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Coordination Chemistry III: Electronic Spectra 11

Cu(H2O)62+ Co(H2O)6

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

2+

Wheel of Color

absorption spectrum of [Cu(H2O)6]2+

Beer-Lambert Law

-log(I/I0) = A = elc : Absorbance

I/I0 : transmittance

e : molar absorptivity (Lmol-1cm-1)

Wheel of Color

absorption spectrum of [Cu(H2O)6]2+ absorption spectrum of [Cr(NH3)6]

3+ (d3)

t2g

eg

t2g

eg

Why 4 or 2 bands?

Wheel of Color

absorption spectrum of [Cu(H2O)6]2+ absorption spectrum of [Cr(NH3)6]

3+ (d3)

t2g

eg

t2g

eg

Why 4 or 2 bands?

Because the transitions occur between states.

An electron configuration can have several states.

Possible states (microstates) of carbon (1s22s22p2)

and many others ..... (think Pc and Pe)

Strategy to understand the electronic spectra of complexes

1. Determine free-ion (or in uniform field) term symbols.

2. Determine how these terms split in a weak field.

3. Determine how these terms split in a strong field.

4. Correlate these with Tanabe-Sugano diagram.

Terms : energy levels (or states) of a particular configuration

Terms (Term Symbols)

Quantum numbers of single electron atoms (ions)

Y = Rnl(r)·Q lm (q)·Flm (f)·ym l l s

n : principal quantum number (n = 1,2,3,4....)

l : (orbital) angular momemtum quantum number (l = 0, 1,...., n-1)

ml : angular momemtum magnetic quantum number (l = -n, -n+1,...., n)

ms : spin magnetic quatum number (ms = -½ , ½ )

Quantum numbers of single

electron atoms (ions)

Quantum numbers of

multielectron atoms (ions)

Quantum numbers of multielectron atoms (ions)

Two schemes for describing interactions (couplings) between electrons

1. Russell-Saunders coupling (L-S coupling)

a. Orbit-orbit interaction (coupling) :

ML = Sml L : total orbital angular momentum quantum number

b. Spin-spin interaction (coupling) :

MS = Sms S : total spin angular momentum quantum number

c. L-S coupling :

J = L + S : total angular moment quantum number

2. j-j coupling (spin-orbit interaction)

jn = ln + sn J = Sjn : total angular moment quantum number

In light atoms, the interactions between the orbital angular momenta of individual electrons is

stronger than the spin-orbit coupling between the spin and orbital angular momenta. These

cases are described by "L-S coupling". However, for heavier elements with larger nuclear

charge, the spin-orbit interactions become as strong as the interactions between individual

spins or orbital angular momenta. We won't study the latter in this course.


Quantum numbers of

multielectron atoms(ions)


Russell-Saunders coupling (L-S coupling)





c. L-S coupling :


J = |L-S|, |L-S|+1, ... , L+S


Free Ion Term Symbols


Russell-Saunders coupling (L-S coupling)





c. L-S coupling :


J = |L-S|, |L-S|+1, ... , L+S


Term symbol

2S+1LJ

2S+1 : spin multiplicity

States : L = 0 (S), 1(P), 2(D), 3(F), 4(G), 5(H), 6(I),...

Free Ion Term Symbols Terms (Term Symbols)

Term symbol

2S+1LJ

2S+1 : spin multiplicity

States : L = 0 (S), 1(P), 2(D), 3(F), 4(G), 5(H), 6(I),...

1S MS = 0

ML=0 x

2S MS = -1/2 MS = +1/2

ML=0 x x

1 microstate 2 microstates

3P MS = 1 MS = 0 MS = -1

ML=1 x x x

ML=0 x x x

ML=-1 x x x

9 microstates


A systematic approach to term symbols 1. Determine the possible values of ML and MS.

