Valence Bond Theory

Valence Bond Theory

1. Valence Bond Theory
(VBT)

2. Natureofmetal-ligandbondingincomplexcompounds
•WehavealreadysaidthatWernerwasthefirsttoexplainthenature
ofbondingincomplexcompounds.
•However,withtheadvancementoftheoriesofvalence,modem
theorieshavebeenproposedtoexplainthenatureofmetal-ligand
bondingincomplexes.
•Thesetheoriescanalsoexplainthe:
–Colour
–Geometry
–Magneticproperties
ofthecomplexcompounds.
•Thesemodemtheoriesare:
–ValenceBondTheory,VBT(duetoL.PaulingandJL.Slater,
1935)
–CrystalFieldTheory,CFT(duetoH.Brethe,1929andVanVleck,
1932)
–LigandFieldTheory,LFTorMolecularOrbitalTheory,MOT(due
toIVanVleck,1935).
•Hereweshalldiscussonlyvalencebondtheoryandcrystalfieldtheory.

3. ValenceBondTheory,VBT
•ThistheoryismainlyduetoPauling.
•Itdealswiththeelectronicstructureofthecentralmetalioninits
groundstate,kindofbonding,geometryandmagneticpropertiesof
thecomplexes.
Assumptionsofvalencebondtheory
•Thistheoryisbasedonthefollowingassumptions:
1.Thecentralmetalatomorion(asthecasemaybe)makesavailablea
numberofemptys,panddatomicorbitalsequaltoitscoordination
number.
•Thesevacantorbitalshybridisetogethertoformhybridorbitals
whicharethesameinnumberastheatomicorbitalshybridising
together.
•Thesehybridorbitalsarevacant,equivalentinenergyandhave
definitegeometry.
•Importanttypesofhybridisationoccuringinthefirstrowtransition
metal(3dmetals)complexesandthegeometryofthecomplexesare
giveninfollowingtable.

5. 2.Theligandshaveatleastoneσ-orbitalcontainingalonepairof
electrons.
3.Vacanthybridorbitalsofthemetalatomorionoverlapwiththe
filled(containinglonepairofelectrons)σ-orbitalsoftheligandsto
formligand→metalσ-bond(representedas
•Thisbondwhichisgenerallyknownascoordinatebondisaspecial
typeofcovalentbondandshowsthecharacteristicsofboththe
overlappingorbitals.
•However,italsopossessesaconsiderableamountofpolarity
becauseofthemodeofitsformation.
4.Thenon-bondingelectronsofthemetalatomorionarethen
rearrangedinthemetalorbitals(viz.pured,sorporbitalsasthe
casemaybe)whichdonotparticipateinformingthehybridorbitals.
•Therearrangementofnon-bondingelectronstakesplaceaccording
toHund'srule.

6. Geometryof6-coordinatedcomplexions
•Examplesof6-coordinatedcomplexionsformedbysometransition
metalsaregiveninfollowingtable.
•Inallthesecomplexionsthecoordinationnumberofthecentral
metalatomorionissixandhencethesecomplexionshave
octahedralgeometry.
•Thisoctahedralgeometryarisesduetod
2
sp
3
orsp
3
d
2
hybridisation
ofthecentralmetalatomorion.
•Whattypeofhybridisation(i.e.,whethersp
3
d
2
ord
2
sp
3
)willoccur
dependsonthenumberofunpairedorpairedelectronspresentin
thecomplexion.
•d
2
sp
3
orsp
3
d
2
hybridisationisalsocalledoctahedralhybridization.
•Octahedralcomplexesinwhichthecentralatomisd
2
sp
3
hybridised
arecalledinner-orbitaloctahedralcomplexeswhiletheoctahedral
complexesinwhichthecentralatomissp
3
d
2
hybridisedarecalled
outer-orbitaloctahedralcomplexes.
•Nowletusseehowd
2
sp
3
/sp
3
d
2
hybridisationtakesplacein
octahedralcomplexes.

