Chapter 4. Molecular Symmetry - KNUbh.knu.ac.kr/~leehi/index.files/Coordination_Chemistry...Valence Bond Theory (VBT) : Hybridization. Description of atomic orbital types used to share

Coordination Chemistry II: Bonding 10

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

dz2, dx2-y2

dxy, dyz, dzx t2

e

Dt

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

D1

D2

D3

d Do

Experimental Facts Thermodynamic Data

[Fe(H2O)6]3+ + SCN- (aq) [FeSCN(H2O)5]

2+ + H2O

[Cu(H2O)6]2+ + 4NH3 (aq) [Cu(NH3)4(H2O)2]

2+ + 4H2O

stability constant (formation constant), K

K1 = [Fe3+][SCN-]

[FeSCN2+]

= 9 x 102

K4 = [Cu2+][NH3]

4

[Cu(NH3)42+]

= 1 x 1013

Q) Why is SCN- (or NH3)

more favorable to Fe(III)

(or Cu(II)) than H2O?

Q) Why do Ag(I) and

Cu(II) have the reverse

order of favoring

ligands?

* HSAB

Experimental Facts Thermodynamic Data

[Cd(H2O)6]2+ + 4 CH3NH2

[Cd(CH3NH2)4(H2O)2]2+ + 4H2O

[Cd(H2O)6]2+ + 2 en [Cd(en)2(H2O)2]

2+ + 4H2O

DHo = -57.3 kJ/mol

K4 = 3.31 x 106

DHo = -56.5 kJ/mol

K2 = 3.98 x 1010

[Ni(CH3NH2)6]2+ + 4 H2O

Ni(OH)2(s) + 6 CH3NH3+ + 4 OH- [Ni(en)3]

2+ Stable in aq soln

Chelate effect: the enhanced affinity of chelating ligands for a metal ion compared to the affinity of a

collection of similar nonchelating (monodentate) ligands for the same metal.

[Cu(H2O)6]2+

Experimental Facts Magnetic Susceptibility

SQUID (Superconducting QUantum Interference Device)

Gouy method


Magnetic Susceptibility (c) = the degree of magnetization of a material

in response to a magnetic field = M/H

Ferromagnetism : T < TC

Antiferromagnetism : T < TN

Paramagnetism : competition between

magnetic and thermal motion

c

T (K) TC TN

paramagnetic

ferromagnetic

antiferromagnetic

TC : Curie Temperature

TN : Neel Temperature

Curie Law : c = C/T

Curie-Weiss Law : c = C/(T-q)

All magnetic materials should have unpaired electrons.


Magnetic Susceptibility (c) Gives information of the magnetic moment (m) of a material

m = 2.828 (cT)1/2 mB (mB : Bohr magneton = magnetic moment of a single electron)

Two sources of magnetic moment – spin (S) and angular(L) motions of electrons

spin quantum number orbital (angular momentum) quantum number

mS+L = g [J(J+1)]1/2 mB

Landé g-factor (gyromagnetic ratio) = 1 + J(J+1) + S(S+1) – L(L+1)

mS+L = g [S(S+1) + 0.25L(L+1)]1/2 mB

total angular momentum quantum number

2J(J+1)

When spin-orbit coupling is negligible,

true for most cases except heavy metals such as Lanthanides

Theoretically,


mS+L = g [S(S+1) + 0.25L(L+1)]1/2 mB

2

Landé g-factor (gyromagnetic ratio)

= 1 + J(J+1) + S(S+1) – L(L+1)

2J(J+1)

mS = g [S(S+1)]1/2 mB

In most cases, L is effectively quenched,

J = S, L = 0 g = 2,

gfree electron = 2.0023

0 0

1 ½

0 0

1 ½

1 ½

1 ½

Why is L quenched in crystal field ?

Q) Why do the transition metal ions

have so much diversified magnetic

moments (spin states)?

Experimental Facts Electronic Spectra

Cu(H2O)62+

Co(H2O)62+

Ni(H2O)62+

Fe(H2O)62+

Co(II)

Q) Why such colors?

