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Mario Barbatti Institute for Theoretical Chemistry University of Vienna

Photochemistry: adiabatic and nonadiabatic molecular dynamics with  multireference ab initio methods . Mario Barbatti Institute for Theoretical Chemistry University of Vienna. COLUMBUS in BANGKOK (3-TS 2 C 2 ) Apr. 2 - 5, 2006 Burapha University, Bang Saen, Thailand. Outline

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Mario Barbatti Institute for Theoretical Chemistry University of Vienna

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  1. Photochemistry: adiabatic and nonadiabatic molecular dynamics with  multireference ab initio methods  Mario Barbatti Institute for Theoretical Chemistry University of Vienna COLUMBUS in BANGKOK (3-TS2C2) Apr. 2 - 5, 2006 Burapha University, Bang Saen, Thailand

  2. Outline • First Lecture: An introduction to molecular dynamics • Dynamics, why? • Overview of the available approaches • Second Lecture: Towards an implementation of surface hopping dynamics • The NEWTON-X program • Practical aspects to be adressed • Third Lecture: Some applications: theory and experiment • On the ambiguity of the experimental raw data • On how the initial surface can make difference • Intersection? Which of them? • Readressing the DNA/RNA bases problem

  3. Outline • First Lecture: An introduction to molecular dynamics • Dynamics, why? • Overview of the available approaches • Second Lecture: Towards an implementation of surface hopping dynamics • The NEWTON-X program • Practical aspects to be adressed • Third Lecture: Some applications: theory and experiment • On the ambiguity of the experimental raw data • On how the initial surface can make difference • Intersection? Which of them? • Readressing the DNA/RNA bases problem

  4. Part IAn Introduction to Molecular Dynamics Cândido Portinari, Café, 1935

  5. Dynamics, why?

  6. Energy (eV) Singlet Triplet 10 VR Ph Fl PA 0 Nuclear coordinates ab initio dynamics conical intersection 10-102 fs intersystem crossing 105-107 fs avoided crossing 102-104 fs Photoinduced chemistry and physics PA – photoabsorption 1 fs VR – vibrational relaxation 102-105 fs Fl – fluorescence 106-108 fs Ph – phosforescence 1012-1017 fs

  7. Dynamics, why? • Why dynamics simulations are needed? • Estimate of specific times (lifetimes, periods); • Estimate of the kind and relative importance of the several available nuclear motions (reaction paths, vibrational modes). • When is it not adequate to reduce the dynamics to the motion on a sole adiabatic potential energy surface? • Electron transfer (high kinetic energy); • Dynamics at metal surfaces (high DoS); • Photoinduced chemistry (multireference states). • Radiationless processes in molecules and solids (conical intersections);

  8. Main objective: relaxation path Ben-Nun, Molnar, Schulten, and Martinez. PNAS99,1769 (2002).

  9. An example to start: the ultrafast deactivation of DNA/RNA bases

  10. An example: photodynamics of DNA basis Lifetimes of the excited state of DNA/RNA basis: Canuel et al. JCP 122, 074316 (2005) Maybe the fast deactivation times for the DNA/RNA basis can provide some explanation to the photostability of DNA/RNA under the UV solar radiation.

  11. An example: photodynamics of DNA basis What has theory to say? C2 pp*/S0 crossing Marian, JCP 122, 104314 (2005) Chen and Li, JPCA 109, 8443 (2005) Perun, Sobolewski and Domcke, JACS 127, 6257 (2005)

  12. An example: photodynamics of DNA basis What has theory to say? reaction coordinate np*/S0 crossing Chen and Li, JPCA 109, 8443 (2005) Perun, Sobolewski and Domcke, JACS 127, 6257 (2005)

  13. An example: photodynamics of DNA basis What has theory to say? ps*/S0 crossing Sobolewski and Domcke, Eur. Phys. J. D 20, 369 (2002)

  14. An example: photodynamics of DNA basis What has theory to say? Our own simulations (TD-DFT(B3LYP)/SVP) do not show any crossing at all.

