)<Δ
o
(5d)]
Note:ThelargestΔ
o
sarefoundincomplexesofmetalionsfromthe
thirdrowofthetransitionmetalswithchargesofatleast+3and
ligandswithlocalizedlonepairsofelectrons.
3.Theoxidationstateofthemetal
•Generally,thehighertheoxidationstateofthemetal,thegreaterthe
crystalfieldsplitting.
Δ
o
for 2
nd
→ 50% greater then for first transition series
Δ
o
for 3
rd
→ 25% greater then for second transition series

133. •Thus,mostcobalt(II)complexesarehighspinasaresultofthe
smallcrystalfieldsplitting,whereasalmostallcobalt(III)
complexesarelowspinasaresultofthemuchlargersplittingby
the3+ion.
4.Principalquantumnumberofthemetal
•∆
0
increasesabout30%to50%from3d
n
to4d
n
andbythesame
amountagainfrom4d
n
to5d
n
complexes.
•Foraseriesofcomplexesofmetalsfromthesamegroupinthe
periodictablewiththesamechargeandthesameligands,the
magnitudeofΔ
o
increaseswithincreasingprincipalquantum
number:
Δ
o
(3d) < Δ
o
(4d) < Δ
o
(5d)
•Thedataforhexaamminecomplexesofthetrivalentgroup9metals
illustratethispoint:
Co(II) → H.S
Co(III) → L.S
(3d
6
)
(4d
6
)
(5d
6
)

134. •TheincreaseinΔ
o
withincreasingprincipalquantum
numberisduetothelargerradiusofvalenceorbitalsdowna
column.
•Inaddition,repulsiveligand–ligandinteractionsaremost
importantforsmallermetalions.
•Relativelyspeaking,thisresultsinshorterM–Ldistances
andstrongerdorbital–ligandinteractions.
5.Thenumberoftheligands
•Thecrystalfieldsplittingisgreaterforalargernumberof
ligands.
•Forexample,∆
oct
,thesplittingforsixligandsinan
octahedralenvironment,ismuchgreaterthan∆
tet
,the
splittingforfourligandsinatetrahedralenvironment.
If ∆ → greater → large number of ligands
Six ligands→ ∆ should be large
Four ligands→ ∆ should be small

135. •TheincreaseinΔ
o
withincreasingprincipalquantum
numberisduetothelargerradiusofvalenceorbitalsdowna
column.
•Inaddition,repulsiveligand–ligandinteractionsaremost
importantforsmallermetalions.
•Relativelyspeaking,thisresultsinshorterM–Ldistances
andstrongerdorbital–ligandinteractions.
5.Thenumberoftheligands
•Thecrystalfieldsplittingisgreaterforalargernumberof
ligands.
•Forexample,∆
oct
,thesplittingforsixligandsinan
octahedralenvironment,ismuchgreaterthan∆
tet
,the
splittingforfourligandsinatetrahedralenvironment.
If ∆ → greater → large number of ligands
Six ligands→ ∆ should be large
Four ligands→ ∆ should be small

136. 6.Thenatureoftheligands
•Experimentally,itisfoundthattheΔ
o
observedfora
seriesofcomplexesofthesamemetaliondepends
stronglyonthenatureoftheligands.
•Foraseriesofchemicallysimilarligands,themagnitude
ofΔ
o
decreasesasthesizeofthedonoratomincreases.
•Forexample,Δ
o
valuesforhalidecomplexesgenerally
decreaseintheorderF
−
>Cl
−
>Br
−
>I
−
becausesmaller,
morelocalizedcharges,suchasweseeforF
−
,interact
morestronglywiththed-orbitalsofthemetalion.
•Inaddition,asmallneutralligandwithahighlylocalized
lonepair,suchasNH
3
,resultsinsignificantlylargerΔ
o
valuesthanmightbeexpected.
•Becausethelonepairpointsdirectlyatthemetalion,the
electrondensityalongtheM–Laxisisgreaterthanfora
sphericalanionsuchasF
−
.