7. d
2
sp
3
Hybridizationininnerorbitaloctahedralcomplexes
•Thistypeofhybridisationtakesplaceinthoseoctahedral
complexeswhichcontainstrongligands.
•Onthebasisoftheorientationofthelobesofd-orbitalsinspace,
theseorbitalshavebeenclassifiedintotwosetsviz.t
2g
ord
ε
ande
g
ord
r
.
•t
2g
setconsistsofd
xy
,d
yz
,andd
zx
orbitalswhilee
g
sethasd
z
2
and
d
x
2
-
y
2
orbitals.
•Intheformationofsixd
2
sp
3
hybridorbitals,two(n-1)d-orbitals
ofe
g
set[i.e.,(n-1)d
z
2
and(n-1)d
x
2
-
y
2
orbitals],onensandthree
np(np
x
,np
y
andnp
z
)orbitalscombinetogetherandformsixd
2
sp
3
hybridorbitals.
•Thusweseethatthetwod-orbitalsusedind
2
sp
3
hybridisationarefrom
penultimateshell[i.e.(n-1)
th
shell]whilesandthreep-orbitalsarefrom
ultimateshell(i.e.,nthshell).
•Thisdiscussionshowsthatincaseofoctahedralcomplexionsof3d
transitionserieselements,twod-orbitalsusedind
2
sp
3
hybridisationare
3d
z
2
and3d
x
2
-
y
2
orbitals(e
g
setoforbitals)whiles-andp-orbitalsare4s
and4porbitals.

8. •Thusd
2
sp
3
hybridisationtakingplaceinsuchcomplexescanbe
representedas3d
x
2
-y
2
.3d
z
2
.4s.4p
x
.4p
y
.4p
z
(d
2
sp
3
).
•Sincetwod-orbitalsusedind
2
sp
3
hybridisationbelongtoinner
shell[i.e.,(n-1)
th
shell],theoctahedralcomplexcompounds
resultedfromd
2
sp
3
hybridisationarecalledinnerorbitaloctahedral
complexes.
•Sincethesecomplexeshavecomparativelylessernumberof
unpairedelectronsthantheouter-orbitaloctahedralcomplexes(see
lateron),thesecomplexesarealsocalledlowspinorspinpaired
octahedralcomplexes.
•Itisduetothepresenceofstrongligandsininner-orbitaloctahedral
complexesof3dtransitionseriesthattheelectronspresentin3d
z
2
and3d
x
2
-y
2
orbitals(e
g
set)areforcedtooccupy3d
xy
,3d
yz
,and3d
xz
orbitals(t
2g
set)andthus3dorbitalsofe
g
setbecomevacantand
hencecanbeusedin3d
x
2
-y
2
.3d
z
2
.4s.4p
x
.4p
y
.4p
z
(d
2
sp
3
)
hybridisation.
•Nowletusdiscussthestructureofsomeoctahedralcomplexionsof
3dtransitionserieselementswhichresultfromd
2
sp
3
hybridisation.

9. 1.Ferricyanideion,[Fe(CN)
6
]
3-
[Alsocalledhexacynoferrate
(III)ion]
•InthisionthecoordinationnumberofFeissixandhencethe
givencomplexionisoctahedralinshape.
•Inthision,FeispresentasFe
3+
ionwhosevalence-shell
configurationis3d
5
ort
3
2g
e
2
g
(Fe=3d
6
4s
2
4p
0
,Fe
3+
=3d
5
=
t
3
2g
e
2
g
)asshowninfollowingfigure.
•AccordingtoHund'srule,eachofthefiveelectronsin3d
orbitalsisunpairedinfreeFe
3+
ion(uncomplexedion)and
hencethenumberofunpairedelectrons(n)isequalto5.
•However,magneticstudyof[Fe(CN)
6
]
3-
ionhasshownthat
thisionhasoneunpairedelectron(n=1)andhenceis
paramagnetic.
•Thus,intheformationofthision,twoelectronsofe
g
setof3d
orbitals(i.e.,3d
z
2
and3d
x
2
-y
2
orbitals)pairupwiththethree
electronsoft
2g
setoforbitals(i.e.,3d
xy
,3d
yz
and3d
zx
orbitals).

10. •Thisresultsinthate
g
setoforbitalsbecomesvacantandis
usedind
2
sp
3
hybridisation.
•Thisalsoresultsinthatthevalence-shellconfigurationofFe
3+
iongetschangedfromt
3
2g
e
2
g
tot
5
2g
e
0
g
andthusthenumberof
unpairedelectronsin3dorbitalnowbecomesequalto1.
•Now3d
x
2
-y
2
,3d
z
2
(e
g
set),4sandthree4p(4p
x
,4p
y
and4p
z
orbitalscombinetogetherandgiverisetotheformationofsix
3d
z
2
.3d
x
2
-y
2
.4s.4p
x
.4p
y
.4p
z
hybridorbitals(d
2
sp
3
hybridisation).
•Eachofthesehybridorbitalsisvacant.
•EachofthesixCN
-
ions(ligands)donatesitslonepairof
electronstod
2
sp
3
hybridorbitalsandsix coordinate
bondsareestablished.
•Theabovediscussionshowsthat[Fe(CN)
6
]
3-
ionhasoneunpaired
electronandhenceisparamagnetic.
•Itisaninnerorbitaloctahedralcomplexion,sinceitisformedby
d
2
sp
3
hybridisation.