  15. An example: photodynamics of DNA basis What has theory to say? • The static calculations have being done in good levels, for instance: • MRCI in Matsika, JPCA 108, 7584 (2004); • CAS(14,11) in Chen and Li, JPCA 109, 8443 (2005); • DFT/MRCI in Marian, JCP 122, 104314 (2005). • However, the system can present conical intersections but never access them due to energetic or entropic reasons. • The dynamics calculations are not reliable enough: they miss the MR and the nonadiabatic characters. To address the problem demands nonadiabatic dynamics with MR methods. We will come back to the adenine deactivation later …

  16. Overview of the available approaches

  17. The minimum energy path: the midpoint between static and dynamics approaches

  18. R2 Hypersphere Emin v0 R2eq Emax R1 R1eq Minimum energy path in two steps • Determine the initial • displacement vector (IRD) 2. Search for the minimum energy path Celany et al. CPL 243, 1 (1995) Schlegel, J. Comp. Chem. 24, 1514 (2003)

  19. Minimum energy path Three qualitatively distinct MEPs Garavelli et al., Faraday Discuss. 110, 51 (1998).

  20. Minimum energy path • Advantages: • Explore the most important regions of the PES. • Its equivalent to “one trajectory damped dynamics”. • Clear and intuitive. • Disadvantages: • Only qualitative temporal information. • Neglects the kinetic energy effects. • No information on the importance of each one of multiple MEPs. • No information on the efficiency of the conical intersections. Garavelli et al., Faraday Discuss. 110, 51 (1998). Cembran et al. JACS 126, 16018 (2004).

  21. SiCH4: MRCI/CAS(2,2)/6-31G* Also for SiCH4 one expects the basic scenario torsion+decay at the twisted MXS. 68% of trajectories follow the torsional coordinate, but do not reach the MXS die to the in-phase stretching-torsion motion. The lifetime of the S1 state is 124 fs. This and other movies are available at: homepage.univie.ac.at/mario.barbatti

  22. SiCH4: MRCI/CAS(2,2)/6-31G* The other 32% follow the stretch-bipyramidalization path. And reaches quickly the bipyramid. region of seam. The lifetime of the S1 state is 58 fs. This and other movies are available at: homepage.univie.ac.at/mario.barbatti

  23. SiCH4 Zechmann, Barbatti, Lischka, Pittner and Bonačić-Koutecký, CPL 418, 377 (2006)

  24. The time-dependent self-consistent field: the basis for everything

  25. Total wave function Time-dependent self consistent field (TD-SCF) Dirac, 1930 Time-dependent SCF Time dependent Schrödinger equation (TDSE)

  26. Wave packet dynamics • Time evolution - I • Wave packet propagation • 1) The nuclear wave function is expanded as: • f is the number of nuclear coordinates (<< 3N). MCTDH (multiconfigurational time-dependent Hartree) (Meyer, Manthe and Cederbaum, CPL 165, 73 (1990)) 2) Solve TDSE using c. z Hermite/Laguerre polynomials (DVR, discrete variable representation) z Plane waves (FFT, fast Fourier transform) Advantage: it is the most complete treatment Limitation: it is quite expansive to include all degrees of freedom

  27. Wave packet dynamics C. Lasser, TU-München

  28. H Wave packet: example HBQ O N de Vivie-Riedle, Lischka et al. (2006)

  29. Multiple spawning • Time evolution - II • Multiple Spawning dynamics (Martínez et al., JPC 100, 7884 (1996)) Nuclear wave function is expanded as a combination of gaussians: The centroids RC and PC are restricted to move classically. Advantage: very reliable quantitative results Limitation: it is still quite expansive

  30. Semiclassical approaches • Time evolution - III • Mean Field; Surface Hopping. Nuclear wave function is restricted to be a product of dfunctions: RC is restricted to move classically. Advantage: large reduction of the computational effort Limitation: they cannot account for nuclear quantum effects

