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M. Stener

A TDDFT study on the dichroism in the photoelectron angular distribution from a chiral transition metal compound. M. Stener. Dipartimento di Scienze Chimiche Universit à degli Studi di Trieste Via L. Giorgieri 1, 34127 TRIESTE - ITALY.

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M. Stener

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  1. A TDDFT study on the dichroism in the photoelectron angular distribution from a chiral transition metal compound M. Stener Dipartimento di Scienze Chimiche Università degli Studi di Trieste Via L. Giorgieri 1, 34127 TRIESTE - ITALY Gordon Research Conference on Photoions, Photoionization & Photodetachment January 31st - February 5th, 2010 Hotel Galvez Galveston, TX

  2. GAS PHASE EXPERIMENT (RANDOMLY ORIENTED MOLECULES) PARTIAL DIFFERENTIAL CROSS SECTION: In this work only Electric Dipole (E1) transition moments are considered:

  3. CHIRAL MOLECULES AND CIRCULARLY POLARIZED LIGHT : Cross section D: Dichroism : Asymmetry parameter • emission angle: between photoelectron k and light propagation • mr: +1 or -1 for left/right circular polarization • D has opposite sign for enantiomeric pairs • Dichroism D: Circular Dicroism in Angular Distribution (CDAD)

  4. Theoretical Method • Esplicit treatment of photoelectron continuum • Multicentric B-spline basis set • Formalism: TDDFT • Parallel implemetation • Large matrices dim(H)  20000, 1 energy point: 1h with 256 cpu M. Stener, G. Fronzoni and P. Decleva, J. Chem. Phys., 122 234301(1-11) (2005). M. Stener G. Fronzoni and P. DeclevaChem. Phys., 361, 49 - 60 (2009). What is new? • First TDDFT calculation of dichroic parameter D • First application on a chiral transition metal compound • First calculation of dichroism D over autoionization resonance (only TDDFT can do it!)

  5. Previous applications (Kohn-Sham) Circular Dichroism in Angular Distribution of Photoelectrons from Chiral Molecules: S(-) methyl-oxirane • Good agreement KS Theory vs. Exp. • Dichroism decays to zero within few eVs above threshold S. Stranges, S. Turchini, M. Alagia, G. Alberti, G. Contini, P. Decleva, G. Fronzoni, M. Stener, N. Zema and T. Prosperi J. Chem. Phys. 122 244303 (1-6) (2005).

  6. Chiral transition metal compound: D-Co(acac)3 D3 point group symmetry

  7. PES D-Co(acac)3 C B’’ K L B’ M

  8. Electronic structure: D-Co(acac)3 (acac)3 Co acac Co(acac)3 4p 3d 3p LP- LP+

  9. PES D-Co(acac)3 K K: 30e L L: 18a1 + 15a2 M M: 29e + 14a2 B’ B’: 28e B”: 27e + 17a1 B’’

  10. Electronic structure: D-Co(acac)3 30e: Co 3d – 3p antibonding

  11. Electronic structure: D-Co(acac)3 18a1: Co 3d

  12. Electronic structure: D-Co(acac)3 15a2: 3p

  13. Electronic structure: D-Co(acac)3 29e: Co 3d – 3p bonding

  14. Electronic structure: D-Co(acac)3 14a2: ligand LP-

  15. Electronic structure: D-Co(acac)3 28e: ligand LP-

  16. Electronic structure: D-Co(acac)3 17a1: ligand LP+

  17. Electronic structure: D-Co(acac)3 27e: Co 3d + ligand LP+ bonding

  18. Electronic structure: D-Co(acac)3 31e: Co 3d + ligand LP+ antibonding

  19. Co(acac)3: “Giant Autoionization” E Direct ionization E = 0 (30e)-1 M+ Autoionization Co(3p)-1 Co(31e)+1 M* Excitation “Giant” because the same principal Q.N.: Co 3p → Co 3d GS: Cr(3p)6 (…) (30e)6 (31e)0 M

  20. Dichroism: D-Co(acac)3 30e: Co 3d – 3p antibonding 18a1: Co 3d “Giant” autoionization: Co 3p → 3d Similar! Different!

  21. Dichroism: D-Co(acac)3 28e: ligand LP- • Small Co 3d contribution: • Very weak resonance in cross section • But … very strong ‘window’ resonance in dichroism!!! • D is very sensitive!