12. 2.Ferrocyanideion,[Fe(CN)
6
]
4-
[Alsocalledhexacyanoferrate(II)
ion]
•Inthision,sincethecoordinationnumberofFeissix,thegiven
complexionhasoctahedralgeometry.
•Inthision,FeispresentasFe
2+
ionwhosevalence-shell
configurationis3d
6
4s
0
4p
0
ort
4
2g
e
2
g
4s
0
4p
0
whichshowsthatFe
2+
ionhas4unpairedelectrons.
•Magneticstudieshave,however,shownthatthegivencomplexion
isdiamagneticandhenceithasnounpairedelectrons(n=0).
•Henceinordertogetalltheelectronsinthepairedstate,two
electronsofe
g
orbitalsaresenttot
2g
orbitalssothatnbecomes
equaltozero.
•SinceCN
-
ions(ligands)arestrongligands,theyarecapableof
forcingthetwoelectronsofe
g
orbitalstooccupyt
2g
orbitalsandthus
makealltheelectronspaired.
•Nowfortheformationof[Fe(CN)
6
]
4-
ion,two3dorbitalsofe
g
set,
4sorbital(oneorbital)andthree4porbitals(allthesesixorbitalsare
vacantorbitals)undergod
2
sp
3
hybridisation(seefollowingfigure).

13. •Itisduetod
2
sp
3
hybridisationthat[Fe(CN)
6
]
4-
ionisaninnerorbital
octahedralcomplexion.
•TheelectronpairdonatedbyCN
-
ion(ligand)isaccommodatedineachof
thesixd
2
sp
3
hybridorbitalsasshowninfollowingfigure.

14. 3.Pentacyanonitrosylferrate(II)ion,[Fe
2+
(CN)
5
(NO
+
)]
2-
(Also
callednitroprussideion)
•SincethecoordinationnumberofFeissix,thegivenionhas
octahedralgeometry.
•Pauling(1931)andSidgwick(1935)havesuggestedthatNOis
presentasNO
+
ion(nitrosylion)whichisatwo-electrondonor.
•NO
+
ionisobtainedwhenNOmolecule(5+6=11electrons)
losesitsunpairedelectronresidinginitsπ*
y
molecularorbital
[MolecularorbitalconfigurationofNOmoleculeis(σ
b
2s
)
2
(σ*
2s
)
2
(σ
b
x
)
2
(π
b
y
)
2
(π
b
z
)
2
(π*
y
)
1
.Thusmolecularorbitalconfigurationof
NO
+
ion(5+6-1=10electrons)is(σ
b
2s
)
2
(σ*
2s
)
2
(σ
b
x
)
2
(π
b
y
)
2
(π
b
z
)
2
(π*
y
)
0
.
•ThepresenceofNO
+
ioninthegivencomplexionindicatesthat
FeispresentasFe
2+
ion(Fe
2+
=3d
6
4s
0
=t
4
2g
e
2
g
4s
0
havingn=
0).
•Magneticmomentvalueof[Fe(CN)
5
(NO)]
2-
ionhasshownthat
thegivenionhasnounpairedelectron(n=0)andhenceis
diamagnetic.

15. •Inordertoaccountforitsdiamagneticcharacter,itisassumed
thatthetwoelectronsofe
g
orbitalsareforcedtooccupythet
2g
orbitalssothatwehavealltheelectronsinthepairedstateand
two3dorbitalsofe
g
setbecomevacantandhenceavailablefor
d
2
sp
3
hybridisation.
•Thusthegivenionresultsfromd
2
sp
3
hybridisationandhenceis
inner-orbitaloctahedralcomplexion(seefollowingfigure).

17. 4.Cobalticnitriteion,[Co(NO
2
)
6
]
3-
[Alsocalledhexanitrocobaltate
(III)ion]
•ItisevidentfromthefactthatsincethecoordinationnumberofCo
3+
ionis6,thegivencomplexionhasoctahedralgeometry.
•Magneticstudieshaveshownthatthegivencomplexionhasno
unpairedelectronsandhencetheionisdiamagnetic.
•Itisduetodiamagneticcharacterthatallthesixelectronsofthe
valenceshellofCo
3+
ion(Co
3+
=3d
6
4s
0
4p
0
ort
4
2g
e
2
g
4s
0
4p
0
)are
pairedint
2g
setoforbitalsande
g
setbecomesvacant,i.e.,the
configurationofCo
3+
ioninthecomplexionist
6
2g
e
0
g
4s
0
4p
0
.
•Thuse
g
orbitalsbecomevacantandhenceareusedind
2
sp
3
hybridisation.ItisduetostrongcharacterofNO
-
2
ions(ligands)that
thetwoelectronsofe
g
setareforcedtooccupyt
2g
orbitals.(see
followingfigure).

