chapter 10. coordination chemistry ii: bonding -...

1

Chapter 10.Coordination Chemistry II:

Bonding

Experimental Fact 1 (Thermodynamics)

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

2

Experimental Fact 2 (Magnetic Properties)

SQUID (Superconducting QUantum Interference Device)

Magnetic Susceptibility (χ)


Magnetic Susceptibility (χ) = the degree of magnetization of a materialin response to a magnetic field = M/H

χ

T (K)TCTN

paramagnetic

ferromagnetic

antiferromagnetic

TC : Curie TemperatureTN : Neel Temperature

Curie Law : χ = C/T

Curie-Weiss Law : χ = C/(T-θ)

Ferromagnetism : T < TC

Antiferromagnetism : T < TN

Paramagnetism : competition between magnetic coupling and thermal motionAll magnetic materials should have unpaired electrons.

3


Magnetic Susceptibility (χ)

Gives information of the magnetic moment (µ) of a material

µ = 2.828 (χT)1/2 µΒ (µΒ : 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

µS+L = g [J(J+1)]1/2 µΒ

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

µS+L = g [S(S+1) + 0.25L(L+1)]1/2 µΒ

total angular momentum quantum number

2J(J+1)

When spin-orbit coupling is negligible,true for most cases except heavy metals such as Lanthanides


µS+L = g [S(S+1) + 0.25L(L+1)]1/2 µΒ

µS = g [S(S+1)]1/2 µΒIn most cases, L is effectively quenched,

J = S g = 2, gfree electron = 2.0023

2

4


µS = g [S(S+1)]1/2 µΒWhy is L quenched in crystal field ?

0

10011

0

00

1/2

1/21/2

Experimental Fact 3 (Colors of Aqueous Solutions)

Cu(H2O)62+ Co(H2O)6

2+ Ni(H2O)62+ Fe(H2O)6

2+

5

Experimental Fact 1, 2, 3stability constant (formation constant), K

K1 = [Fe3+][SCN-]

[FeSCN2+]= 9 x 102

Why?

Have to know the characteristics of the bondingsand the electronic structures of complexes.

010011

0

001/2

1/21/2

Bonding Theories of Complexes

Valence Bond Theory (VBT)

Crystal Field Theory (CFT)

Ligand Field Theory (LFT)

6

Valence Bond Theory (VBT) : HybridizationFirst attempt of quantum mechanical explanation of chemical bonding

Ψ = φΑ(1)φΒ(2)Ψ = φΑ(1)φΒ(2)+φΑ(2)φΒ(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

Valence Bond Theory (VBT) : HybridizationHCl

Cl2

C

H

HH

90o90o

90o

and one H at not defined position

???

tetrahedral,4 equivalent bonds

CH4

4H + C H C HH

H

A σ bond centers along the internuclear axis.

σ bond

σ bond

7

109.5o

Valence Bond Theory (VBT) : HybridizationHybridization : 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

Valence Bond Theory (VBT) : HybridizationCH4

sp3

sp3 hybrid a.o.s:

C(sp3)tetrahedral σ(sp3

C + 1sH)

4HCH

H HH

109.5o

2p2s sp3N

3

σ(sp3N + 1sH)

NH H

H

lone pair in sp a.o.sp3 hybridized

NH3

H2O

Osp32s

2psp3 hybridized

lone pairs in sp3 a.o.s

OH

Hσ(sp3

O + 1sH)H-O-H

N

H

HH

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Valence Bond Theory (VBT) : Hybridization

BF3

sp2

trigonal planar,3 equivalent bonds

B

H

H H

Valence Bond Theory (VBT) : Hybridizationsp2

C2H4

all six atoms liein the same plane

σ-bond π-bond

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

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Valence Bond Theory (VBT) : Hybridizationsp

linear

Valence Bond Theory (VBT) : Hybridizationsp

linear

linear

H-C≡C-H

10

Valence Bond Theory (VBT) : Hybridizationdsp3 PCl5

A

B

B

B

B

BA

B

B

B

B

B

trigonal bipyramid

PCl5

Valence Bond Theory (VBT) : Hybridizationd2sp3 SF6

A

B

B

B

B

B

B

A

B

B

B

B

octahedral

B

B

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The Localized Electron Model : A Summary•Draw the Lewis structure(s)•Determine the arrangement of electron pairs (VSEPR model).•Specify the necessary hybrid orbitals.

Valence Bond Theory (VBT) : Hybridization

Ex) What is the hybridization of each indicated atom in the following molecule? How many σ and π bonds are in the molecule?

HC

HC

C OO

C

H

H

H

CN

sp3sp3

sp

sp2 sp2

sp2

12 σ bonds and 4 π bonds

How many lone pair electrons?

