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Chemical Bonding
Lecture 12: Ligand Field Theory
5/25/2012
Spring 2012
Crystal Field Theory (CFT)
Oh
x
---Atomic Orbitals of M
z
y
Oh
E
8C3
6C2
6C4
3C2 =(C4)2
i
6S4
8S6
3σh
6σd
Eg
2
-1
0
0
2
2
0
-1
2
0
(2z2-x2-y2, x2-y2)
T2g
3
0
1
-1
-1
3
-1
0
-1
1
(xz, yz, xy)
Crystal Field Splitting Δ
d orbitals in the field of point charges on octahedral geometry
Sorce from: http://en.wikipedia.org/wiki/Category:Chemical_bonding
Energy/∆oct
Crystal field splitting of d orbitals
d-d Transition in CFT
Hexaaquatitanium(III)
Solution
• Colors of transition-metal ions are
often determined by d-d transitions
• Transition energy determined by CF
splitting  metal-ligand interactions!!
νmax=20300 cm-1
chνmax
light
(495 nm)
ν/cm-1
http://www.chem1.com/acad/webtext/chembond/cb09.html
The optical absorption spectrum
of [Ti(H2O)6]3+
t2geg transition energy can be used as a probe to determine Δo, i.e. strength of M-L
coordination bond.
Absorbs at longer wavelength
Absorbs at shorter wavelength
Figure from Oxtoby, Gillis, & Campion, Principles of Modern Chemistry, 6th Edition.
Fig. 8-18, p. 369
Spectrochemical Series
I- < Br- < S2- < SCN- < Cl- < NO3- < N3- < F- < OH- < C2O42- < H2O < NCS- < CH3CN < py (pyridine) < NH3
< en (ethylenediamine) < bipy (2,2'-bipyridine) < phen (1,10-phenanthroline) < NO2- < CN- < CO
Sorce from: http://en.wikipedia.org/wiki/Category:Chemical_bonding
Spin states: Strong field --- low spin; weak field --- high spin
e.g. in Oh for d4~ d7 HS <-> LS
Cr(II) d4
Co(III) d6
Weak Field
High Spin
Δ1 < P
dz2 dx
Δ1
dz2 dx
d xy d xz
2
−y 2
Δ2
2
dz2 dx
2
d xy d xz
d yz
d x2 −y 2
−y 2
d xy d xz d yz
−y 2
d yz
dz2
Energy
Energy
Low Spin
Δ2 > P
Strong Field
d xy d xz d yz
High Spin Complex Low Spin Complex
[CoF6]3[Co(NH3)6]3+
Δ< P
Δ> P
P: energy required to pair two electrons (pairing energy)
Crystal Field Stabilization Energy (CFSE)
( d z 2 , d x2 −y 2 )
3/5 Δo
= 0.6Δo
Δo
Energy
-2/5 Δo
= -0.4Δo
( d xy , d xz , d yz )
Free ion
Uniform Field
Octahedral Field
3
 2

∆o × 2 +  − ∆o × 4 
5
 5

2
= − ∆ o = −0.4∆ o
5
HS: CFSE =
d6
CFSE=0
2
5
12
= − ∆ o = −2.4∆ o
5
LS:CFSE = − ∆ o × 6
Silde from C. J. Ballhausen (http://www.quantum-chemistry-history.com/Ballhau1.htm)
Lower-Symmetry Crystal Field Splitting
D4h
Oh
D4h
Elongated
octahedron
d
(b1g)
x2-y2
eg
Square planar
b1g
+β
-β
dz2
b2g
(a1g)
dxy (b2g)
t2g
dxz
eg
a1g
dyz
eg
Effect of D4h distortion on the energies of the d orbitals.
Spectrochemical Series: Problem of CFT
I- < Br- < S2- < SCN- < Cl- < NO3- < N3- < F- < OH- < C2O42- <
H2O < NCS- < CH3CN < py (pyridine) < NH3 <
en (ethylenediamine) < bipy (2,2'-bipyridine) <
phen (1,10-phenanthroline) < NO2- < CN- < CO
CFT is not a proper theory for metal-ligand bonding  it
can’t even explain the strength of metal-ligand interactions in
the spectrochemical series!!
Ligand Field Theory
• Crystal Field Theory:
Simple ionic model →
does not accurately describe covalent bonding.
• Ligand Field Theory:
Simple molecular orbital theory for metal complexes.