19. 5.InnerorbitaloctahedralcomplexesofCo(+2)
•Examplesofsuchcomplexesare[Co(NO
2
)
6
]
4-
and[Co(CN)
6
]
4-Boththeseionsareparamagneticcorrespondingtothepresence
ofoneunpairedelectron.
•Thevalence-shellelectronicconfigurationofCo
2+
ioninitsfree
stateis3d
7
4s
0
4p
0
5s
0
ort
5
2g
e
2
g
4s
0
4p
0
5s
0
whichshowsthat
thisionhas3unpairedelectrons.
•Paulinghassuggestedthat,inordertohaveonlyoneunpaired
electron,oneelectronofe
g
orbitalsisforcedtooccupyt
2g
orbitalsandtheotherelectronofe
g
setispromotedtothehigher
energyvacant5sorbital.
•ThusnowtheconfigurationofCo
2+
ionbecomest
6
2g
e
0
g
4s
0
4p
0
5s
1
inwhichthenumberofunpairedelectronsisequaltoone
andboth3dorbitalsofe
g
setbecomeemptyandhenceare
availableford
2
sp
3
hybridisation.
•Theformationof[CoL
6
]
4-
ion(L=NO
-
2
orCN
-
)byd
2
sp
3
hybridisationhasbeenshowninfollowingfigure.

20. •Thepresenceofunpairedelectronin5sorbitalis
supportedbythefactthat,since5sorbitalisofveryhigh
energy,thesingleelectronresidinginitshouldbe
unstableandhenceshouldbeeasilylost.
•Experimentallyithasbeenfoundtobetrue.
•When[CoL
6
]
4-
ionisacteduponbyairorH
2
O
2
,the
unpairedelectronislostand[Co
2+
L
6
]
4-
ionisoxidisedto
[Co
3+
L
6
]
3-
ion.
•ThuswefindthatCo(+2)lowspin(innerorbital)
octahedralcomplexesareunstable(arelabile)andhence
areeasilyoxidisedtoCo(+3)complexesbyairorH
2
O
2
.
•Consequentlysuchcomplexesshouldbepreparedinan
inertatmosphere.

22. 6.Hexachloroplatinate(IV)ion,[PtC1
6
]
2-
•SincethecoordinationnumberofPt
4+
ionissix,thegivencomplex
ionisoctahedralinshape.
•Valence-shellconfigurationofPt
4+
is4f
14
5d
6
6s
0
6p
0
or4f
14
t
4
2g
e
2
g
6s
0
6p
0
whichhas4unpairedelectrons(n=4).
•Magneticstudyof[PtC1
6
]
2-
ionhasshownthatthisionhasno
unpairedelectron(n=0)andhenceisdiamagnetic.
•Thusintheformationofthisionbothelectronsofe
g
orbitals(5d
z
2
and5d
x
2
-y
2
orbitals)areforcedtooccupyt
2g
orbitals(5d
xy
,5d
yz
and
5d
zx
orbitals)andthusthenumberofunpairedelectronsbecomes
equaltozero(n=0)andalsoe
g
orbitalsbecomeavailableford
2
sp
3
hybridisation.
•Thuswefindthat[PtC1
6
]
2-
ionresultsfromd
2
sp
3
hybridisationof
Pt
4+
ion(seefollowingfigure).
•Examplesofsomeinner-orbitaloctahedralcomplexesaregivenin
followingtable.