Valence Bond Theory

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)

5d6s

6p

from ligands5ddsp2 hybrids

6p

4 dsp2 hybrids (abstract figure)

3d4s

4p

3dsp3 hybrids

from ligands

4 sp3 hybrids (abstract figure)

12

Valence Bond Theory

Octahedral

Co3+ ([Ar]3d6)[Co(NH3)6]3+ : diamagnetic

3d4s

4p

[CoF6]3- : paramagneticOctahedral

4d

3dd2sp3 hybrids

from ligands3d

sp3d2 hybrids

4d

from ligands

Valence Bond Theory

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.•Mnay 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.

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Crystal Field Theory

• Developed to explain metal ions in crystalcalled Crystal Field Theroy (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

LL

bigger repulsionhigher energy level


dfree ion

Uniform Field (Spherical Field)

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dfree ion


Octahedral Field

dz2, dx2-y2

dxy, dyz, dzx


dfree ion


Octahedral Field

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

0.6∆o

0.4∆o

∆o (=10Dq): ligand splitting

parameter

15


Octahedral Field (Oh)

dz2, dx2-y2

dxy, dyz, dzxt2g

eg

Uniform FieldTetragonal elongation (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g



dz2, dx2-y2

dxy, dyz, dzxt2g

eg


dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

Tetragonal compression (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

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dz2, dx2-y2

dxy, dyz, dzxt2g

eg


dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

Square-planar field (D4h)

dx2-y2

dxy

dz2

dyz, dzx eg

a1g

b1g

b2g

∆1

∆2

∆3



dz2, dx2-y2

dxy, dyz, dzxt2g

eg

Uniform FieldCubic Field

dz2, dx2-y2

dxy, dyz, dzx

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dz2, dx2-y2

dxy, dyz, dzxt2g

eg

Uniform FieldCubic Field

dz2, dx2-y2

dxy, dyz, dzx

Tetrahedral Field (Td)

dz2, dx2-y2

dxy, dyz, dzxt2

e∆t ≈ 4/9 ∆o


Octahedral (Oh)

dz2, dx2-y2

dxy, dyz, dzx

t2g

eg

Uniform Field Tetrahedral (Td)

dz2, dx2-y2

dxy, dyz, dzxt2

e

∆t

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

Square-planar (D4h)

dx2-y2

dxy

dz2

dyz, dzx

eg

a1g

b1g

b2g

∆1

∆2

∆3

d

Tetragonal elongation (D4h)

∆o

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Why are complexes formed in crystal field theory? Crystal Field Stabilization Energy (CFSE)

or Ligand Field Stabilization Energy (LFSE)

Octahedral Field

t2g

eg

0.6∆o

0.4∆o

d3 LFSE of d3 in octahedral structure= (-0.4∆o) x 3 = -1.2 ∆o

LFSE : the stabilization of the d electronsbecause of metal-ligand environments

Crystal Field TheoryElectron 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 (Πc + Πe)= -0.6 ∆o + 3Πe

LFSE + pairing energy (Πc + Πe)= -1.6 ∆o + Πc + 3Πe

Πc : Coulombic energyΠe : Exchange energy (=exchanges between the same spins at the same

energy )

∆E = strong field - weak field= -∆o + Πc

∆E > 0 weak field (high spin)∆E < 0 strong field (low spin)

∆o < Πc

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Ligand Field Stabilzation Energies (Oh)


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 ∆o

Spectrochemical Series for LigandsCO > 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+

20


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+

[Co(H2O)]3+ is the only low-spinagua complex.



0

10011

0

00

1/2

1/21/2

Spin States (Oh)

s½13/225/223/21½0

½13/211/201/21½0

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A thermodynamic concequence of LFSE(Hydration Enthalpy)

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

M2+M3+

relatively small compared to LFSE

and LFSE

: mostly comes from LFSE

Ligand Field Stabilzation Energies (Td)


dz2, dx2-y2

dxy, dyz, dzxt2

e

∆t

d 0.4∆t

0.6∆t

tetrahedral field

∆t (≈4/9 ∆o) : all high-spin configuration

Zn2+

Cu2+

Ni2+

Co2+

Fe2+

Mn2+

Cr2+

Cr3+

V3+

Ti3+

ex

½-0.4e4t259

00e4t2610

1-0.8e4t248

3/2-1.2e4t237

2-0.6e3t236

5/20e2t235

2-0.4e2t224

3/2-0.8e2t213

1-1.2e22

½-0.6e11

Spin States (S)LFSEs (∆t)electron configurationsd electrons

22


CFT explains well the magnetic propertiesand 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

Ψ = cAφA + cΒφB

|cA| = |cΒ|

|cA| > |cΒ| |cA| >> |cΒ||cA| = |cΒ|

|cA| < |cΒ||cA| << |cΒ|

N atomic orbitals => N molecular orbitalsSymmetry match of atomic orbitalsRelative energy of atomic orbitals

3 things to consider to form MOs

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Ligand Field Theory

3 things to consider to form MOs

bonding bonding nonbonding

N atomic orbitals => N molecular orbitalsSymmetry match of atomic orbitalsRelative energy of atomic orbitals

Ligand Field Theory

Two Primary Influences to Ligand Field1) Geometries – Oh, Td, D4h ...

