8/12/2019 2-UV (1)

1/35

8/12/2019 2-UV (1)

2/35

2

UV-visible spectroscopyligand p*

(1) metal-metal (d-d) transition

s

*metal-ligand metal d

(2) charge transfer (MLCT)

ligand-metal n(LMCT) metal d

n(3) ligand-centered transition ligand p

s

instrument sample

energy energy energy outputsource selector analyzer

computerelectric connection

light path

absorbance IoA = log = ecl

I

e: extinction coefficient

c: concentration mol/L (M)

l: path length (cm)

8/12/2019 2-UV (1)

3/35

3

selection rules

1. only one electronis involved in any transition

2. there must be no net change of spin S = 0

3. it must involve an overall change in orbitalangular momentum of one unit L = 1

4. Laporte(or parity) selection ruleonly g uand u g transitions are allowed

vibronic couplinginteraction between electronicand vibrational modes

electronic transition e

Laporte allowed(charge transfer) 10000

(100050000)

Laporte forbidden(d-d transition)spin allowed; noncentrosymmetiric 100200

(200250)

spin allowed; centrosymmetric 5100

(20100)

spin forbidden 0.011

(< 1)

8/12/2019 2-UV (1)

4/35

4

[Co(H2O)6]2+

[CoCl4]2-

[Mn(H2O)6]2+

8/12/2019 2-UV (1)

5/35

5

d-d transition crystal field splitting

o size and charge of the metal ion and ligands

4d metal ~50% larger than 3d metal

5d metal ~25% larger than 4d metal

5d > 4d > 3dcrystal field stabilization energy (CFSE)

spin-pairing energy

high-spin/low spin configuration d4 ~ d7

d4

8/12/2019 2-UV (1)

6/35

6

other shapes

tetrahedral

t= 4/9 o

tetrahedron octahedron elongated squareoctahedron planar

8/12/2019 2-UV (1)

7/35

7

d1 [Ti(H2O)6]3+

hole formalism

d2 possible electronpossible arrangements of electrons transitions

hu = Do

8/12/2019 2-UV (1)

8/35

8

Russell-Saunders term symbolsfor free atoms and ions

S: total spin quantum number Sms

L : total orbital angular quantum number Sml

L = 0, 1, 2, 3, 4, ..S P D F G1 3 5 7 9

J: total angular quantum number L+S, ,L -S

d2configuration 10! = 45 microstates

8! 2!

S +1 0 -1L

4 (2+ 2-)

3 (2+

1+

) (2+

1-

) (2-

1+

) (2-

1-

)

(1+ 1-)2 (2+ 0+) (2+ 0-) (2- 0+) (2- 0-)

(1+ 0+) (1+ 0-) (1- 0+) (1- 0-)1 (2+-1+) (2+ -1-) (2- -1+) (2- -1-)

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

(2+ -2+) (2+ -2-) (2- -2+) (2- -2-)

1G 3F 1D 3P 1S9 + 21 + 5 + 9 + 1 = 45

ground term

2S+1LJ

8/12/2019 2-UV (1)

9/35

9

splitting of terms in various chemical

environmentsd orbitals in Ohenvironment

consider pure rotational O subgroup

rotation by angle a ==> R(r), Q(q), sinvariantonly F(f) will be altered

F

(f) = eimf ==>F

(f + a) = eim(f + a)m= 2, 1, 0, -1, -2

e2if e2i f + a)

eif ei f + a)e0 ======> e0e-if e-i f + a)

e-2if e-2i f + a)

states for dnsystems in Russell-Saunders coupling

8/12/2019 2-UV (1)

10/35

10

transformation matrix

e2ia 0 0 0 0

0 eia 0 0 0

0 0 e0 0 0

0 0 0 e-ia 0

0 0 0 0 e-2ia

sum of the diagonal elements

sin(l+ 1/2)ac (a) =

sin(a/2)

for d orbitals

sin(5p/2)c (E) = 5 c (C

2) == 1

sin(p

/2)

sin(5p/3) sin(5p/4)c (C

3) == -1 c (C

4) == -1

sin(p/3) sin(p/4)

==>G

= eg+ t2g

8/12/2019 2-UV (1)

11/35

11

splitting of one-electron levels in an Ohenvironment

splitting of one-electron levels in various symmetries

8/12/2019 2-UV (1)

12/35

12

determine the spin multiplicity of each termd2configuration in O

henvironment

(i) t2g2 aA1g+

bEg+cT1g +

dT2gtotal degeneracy 15

a b c d

I 1 1 1 3

II 1 1 3 1

III 3 3 1 1

(ii) t2g1

eg1 a

T1g +b

T2gtotal degeneracy 24

only possibility 1T1g

1T2g

3T1g

3T2g

(iii) eg2 aA1g+

bA2g+cEg

total degeneracy 6

a b c

I 1 3 1

II 3 1 1

1

S 1

A1g1G 1A

1g1E

g1T

1g1T

2g

3P 3T1g1D 1E

g1T

2g

3F 3A1g 3T1g

3T2g

8/12/2019 2-UV (1)