24. sp
3
d
2
Hybridisationinouteroctahedralcomplexes
•Thistypeofhybridisationtakesplaceinthoseoctahedralcomplex
ionswhichcontainweakligands.
•Weakligandsarethosewhichcannotforcetheelectronsofd
z
2
and
d
x
2
-y
2
orbitals(e
g
set)oftheinnershelltooccupyd
xy
,d
yz
andd
zx
orbitals(t
2g
set)ofthesameshell.
•Thusinthishybridisation,(n—1)d
z
2
and(n—1)d
x
2
-y
2
orbitals
arenotavailableforhybridisation.
•Inplaceoftheseorbitals,weusend
z
2
andnd
x
2
-y
2
orbitals(Thesed-
orbitalsbelongtotheoutershell)andhencesp
3
d
2
hybridisationcan
berepresentedasns.np
x
.np
y
.np
z
.nd
z
2
.nd
x
2
-y
2
.
•Thishybridisationshowsthatallthesixorbitalsinvolvedin
hybridisationbelongtothehigherenergylevel(outershell).
•Thisdiscussionshowsthatincaseofoctahedralionof3dtransition
series,d-orbitalsusedinhybridisationare4d
z
2
and4d
x
2
-y
2
orbitals.
•Sincetwod-orbitalsarefromtheoutershell(i.e.,nthshell),the
octahedralcomplexesresultedfromsp
3
d
2
hybridisationarecalled
outerorbitaloctahedralcomplexes.

25. •Sincethesecomplexeshavecomparativelygreaternumberof
unpairedelectronsthantheinnerorbitaloctahedralcomplexes,
thesearealsocalledhighspinorspinfreeoctahedralcomplexes.
•Nowletusdiscussthestructureofsomeoctahedralcomplexionsof
3dtransitionserieselementswhichareformedbysp
3
d
2
hybridisation.
1.Hexafluroferrate(III)ion,[FeF
6
]
3-
•Inthision,thecoordinationnumberofFeissixandhencethegiven
complexionhasoctahedralgeometry.
•HereironispresentasFe
3+
whosevalenceshellelectronic
configurationis3d
5
4s
0
4p
0
ort
3
2g
e
2
g
4s
0
4p
0
.
•Eachofthefiveelectronsisunpairedandhencen=5.
•Magneticpropertiesofthegivenionhavealsoshownthattheion
hasfiveunpairedelectronsandhenceisparamagentic
correspondingtothepresenceoffiveunpairedelectrons.
•Thustwoelectronsresidingine
g
orbitalscannotbeforcedto
occupyt
2g
orbitalsaswehavedoneincaseof[Fe(CN)
6
]
3-
ion,
otherwisethenumberofelectronswouldbecomeequaltoone.

26. •Thuswefindthatincaseofthegivenion,thetwod-orbitalsusedin
hybridisationare4d
z
2
and4d
x
2
-y
2
andsandporbitalsare4sand4p.
•Thusthegivenionresultsfrom(4s)(4p
3
)(4d
z
2
)(4d
x
2
-y
2
)hybridisationas
showninfollowingfigure.
•Thisdiscussionshowsthatintheformationof[FeF
6
]
3-
iontheoriginal
valence-shellconfigurationofFe
3+
ionisnotdisturbed.

27. 2.Pentaquanitrosoniumiron(I)ion,[Fe
+
(NO
+
)(H
2
O)
5
]
2+
ion
•ThisionisobtainedwhenNOgasispassedthrougha
freshly-preparedaqueoussolutionofFeSO
4
.
•SincethecoordinationnumberofFeatomissix,thegiven
ionhasoctahedralgeometry.
•Themagneticmomentofthisionhasbeenfoundtobe
equalto3.89B.M.whichshowsthatthegivenionhas
threeunpairedelectrons,i.e.,FeispresentasFe
+
ion(Fe
+
=3d
6
4s
1
or3d
7
4s
0
ort
5
2g
e
2
g
4s
0
havingn=3).
•Inordertoshow+2chargesonthecomplexion,NOis
assumedtobepresentasnitrosylcation(NO
+
)whichisa
two-electrondonor.

28. •Inordertoshowthepresenceofthreeunpairedelectrons
inthegivenion,t
5
2g
e
2
g
configurationofFe
+
ionisnot
disturbed.
•Thismeansthatd
2
sp
3
hybridisationschemecannotbeused
toaccountforthepresenceofthreeunpairedelectrons
(d
2
sp
3
hybridisationgivesoneunpairedelectronwhich
wouldnotbepresentint
2g
setoforbitalsbutinsomeother
orbital).
•Weassumethatthegivenionresultsfromsp
3
d
2
hybridisationandhencethegivenionisanouter-orbital
octahedralion(seefollowingfigure).