2) Types of Ligands – σ-donor, π-donor, π-acceptor

σ-donor ligands : H-, NH3 ...

M :H M :NH3

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

X-M

px

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Ligand Field Theory

Two Primary Influences to Ligand Field1) Geometries – Oh, Td, D4h

2) Types of Ligands – σ-donor, π-donor, π-acceptor

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

C=OM

Ligand Field TheoryConstructing MOs of Transition-Metal Complexes

MLn:Assume central metal ion, M, has available s,p, and d orbitals : 9 orbitalsAssume ligands, L, have s and p orbitals : 4n orbitals combination of

the 4n orbitals makes σ-donor, π-donor, and π-acceptor orbitals

Ms : A1g

px, py, pz : T1udz2, dx2-y2 :,Eg

dxy, dyz, dzx : T2g

: representations of σ-donor orbitals

L

Oh (ML6) with σ-donor ligands

Γσ 6 0 0 2 2 0 0 0 4 2

Γσ = T1u + Eg + A1g

25

Ligand Field TheoryOh (ML6) with σ-donor ligands

Ms : A1g


dxy, dyz, dzx : T2g

Γσ = T1u + Eg + A1g

L6M ML6

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


SymmetryAdaptedOrbitals

M ML6

Think about what theseorbitals look like.

L6

26

M ML6 L6



Ligand Field TheoryOh (ML6) with π-acceptor, donor ligands

Ms : A1g


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

L

Γπ 12 0 0 0 -4 0 0 0 0 0

Γπ = T1g + T2g + T1u + T2u

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Ligand Field Theory

M ML6

Γπ = T1g + T2g + T1u + T2uOh (ML6) with π-acceptor, donor ligands

X-M

C=OM

L6

Ligand Field Theory

Γπ = T1g + T2g + T1u + T2uOh (ML6) with π-acceptor, donor ligands

X-M

C=OM

Spectrochemical Series for LigandsCO > CN- > PPh3 > NO2

- > phen > bipy > en > NH3 > py > CH3CN > NCS- > H2O > C2O4

2- > OH- > RCO2- > F- > N3

- > NO3- >

Cl- > SCN- > S2- > Br- > I-

π acceptor π donor(strong field ligand) (weak field ligand)

Metal-to-ligand (M L) π bonding(π back-bonding)

increases metal-ligand bond strength

Ligand-to-metal (L M) π bondingdecreases metal-ligand bond strength

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Ligand Field TheoryD4h (ML4) with σ-donor ligands (square planar)

Ms : A1g

px, py : Eupz : A2u

dz2 : A1gdx2-y2 :,B1g dxy : B2g

dyz, dzx : Eg

Γσ = A1g + B1g + Eu


L

Γσ 4 0 0 2 0 0 0 4 2 0

Ligand Field Theory

Ms : A1g

px, py : Eupz : A2u


dyz, dzx : Eg


M ML4

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

L4

29

Ligand Field Theory

L4M ML4

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


Think about what theseorbitals look like.

Ligand Field TheoryD4h (ML4) with π-acceptor, donor ligands (square planar)

Ms : A1g

px, py : Eupz : A2u


dyz, dzx : Eg



L

Γσ 4 0 0 2 0 0 0 4 2 0

: representations of π ligand orbitals

Γπ 8 0 0 -4 0 0 0 0 0 0

Γπ = A2g + B2g + Eu + A2u + B2u + Eg

30


Ms : A1g

px, py : Eupz : A2u


dyz, dzx : Eg


Γπ = A2g + B2g + Eu + A2u + B2u + Eg

(Γπ = Γ║ + Γ┴)

in-plane out-of-plane

[Pt(CN)4]2-


up and downdepending on ligands

∆1 >> ∆2, ∆3

d8 (sq. pl) low-spin

allways b1g > a1g, eg, b2g

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Ligand Field Theory

Ms : A1

px, py, pz : T2dz2, dx2-y2 :,E

dxy, dyz, dzx : T2

Γσ = A1 + T2

Td (ML4)