2. Determine the electron configurations that are allowed by the Pauli principle.

3. Set up a chart of microstates.

4. Resolve the chart of microstates into appropriate atomic states (terms).

Possible states (microstates) of carbon (1s22s22p2)

+ ½

- ½

+ ½

- ½

+ ½

- ½

+ ½

- ½

+ ½

- ½

ml

p2

1s 2s 2p 1s 2s 2p

0 0 1 0 -1 0 0 1 0 -1

ms + ½ + ½

(1+, 0+) (1+, 1-)


p2

l1 = l2 = 1

s1 = s2 = ½

ML = 2, 1, 0, -1, -2

MS = 1, 0, -1










1. Max MS = 0 : S = 0 MS = 0

Max ML = 2 : L = 2 ML = 2,1,0,-1,-2 1D ( 5 microstates)

2. Max MS = 1 : S = 1 MS = 1,0,-1

Max ML = 1 : L = 1 ML = 1,0,-1 3P ( 9 microstates)

3. Max MS = 0 : S = 0 MS = 0

Max ML = 0 : L = 0 ML = 0 1S ( 1 microstate)






p2

1D 3P 1S

1D2 3P2,

3P1,3P0

1S0

mJ = 2,1,0,-1,-2

mJ = 2,1,0,-1,-2

mJ = 1,0,-1

mJ = 0 mJ = 0

How about energy levels?


Hund's rule (for groundstate term symbol)

1. The term with maximum multiplicity lies lowest in energy

2. For a given multiplicity, the term with the largest value of L lies lowest in energy.

3. For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.

When the shell is more than half full, the opposite rule holds (highest J lies lowest).

p2

1S, 1D

3P

1D

1S

3P

1D2

1S0

3P1

3P2

3P0

p2

1D 3P 1S

1D2 3P2,

3P1,3P0

1S0

mJ = 2,1,0,-1,-2

mJ = 2,1,0,-1,-2

mJ = 1,0,-1

mJ = 0 mJ = 0

How about energy levels?


p1 l1 = 1

s1 = ½

L = 1

S = ½ 2P (2P3/2,

2P1/2)

p3 l1 = l2 = l3 = 1

s1 = s2 = s3 = ½

ML = 3, 2, 1, 0, -1, -2, -3

MS = 3/2, 1/2, -1/2, -3/2

p2 1D(1D2), 3P(3P2,

3P1,3P0),

1S(1S0)

p3 MS

3/2 1/2 -1/2 -3/2

ML 2 1+,1-,0+ 1+,1-,0-

1 (1+,0+,0-) (1+, 1-,-1+) (1-,0+,0-)(1+,1-,-1-)

0 1+,0+,-1+ 1+,0+,-1-

1+,0-,-1+

1-,0+,-1+

1+,0-,-1-

1-,0+,-1-

1-,0-,-1+

1-,0-,-1-

-1 x x x x

-2 x x

2D (2D5/2, 2D3/2),

2P(2P3/2, 2P1/2) 4S (4S3/2)


p1 l1 = 1

s1 = ½

L = 1

S = ½ 2P (2P3/2,

2P1/2)

p3 l1 = l2 = l3 = 1

s1 = s2 = s3 = ½

ML = 3, 2, 1, 0, -1, -2, -3

MS = 3/2, 1/2, -1/2, -3/2

p2 1D(1D2), 3P(3P2,

3P1,3P0),

1S(1S0)

2D (2D5/2, 2D3/2),

2P(2P3/2, 2P1/2) 4S (4S3/2)

p4 same as p2

p5 same as p1

p6 L =0, S = 0 1S (1S0)

s1d1 l1 = 0, l2 = 2

s1 = s2 = ½

L = 2

S = 1, 0

3D (3D3, 3D2,

3D1)

1D (1D2)

d1 l1 = 2

s1 = ½

L = 2

S = ½ 2D (2D5/2,

2P3/2)


d2 l1 = l2 = 2

s1 = s2 = ½

ML = 4, 3, 2, 1, 0, -1, -2, -3, -4

MS = 1, 0, -1

d2 MS

1 0 -1

ML

4 2+,2-

3 2+,1+ 2+,1-

2-,1+

2-,1-

2 2+,0+ 2+,0- 2-,0+

1+,1-

2-,0-

1 1+,0+

2+,-1+

1+,0- 1-,0+

2+,-1- 2-,-1+

1-,0-

2-,-1-

0

1+,-1+

2+,-2+

0+,0-

1+,-1- 1-,-1+

2+,-2- 2-,-2+

1-,-1-

2-,-2-

-1 x x x x x x x x

-2 x x x x x

-3 x x x x

-4 x

1G 3F 1D

3P

1S

terms

d2

1S

3F

1D

3P

1G


d2 l1 = l2 = 2

s1 = s2 = ½

ML = 4, 3, 2, 1, 0, -1, -2, -3, -4

MS = 1, 0, -1

1G 3F 1D

3P

1S

terms

d2

1S

3F

1D

3P

1G

by Hund's rule

in reality

d2

1G

3F

1S

1D

3P


Short-cut to ground-state term symbols : make max S and max L

ml 2 1 0 -1 -2

d1 S = ½ , L=2 2D

d2 S = 1 , L=3 3F

d4 S = 2 , L=2 5D

d7 S = 3/2 , L=3 4F

Splittings of free-ion terms

in a chemical environment

t2g

eg

d

2S+1T2g (triply degenereate)

2S+1Eg (doubly degenerate)

2S+1D

Oh

Oh

spin multiplicity remains the same.

In Weak Field


in a chemical environment In Weak Field

Splitting of One-Electron Levels in Various Symmetries

Levels Oh Td D4h

s a1g a1 a1g

p t1u t2 a2u+eu

d eg+t2g e+t2 a1g+b1g+b2g+eg

f a2u+t1u+t2u a2+t1+t2 a2u+b1u+b2u+2eu

g a1g+eg+t1g+t2g a1+e+t1+t2 2a1g+a2g+b1g+b2g+2eg

h eu+2t1u+t2u e+t1+2t2 a1u+2a2u+b1u+b2u+3eu

i a1g+a2g+eg+t1g+2t2g a1+a2+e+t1+2t2 2a1g+a2g+2b1g+2b2g+3eg



Terms Oh Td D4h

S A1g A1 A1g

P T1g T1 A2g+Eg

D Eg+T2g E+T2 A1g+B1g+B2g+Eg

F A2g+T1g+T2g A2+T1+T2 A2g+B1g+B2g+2Eg

G A1g+Eg+T1g+T2g A1+E+T1+T2 2A1g+A2g+B1g+B2g+2Eg

H Eg+2T1g+T2g E+2T1+T2 A1g+2A2g+B1g+B2g+3Eg

I A1g+A2g+Eg+T1g+2T2g A1+A2+E+T1+2T2 2A1g+A2g+2B1g+2B2g+3Eg

* Assuming all free-ion terms arising from dn configurations.

Splitting of Multi-Electron Levels in Various Symmetries



Terms Oh

S A1g

P T1g

D Eg+T2g

F A2g+T1g+T2g

G A1g+Eg+T1g+T2g

H Eg+2T1g+T2g

I A1g+A2g+Eg+T1g+2T2g

Splitting of Multi-Electron Levels in Various Symmetries

d2

1G

3F

1S

1D

3P

free-ion electron configuration

free-ion terms

in weak field (Oh)


in a chemical environment In Strong Field

d2

In extremely (∞) strong field

t2geg

eg2

t2g2

What will happen when the field relaxes?

(Looking for splittings in strong field)



d2


t2geg

eg2

t2g2

t2g2

T2g x T2g

T2g 3 0 1 -1 -1 3 -1 0 -1 1

T2g x T2g = A1g + Eg + T1g + T2g

9 0 1 1 1 9 1 0 1 1

number of the microstates of t2g2 configuration = 15

T2g x T2g = aA1g + bEg + cT1g + dT2g

assume the spin multiplicities of the irreducible representations as

possible combinations of a, b, c, d number of microstates = a+2b+3c+3d

(1,1,1,3), (1,1,3,1), (3,3,1,1), (2,2,2,1), (2,2,1,2), (1,1,2,2)

t2g2 1A1g + 1Eg + 1T1g +

3T2g 1A1g + 1Eg + 3T1g + 1T2g

3A1g + 3Eg + 1T1g + 1T2g

2A1g + 2Eg + 2T1g + 1T2g

2A1g + 2Eg + 1T1g + 2T2g 2A1g + 2Eg + 1T1g + 2T2g

In Strong Field (Oh)

no spin doublet in the

free-ion terms

3 possiblities



d2


t2geg

eg2

t2g2

eg2

Eg x Eg

Eg

Eg x Eg = A1g + A2g + Eg

number of the microstates of eg2 configuration = 6

Eg x Eg = aA1g + bA2g + cEg

assume the spin multiplicities of the irreducible representations as

possible combinations of a, b, c number of microstates = a+b+2c

(1,1,2), (2,2,1), (3,1,1), (1,3,1)

eg2 1A1g + 1A2g + 2Eg

2A1g + 2A2g + 1Eg 3A1g + 1A2g + 1Eg 1A1g + 3A2g + 1Eg

no spin doublet in the free-ion terms

2 possiblities

2 -1 0 0 2 2 0 -1 2 0

4 1 0 0 4 4 0 1 4 0




d2


t2geg

eg2

t2g2

3 0 1 -1 -1 3 -1 0 -1 1

t2g1 eg

1

Eg

T2g x Eg = T1g + T2g

number of the microstates of t2geg configuration = 24

t2geg 1T1g + 1T2g + 3T1g + 3T2g

T2g x Eg

T2g

6 0 0 0 -2 6 0 0 -2 0

2 -1 0 0 2 2 0 -1 2 0



in a chemical environment In Strong Field (Oh)

d2


t2geg

eg2

t2g2

1T1g + 1T2g + 3T1g + 3T2g

3A1g + 1A2g + 1Eg 1A1g + 3A2g + 1Eg

1A1g + 1Eg + 1T1g +3T2g

1A1g + 1Eg + 3T1g + 1T2g

3A1g + 3Eg + 1T1g + 1T2g

in strong field (Oh)

not complete yet but can imagine

how to split in strong field !!


in a chemical environment Correlation

d2


t2geg

eg2

t2g2

1T1g + 1T2g + 3T1g + 3T2g

3A1g + 1A2g + 1Eg 1A1g + 3A2g + 1Eg

1A1g + 1Eg + 1T1g +3T2g

1A1g + 1Eg + 3T1g + 1T2g

3A1g + 3Eg + 1T1g + 1T2g


not complete yet but can imagine

how to split in strong field !!

t2geg

eg2

t2g2

1T1g + 1T2g + 3T1g + 3T2g


3A1g + 1A2g + 1Eg 1A1g + 3A2g + 1Eg

1A1g + 1Eg + 1T1g +3T2g

1A1g + 1Eg + 3T1g + 1T2g

3A1g + 3Eg + 1T1g + 1T2g


in weak field (Oh)

how to correlate

1. 1-to-1 correspondence

between the states at weak

field and strong field

2. non-crossing rule :

states of the same spin

degeneracy and symmetry

cannot cross.


in a chemical environment Correlation

Correlation

Diagram

d2 (Oh) Tanabe-Sugano Diagrams

(/10)

d2 (Oh) Tanabe-Sugano Diagrams

The lowest-energy state is plotted along the

horizontal axis.

D : ligand field splitting

B : Racah parameter, a measure of the

repulsion between terms of same multiplicity

E : the energy (of excited state) above the

ground state

15B

(/10)

d3 (Oh), d4 (Oh) Tanabe-Sugano Diagrams

d3 (Oh) d4 (Oh)

(/10) (/10)


d5 (Oh) d6 (Oh)

(/10) (/10)


d7 (Oh)

d8 (Oh)

(/10) (/10)

Selection Rules Electronic Spectra

Data obtained

1. Transition energies (frequency positions in a spectrum)

2. Intensities of the bands

3. Widths of the bands

Intensities of the bands (Selection rules)

1. Spin selection rule : DS = 0

2. Laporte selection rule : g ↔ u

Relaxation of selection rules

1. Vibronic coupling relaxes Larpote selection rule.

Oh, e ~ 10 ~50 for d-d transitions with g ↔ g

Td, e ~ 500 for d-d transitions

2. Spin-orbit coupling relaxes spin selection rule.

e ≤ 1 for DS≠0

(/10)

Any transition expected?

d2 (Oh)


(/10)

d2 (Oh) [V(H2O)6]2+

3T1g(F) 3T1g(P) 3T1g(F) 3T2g

3T1g(F) 3A2g : UV region


absorption spectrum of [Cr(NH3)6]3+ (d3)

d3 (Oh)

(/10)

[M(H2O)6]3+ Electronic Spectra

[M(H2O)6]2+ Electronic Spectra

Symmetry Labels for Configurations Electronic Spectra

?