30. 3.Outer-orbitaloctahedralcomplexesofNi(+2)
•OctahedralcomplexesofNi
2+
ionareouter-orbitaloctahedral
complexes(sp
3
d
2
hybridisation).
•Theformationofinner-orbitaloctahedralcomplexesofNi
2+
ion
(Ni
2+
=3d
8
=t
6
2g
e
2
g
)isnotpossible,sincethetwounpaired
electronspresentine
g
setoforbitalscannotbesenttot
2g
orbitals
whicharealreadycompletelyfilled.
•Thuse
g
orbitalscannotbemadeemptyford
2
sp
3
hybridisation.
•OuterorbitalcomplexesofNi
2+
ionareparamagnetic
correspondingtothepresenceoftwounpairedelectronspresentin
e
g
orbitals.
•Asanexampleletusseehowsp
3
d
2
hybridisationtakesplacein
[Ni(NH
3
)
6
]
2+
ion(Seefollowingfigure).
•Examplesofsomeouter-octahedralcomplexesaregivenin
followingtable.

40. Geometryof4-coordinatedcomplexions
•Examplesof4-coordinatedcomplexionsformedbysome
transitionmetalsaregiveninfollowingtable.
•Inthesecomplexionsthecoordinationnumberofthecentral
metalatomorionisfour.
•Suchcomplexionsmayhaveeithersquareplanarortetrahedral
geometry,dependingonwhetherthecentralatomorionis
dsp
2
orsp
3
hybridised.
•Whattypeofhybridisation(i.e.,whetherdsp
2
orsp
3
)thecentral
metalatomorionofa4-coordinatedcomplexionundergoes
dependsonthenumberofunpairedorpairedelectrons
presentinthecomplexion.
Squareplanarcomplexions
•Hereweshallconsiderthefollowingcomplexions.
1.[Ni(CN)
4
]
2-
ion
•Inthiscomplexion,sincethecoordinationnumberofNi
2+
ionis
4,thegivencomplexionmaybesquareplanarortetrahedralin
shape.
Important
↓
Important
↓

41. •Inordertodecidewhetherthegivencomplexionis
squareplanarortetrahedral,wetakethehelpofmagnetic
propertyofthecomplexion.
•Experimentallyithasbeenshownthat[Ni(CN)
4
]
2-
ionhas
nounpairedelectron(n=0)andhenceisdiamagnetic.
•Twocasesarise:
(a)When[Ni(CN)
4
]
2-
ionhastetrahedralgeometry
•InthiscaseNi
2+
ionissp
3
hybridisedasshownin
followingfigure.
•sp
3
hybridisationschemegiveninfollowingfigureshows
that[Ni(CN)
4
]
2-
ionhastwounpairedelectrons(n=2).

43. (b)When[Ni(CN)
4
]
2-
ionhassquareplanargeometry
•Forgettingthisgeometry,Ni
2+
ionshouldbedsp
2hybridised.
•Inthishybridisation,duetotheenergymadeavailableby
theapproachoffourCN
-
ions(ligands),thetwounpaired
3d-electronsarepairedup,thereby,makingoneofthe3d
orbitalsempty.
•Thisempty3dorbital(whichis3d
x
2
-y
2
orbital)isusedin
dsp
2
hybridisation.
•Thishybridisationmakesalltheelectronspaired(n=0)
asshowninfollowingfigure.

45. Conclusion
•Wehavesaidabovethatexperimentshaveshownthat
[Ni(CN)
4
]
2-
ionhasnounpairedelectron(n=0)and
henceisdiamagnetic.
•Thismagneticpropertyconfirmsthefactthat[Ni(CN)
4
]
2-
ionhassquareplanargeometrywithn=0andnot
tetrahedralgeometrywithn=2.
2.[Cu(NH
3
)
4
]
2+
ion
(OxidationofCu
2+
toCu
3+
doesnotoccur)
•SincethecoordinationnumberofCu
2+
ionis4,thegiven
complexionhaseithersquareplanarortetrahedral
geometry.
•Squareplanargeometryarisesduetodsp
2
hybridisationof
Cu
2+
ionasshowninfollowingfigurewhiletetrahedral
geometryisduetosp
3
hybridisationofCu
2+
ionasshown
infollowingfigure.

46. Square planar geometry
↓
dsp
2

47. Tetrahedral geometry
↓
sp
3

48. •Asisevidentfromabovefiguresthatinboththegeometries,
[Cu(NH
3
)
4
]
2+
ionhasoneunpairedelectron(n=1).
•Insquareplanargeometry,theunpairedelectronresidesin4p
orbitalwhileintetrahedralgeometrythiselectronispresentin
3dorbital.
•Theabovediscussionshowsthatthemagneticpropertyof
[Cu(NH
3
)
4
]
2+
ioncannotbehelpfulindecidingastowhatis
theexactgeometryof[Cu(NH
3
)
4
]
2+
ion.
•However,physicalmeasurementshaveindicatedthatthe
tetrahedralgeometryfor[Cu(NH
3
)
4
]
2+
ionisnotpossible.
•Nowifthesquareplanargeometryfor[Cu(NH
3
)
4
]
2+
ionis
supposedtobecorrect,theunpairedelectronpresentinthe
higherenergy4porbital(dsp
2
hybridisation)shouldbe
expectedtobeeasilylost,i.e.,[Cu(NH
3
)
4
]
2+
ion(Cu=+2)
shouldbeeasilyoxidisedto[Cu(NH
3
)
4
]
3+
ion(Cu=+3)by
losingtheunpairedelectronresidingin4porbital.