Experimental Facts

Why?

Have to know the characteristics of the

bondings and the electronic structures of

the complexes.

Valence Bond Theory (VBT) : Hybridization. Description of atomic orbital types used to share

electrons or hold lone pairs to form bonds.

Crystal Field Theory (CFT) : Electrostatic approach. Describing the split of d-orbtal energies in crystal

field. No description of bonds.

Ligand Field Theory (LFT) : Molecular orbital (MO) theory approach to describe the bonds and

electronic structures of the transition metal complexes.

Angular Overlap Method : Estimation of the relative magnitude of MOs.

Theories of Bonding and Electronic

Structure of Complexes

Theories of Bonding and Electronic

Structure of Complexes Valence Bond Theory

(Hybridization)

First attempt of quantum mechanical explanation of chemical bonding

Y = fA(1)fB(2) Y = fA(1)fB(2)+fA(2)fB(1)

Each electron is free to migrate to the other atom.

Probability to find 2e-’s between two nuclei is high.

bonding

Think forming of a bond as Overlap of atomic orbitals

109.5o

Hybridization : the concept of mixing atomic orbitals to form new hybrid

orbitals suitable for the qualitative description of atomic bonding

properties.

CH4

sp3

four sp3 orbitals

Theories of Bonding and Electronic Structure of Complexes

Valence Bond Theory

(Hybridization)

HCl

Cl2

C

H

H

H

90o

90o

90o

and one H at not defined position

???

tetrahedral,

4 equivalent bonds

CH4

4H + C H C H

H

H

A s bond centers along the internuclear axis.

s bond

s bond


Valence Bond Theory

(Hybridization)

CH4

sp3

s p 3 h y b r i d a . o . s :

C ( s p 3 )

t e t r a h e d r a l s ( s p 3 C

+ 1 s H

)

4 H C

H

H H

H

109.5o

H2O

O s p 3 2 s

2 p

s p 3 h y b r i d i z e d

l o n e p a i r s i n s p 3 a . o . s

O

H

H

s ( s p 3 O

+ 1 s H

) H-O-H

2 p

2 s s p 3 N

3

s ( s p 3 N

+ 1 s H

) N

H H

H

l o n e p a i r i n s p a . o .

s p 3 h y b r i d i z e d

NH3

N

H

H H


Valence Bond Theory

(Hybridization)

BF3

sp2

trigonal planar,

3 equivalent bonds

B

H

H H


Valence Bond Theory

(Hybridization)

sp2

C2H4

all six atoms lie

in the same plane

s-bond p-bond

A p bond occupies the space above and below the internuclear axis.


Valence Bond Theory

(Hybridization)

sp

linear


Valence Bond Theory

(Hybridization)

linear

linear

H-C≡C-H

sp

Valence Bond Theory

(Hybridization)


dsp3 PCl5

A

B

B

B

B

B A

B

B

B

B

B

trigonal bipyramid

PCl5

Valence Bond Theory

(Hybridization)


d2sp3 SF6

A

B

B

B

B

B

B

A

B

B

B

B

octahedral

B

B

Valence Bond Theory

(Hybridization)


Hybridization of metal s, p, d orbitals

Metal or Metal Ion (Lewis Acid) + Ligand (Lewis base) => Formation of Complex

Square planar (dsp2)

Pt2+ ([Xe]4f145d8)

PtCl42- : diamagnetic

Ni2+ ([Ar]3d8)

NiCl42- : paramagnetic

Tetrahedral (sp3)

5d 6s

6p

from ligands 5d dsp2 hybrids

6p

4 dsp2 hybrids (abstract figure)

3d 4s

4p

3d

sp3 hybrids

from ligands

4 sp3 hybrids (abstract figure)

Valence Bond Theory

(Hybridization)


3d 4s

4p

Octahedral

Co3+ ([Ar]3d6)

[Co(NH3)6]3+ : diamagnetic [CoF6]

3- : paramagnetic

Octahedral

4d

3d d2sp3 hybrids

from ligands 3d

sp3d2 hybrids

4d

from ligands

Valence Bond Theory

(Hybridization)


VBT has great importance of developing bonding theory for coodination compounds.

