Femtochemistry: A theoretical overview

1. Femtochemistry: A theoretical overview Introduction Mario Barbatti mario.barbatti@univie.ac.at This lecture can be downloaded at http://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture1.ppt

2. settling the bases: photochemistry, excited states, and conical intersections

3. Photochemistry & Photophysics • Stating the problem: • What does happen to a molecule when it is electronically excited? • How does it relax and get rid of the energy excess? • How long this process take? • What products are formed? • How does the relaxation affect or is affected by the environment? • Is it possible to interfere and to control the outputs?

4. Why to study it?

5. Why to study it? Pump-probe experiments based on ultra-fast laser pulses have increased the resolution of the chemical measurements to the femtosecond (10-15 s) time scale.

6. The need for Theory Theory is necessary to map the ground and excited state surfaces and to model the mechanisms taking place upon the photoexcitation. Theory is indispensable to deconvolute the raw time-resolved experimental information and to reveal the nature of the transition species. In particular, excited-state dynamics simulations can shed light on time dependent properties such as lifetimes and reaction yields.

7. P ~ |j|m|i|2 t ~ ns Basic process I: Radiative decay (fluorescence)

8. j| |i P ~ v  N t~ fs Basic process II: Non-radiative decay

9. The Static Problem • How are the excited state surfaces? • 2. For which geometries does the molecule have conical intersections? • 3. Can the molecule reach them?

10. Conical intersections formamide pyridone Antol et al. JCP 127, 234303 (2007) Barbatti et al., Chem. Phys. 349, 278 (2008)

11. Primitive conical intersections

12. Conical intersections: Twisted-pyramidalized Barbatti et al. PCCP 10, 482 (2008)

13. Paths to conical intersections: Adenine

14. The Dynamics Problem At a certain excitation energy: 1. Which reaction path is the most important for the excited-state relaxation? 2. How long does this relaxation take?

15. about methods & programs

16. General methodology

17. Programs • COLUMBUS • MRCI, MCSCF • Analytical gradients and non-adiabatic couplings • www.univie.ac.at/columbus • Lischka et al. PCCP 3, 664 (2001) • NEWTON-X • Mixed quantum-classical dynamics (surface hopping) • Excited-state Born-Oppenheimer dynamics • Absorption/emission spectrum simulation • General, modular, flexible • Interfaces to COLUMBUS, TURBOMOLE, DFTB • www.univie.ac.at/newtonx • Barbatti et al., J. Photochem. Photobio. A 190, 228 (2007)

18. 1 For a fixed nuclear geometry, solve time-independent Schrödinger Eq. for electrons. Get the energy gradient and the couplings 2 Use the energy gradient to update the nuclear geometry according to the Newton`s Eq. 3 For the new nuclear geometry (only!), solve the SC-TDSE and correct classical solution by performing a hopping if necessary. i) Go back to step 1 and repeat the procedure until the end of the trajectory. 4 ii) Repeat procedure for a large number of trajectories to have the “classical wave packet”. 5 iii) MQCD methods: surface hopping

19. Transition probability is evaluated at each time step A stochastic algorithm decides on which surface the molecule will continue Classical nuclear motion on the on-the-fly BO surface MQCD methods: surface hopping E Q Tully, J. Chem. Phys. 93, 1061 (1990)

20. Chair Twisted-chair Envelope Q Screw-boat q f Boat Cremer-Pople parameters Ex.: 1S6 = Screw-boat with atoms 1 above the plane and 6 below Cremer and Pople, JACS 97, 1358 (1975)

21. dynamics: adenine

22. Photochemical process B A

23. Photophysical process A

24. A short lifetime can enhance the photostability because the molecule does not remain long enough in the reactive excited state so as to have chance to isomerize.

25. This effect might have constituted an evolutionary advantage for the five nucleobases forming DNA and RNA.

26. