Ligand field theory - Supratim Chakraborty

Brief introduction about 'Ligand Field Theory'

1. Ligand Field Theory
Centre for Nano and Material Sciences,
Jain University,
Jain Global Campus, Bangalore –562112,
Karnataka, INDIA
Presented by: Supratim Chakraborty

2. Ligand Field Theory
Goldberg Chem. Ber.1906, 39, 1691
Crystal Field Theory (CFT):
•CrystalFieldTheorywaspostulatedbyHansBetheandVanVleckinearly
1930s
•Itexplainsthebondingbetweencoordinationcompoundsaselectrostatic
interactionbetweenpositivelychargedmetalionsandnegativelycharged
ligands.
•Incaseofneutralligandsdipoleinteractionbetweenmetalionandligandis
takenintoaccount.
•CFTworkswellwithsmallelectronegativeligandssuchasF
-
,Cl
-
,andOH
2but
notwithneutralligandssuchascarbonmonoxide(CO).
•However,toexplaincomplexpropertiessuchasvariableoxidationstate,
catalyticproperties,magneticpropertiesandelectronicspectramore
sophisticatedtreatmentwasrequired.Thatcameintermsofligandfield
theory(LFT).

3. Ligand Field Theory
Splitting of d –orb in presence of ligand:
•dz
2
anddx
2
-y
2
orbitalsarepointeddirectlytowardstheaxis;ZaxisandX,Yaxis
respectively.
•Whereas,d
xy,d
yz,andd
zxarepointedbetweentheaxis;(X&Y),(Y&Z),and(Z&X)
respectively.
Essentials of Coordination Chemistry
http://dx.doi.org/10.1016/B978-0-12-803895-6.00001-X

4. Ligand Field Theory
Splitting of d –orb in octahedral complexes:
Approach of ligand inoctahedral field:
Pointeddirectlytowards
theapproachof6ligands
Notinthesame
directionsasligands
5degenerate
d–orbitalsof
freeions
Splittingofd
–orbitalsin
octahedral
field
•dz
2
anddx
2
-y
2
orbitals(e
g)are
higherinenergy;Energygap=
3/5Δ
O
•Whereas,d
xyd
yzandd
zxorbitals
(t
2g)areloweredinenergy;
Energygap=2/5Δ
O
•Example:[Cr(III)Cl
6]
3-
Repulsionbetweenligandandmetalremoves
thedegeneracybetweenthe5d–orbitals.

5. Ligand Field Theory
Splitting of d –orb in tetrahedral complexes:
Farfromtheapproach
oftheligands
Moretowards
thedirection
oftheligands
Approach of ligand intetrahedral field:
5degenerate
d–orbitalsof
freeions
Splittingofd–
orbitals in
tetrahedralfield
•d
xyd
yzandd
zxorbitals(t
2g)arehigherin
energy;Energygap=2/5Δ
t
•Whereas,dz
2
anddx
2
-y
2
orbitals(e
g)are
loweredinenergy;Energygap=3/5Δ
t
•Example:[Fe(VI)O
4]
2-
Unlikeoctahedralasonly4ligandsare
approachingintetrahedralsotheelectrostatic
repulsioniscomparativelylessandΔ
t=4/9Δ
o
X
Y
Z
M
n+

6. Ligand Field Theory
Splitting of d –orb in presence of ligands:
Compression of trans ligand
d
(in)andd
(out)distortionsof
octahedralfield:
•Squareplannercomplexeshave
similartypeofsplittingasd
(out)
geometry.
•JahnTellerdistortion:“Theshapeof
transitionmetalcomplexesis
determinedbythetendencyof
electronpairstooccupypositionas
farawayaspossible.”
d
(in)
Removal of trans ligand
d
(out)

7. Ligand Field Theory
Splitting of d –orb in low symmetry environments:
https://en.wikipedia.org/wiki/Crystal_field_theory

8. Splitting of d –orb in low symmetry environments:
Ligand Field Theory
https://en.wikipedia.org/wiki/Crystal_field_theory

9. Ligand Field Theory
InLigandFieldTheoryspecificelectronicinteractionsbetweenligandsandmolecular
orbitalsaretakenintoaccount.
Duetothedirectionalnatureoftheapproachingligandsintheoctahedralfieldonlythe
followingligandsofthemetalswillgoingtointeractwiththeligands:s,p
x,p
y,p
z,d
z2andd
x2–y2.
Bonding BondingLigand Orb Ligand Orb
S orb
p
xorb
p
yorb
p
zorb
d
z2orb
d
x2-y2orb