But •It is highly unlikely to use 4d orbital which is high in energy.

•Many electronic spectra (such as charged complexes) are not well explained.

Today, we rarely use it.

Forget VBT

But, don't foget that VBT is still a good subject for exams.

Valence Bond Theory

(Hybridization)


• Developed to explain metal ions in crystal called Crystal Field Theory (CFT)

• Also useful for coordination compounds

• Repulsion between d-orbital e- ligand e-

splitting of energy levels of d-orbitals

Ex) dx2-y2 and dxy orbitals in octahedral field

L

L

L

L

L L

L

L

L

L

L

L

bigger repulsion

higher energy level

Theories of Bonding and Electronic Structure of Complexes Crystal Field Theory

d

free ion

Uniform Field (Spherical Field)


d

free ion


Octahedral Field

dz2, dx2-y2

dxy, dyz, dzx


d

free ion


Octahedral Field

dz2, dx2-y2

dxy, dyz, dzx t2g

eg

0.6Do

0.4Do

Do (=10Dq)

: ligand splitting

parameter


Octahedral Field (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field

Tetragonal elongation (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g


Tetragonal compression (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g Octahedral Field (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field


dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g


dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g Octahedral Field (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field


dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

Square-planar field (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

D1

D2

D3



dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field Cubic Field

dz2, dx2-y2

dxy, dyz, dzx



dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field Cubic Field

dz2, dx2-y2

dxy, dyz, dzx

Tetrahedral Field (Td)

dz2, dx2-y2

dxy, dyz, dzx t2

e

Dt ≈ 4/9 Do


Octahedral (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field Tetrahedral (Td)

dz2, dx2-y2

dxy, dyz, dzx t2

e

Dt

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

Square-planar (D4h)

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

D1

D2

D3

d


Do


Why are complexes formed in crystal field theory?

Crystal Field Stabilization Energy (CFSE)

or Ligand Field Stabilization Energy (LFSE)

Octahedral Field

t2g

eg

0.6Do

0.4Do

d3 LFSE of d3 in octahedral structure

= (-0.4Do) x 3 = -1.2 Do

LFSE : the stabilization of the d electrons because of the metal-ligand environments


Crystal Field Theory

: CFSE, LFSE

Electron

configuration

(Oh)

t2g1 t2g

2 t2g3 t2g

3eg1 t2g

3eg2

t2g4eg

2 t2g5eg

2 t2g6eg

2 t2g6eg

3 t2g6eg

4

t2g1 t2g

2 t2g3 t2g

4 t2g5

t2g6 t2g

6eg1 t2g

6eg2 t2g

6eg3 t2g

6eg4

weak field, strong field ?

LFSE + pairing energy (Pc + Pe)

= -0.6 Do + 3Pe

LFSE + pairing energy (Pc + Pe)

= -1.6 Do + Pc + 3Pe

Pc : Coulombic energy

Pe : Exchange energy (=exchanges

between the same spins at the same energy )

DE = strong field - weak field

= -Do + Pc

DE > 0 weak field (high spin)

DE < 0 strong field (low spin)



: CFSE, LFSE

Ligand Field Stabilization Energies and Spin States (Oh)

Weak field (high spin) Strong field (low spin)



: CFSE, LFSE

What determines ∆? ∆ depends on the relative

energies of the metal ions and ligand orbials and

on the degree of overlap.

Octahedral (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

d Do

Spectrochemical Series for Ligands

CO > CN- > PPh3 > NO2- > phen > bipy > en > NH3

> py > CH3CN > NCS- > H2O > C2O42- > OH-

> RCO2- > F- > N3

- > NO3- > Cl- > SCN- > S2- > Br-

> I-

π acceptor π donor

(strong field ligand) (weak field ligand)

Spectrochemical Series for Metal Ions

(ox # ↑,ᇫ↑)

smaller size and higher charge

(down a group in periodic table, ᇫ↑)

greater overlap between 4d and 5d orbitals and

ligand orbitals, decreasing pairing energy

Pt4+ > Ir3+ > Pd4+ > Ru3+ > Rh3+ > Mo3+ > Mn4+

> Co3+ > Fe3+ > V2+ > Fe2+ > Co2+ > Ni2+ > Mn2+



: CFSE, LFSE

[Co(H2O)]3+ is the only low-spin

agua complex.


(ox # ↑,ᇫ↑)





Pt4+ > Ir3+ > Pd4+ > Ru3+ > Rh3+ > Mo3+ > Mn4+

> Co3+ > Fe3+ > V2+ > Fe2+ > Co2+ > Ni2+ > Mn2+



: CFSE, LFSE

Spin States (Oh)

s ½

1

3/2

2

5/2

2

3/2

1

½

0

½

1

3/2

1

1/2

0

1/2

1

½

0



: CFSE, LFSE



: CFSE, LFSE

Magnetochemical Series

Measure pyrrole 1H chemical shift in Fe(III)X(TPP) :

useful for distinguishing weak ligads

H

I- > ReO4- (66.7 ppm) > CF3SO3

- (47.9) > ClO4- (27.7)

AsF6- (-31.5) > CB11H12

- (-58.5)

weaker

Full series

(2015)

For weak ligand, admixed (in between S = 5/2 and S = 3/2) states are observed.

Qualitative observation of LFSE in thermodynamic data (Hydration Enthalpy)

M2+(g) + 6H2O(l) [M(H2O)6]2+ : DHhyd [∝x (= z2/r) in first order]



: CFSE, LFSE

Corrected with spin-orbit splittings,

relaxation effect from the contraction of

the metal-ligand distances, and

interelectronic repulsion energy, and

LFSE. But mostly the differences

between the experimental and corrected

values are from LFSE.

: mostly comes

from LFSE

Measured by M2+(g) + 6H2O(l) + 2H+ + 2e-

[M(H2O)6]2+ + H2(g)

Ligand Field Stabilzation Energies (Td)

dz2, dx2-y2

dxy, dyz, dzx t2

e

Dt

d 0.4Dt

0.6Dt

tetrahedral field

Dt (≈4/9 Do) : all high-spin configuration

d electrons ex electron configurations LFSEs (Dt) Spin States (S)

1 Ti3+ e1 -0.6 ½

2 V3+ e2 -1.2 1

3 Cr3+ e2t21 -0.8 3/2

4 Cr2+ e2t22 -0.4 2

5 Mn2+ e2t23 0 5/2

6 Fe2+ e3t23 -0.6 2

7 Co2+ e4t23 -1.2 3/2

8 Ni2+ e4t24 -0.8 1

9 Cu2+ e4t25 -0.4 ½

10 Zn2+ e4t26 0 0



: CFSE, LFSE

CFT explains

well the magnetic properties

and in some degree the electronic spectra of the complexes.

However, there is no explaination of the bondings.

In other words, the purely electrostatic approach does not allow for the lower

(bonding) molecular orbitals, and thus fail to provide a complete picture of the

electron structures of complexes.

CFT and MO theory combined complete theory

Ligand Field Theory

(Bonding Theory of Transition-Metal Complexes)

Constructring MOs to explain the electronic structure, magnetic

properties, and bondings.


Ligand Field Theory

N atomic orbitals => N molecular orbitals

Symmetry match of atomic orbitals

Relative energy of atomic orbitals

3 things to consider to form MOs

Orbital interactions

in Oh complexes


Ligand Field Theory

N atomic orbitals => N molecular orbitals

Symmetry match of atomic orbitals

Relative energy of atomic orbitals

3 things to consider to form MOs

|cA| = |cB|

|cA| > |cB| |cA| >> |cB| |cA| = |cB|

|cA| < |cB| |cA| << |cB|

bbaa cc +=Y


Ligand Field Theory

Two Primary Influences to Ligand Field

1) Geometries – Oh, Td, D4h ...