13/35

13

method of descending symmetryconsider d2ion in O

henvironment

from correlation table for group Oh

(i) t2g2 A1g Eg T1g T2g

lowering the symmetry to C2h t2g ag+ag +bg

t2g t2g=1A1g

1Eg3T1g

1T2g

possible spin 1 1 1 3

multiplicity 1 1 3 1 3 3 1 1

corresponding 1Ag1Ag

3Ag1Ag

representations 1Bg3Bg

1Agin C2h

3Bg1Bg

ag

ag

Ag

====>

1Ag

ag ag Ag ====>1Ag

3Ag

ag bg Bg ====>1Bg

3Bg

ag ag Ag ====>1Ag

ag bg Bg ====>1Bg

3Bg

bg bg Ag ====>1Ag

===> total 41Ag+ 3Ag+ 21Bg+ 23Bg

8/12/2019 2-UV (1)

14/35

14

(ii) eg2 A1g A2g Eg

lowering the symmetry to D4h eg a1g + b1g

a1g2 A1g possible spin multiplicity

1A1g

a1g

b1g

B1g

possible spin multiplicity 1B1g

3B1g

b1g2 A1g possible spin multiplicity 1A1g==> D

4h O

h

1A1g1A1g

3B2g3A1g

1A1g1B1g

1Eg

(iii) t2g1eg

1 ????

consider d2ion in Tdenvironment

from splitting of energy level in Tdsymmetry3F 3A2

3T13T2

1D 1E 1T23P 3T11G 1A1

1E 1T11T2

1S 1A1

electron configurations

e2 A1

A2

E total degeneracy 6

et2 T1 T2 total degeneracy 24

t22 A1 E T1 T2 total degeneracy 15

assign the correct spin multiplicity ???

8/12/2019 2-UV (1)

15/35

15

splitting of the terms for d2ion in several pointgroups

8/12/2019 2-UV (1)

16/35

16

correlation diagram for a d2ion in Oh

environment

8/12/2019 2-UV (1)

17/35

17

correlation diagram for a d2ion in Td

environment

8/12/2019 2-UV (1)

18/35

18

Orgel diagramsd1, d6/d4, d9

u= 10 Dq

E T2 T2g Eg

Eg T2 g T2 E

d1, d6 tetrahedral d1, d6 octahedral

d4, d9 octahedral d4, d9 tetrahedral

8/12/2019 2-UV (1)

19/35

19

d2, d7/d3, d8

A2T2 u1= 10Dq T1T2 u1= 8Dq+ c

A2T1(F) u2= 18Dq - c T1(F)T1(P) u2= 18Dq+ c

A2T1(P) u1= 15B+ 12Dq+ cT1A2 u3= 15B+ 6Dq+ 2c

d2, d7 tetrahedral Dq d2, d7 octahedral

d3

, d8

octahedral d3

, d8

tetrahedral

cm-1

8/12/2019 2-UV (1)

20/35

20

8/12/2019 2-UV (1)

21/35

21

Tanabe-Sugano diagrams

8/12/2019 2-UV (1)

22/35

22

8/12/2019 2-UV (1)

23/35

8/12/2019 2-UV (1)

24/35

24

magnitude of o

Mn(II) < Ni(II)

8/12/2019 2-UV (1)

25/35

25

Jrgensen prediction of 10Dqand B

10Dq= f g (cm-1 10-3)

B = Bo(1 h k)

Bo: free ion interelectronic repulsion parameter

Jahn-Teller distortions

distortion will occur whenever the resulting splittingenergy levels yields additional stabilization

__ dx2-y2 __ dz2

eg __ __

__ dz2 __ dx2-y2

or

__ dxy__ __d

xz, d

yz

t2g __ __ __

__ __ dxz, dyz

__ dxy

8/12/2019 2-UV (1)

26/35

26

[M(H2O)

6]n+

Ti3+(d1)

V3+(d2)

Cr3+(d3)

Mn2+(d5)

Fe2+(d6)

Co2+(d7)

Ni2+(d8)

Cu2+(d9)

Cr2+(d4)

8/12/2019 2-UV (1)

27/35

27

d1

d2

8/12/2019 2-UV (1)

28/35

28

d3

8/12/2019 2-UV (1)

29/35

29

d3

8/12/2019 2-UV (1)

30/35

30

d4

d5

8/12/2019 2-UV (1)

31/35

31

d6

8/12/2019 2-UV (1)

32/35

32

d6

8/12/2019 2-UV (1)

33/35

33

d6

8/12/2019 2-UV (1)

34/35

34

d7

8/12/2019 2-UV (1)

35/35

d8

d9