10. Ligand Field Theory
x
2
–y
2
z
2
xyyzzx
x
2
–y
2
z
2
xyyzzx
L1 L2
L1 L2
•Amongthesixdorbitalsonlydz
2
anddx
2
-y
2
orbitalsarepointeddirectlytowardstheaxis;Z
axisandX,Yaxisrespectively.
•Thosetwoorbitalswillgoingtointeractdirectly
withthe2ligands(L1andL2).
•Fromtheinteractionbetweenthetwoligand
orbitalsanddz
2
anddx
2
-y
2
orbitalstherewillbe
theformationoftwob.o.andtwoa.o.
•Asthea.o.areclosetotheenergyofthed
orbitalssotheywilllooklikethedorbitals.
•Whereasb.o.beingclosetoenergyoftheligand
orbitalswillresembletheshapeofligandorbitals.
•Thexy,yz,andzxwillgoingtoremainasnon
bondingorbitals.
Interaction of d –orbitals with ligands:
dz
2
Ligand dx
2
-y
2
Ligand
Non bonding
(t
2g)
Anti bonding
(e
g*)
Bonding (e
g)

11. Ligand Field Theory
Interaction of s, p, and d –orbitals with ligands:
•Overallinteractionsofligand
orbitalswiththemetalorbitals
isverycomplicated.
•E
gorbitalswillgoingtointeract
directlydz
2
anddx
2
-y
2
orbitals.
•A1gorbitalsfromtheligandwill
goingtointeractwithsorbitals
•T1Uorbitalsoftheligandswill
interactwiththepx,py,andpz
orbitals.
S orb A
1g
p
x p
y p
z
T
1uorbitals

12. Ligand Field Theory
The importance of Ligand Field Theory:
5degenerate
d–orbitalsof
freeions
Splittingof
d –
orbitalsin
octahedral
field
Intermsoftheabilityoftheligandstosplitthe
dorbitalstheyareclassifiedeitherasweakfield
orstrongfield.
Theserieswhichliststheligandsintermsof
theirsplittingabilityiscalledthe
spectrochemicalseries.
I-< Br-< SCN-~Cl-< F-< OH-~ ONO-< C
2O
4
2-
< H
2O < NCS-< EDTA
4-
< NH
3~ pyr~ en <
bipy< phen< CN-~ CO
Spectrochemicalseries:
What the CFT fails to explain is why CO > H
2O > C
2O
4
2-
>EDTA
4-
> I
-
?
Fromthepointofviewofelectrostaticrepulsiontheordershouldbereverse
i.e.,
EDTA
4-
>C
2O
4
2-
>I
-
>H
2O>CO.ThiscanbeexplainedbyLigandFieldTheory.
http://wwwchem.uwimona.edu.jm/courses/LFT.html

13. Ligand Field Theory
Δ
Δ
Δ
t
2g
e
g* e
g*e
g*
π
π
π*
π*
πorbital
of I
-
π* orbital
of CN
-
πbonding of ligands with the metal orbitals:
Sigmabondingofligands
withthemetalorbitals
[M(II)(H
2O)
6]
2+
[M(II)(CN)
6]
4-
[M(II)(I)
6]
4-
M CO
Metal Ligand back bonding
πorbitalsfromI
-
arelowerin
energythanmetalt
2gorbitals.So
theeffectiveandexperimentalΔ
valuebecomessmaller.Δ(I
-
)
π*orbitalsfromCN
-
arehigherin
energythanmetalt
2gorbitals.Sothe
effectiveandexperimentalΔvalue
becomesbigger.Δ(CO/CN
-
)
πacceptor ligands
Ligand Metal back bonding
πdonor ligands
Absenceofanyπorbitalsand
metalinteractionhaskeptthe
valueofΔinstandardregion.
<<
Δ(H
2O)

14. Summary:
Ligand Field Theory
•LigandFieldTheorywaspostulatedbyOrgelandGriffithin1950s.
•Itisamodifiedversionofcrystalfieldtheoryandmolecularorbitaltheory.
•BytheuseofCFTitispossibletoexplaincoordinationcompoundsof
differentgeometriessuchasoctahedral,tetrahedral,squareplanner,
squarepyramidal,pentagonalbipyramidaletc.
•TwomajoraspectsofLigandFieldTheoryissigmabondingandpi
bonding.
•CFTworkswellwithsmallelectronegativeligandssuchasF
-
,Cl
-
,andOH
2
butnotwithneutralligandssuchascarbonmonoxide(CO).
•Thecharacteristicbehaviorofstrongfieldligandssuchascarbon
monoxide(CO)orcyanide(CN
-
)pibondingaspectofLFTbecomes
important.(someunusualchangesinthissentencestructurethatIcannot
rememberdoingbutnoticedduringpresenting)