137. •Theexperimentallyobservedorderofthecrystalfield
splittingenergiesproducedbydifferentligandsiscalled
thespectrochemicalseries.
•Thecommonligandscanbeorderedonthebasisofthe
effectthattheyhaveonthecrystalfieldsplitting.
•Amongthecommonligands,thesplittingislargestwith
carbonylandcyanideandsmallestwithiodide.
•Theorderingformostmetalsis:
Generalguidelinesfororderingtheligands
•Thegeneralguidelinesfororderingtheligandsis:
–Halides<oxygendonors<nitrogendonors<carbondonors
•Thus,foraparticularmetalion,itistheligandthat
determinesthevalueofthecrystalfieldsplitting.

138. •Considerthed
6
iron(II)ion.
•Accordingtocrystalfieldtheory,therearethetwospin
possibilities:highspin(weakfield)withfourunpaired
electronsandlowspin(strongfield)withallelectronspaired.
•Wefindthatthehexaaquairon(II)ion,[Fe(OH
2
)
6
]
2+
,possesses
fourunpairedelectrons.
•Thewaterligands,beinglowinthespectrochemicalseries,
produceasmall∆
oct
;hence,theelectronsadoptahigh-spin
configuration.
•Conversely,thehexacyanoferrate(II)ion,[Fe(CN)
6
]
4-
,isfound
tobediamagnetic(zerounpairedelectrons).
•Cyanideishighinthespectrochemicalseriesandproducesa
large∆
oct
;hence,theelectronsadoptalow-spinconfiguration.
•ThevaluesofΔ
o
listedinfollowingtable(Δillustratethe
effectsofthechargeonthemetalion,theprincipalquantum
numberofthemetal,andthenatureoftheligand.

139. Table. Crystal field splitting energies for some octahedral (Δ
o
)* and
tetrahedral (Δ
t
) transition-metal complexes.

140. 7.Colorsoftransition-metalcomplexes
•Thestrikingcolorsexhibitedby
transition-metalcomplexesarecaused
byexcitationofanelectronfroma
lower-energydorbitaltoahigher-energy
dorbital,whichiscalledad–dtransition
(followingfigure).
•Foraphotontoeffectsuchatransition,
itsenergymustbeequaltothedifference
inenergybetweenthetwodorbitals,
whichdependsonthemagnitudeofΔ
o
.
Figure.A d–d Transition. In a d–d transition, an electron in one
of the t
2g
orbitalsof an octahedral complex such as the
[Cr(H
2
O)
6
]
3+
ion absorbs a photon of light with energy equal to
Δ
o
, which causes the electron to move to an empty or singly
occupied e
g
orbital.

141. •Thecolorweobservewhenwelookatanobjectora
compoundisduetolightthatistransmittedorreflected,
notlightthatisabsorbed,andthatreflectedor
transmittedlightiscomplementaryincolortothelight
thatisabsorbed.
•Thusagreencompoundabsorbslightintheredportion
ofthevisiblespectrumandviceversa,asindicatedby
thecolorwheel.

142. •Becausetheenergyofaphotonoflightisinversely
proportionaltoitswavelength,thecolorofacomplex
dependsonthemagnitudeofΔ
o
,whichdependsonthe
structureofthecomplex.
•Forexample,thecomplex[Cr(NH
3
)
6
]
3+
hasstrong-field
ligandsandarelativelylargeΔ
o
.
•Consequently,itabsorbsrelativelyhigh-energyphotons,
correspondingtoblue-violetlight,whichgivesitayellow
color.
•Arelatedcomplexwithweak-fieldligands,the
[Cr(H
2
O)
6
]
3+
ion,absorbslower-energyphotons
correspondingtotheyellow-greenportionofthevisible
spectrum,givingitadeepvioletcolor.
•Wecannowunderstandwhyemeraldsandrubieshave
suchdifferentcolors,eventhoughbothcontainCr
3+
inan
octahedralenvironmentprovidedbysixoxideions.

143. •Althoughthechemicalidentityofthesixligandsisthesamein
bothcases,theCr–Odistancesaredifferentbecausethe
compositionsofthehostlatticesaredifferent(Al
2
O
3
inrubies
andBe
3
Al
2
Si
6
O
18
inemeralds).
•Inruby,theCr–Odistancesarerelativelyshortbecauseofthe
constraintsofthehostlattice,whichincreasesthedorbital–
ligandinteractionsandmakesΔ
o
relativelylarge.
•Consequently,rubiesabsorbgreenlightandthetransmittedor
reflectedlightisred,whichgivesthegemitscharacteristiccolor.
Inemerald,theCr–Odistancesarelongerduetorelativelylarge
[Si
6
O
18
]
12−
silicaterings;thisresultsindecreaseddorbital–
ligandinteractionsandasmallerΔ
o
.
•Consequently,emeraldsabsorblightofalongerwavelength
(red),whichgivesthegemitscharacteristicgreencolor.
•Itisclearthattheenvironmentofthetransition-metalion,which
isdeterminedbythehostlattice,dramaticallyaffectsthe
spectroscopicpropertiesofametalion.

