1. Photochemistry: adiabatic and nonadiabatic molecular dynamics with multireference ab initio methods 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

2. Outline First Lecture: An introduction to molecular dynamics 1.Dynamics, why? 2.Overview of the available approaches Second Lecture: Towards an implementation of surface hopping dynamics 1.The N EWTON -X program 2.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 1.Dynamics, why? 2.Overview of the available approaches Second Lecture: Towards an implementation of surface hopping dynamics 1.The N EWTON -X program 2.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 I An Introduction to Molecular Dynamics Cândido Portinari, Café, 1935

5. Dynamics, why?

6. Singlet Triplet Photoinduced chemistry and physics avoided crossing 10 2 -10 4 fs conical intersection 10-10 2 fs PA – photoabsorption 1 fs VR – vibrational relaxation 10 2 -10 5 fs Energy (eV) 0 10 Nuclear coordinates Ph Fl PA VR Fl – fluorescence 10 6 -10 8 fs intersystem crossing 10 5 -10 7 fs Ph – phosforescence 10 12 -10 17 fs ab initio dynamics

7. 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) Photoinduced chemistry (multireference states). Radiationless processes in molecules Radiationless processes in molecules and solids (conical intersections); 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).

8. Main objective: relaxation path Ben-Nun, Molnar, Schulten, and Martinez. PNAS 99,1769 (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: UV solar radiation 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. Canuel et al. JCP 122, 074316 (2005)

11. An example: photodynamics of DNA basis What has theory to say?  */S 0 crossing Marian, JCP 122, 104314 (2005) Chen and Li, JPCA 109, 8443 (2005) Perun, Sobolewski and Domcke, JACS 127, 6257 (2005) C2C2

12. An example: photodynamics of DNA basis What has theory to say? n  */S 0 crossing Chen and Li, JPCA 109, 8443 (2005) Perun, Sobolewski and Domcke, JACS 127, 6257 (2005) reaction coordinate

13. An example: photodynamics of DNA basis What has theory to say?  */S 0 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. Minimum energy path in two steps Celany et al. CPL 243, 1 (1995) E max E min v0v0 Hypersphere R1R1 R2R2 R 1 eq R 2 eq 1.Determine the initial displacement vector (IRD) 2. Search for the minimum energy path Schlegel, J. Comp. Chem. 24, 1514 (2003)

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

20. Minimum energy path Garavelli et al., Faraday Discuss. 110, 51 (1998). Cembran et al. JACS 126, 16018 (2004). 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.

21. SiCH 4 : MRCI/CAS(2,2)/6-31G* Also for SiCH 4 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 S 1 state is 124 fs. This and other movies are available at: homepage.univie.ac.at/mario.barbatti

22. SiCH 4 : 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 S 1 state is 58 fs. This and other movies are available at: homepage.univie.ac.at/mario.barbatti

23. SiCH 4 Zechmann, Barbatti, Lischka, Pittner and Bonačić-Koutecký, CPL 418, 377 (2006)

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

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

26. Time evolution - I Wave packet propagation 1) The nuclear wave function is expanded as: f is the number of nuclear coordinates (<< 3N). Wave packet dynamics MCTDH (multiconfigurational time-dependent Hartree) (Meyer, Manthe and Cederbaum, CPL 165, 73 (1990)) 2) Solve TDSE using .   Hermite/Laguerre polynomials (DVR, discrete variable representation)   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. C. Lasser, TU-München Wave packet dynamics

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

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

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

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

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

33. TDSE and Multiconfigurational expansion where Time derivativeNonadiabatic coupling vector Population: Two electronic states are coupled via non-diagonal terms in the Hamiltonian H ij and by the nonadiabatic coupling vector h ij. Diabatic representation:  i  h ij = 0. Adiabatic representation: {  i }  H ij = 0 (i ≠ j).

34. 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)) At each time, the dynamics is performed on an average of the states: In the adiabatic representation H ii = E i (R),  E i, and h ji are obtained with traditional quantum chemistry methods. a ji is obtained by integrating Nuclear motion is obtained by integrating the Newton eq.

35. Surface hopping At each time, the dynamics is performed on one unique adiabatic state. In the adiabatic representation H ii = E i (R),  E i, and h ji are obtained with traditional quantum chemistry methods. a ji 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. Advantages: Computationally cheap; correct assymptotic behavior; easy interpretation of results Limitations: Forbidden hops; ad hoc conservation of energy We will discuss this approach in detail later…

36. Mean Field and Surface hopping t E t E 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. Let`s start again, but now with a multiconfigurational wave function. And with Multiconfigurational approach in polar coordinates the same equation as before E kk new terms where and High order coupling

39. Approximation 1: Classical independent trajectories where and

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

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

42. Approximation 2: Classical coupled trajectories where and

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

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

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

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

47. Worth, hunt and Robb, JPCA 127, 621 (2003). Comparison between methods Oscillation patterns are not necessarily quantum interferences Butatriene cation Barbatti, Granucci, Persico, Lischka, CPL 401, 276 (2005). Ethylene

48. Hierarchy of methods Quantum Classical Multiple spawning (MS) R1R1 R2R2 t Surface hopping and Ehrenfest dynamics independent trajectories R1R1 R2R2 t Bohmian dynamics (CLSE, VCA) interacting trajectories R1R1 R2R2 t Wave packet (MCTDH) R1R1 R2R2 t

49. Next lecture: How to implement the surface hopping dynamics The on-the-fly surface-hopping dynamics program N EWTON -X 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