electronic circular dichroism of transition metal complexes within tddft

Electronic Circular Dichroism of Transition Metal Complexes

within TDDFTJing Fan

University of Calgary

1

Objectives To understand, experimental CD spectra, quantum

mechanical calculations of electronic structure and CD based on TDDFT

To elucidate the origin of CD in typical transition metal complexes, relationship between CD and molecular geometry

To evaluate the reliability and accuracy of TDDFT for transition metal compounds

2

3

Complexes Studied:Trigonal Dihedral:

− both - and π-bonded complexes: [M(L-L)3]n+ (M = Co, Cr; L =

ox, acac, thiox, etc.)(d-to-d, LMCT, MLCT, LC)

− complexes with conjugated ligands: [M(L-L)3]2+ ( M = Fe, Ru, Os; L = bpy, phen)(LC exciton CD )

Trigonal bipyramidal: − complexes with conjugated ligands [M(L)X]+ (M = Cu, Zn; L = MeTPA, MeBQPA, MeTQA; X = Cl-, NCS-)(LC exciton CD)

− -bonded complexes: [M(en)3]3+ (M = Co, Cr) (d-to-d, LMCT)

4

Computational Details ADF package Basis sets (STO): • ligand atoms: frozen core triple- polarized “TZP” -C, N, O (1S); S (2p) • metal atoms: -Co, Cr : TZP (2p); -Fe, Ru, Os: TZ2P (2p, 3d, 4f) Functionals: VWN (LDA) + BP86 (GGA) Relativistic effect for Fe group metals (scalar ZORA) Un-restricted calculations for Cr(III) The “COnductor-like continuum Solvent MOdel” (COSMO) of solvation

-bonded Complexes : [Co(en)3]3+ and [Cr(en)3]3+

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H2N NH2

en:d-d LMCT

• Calculated E are systematically overestimated for the d-d region (by ~5,500 cm-1); underestimated for the LMCT region (by ~6,000 cm-1)

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Lowest singlet excited states and their splitting in D3 symmetry

Assignment of Transitions

(1A2)

(2E)

(3E)

(2A2)

(1E)

Λ-[Co(en)3]3+

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Why Optically Active?

1A1g 1T1g d-d transitions: magnetically allowed1A1g 1T1u LMCT transitions: electrically allowed

electric transition dipole moment

magnetic transition dipole moment

€

R0λ = Im 0 ˆ Θ λ ⋅ λ ˆ M 0

Rotatory Strengths:

8

Metal d-orbitals:

€

eg:1(− 1/3dx2−y2 + 2/3dyz)

€

eg:2( 1/3dxy − 2/3dxz)

€

t2g:1(dz2 )

€

t2g:2( 2/3dx2−y2 + 1/3dyz)

€

t2g:3(− 2/3dxy − 1/3dxz)

dσ1 dσ2

dπ2dπ1 dπ3

L-orbitals:

Symmetry Metal and Ligand Frontier Orbitals

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• Metal-ligand orbital interactions

€

a1σ

€

a2σ

€

1ˆ e xσ

€

1ˆ e yσ

€

2ˆ e xσ

€

2ˆ e yσ

CH2H2C

H2N NH2

CH2H2C

H2N NH2

Origin of Optical Activity

9

In general

,

,

,

,

ExpressionOverlaps

S(d1,1ex )

S(d2 ,1ey )

S(d1,2ex )

S(d2 ,2ey )

S(d1,a1 )

S(d 2 ,1ex )

S(d 3 ,1ey )

S(d 2 ,2ex )

S(d 3 ,2ey )

€

b

2a

1

2(b2 − a2 sin2 ω

b2 ) + (a2 sin2ω

b2 ) ⎡

⎣ ⎢

⎤

⎦ ⎥Sσ '

€

(1

2sinω + cosω)Sσ '

3 3

2(

a2 cos2a2 b2

1

3)S

€

−b

2a(b2 − a2 sin2 ω

b2) −

1

2(a2 sin2ω

b2)

⎡

⎣ ⎢

⎤

⎦ ⎥Sσ '

€

−(sinω −1

2cosω)Sσ '

Semi-quantitative Metal-ligand Orbital Overlaps

€

Sσ ' =3ab

a2 + b2Sσ

b

€

aM

N

N

N

N

N

N

-0.160 S-0.021 S0,

-0.102 S0.096 S0,

0.287 S0.047 S0

0.013 S-0.001 S0,

1.193 S1.220 S1.225 S,

Case IIICase II Case IOverlaps

S(d1,a1 )