144. Gem-quality crystals of ruby and emerald.
The colors of both minerals are due to the presence of small amounts of Cr
3+
impurities in octahedral sites in an otherwise colorless metal oxide lattice.
Emerald (درمز)Ruby (توقاي)

145. Limitationsofcrystalfieldtheory
•Crystalfieldtheoryissurprisinglyusefulwhenoneconsidersits
simplicity.
•However,ithaslimitations.
•CFTconsidersonlythemetaliond-orbitalsandgivesno
considerationatalltoothermetalorbitalssuchass,p
x
,p
y
andp
z
orbitalsandligandπ-orbitals.
•Therefore,toexplainallthepropertiesofthecomplexes
dependentontheπ-ligandorbitalswillbeoutsidethescopeof
CFT.
•CFTdoesnotconsidertheformationofπ-bondingincomplexes.
•Althoughwecaninterpretthecontrastingmagneticpropertiesof
high-andlow-spinoctahedralcomplexesonthebasisofthe
positionsofweak-andstrong-fieldligandsinthespectrochemical
series,crystalfieldtheoryprovidesnoexplanationastowhy
particularligandsareplacedwheretheyareintheseries.

146. •CFTisunabletoaccountsatisfactorilyfortherelativestrengthsof
ligands,e.g.,itgivesnoexplanationastowhyH
2
Oappearsinthe
spectrochemicalseriesasastrongerligandthanOH
-
.
•AccordingtoCFT,thebondbetweenthemetalandligandis
purelyionic.
•Itgivesnoaccountofthepartlycovalentnatureofthemetal-
ligandbonds.
•Thustheeffectsdirectlydependentoncovalencycannotbe
explainedbyCFT.

147. Applicationsofcrystalfieldtheory
•Thefollowingpropertiesoftransitionmetalcomplexescanwillbe
explainedonthebasisofCFT.
•UsesofCFSEvalues
•WiththehelpofCFT,wehavecalculatedtheCFSEvaluesford
x
configurationofthecentralmetalioninoctahedralandinhighspin
tetrahedralcomplexes.
•WiththehelpofCFSEvalueswecanexplainthefollowing:
1.Crystalstructureofspinels
•Mixedoxidesofthegeneralformula,A
2+
B
2
3+
O
4
arecalledspinals
afterthenameofthemineralspinel,MgAl
2
O
4
ionsmaybeof
differentmetalsorofthesamemetal.
•Inspinalsoxygenatomarearrangedinacubicclose-packed
lattice.
•Insuchlatticeseachoxygenatomhas12otheroxygenatoms
equidistantfromitandtheholesbetweenoxygenatomsareoftwo
types:

148. •Octahedralholeswhicharesocalledbecausetheseare
surroundedbysixoxygenatoms.Thereisoneofsuchholesfor
eachoxygenatom.
•Tetrahedralholeswhicharesocalledsincetheseare
surroundingbyfouroxygenatoms.Thesearetwosuchholes
foreachoxygenatoms.Thesearesmallerthentheoctahedral
holes.Therearetwiceasmanytetrahedralholesasthereare
octahedralholes.Thecationsoccupytheoctahedraland
tetrahedralholes,sincethesearelargeenoughtobefilledby
cations.
•SpinalsofA
2+
B
2
3+
O
4
typeareclassifiedasnormalorsimpleand
inversespinals.
•InnormalspinelsalltheA
2+
cationsoccupyoneoftheeight
availabletetrahedralholesandallB
3+
cationsoccupyhalfofthe
availableoctahedralholes.
•NormalspinelsarerepresentedasA
2+
[B
2
3+
]O
4.
•Thisrepresentationshowsthatthecationsoutsidethebracketoccupythe
tetrahedralholesandcationsinsidethebracketoccupytheoctahedralholes.