49. •However,experimentshaveshownthattheoxidationof
[Cu(NH
3
)
4
]
2+
to[Cu(NH
3
)
4
]
3+
asshownabovedoesnotoccur.
•Thenhowtoexplainthegeometryof[Cu(NH
3
)
4
]
2+
ion.
Huggin'ssuggestion
•Hugginhassuggestedthat[Cu(NH
3
)
4
]
2+
ionhassquare
planargeometryandCu
2+
ionissp
2
d[(4s)(4p)
2
(4d)]
hybridisedasshowninfollowingfigure.
•Theunpairedelectronresidesin3dorbital.
Conclusion
•[Cu(NH
3
)
4
]
2+
ion→squareplanargeometry
•Cu
2+
ion→sp
2
d[(4s)(4p)
2
(4d)]hybridised
•Unpairedelectron→3dorbital
(Does not possible)

50. Square planar geometry
↓
4(sp
2
d)

51. 3.[Ni(dmg)
2
]
0
molecule
•Inthiscomplexcompound,NiispresentasNi
2+
ion(Ni
2+=3d
8
4s
0
).
•dmgisanegatively-chargedionwhichactsasabidentate
ligand.
•Magneticmeasurementshaveshownthat[Ni(dmg)
2
]
0
has
nounpairedelectrons(n=0)andhassquareplanar
geometrywhicharisesbecauseofdsp
2
hybridisationof
Ni
2+
ion.
•Forgettingdsp
2
hybridisation,one3dorbitalshouldbe
vacant.
•Inordertomake3dorbitalvacant,twounpairedelectrons
presentin3dorbitalsareforcedtogetpaired(see
followingfigure).

53. Tetrahedralcomplexions
•Hereweshalldiscussthestructureofthefollowing
complexcompoundswhichhavetetrahedralgeometry.
1.Ni(CO)
4
molecule(Ni→zerooxidationstate)
•InthiscomplexcompoundNiisinzerooxidationstate
andhasitsvalence-shellconfigurationas3d
8
4s
2
.
•Thiscompoundhastetrahedralgeometrywhicharisesdue
tosp
3
hybridisationofNiatom.
•ThemagneticstudiesofNi(CO)
4
haveindicatedthatthis
moleculeisdiamagnetic(n=0),showingthatthetwo4s
electronsareforcedtopairupwith3dorbitals.
•Thisresultsinsp
3
hybridisationandNi(CO)
4
molecule
hastetrahedralstructure(seefollowingfigure).

55. 2.[NiCl
4
]
2-
ion(Ni→+2oxidationstate)
•ThiscomplexionhasNi
2+
ionwhosevalence-shellconfigurationas
3d
8
4s
0
.
•Magneticmeasurementsrevealthatthegivenionisparamagnetic
andhastwounpairedelectrons(n=2).
•Thisispossibleonlywhenthisionisformedbysp
3
hybridisation
andhastetrahedralgeometry(seefollowingfigure).

58. Tofindoutthenumberofunpairedelectronsinagivencomplex
ion
•Thenumberofunpairedelectrons(n)presentinagivencomplex
iondependsonthegeometryofthecomplexionandthetypeof
hybridisationundergonebythecentralmetalatomorion.
•Thisisevidentfromfollowingtableinwhichwehaveshowna
relationbetweenthenumberofunpairedelectronsandgeometries
ofthecomplexions.

59. LimitationsofVBT
1.VBTcannotaccountfortherelativestabilitiesfordifferent
shapesanddifferentcoordinationnumbersinmetal
complexes,e.g.,itcannotexplainsatisfactorilyastowhy
Co(+2)(d
7
system)formsbothoctahedralandtetrahedral
complexeswhileNi(+2)(d
8
system)rarelyformstetrahedral
complexes.
•Similarly,Fe(+3)(d
5
system)formsbothtetrahedraland
octahedralcomplexeswhileCr(+3)(d
3
system)givesonly
octahedralcomplexes.
2.VBTcannotexplainastowhyCu(+2)formsonlyone
distortedoctahedralcomplexesevenwhenallthesixligands
areidentical.
3.Thistheorycannotaccountfortherelativeratesofreactionsof
analogousmetalcomplexes,e.g.[Mn(phen)
3
]
2+
dissociates
instantaneuslyinacidicaqueoussolutionwhile[Fe(phen)
3
]
2+
dissociatesataslowrate.

