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Ultrafast processes in molecules

Ultrafast processes in molecules. XI – Surface hopping with correlated single reference methods. Mario Barbatti barbatti@kofo.mpg.de. Energy. Static EC. Time. D ynamic Electron Correlation.

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Ultrafast processes in molecules

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  1. Ultrafast processes in molecules XI – Surface hopping with correlated single reference methods Mario Barbatti barbatti@kofo.mpg.de

  2. Energy Static EC Time Dynamic Electron Correlation If DEC is needed everywhere and SEC only at the intersection, why choosing CASSCF (only SEC) for dynamics?

  3. SR can describe the relaxation through the manifold of excited states until: • The minimum of the first excited state is found (Kasha’s rule) • The crossing to the ground state is found • We can get information on: • Lifetimes • Reaction pathways distributions • We can’t get information on: • Photoisomerization quantum yield • Ground-state vibrational relaxation

  4. TDDFT has been the SR choice for a number of groups: • Bonačić-Koutecký, Mitrić • Tavernelli • Tapavicza, Furche • Ourselves • And about Coupled-Cluster? • Curchod, Rothlisberger, Tavernelli, ChemPhysChem14, 1314 (2013)

  5. Coupled-Cluster • Sneskov and Christiansen, WIREs 2, 566 (2011)

  6. Coupled-Cluster Excitation operator ith-order b b a a i i j j amplitudes • Sneskov and Christiansen, WIREs 2, 566 (2011)

  7. Coupled-Cluster • Choose a truncation level • Insert this Ansatz into TDSE • Get a set of nonlinear equations for the amplitudes and ground-state energy • Sneskov and Christiansen, WIREs 2, 566 (2011)

  8. Coupled-Cluster Truncation produces a well defined hierarchy of methods: CCS < CCSD < CCSDT < ··· CC3, CCSD(T) With some exotic flavors • Sneskov and Christiansen, WIREs 2, 566 (2011)

  9. For excited states, the important quantity is the CC Jacobian matrix A: • Response Theory shows that: • Excited-state energies W are eigenvalues of A • Contribution R from each determinant is the eigenvector • The problem is to solve

  10. Jacobian is not a symmetric matrix! ===================================== Left and right eigenvalues converged to the same Results within 0.42E-07 a.u.

  11. CC is time-consuming… CCS < CCSD < CC3 < CCSD(T) < CCSDT < ··· CC2 CIS(D∞)

  12. CC is very accurate • Schreiber, Silva-Junior, Sauer, Thiel, J ChemPhys128, 134110 (2008)

  13. CC doesn’t work well for degenerated excited states Non-symmetric Jacobian→eigenvalues (energies) may be imaginary CCS < CIS(D∞ ) < CC2 < CCSD < CC3 < CCSD(T) < CCSDT < ··· Build a symmetric Jacobian: • Hättig, Köhn, J ChemPhys 117, 6939 (2002)

  14. ADC(2) CCS < CIS(D∞ ) < CC2 < CCSD < CC3 < CCSD(T) < CCSDT < ··· ADC(2): Algebraic Diagrammatic Construction scheme up to second order ADC(2) is not strictly a CC method It is a excited-state propagator for ground-state MP2 (Schirmer1982) These excited states are equivalent to the symmetrized CIS(D∞) Trofimov, Krivdina, Weller, Schirmer, ChemPhys329, 1 (2006)

  15. For surface hopping, we need nonadiabatic couplings Fkl They are used to compute transition probabilities Analytical nonadiabatic coupling vectors are available only for EOM-CC (CFour) • Tajti and Szalay, J. Chem. Phys. 131, 124104 (2009)

  16. But we follow another way For the probabilities, we don’t need F, we need F.v In the 1990s, Hammes-Schiffer and Tully showed that Overlap of electronic wavefunction in different time steps • Hammes-Schiffer and Tully, J Chem Phys 101, 4657 (1994)

  17. Couplings based on such overlaps have been used by several authors with: • MRCI • CASSCF • TDDFT • TDDFTB • Barbatti, WIREs1, 620 (2011)