• Similar to previous MO treatment:
Build ligand group orbitals, combine them with metal
atomic orbitals of matching symmetry to form MO’s.
• With focus on bonding with d-orbitals.
Coordination Bonding (dative bonds)
Source from: http://www.chemistry.wustl.edu/~courses/genchem/Tutorials/Hemoglobin/151_T3_hemoglobin.htm
Coordination Bonding (dative bonds)
Metal ion:
Electron acceptor
(Lewis acid)
chelates
Ligand:
Electron donor
(Lewis base)
Source from: http://www.chemistry.wustl.edu/~courses/genchem/Tutorials/Hemoglobin/151_T3_hemoglobin.htm
Common Ligands
Ligand
Structure
Name
Ligand
I-
Iodide ion
Br-
Bromide ion
F-
Fluoride ion
Cl-
Chloride ion
OH-
Hydroxide ion
CO
Carbon monoixde
CN-
Cyanide ion
SCN-
Thiocyanate ion
H2O
water
NH3
ammonia
Oxalate ion
Acetylacetoneate
ion
Structure
phenanthroline
ethylenediammine
Name
Chelating Ligands
Bidentate
ligands
EDTA:
ethylenediaminetetra-acetate ion
MOs for NH3
3a1
2a1
Character table for C3v group
C3v
E
2C3
3 σv
Linear, Rotations
Quadratic
A1
1
1
1
z
x2 + y2, z2
A2
1
1
-1
Rz
E
2
-1
0
(x,y), (Rx, Ry)
(x2-y2, xy), (xz, yz)
MOs for CO
https://wiki.fysik.dtu.dk/dacapo/Solution_3
Ligand Field Theory--- MOs of M and L
Metal-Ligand Bonding Character
Metal Ligand σ Bond
σ Bond
Metal sp3d2
Metal Ligand π Bond
d-p π Bond
L
Ligand σ donor
d x2 −y 2 , d z 2
Metal
Ligand
Ligands of σ-donor :
NH3, F-, Cl-, Br-, CN-, CO, NCS-,
OH-, en, EDTA-4…
Ligands of π-donor : Cl-, Br-, H2O…
Ligands of π-acceptor : CO, CN-, N2…
Ligand Field Theory--- MOs of M and L
Ligand can be π donor or π acceptor
Metal Ligand σ Bond
π donor
Transfer
L(π ) Charge


→ M (d )
LMCT
e.g. X- (halide), HO-, RCOOσ Bond
L
empty
d
Ligand σ donor
Metal sp3d2
full
π
d x2 −y 2 , d z 2
M
L
M
σ donor
e.g. NH3, H2O, H-
full
e.g. CO,
MLCT
CN-,
( )
PR3
π
full
d
empty
σ
M
L
π acceptor M (d ) Charge
 Transfer
→ L π*
LMCT
empty
Complex
L
d
M
M
Complex
L
L
M
Complex
L
AX6 system (Oh)
Oh
E
8C3
6C2
6C4
3C2( = C42)
i
6S4
8S6
3σh
6 σd
A1g
1
1
1
1
1
1
1
1
1
1
A2g
1
1
-1
-1
1
1
-1
1
1
-1
Eg
2
-1
0
0
2
2
0
-1
2
0
T1g
3
0
-1
1
-1
3
1
0
-1
-1
T2g
3
0
1
-1
-1
3
-1
0
-1
1
A1u
1
1
1
1
1
-1
-1
-1
-1
-1
A2u
1
1
-1
-1
1
-1
1
-1
-1
1
Eu
2
-1
0
0
2
-2
0
1
-2
0
T1u
3
0
-1
1
-1
-3
-1
0
1
1
T2u
3
0
1
-1
-1
-3
1
0
1
-1
Γσ
6
0
0
2
2
0
0
0
4
2
Z
A
X
x2 + y2 +z2
(2z2–x2–y2, x2 –y2)
(Rx, Ry, Rz)
(xy, xz, yz)
(x, y, z)
Γσ = A 1g + Eg +T1u
Y
A1g : s
Eg : dz2, dx2-y2
T1u : px, py, pz
A1g + Eg +T1u
AX6 system (Oh)
Oh
E
8C3
6C2
6C4
3C2( = C42)
i
6S4
8S6
3σh
6 σd
A1g
1
1
1
1
1
1
1
1
1
1
A2g
1
1
-1
-1
1
1
-1
1
1
-1
Eg
2
-1
0
0
2
2
0
-1
2
0
T1g
3
0
-1
1
-1
3
1
0
-1
-1
T2g
3
0
1
-1
-1
3
-1
0
-1
1
A1u
1
1
1
1
1
-1
-1
-1
-1
-1
A2u
1
1
-1
-1
1
-1
1
-1
-1
1
Eu
2
-1
0
0
2
-2
0
1
-2
0
T1u
3
0
-1
1
-1
-3
-1
0
1
1
T2u
3
0
1
-1
-1
-3
1
0
1
-1
Γπ
12
0
0
0
-4
0
0
0
0
0
x2 + y2 +z2
(2z2–x2–y2, x2 –y2)
(Rx, Ry, Rz)
(xy, xz, yz)
(x, y, z)
T1g + T2g +T1u + T2u