60. 4.Theclassificationofmetalcomplexesonthebasisoftheir
magneticbehaviourintocovalent(inner-orbital)andionic
(outer-orbital)complexesisnotsatisfactoryandisoften
misleading,e.g.,manyoftheso-calledioniccomplexeslike
[Fe
3+
(acac)
3
]
0
havepropertieslikehighvolatility,highsolubility
inorganicsolventsetc.whicharecharacteristicsofcovalent
compounds.
•Alsoitisknownthattheaquoion,[Cr(H
2
O)
6
]
3+
(pKa=3.8at
25°C)isamuchweakeracidthan[Fe(H
2
O)
6
]
3+
(pKa=2.2)and
[Co(H
2
O)
6
]
3+
(pKa=0.7)ions,despitethefactthatonly
[Fe(H
2
O)
6
]
3+
isofouter-orbitaltypewithionicbondingwhilethe
othertwoaquoionsareofouter-orbitaltypewithcovalent
bonding.
•Both[Fe(H
2
O)
6
]
3+
and[Co(H
2
O)
6
]
3+
ionsexchangeH
2
O
18
in
solventinstantaneouslywhile[Cr(H
2
O)
6
]
3+
ionexchangesH
2
O
18
veryslowly.
•Theacidityofanaquometalionisexpectedtoincreasewiththe
increaseofcovalentcharacterofthemetal-oxygenbond.

61. •Butneitherthesequenceofaciditiesnortheexchangeratesofthe
abovementionedthreeaquometalionsareintheorderexpected
fromtheirclassificationintoionicandcovalenttypesonthebasis
ofPauling'sVBT.
5.VBTfailstoexplainthefinerdetailsofmagneticproperties
includingthemagnitudeoftheorbitalcontributiontothemagnetic
moments,e.g.althoughbothtetrahedral(sp
3
hybridisation)and
outer-orbitaloctahedral(sp
3
d
2
hybridisation)complexesofCo(+2)
(d
7
system)havethreeunpairedelectronsandare,therefore,
expectedtohaveμvalueequalto3.87B.M.;thetetrahedral
complexesgenerallyhaveμvalueintherangeof4.4–4.8B.M,
whiletheoctahedralcomplexeshavestillhighervalueofμinthe
rangeof4.7–5.2B.M.
•Theincreaseinthevalueofμisduetotheorbitalcontribution.
•Similaristhecasewithtetrahedralandoctahedralcomplexesof
Ni(+2)(d
8
system).
•VBTcannotexplaintheincreaseinthevalueofμ.
6.VBTcannotinterpretthespectra(colour)ofthecomplexes.

62. 7.Thistheorydoesnotpredictorexplainthemagneticbehavioursof
complexes.
•Thistheoryonlypredictsthenumberofunpairedelectrons.
•Itspredictionevenforthenumberofunpairedelectronsandtheir
correlationwithstereochemistryismisleading.
•Forexampleitwasassumedforlongthatallsquareplanar
complexesofNi(+2)(d
8
system)formedbydsp
2
hybridisationwere
diamagnetic(n=0),whilealltetrahedralcomplexesofNi(+2)
formedbysp
3
hybridisationwereparamagneticduetothepresence
oftwounpairedelectrons(n=2).
•X-raystudyof4-coordinateNi(+2)complexeshasshownthatone
andthesamecomplexcanbeobtainedinbothaparamagneticform
(havingbluecolour)andadiamagneticform(havingyellow
colour).
•VBThasnoexplanationforit.
•VBTcannotexplainthetemperaturedependentparamagnetismof
thecomplexes.

63. 8.VBTcannotgiveanyexplanationfortheorderofreactivitiesofthe
inner-orbitalinertcomplexesofd
3
,d
4
,d
5
andd
6
ionsandofthe
observeddifferencesintheenergiesofactivationinaseriesof
similarcomplexes.
9.Themagneticmomentvaluesofthecomplexesofcertainions(e.g.,
Co
2+
,Ni
2+
,etc.)aremuchhigherthanthoseexpectedbyspin-only
formula.
•VBTcannotexplaintheenhancedvaluesofmagneticmoment.

67. The End