)ˆ2,( 1 xedS )ˆ2,( 2

yedS

)ˆ1,( 2 yedS)ˆ1,( 1

xedS

)ˆ1,( 2 xedS )ˆ1,( 3

yedS

)ˆ2,( 2 xedS )ˆ2,( 3

yedS

Case I: Oh, = 60Case II: D3, = −6.3 Case III: D3, = +6.3-[Co(en)3]3+

1 e ( 3 /2)1e (1/2)2e ,2 e (1/2)1e ( 3 /2)2e

1010

Ene

rgy

(eV

)

MO diagram

MOs as linear combinations of symmetry ligand and metal d-orbitals

na2c(na2)a2

€

na1= c(na1,i)

i

2

∑ χ i

nex,y c(nex,y,i)

i

4

i

(1 a1 ,2 d1)

€

(χ 1 =1ˆ e σ ,χ 2 = 2ˆ e σ ,χ 3 = dσ ,χ 4 = dπ )

€

3e = 0.88661ˆ e σ + 0.1176dπ

€

4 e = −0.09791ˆ e σ + 0.9725dπ

€

5e = 0.8582dσ − 0.77882ˆ e σ

Main components from DFT calculations

bonding

anti-bonding

anti-bonding

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and in terms of one-electron excitations 4e(d) 5e(d)€

R 1A21

( ) = Im A11 ˆ μ 1A2

1 ⋅ 1A21 ˆ m A1

1[ ]

€

R 1A21

( ) =4 2

3c(4ex,1)c(5ey,2) 1ˆ e xσ z 2ˆ e yσ[ ] ⋅ c(5ey,3)c(4ex,4) ⋅ dxy mz dx 2 −y 2 − dxz mz dyz( )[ ]

• Prediction of the Sign of Rotatory Strengths

Band 2:

A11 1A2

1

z

y

x

1 e x

2 e y

positive

negative

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Metal d-orbitals:

€

eg:1(− 1/3dx2−y2 + 2/3dyz)

€

eg:2( 1/3dxy − 2/3dxz)

€

t2g:1(dz2 )

€

t2g:2( 2/3dx2−y2 + 1/3dyz)

€

t2g:3(− 2/3dxy − 1/3dxz)

dσ1 dσ2

dπ2dπ1 dπ3

L-orbitals:

L-orbitals:

€

a1

€

a2

€

1ex

€

1ey

€

2ex

€

2ey

€

a1

€

a2

€

1ex

€

1ey

€

2ey

€

2ex

Metal and Ligand Frontier Orbitals

12

Both - and π-bonded Complexes

13

overlap* overlap

€

S dσ 1,1exσ

( );S dσ 2 ,1eyσ

( )

€

S dσ 1,2exσ

( );S dσ 2 ,2eyσ

( )

€

S dπ1,a1σ

( )

€

S dπ 2 ,1exσ

( );S dπ 3 ,1eyσ

( )

€

S dπ 2 ,2exσ

( );S dπ 3 ,2eyσ

( )

€

b

2a

1

2

b2 − a2 sin2 ω

b2

⎛

⎝ ⎜

⎞

⎠ ⎟+

a2 sin2ω

b2

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥Sσ '

€

1

2sinω + cosω

⎛

⎝ ⎜

⎞

⎠ ⎟Sσ '

€

−3 3

2

a2 cos2ω

a2 + b2−

1

3

⎛

⎝ ⎜

⎞

⎠ ⎟Sσ

€

−b

2a

b2 − a2 sin2 ω

b2

⎛

⎝ ⎜

⎞

⎠ ⎟−

1

2

a2 sin2ω

b2

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥Sσ '

€

−sinω −1

2cosω

⎛

⎝ ⎜

⎞

⎠ ⎟Sσ '

€

S dσ 1,1exπ

( );S dσ 2 ,1eyπ

( )

€

S dσ 1,2exπ

( );S dσ 2 ,2eyπ

( )

€

S dπ1,a1π

( )

€

S dπ 2 ,1exπ

( );S dπ 3 ,1eyπ

( )

€

S dπ 2 ,2exπ

( );S dπ 3 ,2eyπ

( )

€

cosθ1

2sin 2ω − 2cos2ω

⎛

⎝ ⎜

⎞

⎠ ⎟Sπ

€

sinθ 2 cosω − 2sinω( )Sπ

€

3 cosθ sin 2ω( )Sπ

€

−cosθ sin 2ω + 2 cos2ω( )Sπ

€

−sinθ 2cosω + 2 sinω( )Sπ

Symmetry Unique Metal-ligand Orbital Overlaps

€

Sσ ' =3ab

a2 + b2Sσ

€

sinθ =a2 sin 2ω + b2

a2 + b2

€

cosθ =a cosω

a2 + b2 , , .