149. •ExamplefornormalspinelsareMg
2+
[Cr
2
3+
]O
4
,Ni
2+
[Cr
2
3+
]O
4,
Mn
3
O
4
orMn
2+
[Mn
2
3+
]O
4
etc.
•IninversespinelsalltheA
2+
andhalfoftheB
2
3+
cationsarein
octahedralandtheotherhalfoftheB
3+
cationsareintetrahedral
holes.
•InversespinelsarerepresentedasB
3+
[A
2+
B
3+
]O
4.
•Thisformulationshowsthatthetetrahedralholesareoccupiedby
halfoftheionsB
3+
andtheoctahedralholesareoccupiedbyA
2+
IonsandtheremaininghalfB
3+
ions.
•ExamplesofinversespinalsareCuFe
2
O
4
orFe
3+
[Cu
2+
Fe
3+
]O
4
etc.
•NowletusseehowCFThelpsinpredictingthestructureof
spinels.
•ForexamplewiththehelpofCFTitcanbeshownwhytheoxide
Mn
3
O
4
orMn
2+
[Mn
2
3+
]O
4
isanormalspinelwhiletheoxideFe
3
O
4
orFe
2+
[Fe
2
+3
]O
4
isaninversespinel.
•CFSEvaluesinoctahedralandtetrahedralfieldshavebeenused
forinterpretation.

150. •Forthisitisassumedthattheoxideions,O
2-
,likewatermolecules,
produceweakfield.
•CFSEvalues(intermsof∆
0
)inoctahedralandtetrahedralweak
ligandfieldaregivenbelow:
•ItisobviousthatforMn
3+
(d
4
)andFe
2+
(d
6
)ionstheCFSEvalues
aregreaterforoctahedralthanfortetrahedralsites.
•ThusMn
3+
andFe
2+
ionswillpreferentiallyoccupytheoctahedral
sites,maximizingtheCFSEvaluesofthesystem.
•HenceinMn
3
O
4
alltheMn
3+
ionsoccupyoctahedralsatesandall
Mn
2+
ionsareinthetetrahedralsites,i.e.,itisanormalspineland
itsstructureis,therefore,representedasMn
2+
[Mn
2
3+
]O
4
.
•InFe
3
O
4
alltheFe
2+
ionsandhalfoftheFe
3+
ionsareinthe
octahedralsites,whiletheremaininghalfofFe
3+
ionsoccupy
tetrahedralsitesthusitisaninversespinelandis,therefore
representedasFe
3+
[Fe
2+
Fe
3+
]O
4
.

151. 2.Stabilizationofoxidationstates
•CFSEvaluesalsoexplainwhycertainoxidationstatesare
preferentiallystabilizedbycoordinatingwithcertainligands.
•Thefollowingtwoexamplesillustratethisuse:
•AlthoughH
2
Omoleculewhichisaweakligandshouldbe
expectedtocoordinatewithCo
2+
andCo
3+
ionstoformthehigh-
spinoctahedralcomplexesviz.[Co(H
2
O)
6
]
2+
respectively,
experimentsshowthatH
2
OstabilisesCo
2+
ionandnotCo
3+
,i.e.,
[Co(H
2
O)
6
]
2+
ismorestablethan[Co(H
2
O)
6
]
3+
.
•ThisisbecauseofthefactthatCo
2+
hasamuchhighervalueof
CFSEinweakoctahedralconfiguration(CFSE=0.8∆
0
)thanCo
3+
inthesameconfiguration(CFSE=0.4∆
0
).
•IfweconsiderthecoordinationofNH
3
moleculeswithCo
2+
and
Co
3+
ions,itmybeseenthatNH
3
whichisastrongligand
stabilisesCo
2+
ionbyforming[Co(NH
3
)
6
]
3+
ratherthanCo
2+
ions.
•ThisisbecauseofthefactthatCo
3+
ionhasmuchhighervaluesof
CFSEinstrongoctahedralconfiguration(CFSE=2.4∆
0
)than
Co
3+
inthesameconfiguration(CFSE=1.8∆
0
).