  22. Dichroism: D-Co(acac)3 Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) Elettra Sinchrotron (Trieste ITALY)

  23. Dichroism: D-Co(acac)3 Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) Elettra Sinchrotron (Trieste ITALY) Complete disagreement!!!

  24. Dichroism: D-Co(acac)3 Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) Elettra Sinchrotron (Trieste ITALY)

  25. Dichroism: D-Co(acac)3 Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) at Elettra Sinchrotron (Trieste ITALY) Alternative assignment of B’ and B” bands: better agreement!!!

  26. Cross section near the resonance: D-Co(acac)3 Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) Elettra Sinchrotron (Trieste ITALY)

  27. Conclusions • Method: Parallel multicenter B-spline TDDFT continuum. • Calculation of Dichroism (D) of D-Co(acac)3. • Strong sensistivity of D parameter. • Comparison with preliminar experimental dichroism, possible revision of previous assignment. • Co 3p → 3d autoionization: Dichroism sensitive even for ligand orbitals. • Future perspectives: dichroism experiment on Co 3p → 3d autoionization.

  28. Acknowledgments: Trieste University: Prof. Piero Decleva Prof. Giovanna Fronzoni Dott. Daniele Toffoli Dott. Devis Di Tommaso Elettra Sinchrotron Trieste: Dott. Daniele Catone Dott. Tommaso Prosperi Dott. Stefano Turchini Thank you for your attention!

  29. Additional slides

  30. Density Functional Theory for Photoionization: the Kohn-Sham approach hKS : bound and continuum states can be extracted, and photoionization parameters calculated (, , D) • Well known limitation of the KS scheme: • It is static: the response effects to the external time dependent electromagnetic field are neglected

  31. Basis set approach The main issue is proper basis set choice • B-splines: piecewise polynomials defined over an arbitrary grid • Polynomial order k • -Knot sequence {t0 t1 … tn} over [t0, tn] = [0, Rmax]

  32. B-spline functions

  33. One center expansion (OCE) { (r0) } All functions centered on a common origin 0 Multicenter expansion (LCAO) { (r0) }  { 1(r1) }  …  { p(rp) } OCE: very stable and robust, shows smooth but slow convergence with LMAX0 LCAO: converges much more quickly, but less stable, careful choice of numerical parameters. The basis becomes easily overcomplete

  34. Continuum: Kohn-Sham In the basis Hc = ESc Bound states : standard diagonalization Continuum states: Least Squares Approach A(E) = H – ES, N0 lowest eigenvalues ai 0 Works fine, even with N0 a few hundred Poisson equation VC = -4 is solved in the same basis. Gives the coulomb potential VC, avoiding the need of two electron integrals.

  35. Linear response : general theory External TD perturbation, with  frequency (dipole) Induced density by the external field Dielectric susceptibility, not easy to calculate

  36. TDDFT: general theory TDDFT: instead of , use S of a model system of non-interacting electrons and a modified external potential: SCF Coupled, but linear! K(r,r’) (kernel)

  37. TDDFT: Direct (not iterative) algorithm Exploit linearity of the problem: defines the kernel K defines the susceptibility  The Response Equation becomes: To solve : represent the response equation in the B-spline basis set M. Stener, G. Fronzoni and P. Decleva, J. Chem. Phys., 122 234301(1-11) (2005).

  38. Properties Dynamical polarizability: Total cross section: Partial cross section:

  39. Well known limitation of the KS scheme: • It is static: the response effects to the external time dependent electromagnetic field are neglected • The TDDFT includes such response effects: • better agreement with experiment • New effects can be modelled by theory: Autoionization

  40. Cr(CO)6: Autoionization analysis “Giant” autoionization: Cr 3p → Cr 3d Parallel implementation: M. Stener G. Fronzoni and P. DeclevaChem. Phys., 361, 49 - 60 (2009).

  41. Explicit expressions for s, b and D Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.

  42. Explicit expressions for s, b and D Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.

  43. Explicit expressions for s, b and D Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.

  44. Explicit expressions for s, b and D Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.

  45. Photoionization from chiral molecules Linearly polarized light Chiral molecule, Circularly polarized light Forward-Backward asymmetry in the angular distribution Or, switching the polarization of the light at the magic angle P2(cos)=0

  46. Electronic structure: D-Co(acac)3 acac ligand 4p 3p LP- LP+

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