T designates a triply degenerate

asymmetrically occupied state.

E designates a doubly degenerate

asymmetrically occupied state.

A, B designate a non degenerate

symmetrically occupied state.

Ex

d1 Electronic Spectra

[Ti(H2O)6]3+

d1 : l1 = 2, s1 = ½ L=2, S = ½ 2D

eg

t2g

d

Oh

2T2g

2Eg

2D

Oh

2Eg 2T2g

2T2g 2Eg : 1 band ?

b1g

a1g

b2g

eg

2B2g 2Eg

2B1g 2A1g

2D

2T2g

2Eg

Oh

2B1g

2A1g

2B2g

2Eg

D4h

out of visible range

Jahn-Teller distortion

b1g

a1g

b2g

eg

d9 Electronic Spectra

d1 : l1 = 2, s1 = ½ L=2, S = ½ 2D

eg

t2g

d

Oh

2T2g

2Eg

2D

Oh

2Eg 2T2g

2T2g 2Eg : 1 band ?

2D

2T2g

2Eg

Oh

2B1g

2A1g

2B2g

2Eg

D4h

out of visible range

Jahn-Teller distortion [Cu(H2O)6]2+

d9 : 2D

2Eg

2T2g

2Eg 2T2g : 1 band ?

2B2g 2Eg

2B1g 2A1g

2B1g 2A1g

2B2g 2Eg

2Eg

2T2g 2B2g

2Eg

2B1g

2A1g

Hole Formalism Tanabe-Sugano Diagrams

2T2g

2Eg hole

2Eg

2T2g

2T2g

2Eg

d1 (Oh) d9 (Oh)

2D

free ion

• the same free-ion terms

• the same splitting pattern in fields but the

energy levels are reversed.

d1 d9

dn d10-n

Hole Formalism Tanabe-Sugano Diagrams

(/10)

d2 (Oh)

d8 (Oh)

(/10)

Tanabe-Sugano Diagrams

d7 (Oh)

(/10)

d3 (Oh)

(/10)

Hole Formalism


d6 (Oh)

(/10)

d4 (Oh)

(/10)

Hole Formalism

Tanabe-Sugano Diagrams Hole Formalism

• the same free-ion terms

• the same splitting pattern in fields

d1(Td) d9(Oh)

dn(Td) = d10-n(Oh)

2D

2Eg

2T2g

2E

2T2

Oh Td

d1(Td) d9(Oh)

2T2(g)

2E(g) hole

d1(Td) d9(Oh) 2D

Terms Oh Td

S A1g A1

P T1g T1

D Eg+T2g E+T2

F A2g+T1g+T2g A2+T1+T2

G A1g+Eg+T1g+T2g A1+E+T1+T2

H Eg+2T1g+T2g E+2T1+T2

I A1g+A2g+Eg+T1g+2T2g A1+A2+E+T1+2T2

Tanabe-Sugano Diagrams Hole Formalism

d2 (Oh) ◄► d8 (Td) d3 (Oh) ◄► d7 (Td) d4 (Oh) ◄► d6 (Td) d5 (Oh) ◄► d5 (Td)

d6 (Oh) ◄► d4 (Td) d7 (Oh) ◄► d3 (Td) d8 (Oh) ◄► d2 (Td)

Tanabe-Sugano Diagrams Applications (Determination of Do)

d1, d9

2D

2Eg

2T2g

2T2g

2Eg Oh

d1 d9 Do Do

d1 d9

Do Do

[Cu(H2O)6]2+ [Ti(H2O)6]

3+


d4 (hs), d6 (hs)

Oh d4 (hs) d6 (hs)

5Eg 5T2g 5T2g

5Eg

[Fe(H2O)6]2+

[Cr(H2O)6]2+

Do

Do


Orgel Diagram for d1, d4(hs), d6(hs) d9

Orgel diagram

- considers only states with the same spin

multiplicity as that of the ground state.