Γπ = T1g+T2g+T1u+T2u
T1g : None
T2g : dxz, dyz, dxy
T1u : px, py, pz
T2u : None
i
6S4
8S6
3σh
6σd
1
1
1
1
1
1
-1
1
1
-1
1
1
-1
0
0
2
2
0
-1
2
0
0
-1
1
-1
3
1
0
-1
-1
3
0
1
-1
-1
3
-1
0
-1
1
A1u
1
1
1
1
1
-1
-1
-1
-1
-1
A2u
1
1
-1
-1
1
-1
1
-1
-1
1
Eu
2
-1
0
0
2
-2
0
1
-2
0
T1u
3
0
-1
1
-1
-3
-1
0
1
1
T2u
3
0
1
-1
-1
-3
1
0
1
-1
Γσ
6
0
0
2
2
0
0
0
4
2
A1g+Eg+T1u
Γπ
12
0
0
0
-4
0
0
0
0
0
T1g+T2g+T1u+T2u
6C4 3C2 =(C4)2
Oh
E
8C3
6C2
A1g
1
1
1
1
A2g
1
1
-1
Eg
2
-1
T1g
3
T2g
x2+y2+z2
(2z2-x2-y2, x2-y2)
(Rx, Ry, Rz)
(xz, yz, xy)
(x, y, z)
σ interaction
π interaction
Ligand Field Theory (LFT)
---Molecular Orbitals of M-L
Ligand Field Theory was developed during the thirties and fourties of the twentieth century as an expansion of
the electrostatic crystal field theory, which offered a good description of the electronic structure of metal ions in
coordination complexes but was not able to provide a proper explanation for their bonding. It was created by
combining crystal field theory with molecular orbital theory
σ*
4p
px、py、pz
σ*
4s
s
σ*
Oh
Δo
3d
d z 2 d x 2 − y 2 d xy d d
xz
yz
d xy d xz d yz
L (6σ)
σ
A1g+Eg+T1u
σ
Mn+
σ
ML6
X- ligands (Pure σ-donor)
Sorce from: http://en.wikipedia.org/wiki/Category:Chemical_bonding
Ligand Field Theory (LFT)
---Molecular Orbitals of M-L
σ*
σ*
4p
px、py、pz
σ*
4s
s
Δo”
π*
d xy d xz d yz
3d
d z 2 d x 2 − y 2 d xy d d
xz
yz
π
Oh
T1g+T1u+T2u
T2g
filled ligand π or n orbitals
L (6σ)
σ
A1g+Eg+T1u
σ
σ
Mn+
6L ligands (σ-donor + π-donor)
ML6
LMCT (usually weak)
Ligand Field Theory (LFT)
---Molecular Orbitals of M-L
σ*
4p
4s
σ*
px、py、pz
π*
σ*
s
T1g+T1u+T2u
Δo’
3d
Oh
d z 2 d x 2 − y 2 d xy d d
xz
yz
T2g
empty ligand π* orbitals
π or n (12)
d xy d xz d yz
σ
L (6σ)
A1g+Eg+T1u
σ
σ
Mn+
ML6
6L ligands (σ-donor + π-acceptor)
MLCT (usually weak)
LMCT: ligand to metal charge transfer
MLCT: metal to ligand charge transfer
π*
Empty ligand
group orbitals
d z 2 d x2 −y 2
d z 2 d x2 −y 2
d z 2 d x2 −y 2
Δo
MLCT
Δo
’
Δo’’
π*
LMCT
d xy d xz d yz
Filled ligand
group orbitals
π
π Bonding
(π Acceptor)
Δ o ’ > Δo
Strong field
σ Bond only
π
π Bonding
(π Donor)
Δo’’ < Δo
Weak field
σ donor; chelate effect
σ donor; π donor
σ donor; π acceptor
Spectra chemical series
Ligand Field Splitting of ML6 Octahedral Complexes: Δ0 (also often called 10Dq) as an
empirical parameter measured from d-d absorption band
d-d transition
Ligands fields splittings ∆o of ML6 complexes
Ions
Ligands
Cl-
H2O
NH3
en
CN-
21.5
21.9
26.6
10.1
30
d3
Cr3+
13.7
17.4
d2
Mn2+
7.5
8.5
d5
Fe3+
11.0
14.3
(35)
d6
Fe2+
10.4
(32.8)
Co3+
(20.7)
(22.9)
(23.2)
(34.8)
(45.5)
d8
Rh3+
(20.4)
(27.0)
(34.0)
(34.6)
Ni2+
7.5
8.5
10.8
11.5
chνmax
The optical absorption spectrum
of [Ti(H2O)6]3+
Figures from Brown, LeMay & Bursten, Chemistry, The Central Science, 1st Edition
*Values are in multiples of 1000cm-1; entries in parentheses are for low spin complexes.