2) Types of Ligands – s-donor, p-donor, p-acceptor

s-donor ligands : H-, NH3 ..

M :H M :NH3

p-donor ligands : halides, O2-, RO-, RS-, RCO2- ...

X- M

px

p-acceptor ligands : CO, CN-, NO+, RCN ...

s-donor orbital

C=O M

p-acceptor orbital


Ligand Field Theory

Constructing MOs of Transition-Metal Complexes

MLn:

Assume central metal ion, M, has available s,p, and d orbitals : 9 orbitals

Assume ligands, L, have s and p orbitals : 4n orbitals combination of

the 4n orbitals makes s-donor, p-donor, and p-acceptor orbitals

M

s : A1g

px, py, pz : T1u

dz2, dx2-y2 :,Eg

dxy, dyz, dzx : T2g

Oh (ML6) with s-donor ligands

x2+y2+z2


Ligand Field Theory

: representations of s-donor orbitals

L

Gs 6 0 0 2 2 0 0 0 4 2


M

s : A1g

px, py, pz : T1u

dz2, dx2-y2 :,Eg

dxy, dyz, dzx : T2g

x2+y2+z2

Gs = T1u + Eg + A1g


Ligand Field Theory


M

s : A1g

px, py, pz : T1u

dz2, dx2-y2 :,Eg

dxy, dyz, dzx : T2g

Gs = T1u + Eg + A1g

electrons from ligands

frontier orbitals

•electrons from d-orbitals

•same splitting pattern and d-

orbital configuration as in CFT

Why are complexes formed

in ligand field theory?

Because of forming bonding

orbitals


Ligand Field Theory


Symmetry

Adapted

Orbitals

Think about what these

orbitals look like.


Ligand Field Theory


Ligand Field Theory

Oh (ML6) with p-acceptor, p-donor ligands

M

s : A1g

px, py, pz : T1u

dz2, dx2-y2 :,Eg

dxy, dyz, dzx : T2g : representations of p orbitals

L

Gp 12 0 0 0 -4 0 0 0 0 0

Gp = T1g + T2g + T1u + T2u


Ligand Field Theory

Gs = T1u + Eg + A1g

CO (LUMO)

CO (HOMO)

s-donor ligands

p-acceptor +

Gp = T1g + T2g + T1u + T2u Oh (ML6) with p-acceptor, p-donor ligands


Ligand Field Theory

Gs = T1u + Eg + A1g

CO (LUMO)

CO (HOMO)

s-donor ligands

p-acceptor +

Gp = T1g + T2g + T1u + T2u Oh (ML6) with p-acceptor, p-donor ligands

metal-to-ligand (M→L) p bonding

= p backbonding


Ligand Field Theory

Oh (ML6) with p-acceptor, p-donor ligands

X- M

C=O M

Gp = T1g + T2g + T1u + T2u


CO > CN- > PPh3 > NO2- > phen > bipy > en >

NH3 > py > CH3CN > NCS- > H2O > C2O42- > OH-

> RCO2- > F- > N3

- > NO3- > Cl- > SCN- > S2- > Br-

> I-



Metal-to-ligand (ML) p bonding

(p back-bonding)

increases metal-ligand bond strength

(transfer of negative charge away from the metal ion)

Ligand-to-metal (LM) p bonding

decreases metal-ligand bond strength

(more negative charge on the metal ion decrease of

attraction between the metal ion and the ligands)


Ligand Field Theory

D4h (ML4) with s-donor ligands (square planar)

M

s : A1g

px, py : Eu

pz : A2u

dz2 : A1g

dx2-y2 :,B1g

dxy : B2g

dyz, dzx : Eg

Gs = A1g + B1g + Eu

: representations of

s-donor orbitals L

Gs 4 0 0 2 0 0 0 4 2 0


p║-orbitals


p┴-orbitals

G║ = A2g + B2g + Eu

G║ 4 0 0 -2 0 0 0 4 -2 0

G┴ = A2u + B2u + Eg

G┴ 4 0 0 -2 0 0 0 -4 2 0


Ligand Field Theory


M

s : A1g

px, py : Eu

pz : A2u

dz2 : A1g

dx2-y2 :,B1g

dxy : B2g

dyz, dzx : Eg

Gs = A1g + B1g + Eu

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

D1

D2

D3

CFT


Ligand Field Theory

D4h (ML4) with s-donor ligands (square planar) Gs = A1g + B1g + Eu

Symmetry

Adapted

Orbitals Think about what these

orbitals look like.


