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Tom Ziegler Department of Chemistry University of Calgary,Alberta, Canada T2N 1N4

Tuesday November 11 11:30 am - 12:10 pm. Tom Ziegler Department of Chemistry University of Calgary,Alberta, Canada T2N 1N4. Magnetically Perturbed Time Dependent Density Functional Theory. Applications and Implementations. ADF. Solves Kohn-Sham equations Properties

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Tom Ziegler Department of Chemistry University of Calgary,Alberta, Canada T2N 1N4

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  1. Tuesday November 11 11:30 am - 12:10 pm Tom Ziegler Department of Chemistry University of Calgary,Alberta, Canada T2N 1N4 Magnetically Perturbed Time Dependent Density Functional Theory. Applications and Implementations

  2. ADF • Solves Kohn-Sham equations • Properties • NMR, EFG, EPR, Raman, IR, UV/Vis, NLO, CD, … • Potential energy surfaces (transition states, geometry optimization) • Environment effects • QM/MM, COSMO • Relativistic effects • Scalar relativistic effects, spin-orbit coupling • Transition and heavy metal compounds • Uses Slater functions

  3. Inorganic Spectroscopy

  4. Where : Definition of A and B Matrices : Basic Time Dependent Density Functionl Theory Basic Equation : M.E.Casida Gross,E.K.; Kohn W. T. Ziegler,M.Seth,M.Krykunov,J.Autschbach A Revised Electronic Hessian for Approximate Time-Dependent Density Functional Theory SUBMITTED, J.C.P.

  5. Where : Corredted Definition of A and B Matrices : Basic Time Dependent Density Functionl Theory Basic Equation : M.E.Casida Gross,E.K.; Kohn W.

  6. Where : Corredted Definition of A and B Matrices : Basic Time Dependent Density Functionl Theory Basic Equation : M.E.Casida Gross,E.K.; Kohn W. Spin-flip transitions using non-collinear functionals Liu (2004),Ziegler+Wang (2005),Vahtras (2007)

  7. Electric TransitionDipole Moment : Magnetic TransitionDipole Moment : Basic Time Dependent Density Functionl Theory Basic Equation : M.E.Casida Gross,E.K.; Kohn W. Transition Energy :

  8. A A B B C C Absorption Spectra and TD-DFT Transition Energy :

  9. H Inorganic Spectroscopy

  10. Magnetic Circular Dichroism (MCD) Spectroscopy Why MCD and MOR ? In absorption spectroscopy only positive (often overlapping) bands More information about each excited state

  11. Magnetic Circular Dichroism (MCD) Spectroscopy Why MCD ? In MCD bands of different shapes More information about each excited state

  12. Absorbance in dipole approximation. Electric dipole operator: Magnetic Circular Dichroism (MCD) Spectroscopy Origin of MCD ?

  13. Absorbance in dipole approximation. Magnetic Circular Dichroism (MCD) Spectroscopy Origin of MCD ?

  14. Circular Polarized Light Difference in absorbance of left and right circular polarized light Electric dipole operator For circular polarized Light: Magnetic Circular Dichroism (MCD) Spectroscopy Origin of MCD ?

  15. Magnetic Circular Dichroism (MCD) Spectroscopy Origin of MCD ? The difference in absorption of left and right circularly polarized light in the presence of a magnetic field as a function of photon energy

  16. Magnetic Circular Dichroism (MCD) Spectroscopy Origin of MCD ?

  17. Magnetic Circular Dichroism (MCD) Spectroscopy The MCD disprsion P.J.Stephens. Ph.D. Thesis 1964 C(T) A B A

  18. Magnetic Circular Dichroism (MCD) Spectroscopy The MCD disprsion P.J.Stephens. Ph.D. Thesis 1964 Degenerate ground- or (and) excited state Absorption band

  19. Magnetic Circular Dichroism (MCD) Spectroscopy The MCD disprsion P.J.Stephens. Ph.D. Thesis 1964 All cases Absorption band

  20. P o s i t i v e N e g a t i v e C - t e r m C - t e r m Magnetic Circular Dichroism (MCD) Spectroscopy The MCD disprsion P.J.Stephens. Ph.D. Thesis 1964 Space and(or) spin-degenerate ground state Absorption band

  21. Origin of B-Term The B term M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008)

  22. Expression for the B-Term The B term Or by using the identity We thus have M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008)

  23. The Calculation of the B-term The B term : practical calculations We have: Where: Early work: J.Michl, J.Am.Chem.Soc. 100,6801 (1978) TD-DFT calculations

  24. The Calculation of the B-term The B term : practical calculations We have: Where: TD-DFT calculations Solve:

  25. The Calculation of the B-term The B term : practical calculations By differentiation of M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008)

  26. The Calculation of the B-term Affords Here: M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008)

  27. The Calculation of the B-term The B term : practical calculations M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008) Seth+Ziegler JCP,2008,in press

  28. The Calculation of the B-term by Direct Method The B term : Direct method We must solve Seth+Ziegler JCP,2008

  29. The Calculation of the B-term by Direct Method The B term : Direct Method We must solve Pros M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008) Seth+Ziegler JCP,2008,in press Cons

  30. The Calculation of the B-term by Sum-over-State Method The B term : Sum Over State Writing Z(1) in terms of the complete set F(0) affords M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem. Phys. J. Chem. Phys.128, 144105 (2008) Or Seth+Ziegler JCP,2008,134108

  31. The Calculation of the B-term by Sum-over-State Method The B term : Sum Over State Seth+Ziegler JCP,2008,134108 Pros Cons