  31. i) Newton Hamilton-Jacob ii) Classical limit of the Schrödinger equation Nuclear wave function in polar coordinates

  32. (Classical action) Min(S): Euler-Lagrange equation Classical TDSE limit and minimum action Newton Hamilton-Jacob

  33. Population: • Two electronic states are coupled via non-diagonal terms in the Hamiltonian Hij and by the nonadiabatic coupling vector hij. TDSE and Multiconfigurational expansion where Time derivative Nonadiabatic coupling vector • Diabatic representation: {fi} hij = 0. • Adiabatic representation: {fi} Hij = 0 (i ≠ j).

  34. At each time, the dynamics is performed on an average of the states: • In the adiabatic representation Hii = Ei(R), Ei, and hji are obtained with traditional quantum chemistry methods. • aji is obtained by integrating • Nuclear motion is obtained by integrating the Newton eq. Mean Field (Ehrenfest) dynamics Advantage: Computationally cheap Limitation: wrong assymptotical description of a pure state (there is no decoherence) Solution (?): Impose a demixing time (Jasper and Truhlar, JCP 122, 044101 (2005))

  35. We will discuss this approach in detail later… Advantages: Computationally cheap; correct assymptotic behavior; easy interpretation of results Limitations: Forbidden hops; ad hoc conservation of energy Surface hopping • At each time, the dynamics is performed on one unique adiabatic state. • In the adiabatic representation Hii = Ei(R), Ei, and hji are obtained with traditional quantum chemistry methods. • aji is obtained by integrating • Nuclear motion is obtained by integrating the Newton eq. • The transition probability between two electronic states is calculated at each time step of the classical trajectory. • The system can hop to other adiabatic state.

  36. E t E t Mean Field and Surface hopping Mean Field system evolves in a pure state (superposition of several states) Surface Hopping system evolves in mixed state (several independent trajectories)

  37. What are we loosing?

  38. And with the same equation as before Ekk new terms where and High order coupling Multiconfigurational approach in polar coordinates Let`s start again, but now with a multiconfigurational wave function.

  39. Approximation 1: Classical independent trajectories where and

  40. Approximation 1: Classical independent trajectories = 0 where and Example: Surface hopping. Mean Field.

  41. Approximation 1: Classical independent trajectories Example: Surface hopping. Mean Field.

  42. Approximation 2: Classical coupled trajectories where and

  43. Approximation 2: Classical coupled trajectories = 0 where and Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).

  44. Approximation 2: Classical coupled trajectories where Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).

  45. Approximation 3: Coupled trajectories where and Example: Classical Limit Schrödinger Equation (CLSE, Burant and Tully, 2000) (Yarkony, JCP 114, 2601 (2001) One problem: get Dkl

  46. Comparison between methods Tully, Faraday Discuss. 110, 407 (1998). surface-hopping (diabatic) surface-hopping (adiabatic) mean-field wave-packet Landau-Zener Burant and Tully, JCP 112, 6097,(2000)

  47. Ethylene Barbatti, Granucci, Persico, Lischka, CPL401, 276 (2005). Comparison between methods Butatriene cation Worth, hunt and Robb, JPCA 127, 621 (2003). Oscillation patterns are not necessarily quantum interferences

  48. R1 t Wave packet (MCTDH) R2 R1 t Multiple spawning (MS) R1 R2 t Bohmian dynamics (CLSE, VCA) interacting trajectories R2 R1 t Surface hopping and Ehrenfest dynamics R2 independent trajectories Hierarchy of methods Quantum Classical

  49. This lecture: • Dynamics reveal features that are not easily found by static methods • From the full quantum treatment to the classical approach, there are several available methods • Semiclassical approaches (classical nuclear motion + quantum electron treatment) show the best cost-benefit ratio • Next lecture: • How to implement the surface hopping dynamics • The on-the-fly surface-hopping dynamics program NEWTON-X

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