Ligand Field Theory


M

s : A1g

px, py : Eu

pz : A2u

dz2 : A1g

dx2-y2 :,B1g

dxy : B2g

dyz, dzx : Eg

Gs = A1g + B1g + Eu

G║ = A2g + B2g + Eu

G┴ = A2u + B2u + Eg

s-bonding orbitals : ligand s-donor 8 electrons

p-bonding orbitals : ligand p-donor 16 electrons

metal d orbitals

[Pt(CN)4]2-


Ligand Field Theory

up and down

depending on

metals and ligands

D1 >> D2, D3 d8 (sq. pl) low-spin always b1g > a1g, eg, b2g

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

D1

D2

D3

CFT


[Pt(CN)4]2-

[Ni(CN)4]2-: a2u > b1g > a1g > eg > b2g


Ligand Field Theory

Td (ML4)

M

s : A1

px, py, pz : T2

dz2, dx2-y2 :,E

dxy, dyz, dzx : T2

: representations of s-donor orbitals

L

: representations of p ligand orbitals

Gs 4 1 0 0 2

Gp 8 -1 0 0 0

Gs = A1 + T2 Gp = E + T1 + T2


Ligand Field Theory

Td (ML4)

M

s : A1

px, py, pz : T2

dz2, dx2-y2 :,E

dxy, dyz, dzx : T2

Gs = A1 + T2 with s-donors only

a1 + t2

L4 M ML4

t2

a1

e + t2

1t2

1a1

2t2

e

2a1

3t2

dz2, dx2-y2

dxy, dyz, dzx t2

e

Dt

CFT

Symmetry Adapted

Orbitals

Think about the shapes

of the MOs


Ligand Field Theory

Td (ML4)

M

s : A1

px, py, pz : T2

dz2, dx2-y2 :,E

dxy, dyz, dzx : T2

Gs = A1 + T2 with s-donors

Gp = E + T1 + T2

and p-interactions


Ligand Field Theory

Ligand Field Model

• No explicit use of energy

• Difficult to use when considering an assortment of ligands or structures with

symmetry other than Oh, D4h, Td.

Angular Overlap Model

• A variation with the flexibility to deal with a variety of possible geometries and

with a mixture of ligands

• Estimates the strength of interaction between individual ligand orbitals and metal

d orbitals based on overlap between them

• Determine the energy level of a metal d orbital and a ligand orbital in a

coordination complex



s-donor interactions

Basic criteria: the strongest s interaction overlap between dz2 and ligand pz (or hybrid) : es

bonding orbitals: stabilized by es

antibonding orbitals: destabilized by es

The magnitudes of other interactions between d-orbitals and ligand s-orbitals: determined relative to es




Ex) s-donor interactions

of [M(NH3)6]n+

dz2 : strength of s-interaction

= 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3

dx2-y2 :

strength of s-interaction

= 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3

dxy, dyz, dzx :


= 0 + 0 + 0 + 0 + 0 + 0 = 0

ligand 1,6 orbitals :


= 1 + 0 + 0 + 0 + 0 + 0 = 1

ligand 2, 3, 4, 5 orbitals :


= ¼ + ¾ + 0 + 0 + 0 + 0 = 1




Ex) s-donor interactions

of [M(NH3)6]n+

dz2 : strength of s-interaction

= 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3

dx2-y2 :


= 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3

dxy, dyz, dzx :