Tetrahedral Complexes
6σd
Td
E 8C3 3C2 6S4
A1
1
1
1
1
1
A2
1
1
1
-1
-1
E
2
-1
2
0
0
T1
3
0
-1
1
-1
(Rx, Ry, Rz)
T2
3
0
-1
-1
1
(x, y, z)
Γσ
4
1
0
0
2
A1+T2
Γπ
8
-1
0
0
0
E+T1+T2
x2+y2+z2
(2z2-x2-y2, x2-y2)
E : d z 2 , d x2 − y2
(xy, xz, yz)
Weak π interactions
T1 : none
T2 : ( p x , p y , p z ), (d xz , d yz , d xy )
Weak field
d8 most likely
Strong σ & π
interactions
Ligand Field Splitting of ML4 Tetrahedral Complexes
Values of ∆T for representative tetrahedral
complexes
Complexes
Energies of the d orbitals in a
tetrahedral ligand field
∆T/cm-1
VCl4
9010
[CoCl4]2-
3300
[CoBr4]2-
2900
[CoI4]2-
2700
[Co(NCS)4]2-
4700
Δ0 for the tetrahedral case is much smaller than the octahedral case
because in Td:
•Ligands do not approach along the direction of the d orbitals.
•There are only four ligands.
Ligand Field Stabilization Energy (LSFE): Use Δ0 (10Dq) as an empirical parameter to
estimate extra stabilization energy due to ligand-field d-splitting.
Ligand field stabilization energies for octahedral and tetrahedral complexes.
Octahedral
Weak field
Strong field
Weak field
Strong field
Examples
(-Dq)
(-Dq)
(-Dq)
(-Dq)
d0
Ca2+, Sc3+
0
0
0
0
d1
Ti3+
4
4
6
6
d2
V3+
8
8
12
12
d3
Cr3+, V2+
12
12
8
(18)a
d4
Cr2+, Mn3+
6
16
4
(24)a
d5
Mn3+, Fe3+
0
20
0
(20)a
d6
Fe2+, Co3+
4
24
6
(16)a
d7
Co2+
8
18
12
12
d8
Ni2+
12
12
8
8
d9
Cu2+
6
6
4
4
d10
Cu+, Zn2+
0
0
0
0
Configuration
a
Tetrahedral
Theses cases are not realized for regular tetrahedral complexes.
Example:
Lattice enthalpies
Oxides
CaO
TiO
VO
MnO
H (kJ/mol-1)
3460
3878
3913
3810
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http://www.chemistry.wustl.edu/~course
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3_hemoglobin.htm
2012/06/06 visited
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_3
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http://www.larapedia.com/chimica_appu
nti/chimica_appunti_parte_2.html
2012/06/12visited
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Oxtoby, Gillis, & Campion, Principles
of Modern Chemistry, 6th Edition
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Oxtoby, Gillis, & Campion, Principles
of Modern Chemistry, 6th Edition
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Figure from Brown, LeMay & Bursten,
Chemistry, The Central Science, 1st
Edition
http://wpscms.pearsoncmg.com/wps/
media/objects/3662/3750390/Aus_cont
ent_20/Fig20-37.jpg