  32. Other B-term implementations J.Michl J.Am.Chem.Soc. 100, 6801, 1978 HF+CI E.Dalgaard Phys.Rev. A 42 42 1982 J.Olsen; P. Jørgensen J.Chem.Phys. 82 3235 (1985) W.A.Parkinson; J.Oddershede J.Chem.Phys. 94,7251 (1991) W.A.Parkinson; J.Oddershede) Int.J.Quantum Chem. 64,599 (1997) CCSD(T) 7S.Coriani, P.Jørgensen, T.Helgaker J.Chem.Phys. 113,3561,2000 T.Kjœrgaard, B.Jansik, P.Jørgensen,S.Coriani, J.Michl, J.Phys.Chem. A 111,11278 (2007)) M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 144105 (2008) DFT H.Solheim; L.Frediani; K.Rudd; S.Coriani Theor.Chem.Acc 119,231,2007 DFT-SOS M.Seth,T.Ziegler,J.Autschbach J.Chem.Theory.Comp.3,434,2007 M.Krykunov,M.Seth,T.Ziegler,J.Autschbach J.Chem.Phys. 2007,127,244107

  33. Comparison of Sum-over-State and Direct Method for B-terms Convergence of SOS- method for Ethylene Seth+Ziegler JCP,2008

  34. Comparison of Direct Method for B-terms with Experiment S4N2 S4N3+ Exp: J.W.Waluk, J.Michl Inorg.Chem. 21,556,1982) Exp: H.-P.Klein, R.T. Oakley, J.Michl Inorg.Chem. 25,3194 (1986)

  35. Comparison of Direct Method for B-terms with Experiment Exp: H.-P.Klein, R.T. Oakley, J.Michl Inorg.Chem. 25,3194 (1986) Seth+Ziegler JCP,2008 Exp: H.-P.Klein, R.T. Oakley, J.Michl Inorg.Chem. 25,3194 (1986)

  36. Comparison of Direct Method for B-terms with Experiment and other Methods Exp: H.-P.Klein, R.T. Oakley, J.Michl Inorg.Chem. 25,3194 (1986) T.Kjœrgaard, B.Jansik, P.Jørgensen,S.Coriani, J.Michl, J.Phys.Chem. A 111,11278 (2007))

  37. TD-DFT calculations of B-term. W. Hieringer, S. J. A. van Gisbergen, and E. J. Baerends J. Phys. Chem. A 2002, 106, 10380 Furan Thiophene Selenophen Seth+Ziegler JCP,2008,134108 Tellurophen

  38. TD-DFT calculations of B-term. Sum-over-state formulation Norden, B.; Hansson, R.; Pedersen, P. B.; Thulstrup, E. W. Chem.Phys. 1978, 33, 355.

  39. TD-DFT calculations of B-term. Sum-over-state formulation Norden, B.; Hansson, R.; Pedersen, P. B.; Thulstrup, E. W. Chem.Phys. 1978, 33, 355.

  40. TD-DFT calculations of B-term. Sum-over-state formulation Furan Seth+Ziegler JCP,2008,134108

  41. TD-DFT calculations of B-term. Sum-over-state formulation Thiophene Seth+Ziegler JCP,2008,134108

  42. TD-DFT calculations of B-term. Sum-over-state formulation Selonophene Seth+Ziegler JCP,2008,134108

  43. TD-DFT calculations of B-term. Sum-over-state formulation Tellurophen Seth+Ziegler JCP,2008,134108

  44. A-term of MCD Origin of A-term M.Seth,T.Ziegler,J.Chem.Phys. 2004,120,10943 M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 234102 (2008)

  45. The A-term of Magnetic Circular Dichroism (MCD) Spectroscopy The A term Thus M.Seth,T.Ziegler,J.Chem.Phys. 2004,120,10943 M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 234102 (2008)

  46. The A-term of Magnetic Circular Dichroism (MCD) Spectroscopy The A term Here We have Thus M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 234102 (2008)

  47. The A-term of Magnetic Circular Dichroism (MCD) Spectroscopy The A term

  48. Other A-term implementations J.Michl J.Am.Chem.Soc. 100, 6801, 1978 HF+CI Y.Honda, M.Hada, M.Ehara, H.Nakatsuiji,J.Downing,J.Michl , Chem.Phys.Lett 355,219, , 2002 Y.Honda, M.Hada, M.Ehara, H.Nakatsuiji,J.Michl , J.Chem.Phys. 123,164113 (2005) CCSD(T) 7S.Coriani, P.Jørgensen, T.Helgaker J.Chem.Phys. 113,3561,2000 T.Kjœrgaard, B.Jansik, P.Jørgensen,S.Coriani, J.Michl, J.Phys.Chem. A 111,11278 (2007)) DFT M.Seth,T.Ziegler, M.Krykunov, J.Autschbach J.Chem.Phys. J. Chem. Phys.128, 234102 (2008) H.Solheim; ; K.Rudd; S.Coriani ,P.Norman J.Chem.Phys. 128,094193,2008 M.Krykunov,M.Seth,T.Ziegler,J.Autschbach J.Chem.Phys. 2007,127,244107 M.Seth,T.Ziegler, E.J.Baerends J.Chem.Phys. 2004,120,10943 M.Seth,T.Ziegler, J.Chem.Phys. 2007,127,134108

  49. Applications:A/D C6Cl6 D6h Ni(CN)42- D4h Se42+ D4h Te42+ Exp:-0.66 Calc:-0.72 Exp:-0.50 Calc:-0.80 Exp: 0.72 Calc: 0.63 Fe(CN)64- Oh C6H3Br3 D3h Exp: 0.40 Calc: 0.48 Exp: 0.60 Calc: 0.55 M.Seth,T.Ziegler,J.Chem.Phys. 2004,120,10943

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