152. 3.Stereochemistryofcomplexes
•(a)CFSEvaluesalsopredictwhyCu
2+
ionformssquareplanar
complexesratherthantetrahedraloroctahedralcomplexesinboth
thefield.
•ThisisbecauseofthereasonthatCu
2+
hasamuchhigherCFSE
valueinasquareplanarconfiguration(CFSE=1.22∆
0
)thanin
octahedralortetrahedralconfiguration(CFSE=0.18∆
0
).
•(b)MostofthefourcoordinatedcomplexesofNi
2+
aresquare
planarratherthantetrahedral[(NiX
4
)
2-
isanexception,X=Cl
-
,
Br
-
,I
-
].ThisisbecauseCFSEvaluesofd
8
ionarehigherinsquare
planarconfiguration(=1.45∆
0
)thanthoseofthesameionin
tetrahedralconfiguration(=0.36∆
0
).
4.Otherapplication
•WiththehelpofCFT,wecanfindout.
•Thenumberofunpairedelectrons(n)inthecentralmetalionofa
givencomplexionandhencethevalueofmagneticmoment(μ)of
theion.μisgivenby:
•Thus,forn=0,μ=0.0(diamagnetic)

153. n = 1,µ = 1.73 B.M
n = 2, µ = 2.83 B.M
n = 3, µ = 3.87 B.M
n = 4,µ = 4.90 B.M
n = 5, µ = 5.92 B.M
•(Where B.M. = Bohr Magneton, it is unit of magnetic moment)
•Whether the given complex ion is LS.
•Whether the given complex ion is paramagnetic or diamagnetic.

154. Experimentalevidenceformetal-ligandcovalentbonding
incomplexes
•Thefollowingevidenceshavebeenpresentedtoshowthe
metal-ligandcovalentbondingincomplexes.
Electronspinresonancespectra
•MostdirectevidenceisobtainedfromESRspectrumof
complexes,e.g,.ESRspectrumof[Ir
IV
Cl
6
]
2-
ionshowsthat
ithasacomplexpatternofsub-bandswhichiscalledthe
hyperfinestructure.
•Thehyperfinestructurehasbeenexplainedbyassumingthat
certainoftheiridiumorbitalsandcertainorbitalsofthe
surroundingCl
-
ionsoverlaptosuchasextentthatthesingle
unpairedd-electronisnotlocalizedentirelyonthemetalion
butinsteadisabout5%localizedoneachCl
-
ion.
•Suchstudyofothercomplexesalsogivessimilarresults.

155. Nuclearmagneticresonance(NMR)
•NMRstudiesofcomplexeslikeKMnF
3
andKNiF
3
show
thatthemetalt
2g
ande
g
electronspassafractionoftime
aroundtheFlourinenuclei.
Nuclearquadrupoleresonance(NQR)
•TheNQRspectrumofsomeofthesquareplanarcomplexes
ofPt(II)Pd(II)suchas(Pt
2
X
4
)
2-
and(Pd
2
X
4
)
2-
suggestthat
thereisconsiderableamountofcovalencyinthemetal-
ligandbond(i.e.,Pt-XorPd-Xbonds).
•Theunusuallylargeabsorptionbandintensitiesobserved
fortetrahedralcomplexeslike[Co
II
Cl
4
]
2-
havebeen
explainedbysayingthatthemetal-ligandbondshave
appreciablecovalentcharacter.

156. ComparisonBetweenVBTandCFT
•Thepointsshowingthecomparisonbetweenthetwotheoriesare
givenbelow:
•TheinnerorbitaloctahedralcomplexesofVBTarethesameas
thespin-pairedorlow-spinoctahedralcomplexesofCFT.
•Similarlyouter-orbitalcomplexesofVBTarethesameasthe
spin-freeorhigh-spinoctahedralcomplexesofCFT.
•Intheformationofsomeinner-orbitaloctahedralcomplexesof
VBT,thepromotionofanelectronfromd-orbitaltos-orbitalis
required,whileintheformationofspin-pairedoctahedral
complexesofCFTnosuchpromotionisrequired.
•AccordingtoVBT,themetal-ligandbondingincomplexesis
onlycovalent,sinceVBTassumesthatligandelectronsare
donatedtothevacantd-orbitalsonthecentralcation.
•Ontheotherhand,CFTconsidersthebondingtobeentirely
electrostatic.Thus,CFTdoesnotallowtheligandelectronsto
enterthemetald-electrons.