  18. MO coefficients AO integrals for “Double-Molecule” CI coefficients Newton-X CIOVERLAP modulus The couplings can be used not only to get Fkl.v But also to solve Surface Hopping equations with Local Diabatization method • Plasser, Granucci, Pittner, Barbatti, Persico, Lischka, J Chem Phys 137, 22A514 (2012)

  19. We use the eingenvectors R and L to build CIS wavefunctions For TDDFT (Casida 1996):

  20. Test case: adenine

  21. Adenine is great for benchmarking: • a) Dynamics is available at: • MRCIS • OM2/MRCI • FOMO-CI/AM1 • TDDFT (several functionals) • TDDFTB • b) Different dynamics methods have been used: • Surface Hopping • Ehrenfest Dynamics • Quantum wavepacket • c) Gas-phase transient spectra available for several pump wavelengths • Barbatti, Lan, Crespo-Otero, Szymczak, Lischka, Thiel, J Chem Phys 137, 22A503 (2012)

  22. Vertical excitation aBarbatti and Ullrich, PCCP 13, 15492 (2011) b Clark, Peschel, Tinoco, J Phys Chem69, 3615 (1965)

  23. S1 minimum Fluorescence in water (f = 2.6×10-4) Band origin: vapor a Daniels and Hauswirth, Science 171, 675 (1971) bNir, Plutzer, Kleinermanns, de Vries, Eur Phys J D 20, 317 (2002)

  24. Absorption a Clark, Peschel, Tinoco, J Phys Chem69, 3615 (1965)

  25. Initial conditions were sampled in two spectral domains corresponding to different pump excitations Different proportions of excitations into S1, S2 and S3 contribute to each domain

  26. Simulations setup: • 50 Trajectories in each domain (L and M) • Fewest Switches with decoherence correction • 0.5 fs time step for classical equations • 0.025 fs for quantum equations • Max 1000 fs or until E1-E0 < 0.1 eV • RI-CC2 and RI-ADC(2) • aug-cc-pVDZ • 3 excited states • Newton-X / Turbomole 1000 ps ADC(2) trajectory takes 24 days in 4 cores Xenon 2.7 GHz

  27. CC2 trajectories died in less than 100 fs! Non-symmetrical Jacobian is the problem ADC(2) trajectories are perfectly stable They ran until one of the termination criteria was satisfied

  28. Double excitation Single excitation MR Ground state SR Ground state • Nielsen andJanssen, ChemPhysLett310, 568 (1999)

  29. Deactivation to Ground State within 1 ps Margin of error for 90% confidence interval aEvans and Ullrich, J Phys Chem A, 114, 11225 (2010)

  30. Deactivation to Ground State within 1 ps Margin of error for 90% confidence interval aEvans and Ullrich, J Phys Chem A, 114, 11225 (2010)

  31. Deactivation to Ground State within 1 ps • There is no statistical distinction between L and M • SH/ADC(2) is slightly underestimating the deactivation level • Problems with ADC(2) surfaces? • Expt. includes 9H and 7H tautomers • Expt. includes ionization info (Barbatti and Ullrich 2011) aEvans and Ullrich, J Phys Chem A, 114, 11225 (2010)

  32. Trajectories cluster around C2 deformation of the pyrimidine ring C2

  33. Participation of each reaction path in the internal conversion • C2 is the dominant one • C6 is also important • H elimination plays a minor role

  34. There are thermodynamic reasons favoring C2 There are kinetic reasons favoring C2

  35. Only ADC(2) and OM2/MRCI predict right IC • MRCIS overshoots IC • TDDFT underestimates IC • OM2/MRCI underestimates C2 • ADC(2) is the best result so far

  36. To conclude: • SR methods can be very useful for some (not all!) problems in nonadiabatic dynamics • Non-symmetric Jacobians in CC methods are a major problem • ADC(2) showed good potential (accurate and stable) • Lack of hopping to ground state is the main problem

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