- plots the energy levels of the states as LFSE.

d4 (hs) d6 (hs)

Do Do

Do

Do

Orgel Diagram for free-ion D ground state

[d1, d4(hs), d6(hs), d9]


Orgel Diagram for d2, d3, d7(hs), d8

d2

LFSE = -0.8Do

LFSE = 0.2Do

LFSE = 1.2Do

15B

d2

LFSE = -0.8Do

LFSE = 0.2Do

LFSE = 1.2Do

15B

Noncrossing rule

- the states with the same spin

mutiplicity and symmetry cannot cross

but may mix



oct d2, d7

tet d3, d8

oct d3, d8

tet d2, d7

D

D

0.8D

0.8D

-0.6D

1.2D

0.2D

+ 15B

0.2D

-1.2D

0.6D

-0.2D

+ 15B

-0.2D

0.8D : for the case of extremely strong field

Noncrossing rule

- the states with the same spin

mutiplicity and symmetry cannot cross

but may mix



oct d2, d7

tet d3, d8

oct d3, d8

tet d2, d7

D

D

1.2D

0.2D

-1.2D

0.6D - x

-0.2D

-0.6D - x

Orgel Diagram for free-ion F ground state

[d2, d3, d7(hs), d8]



oct d2, d7

tet d3, d8

oct d3, d8

tet d2, d7

D

D

1.2D

0.2D

-1.2D

0.6D - x

-0.2D

-0.6D - x

Orgel Diagram for free-ion F ground state

[d2, d3, d7(hs), d8]

Do

Do/B

E/B


[V(H2O)6]3+

n1= 17,800 cm-1 n2 = 25,700 cm-1

3T1g(F) 3T1g(P) 3T1g(F) 3T2g

3T1g(F) 3A2g : UV region

n2/n1 = 1.44 at Do/B = 31

at Do/B = 31

n1: E/B ~ 29 E = 17,800 cm-1 = 29B B ~ 610 cm-1

n2: E/B ~ 42 E = 25,700 cm-1 = 42B B ~ 610 cm-1

Do = 31B = 19,000 cm-1

31

42

29

Applications (Determination of Do and B)

d2

[Cr(NH3)6]3+

n2= 28,500 cm-1 n1 = 21,500 cm-1

UV

Do

E/B

Do/B


n2/n1 = 1.33 at Do/B = 33

at Do/B = 33 n1: E/B ~ 33 E = Do = 21,500 cm-1 = 33B B ~ 650 cm-1

n2: E/B ~ 44 E = 28,500 cm-1 = 44B B ~ 650 cm-1

33

44

33

Applications (Determination of Do and B)

d3

Tanabe-Sugano Diagrams Applications (Determination of Do and B)

d5(hs), d4-d7(ls)

d4 (Oh) d5 (Oh) d6 (Oh) d7 (Oh)

colorless (for example [Mn(H2O)6]2+)

d4-d7(ls) : difficult to analyze the electronic spectra because of many excited states with the

same spin multiplicity as that of the ground state

[Cu(H2O)6]2+ (d9)

[Cr(NH3)6]3+ (d3)

Charge-Transfer Band

CT

LMCT (CTTM) : ligand

to metal charge transfer

- ligand s (or p)-donor

orbital to metal d-orbital

MLCT (CTTL) :

metal to ligand charge

transfer

- metal d-orbital to

ligand p-acceptor

orbital (CO, CN-, SCN-,

bipy, S2CNR2-)

Both:

very intense : e ~ 50,000

UV/VIS region

LMCT (CTTM) : causes reduction of metal

MLCT (CTTL) : causes oxidation of metal

Charge-Transfer Band

LMCT (CTTM)

MLCT (CTTL)

[IrBr6]2- (d5, Oh) : strong absorption bands at ~600 nm and ~270 nm

Common for complexes with bipy and phen ligands

[MnO4]- (do, Td) : intense purple color (pO empty d)

[IrBr6]3- (d6, Oh) : strong absorption bands at ~250 nm

wheel of color - knubh.knu.ac.kr/~leehi/index.files/coordination_chemistry_electronic... · wheel...

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