157. Assignments
Assignment-1
•Forthecomplexion[Fe(Cl)
6
]
3-
determinethenumberofd
electronsforFe,sketchthed-orbitalenergylevelsandthe
distributionofdelectronsamongthem,listthenumberof
loneelectrons,andlabelwhetherthecomplexis
paramagneticordiamagnetic.
Solution
Step1
•DeterminetheoxidationstateofFe.
•HereitisFe
3+
.
•Basedonitselectronconfiguration,Fe
3+
has5d-electrons.
Step2
•Determinethegeometryoftheion.
•Hereitisanoctahedralwhichmeanstheenergysplitting
shouldlooklike:
Fe
3+
: 1s
2
2s
2
2p
6
3s
2
3p
6
3d
5

158. Step3
•Determinewhethertheligandinducesisastrongorweak
fieldspinbylookingatthespectrochemicalseries.
•Cl
-
isaweakfieldligand(i.e.,itinduceshighspin
complexes).
•Therefore,electronsfillallorbitalsbeforebeingpaired.

159. Step4
•Countthenumberofloneelectrons.
•Here,thereare5electrons.
Step5
•Thefiveunpairedelectronsmeansthiscomplexion
isparamagnetic(andstronglyso).

160. Assignment-2
•Foreachcomplex,predictitsstructure,whetheritishighspinor
lowspin,andthenumberofunpairedelectronspresent.
–[CoF
6
]
3−
–[Rh(CO)
2
Cl
2
]
−
•Given:Complexes
•Askedfor:Structure,highspinversuslowspin,andthenumberof
unpairedelectrons
•Strategy:
•A:Fromthenumberofligands,determinethecoordinationnumber
ofthecompound.
•B:Classifytheligandsaseitherstrongfieldorweakfieldand
determinetheelectronconfigurationofthemetalion.
•C:PredicttherelativemagnitudeofΔ
o
anddecidewhetherthe
compoundishighspinorlowspin.
•D:Placetheappropriatenumberofelectronsinthedorbitalsand
determinethenumberofunpairedelectrons.

161. Solution:
1.A:Withsixligands,weexpectthiscomplextobe
octahedral.
•B:Thefluorideionisasmallanionwithaconcentrated
negativecharge,butcomparedwithligandswithlocalized
lonepairsofelectrons,itisweakfield.Thechargeonthe
metalionis+3,givingad
6
electronconfiguration.
•C:Becauseoftheweak-fieldligands,weexpecta
relativelysmallΔ
o
,makingthecompoundhighspin.
•D:Inahigh-spinoctahedrald
6
complex,thefirstfive
electronsareplacedindividuallyineachofthedorbitals
withtheirspinsparallel,andthesixthelectronispairedin
oneofthet
2g
orbitals,givingfourunpairedelectrons.

162. 2.A:Thiscomplexhasfourligands,soitiseithersquare
planarortetrahedral.
•BandC:Becauserhodiumisasecond-rowtransition
metalionwithad
8
electronconfigurationandCOisa
strong-fieldligand,thecomplexislikelytobesquare
planarwithalargeΔ
o
,makingitlowspin.Becausethe
strongestd-orbitalinteractionsarealongthexandyaxes,
theorbitalenergiesincreaseintheorderd
z
2
,d
yz
,andd
xz
(thesearedegenerate);d
xy
;andd
x
2
−y
2
.
•D:Theeightelectronsoccupythefirstfourofthese
orbitals,leavingthed
x
2
−y
2
orbitalempty.Thusthereareno
unpairedelectrons.

163. Assignment-3
•Foreachcomplex,predictitsstructure,whetheritis
highspinorlowspin,andthenumberofunpaired
electronspresent.
–[Mn(H
2
O)
6
]
2+
–[PtCl
4
]
2−
Answer
[Mn(H
2
O)
6
]
2+
–Octahedral
–Highspin
–Fiveunpairedelectrons
[PtCl
4
]
2−
•Squareplanar
•Lowspin
•Nounpairedelectrons
Mn
2+
=1s
2
2s
2
2p
6
3s
2
3p
6
3d
5
Pt = [Xe] 6s
1
4f
14
5d
9
Pt
2+
= [Xe] 4f
14
5d
8