= 0 + 0 + 0 + 0 + 0 + 0 = 0

ligand 1,6 orbitals :


= 1 + 0 + 0 + 0 + 0 + 0 = 1

ligand 2, 3, 4, 5 orbitals :


= ¼ + ¾ + 0 + 0 + 0 + 0 = 1

stabilization : 12es

destabilization : 0 or (3xn)es

dz2, dx2-y2

dxy, dyz, dzx t2g

eg

Do CFT

Angular overlap model: not a

complete picture of MOs, but

can estimate the energy levels of

the orbitals



p-acceptor interactions



Basic criteria: the strongest p interaction overlap between dxz and ligand p* orbital : ep

ep < es




Ex) p-acceptor interactions

of [M(CN)6]n-

dz2, dx2-y2 :

strength of p-interaction

= 0 + 0 + 0 + 0 + 0 +0

= 0

dxy, dyz, dzx :


= 0 + 1 + 1 + 1 + 1 + 0

= 4

ligand 1, 2, 3, 4, 5, 6

orbitals :


= 0 + 0 + 0 + 0 + 1 + 1

= 2




Ex) Energy level diagram of d-orbitals, s-donor and p-acceptor ligands in octahedral complexes


dz2, dx2-y2 : 0

dxy, dyz, dzx : 4

ligand 1, 2, 3, 4, 5, 6 orbitals : 2


dz2, dx2-y2 : 3

dxy, dyz, dzx : 0

ligand 1,2, 3, 4, 5, 6 orbitals : 1

s-donor + p-acceptor interactions

2ep

p-donor interactions



Basic criteria:

same as in p-acceptor interaction : ep

Ex) p-donor interaction of [MX6]n-

dz2, dx2-y2 : strength of p-interaction

= 0 + 0 + 0 + 0 + 0 +0 = 0

dxy, dyz, dzx : strength of p-interaction

= 0 + 1 + 1 + 1 + 1 + 0 = 4

ligand 1, 2, 3, 4, 5, 6 orbitals :

strength of p-interaction = 0 + 0 + 0 + 0 + 1 + 1 = 2

usually, ep for p-acceptor interation > ep for p-donor interation




Ex) Energy level diagram of d-orbitals, s-donor and p-acceptor ligands in octahedral complexes


dz2, dx2-y2 : 0

dxy, dyz, dzx : 4

ligand 1, 2, 3, 4, 5, 6 orbitals : 2


dz2, dx2-y2 : 3

dxy, dyz, dzx : 0

ligand 1,2, 3, 4, 5, 6 orbitals : 1

s-donor + p-donor interactions



s-donor s-donor

+ p-donor

s-donor

+ p-acceptor

LFT

Magnitudes of es, ep, and D : depend on both ligands and metals

es, ep

• es > ep

• es , ep ↓ as size of X- ↑

and electronegativity of X- ↓ (bond length increase

metal-ligand interaction decrease)

s-donor

+ p-donor

D = 3es - 4ep generally follows the spectrochemical series.



Magnitudes of es, ep, and D : depend on both ligands and metals




CO > CN- > PPh3 > NO2- > phen > bipy > en > NH3

> py > CH3CN > NCS- > H2O > C2O42- > OH-

> RCO2- > F- > N3

- > NO3- > Cl- > SCN- > S2- > Br-

> I-




(ox # ↑,ᇫ↑)





Pt4+ > Ir3+ > Pd4+ > Ru3+ > Rh3+ > Mo3+ > Mn4+

> Co3+ > Fe3+ > V2+ > Fe2+ > Co2+ > Ni2+ > Mn2+

Four- and six coordinate preference



Angular overlap calculation can provide us with some indication of relative stabilities depending on the

number of d electrons and geometries.

ang

ula

r o

ver

lap e

ner

gy

E = 12x(-es) + 5x(0es) + 2x(3es) = -6es

Oh is favorable. Both sq. pl and Oh are favorable.

Four- and six coordinate preference



Angular overlap calculation can provide us with some indication of relative stabilities depending on the

number of d electrons and geometries.

