1. Electronic Circular Dichroism of Transition Metal Complexes within TDDFT Jing Fan University of Calgary 1

2. 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. 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, L  MCT)

4. 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

5.  -bonded Complexes : [Co(en) 3 ] 3+ and [Cr(en) 3 ] 3+ 5 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 )

6. 6 Lowest singlet excited states and their splitting in D 3 symmetry Assignment of Transitions (1A 2 ) (2E) (3E) (2A 2 ) (1E) Λ-[Co(en) 3 ] 3+

7. 7 Why Optically Active? 1 A 1g 1 T 1g d-d transitions: magnetically allowed 1 A 1g 1 T 1u LMCT transitions: electrically allowed electric transition dipole moment magnetic transition dipole moment Rotatory Strengths:

8. 8 Metal d-orbitals: L  -orbitals: Symmetry Metal and Ligand Frontier Orbitals  Metal-ligand Orbital Interaction 8 Metal-ligand orbital interactions Origin of Optical Activity

9. 9 In general,,,, ExpressionOverlaps Semi-quantitative Metal-ligand Orbital Overlaps -0.160 S  -0.021 S  0, -0.102 S  0.096 S  0, 0.287 S  0.047 S  0 0.013 S  -0.001 S  0, 1.193 S  1.220 S  1.225 S , Case IIICase IICase IOverlaps Case I: O h,  = 60  Case II: D 3,  = −6.3  Case III: D 3,  = +6.3   -[Co(en) 3 ] 3+ 1 ˆ e   (  3/2)1e   (1/2)2e ,2 ˆ e   (1/2)1e   (3/2)2e 

10. 10 Energy (eV) MO diagram MOs as linear combinations of symmetry ligand and metal d-orbitals Main components from DFT calculations bonding anti-bonding

11. 11 and in terms of one-electron excitations 4e(d  )  5e(d  ) Prediction of the Sign of Rotatory Strengths Band 2: 1 ˆ e x  2 ˆ e y  positive negative

12. 12 Metal d-orbitals: L  -orbitals: L  -orbitals: Metal and Ligand Frontier Orbitals  Metal-ligand Orbital Interaction 12 Both  - and π-bonded Complexes

13. 13  overlap*  overlap Symmetry Unique Metal-ligand Orbital Overlaps,,. 13 * Only p-orbitals on the N atoms are considered

14. 14 -1.976 S  -2.002 S  -0.892 S  -0.816 S  1.590 S  1.632 S  0.110 S  0 -0.138 S  0  -type 0.059 S  0 -0.064 S  0 -0.034 S  0 1.058 S  1.061 S  0.610 S  0.612 S   -type Case II (D 3 )Case I (O h )Overlaps -1.976 S  -2.002 S  -0.892 S  -0.816 S  1.590 S  1.632 S  0.110 S  0 -0.138 S  0  -type 0.059 S  0 -0.064 S  0 -0.034 S  0 1.058 S  1.061 S  0.610 S  0.612 S   -type Case II (D 3 )Case I (O h )Overlaps Case I: O h Case II: D 3

15. 15 CD spectra - acac  d-to-d, LMCT as well as ML  CT and LC, etc.  Global red-shift applied to the computed excitation energies: Cr(III): –5.0  10 3 cm –1 Co(III): –4.0  10 3 cm –1 theor.expt.

16. - thiox 16

17. 17 a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ  = 0  for ideal octahedrons. c Trigonal splitting of the T 1g 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) <  (A 2 ) Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L) 3 ] n+

18. 18 Rotatory strengths R ( ) and overlaps S(d  2, ) ( ) against  S R /10 -40 cgs  / degree S / S  R(1E 1 ) R(2E 1 ) (1A 2 ) (2E) (1E)

19. 19 a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ  = 0  for ideal octahedrons. c Trigonal splitting of the T 1g 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+

20. 20 Complexes with Conjugated Ligands (Trigonal Dihedral) M: Fe, Ru, Os N-N: bpy, phen [Λ-Os(bpy) 3 ] 2+ E A2A2 Exciton CD (LC π-π* transitions ) For the Λ configuration: R(E) > 0, R(A 2 ) 0 theor. expt.   5

21. 21 Energy (eV) απαπ βπβπ

22. 22 R(A 2 ) 0 for 0 <  < 90  (α π −>β π )

23. Energy Splitting of CD Bands  d-to-d: trigonal splitting of dπ orbitals due to metal-ligand interactions 23 [Co(en) 3 ] 3+ [Cr(en) 3 ] 3+ d-Lσ E A2A2 E A2A2 polar compression (s/h > 1.22)  (E) <  (A 2 ) Co(acac) 3 and Cr(acac) 3 d-Lπ/σ E A2A2 polar elongation (s/h  (A 2 )

24. LC: trigonal splitting of dπ orbitals due to metal-ligand interactions and electron- electron repulsion energy involving different number of ligands 24

25. 25   /  -bonded: d-to-d (might be safe), CT (not safe) Determination of Absolute Configuration by CD   -bonded: d-to-d, L  MCT ✔    /  -bonded (conjugated ligands): LC exciton excitations ✔

26. Complexes with Tripodal Tetradentate Ligands (Trigonal bipyramidal) 26 MeTPAMeBQPAMeTQA Cu