L

Γσ 4 1 0 0 2

: representations of π ligand orbitals

ΓΠ 8 -1 0 0 0ΓΠ = E + T1 + T2

Ligand Field Theory

Ms : A1

px, py, pz : T2dz2, dx2-y2 :,E

dxy, dyz, dzx : T2

Td (ML4)

a1 + t2

ΓΠ = E + T1 + T2

L4M ML4

t2

a1

e + t2

Γσ = A1 + T2

1t2

1a1

2t2

e

2a1

3t2

32

Angular Overlap

Ligand Field Model• No explicit use of energy• Diffucult 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

Angular Overlap σ-donor interactions

basic creterion: the strongest σ interation

overlap between dz2 and ligand pz (or hybrid) : eσ

33



ex) σ-donor interaction of [M(NH3)6]n+

dz2 : strength of σ-interaction = 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3

dx2-y2 : strength of σ-interaction = 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3

dxy, dyz, dzx : strength of σ-interaction = 0 + 0 + 0 + 0 + 0 + 0 = 0

ligand 1,6 orbitals : strength of σ-interaction = 1 + 0 + 0 + 0 + 0 + 0 = 1ligand 2, 3, 4, 5 orbitals : strength of σ-interaction = ¼ + ¾ + 0 + 0 + 0 + 0 = 1

34


ex) [M(NH3)6]n+

dz2 : strength of σ-interaction = 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3

dx2-y2 : strength of σ-interaction = 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3

dxy, dyz, dzx : strength of σ-interaction = 0 + 0 + 0 + 0 + 0 + 0 = 0

ligand 1,6 orbitals : strength of σ-interaction = 1 + 0 + 0 + 0 + 0 + 0 = 1ligand 2, 3, 4, 5 orbitals : strength of σ-interaction = ¼ + ¾ + 0 + 0 + 0 + 0 = 1

stabilization : 12eσ

destabilization : 0 or (3xn)eσ

Angular Overlap π-acceptor interactions

basic creterion: the strongest π interation

overlap between dxz and ligand π* orbital: eπ

eπ < eσ

35



ex) π-acceptor interaction of [M(CN)6]n- (σ-donor interactions are the same as in [M(NH3)6]n+)

dz2, dx2-y2 : strength of π-interaction = 0 + 0 + 0 + 0 + 0 +0 = 0dxy, dyz, dzx : strength of π-interaction = 0 + 1 + 1 + 1 + 1 + 0 = 4

ligand 1, 2, 3, 4, 5, 6 orbitals : strength of π-interaction = 0 + 0 + 0 + 0 + 1 + 1 = 2

36


ex) π-acceptor interaction of [M(CN)6]n- (σ-donor interactions are the same as in [M(NH3)6]n+)



2eπ

Angular Overlap π-donor interactions

usually, eπ for π-acceptor interation > eπ for π-donor interation

37


ex) π-donor interaction of [MX6]n-




ex) π-donor interaction of [MX6]n-



2eπ

π-acceptor interaction

38

Angular Overlap Magnitudes of eσ, eπ, and ∆ : depend on both ligands and metals

high spin low spin

high spin low spin

Angular Overlap Magnitudes of eσ, eπ, and ∆ : depend on both ligands and metals

• eσ > eπ

• eσ , eπ ↓ as size of X- ↑and electronegativity ↓

isoelectronic• eσ , eπ ↑ as nuclear charge ↑

39

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 configuation of a nonlinear complex is orbitally degenerate, the complex will distort to remove the degeneracy and achieve a lower energy.

d9 (Cu(II))

favor

d1 (Ti(III))

favor

Jahn-Teller Effect

Number of d electrons 1 2 3 4 5 6 7 8 9 10High-spin JT w w s w w sLow-spin JT w w w w s s

w = weak JT effect, s = strong JT effect

40

Angular Overlap

Four- and six- coordinate preferencesAngular overlap caculation can provide us with some indication of relative stabilities depending on d electrons and geometries.

angu

lar

over

lap

ener

gy

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

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

Angular Overlap

Four- and six- coordinate preferences

angu

lar

over

lap

ener

gy

Sq. pl is favorable.

41

Angular Overlap

Other shapesConsideration of both group theory and angular overlap can give estimations of the energy levels of the MOs for geometries other than octahedral and square planar.

trigonal bipyramidal ML5 (D3h)

ML

L

L

L

L

D3h E 2C3 3C2 σh 2S3 3σv

Mdz2 : A1'

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

Γσ 5 3 1 3 0 3

Γσ = 2A1' + A2'' + E'

Chelate Effect

42

Experimental Fact 1, 2, 3stability constant (formation constant), K

K1 = [Fe3+][SCN-]

[FeSCN2+]= 9 x 102

010011

0

001/2

1/21/2

Why?Next Story

chapter 10. coordination chemistry ii: bonding -...

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