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* Only p-orbitals on the N atoms are considered

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-1.976 S-2.002 S

-0.892 S-0.816 S

1.590 S1.632 S

0.110 S0

-0.138 S0

-type

0.059 S0

-0.064 S0

-0.034 S0

1.058 S1.061 S

0.610 S0.612 S

-type

Case II (D3)Case I (Oh)Overlaps

€

S dσ 1,1exσ

( );S dσ 2 ,1eyσ

( )

€

S dσ 1,2exσ

( );S dσ 2 ,2eyσ

( )

€

S dπ 2 ,1exσ

( );S dπ 3 ,1eyσ

( )

€

S dπ 2 ,2exσ

( );S dπ 3 ,2eyσ

( )

€

S dσ 1,2exπ

( );S dσ 2 ,2eyπ

( )

€

S dπ 2 ,1exπ

( );S dπ 3 ,1eyπ

( )

€

S dπ 2 ,2exπ

( );S dπ 3 ,2eyπ

( ) -1.976 S-2.002 S

-0.892 S-0.816 S

1.590 S1.632 S

0.110 S0

-0.138 S0

-type

0.059 S0

-0.064 S0

-0.034 S0

1.058 S1.061 S

0.610 S0.612 S

-type

Case II (D3)Case I (Oh)Overlaps

€

S dσ 1,2exσ

( );S dσ 2 ,2eyσ

( )

€

S dπ1,a1σ

( )

€

S dπ 2 ,1exσ

( );S dπ 3 ,1eyσ

( )

€

S dπ 2 ,2exσ

( );S dπ 3 ,2eyσ

( )

€

S dσ 1,2exπ

( );S dσ 2 ,2eyπ

( )

€

S dπ1,a1π

( )

€

S dπ 2 ,1exπ

( );S dπ 3 ,1eyπ

( )

€

S dπ 2 ,2exπ

( );S dπ 3 ,2eyπ

( )

Case I: Oh

Case II: D3

€

S(dσ 1,1exπ );S(dσ 2,1ey

π )

1515

CD spectra- acac

d-to-d, LMCT as well as MLCT and LC, etc.

Global red-shift applied to the computed excitation energies:Cr(III): –5.0 103 cm–1

Co(III): –4.0 103 cm–1

theor. expt.

HC

O

H3C

-O

CH3

acac

- thiox

16

-S

OO

S-thiox

1717

a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0 for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons.

σ-bonded

Early rule proposed for Λ-configuration:Azimuthal contraction ( < 0) positive R(E)Polar compression (s/h > 1.22) (E) < (A2)

Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+

s

h

φ

18

Rotatory strengths R ( ) and overlaps S(d2, ) ( ) against xe1

S

R /

10-4

0 cgs

/ degree

S / S

-80

-60

-40

-20

0

20

40

30 35 40 45 50 55-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

€

R(1A21 )

R(1E1)

R(2E1) (1A2)

(2E)(1E)

b

€

aM

N

N

N

N

N

N

191919

a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0 for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons.

Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+

φ

s

h

20

Complexes with Conjugated Ligands (Trigonal Dihedral)

N

M

N

N

N

N

N

M: Fe, Ru, OsN-N: bpy, phen

[Λ-Os(bpy)3]2+

E

A2

Exciton CD (LC π-π* transitions )

For the Λ configuration: R(E) > 0, R(A2) < 0, υ(A2−E) > 0

theor.expt.

5

21

απ

βπ

22

N

N

N

N

zx

N

N

y N

N

N

N

NN

y'

x'

L1

L2

L3M

y'

x'

NN

short axis

long axis

x'

z'

y'

€

α μy' β π = 2.397, β π lx' α π = −0.2394 R(A2) < 0 and R(E) > 0 for 0 < < 90

(απ−>βπ)

Energy Splitting of CD Bandsd-to-d: trigonal splitting of dπ orbitals due to

metal-ligand interactions

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[Co(en)3]3+

[Cr(en)3]3+

• d-Lσ E

A2

E

A2

polar compression (s/h > 1.22) (E) < (A2)

Co(acac)3

and Cr(acac)3

• d-Lπ/σE

A2

polar elongation(s/h < 1.22) (E) > (A2)

• LC: trigonal splitting of dπ orbitals due to metal-ligand interactions and electron-electron repulsion energy involving different number of ligands

24

€

Eexciton = E(A2 ) − E(Ea ) = E(A2 ) − E(Eb ) = 3κ = 3 π I (1)∫ π I*(1)

1

r12

π II (2)π II* (2)dv1dv2

2525

/-bonded: d-to-d (might be safe), CT (not safe)

Determination of Absolute Configuration by CD

-bonded: d-to-d, LMCT ✔

/-bonded (conjugated ligands): LC exciton excitations ✔

Complexes with Tripodal Tetradentate Ligands (Trigonal bipyramidal)

26

N NM

N

H3C H

NX

N NM

N

H3C H

NX

N NM

N

H3C H

NX

MeTPA MeBQPA MeTQA

Cu Cu Cu