Strong-field sq. pl is favorable.

Angular overlap calculation gives just an approximate. There are many other factors to get a complete picture.

ang

ula

r o

ver

lap

en

erg

y

Application to hydration enthalpy



M2+(g) + 6H2O(l) [M(H2O)6]2+ :

DHhyd [∝x (= z2/r) in first order]

M2+

Assume -1.8 es per each d electron added

(-0.3 es in the textbook is something wrong)

LFSE

weak field octahedral [M(H2O)6]2+ ang

ula

r o

ver

lap

en

erg

y

+ -1.8 es x number of d electrons

Other shapes



Consideration of both group theory and angular overlap model can be used to determine which d orbitals

interact ligand s orbitals and give estimations of the energy levels of the MOs for geometries other than

octahedral and square planar.

trigonal bipyramidal ML5 (D3h)

M

L

L

L

L

L

M

dz2 : A1'

dx2-y2, dxy : E' dyz, dzx : E''

Gs 5 2 1 3 0 3 Gs = 2A1' + A2'' + E'

d e”

e’

a1’

M ML5

e”

e’

a1’ which one?

5 s-donor ligands

Other shapes



trigonal bipyramidal ML5 (D3h)

M

dz2 : A1'

dx2-y2, dxy : E' dyz, dzx : E''

dx2-y2, dxy: strength of s-interaction = 9/8

dyz, dzx : strength of s-interaction = 0

ligands : strength of s-interaction = 1

dz2 : strength of s-interaction = 2¾

2¾ es

9/8 es

es

Jahn-Teller Effect

There cannot be unequal occupation of orbitals with identical orbitals. To avoid such unequal

occupation, the molecule distorts so that these orbitals no longer degenerate. In other words, if the ground

electron configuration of a nonlinear complex is orbitally degenerate, the complex will distort to remove

the degeneracy and achieve a lower energy.

d9 (Cu(II))

In Oh, effect on eg orbital is bigger so that Jahn-Teller elongation usually occurs for d9.

(Why ? : think about the directions of the orbitals)

favor

Jahn-Teller Effect

There cannot be unequal occupation of orbitals with identical orbitals. To avoid such unequal

occupation, the molecule distorts so that these orbitals no longer degenerate. In other words, if the ground

electron configuration of a nonlinear complex is orbitally degenerate, the complex will distort to remove

the degeneracy and achieve a lower energy.

d9 (Cu(II))

[Cu(H2O)6]2+

d(Cu-Oeq) = 1.95 Å

d(Cu-Oax) = 2.38 Å

← [Cu(H2O)6]2+ + NH3 → [Cu(NH3)(H2O)5]

2+ + H2O K1 = 20,000

← [Cu(NH3)(H2O)5]2+ + NH3 → [Cu(NH3)2(H2O)4]

2+ + H2O K2 = 4,000

← [Cu(NH3)2(H2O)4]2+ + NH3 → [Cu(NH3)3(H2O)3]

2+ + H2O K3 = 1,000

← [Cu(NH3)3(H2O)3]2+ + NH3 → [Cu(NH3)4(H2O)2]

2+ + H2O K4 = 200

← [Cu(NH3)4(H2O)2]2+ + NH3 → [Cu(NH3)5(H2O)]2+ + H2O K5 = 0.3

← [Cu(NH3)5(H2O)]2+ + NH3 → [Cu(NH3)6]2+ K6 = very small

[Cu(NH3)6]2+ : difficult to make in aqueous solution. Can be made in ammonical solution.

← [Cu(H2O)6]2+ + 2 en → [Cu(en)2(H2O)5]

2+ + 4 H2O

N

N

OH2

N

N

H2O

Jahn-Teller Effect

d1 (Ti(III))

favor

Why?

Next Story

Experimental Facts

Documents

Chapter 4. Molecular Symmetry - KNUbh.knu.ac.kr/~leehi/index.files/Coordination_Chemistry...Valence Bond Theory (VBT) : Hybridization. Description of atomic orbital types used to share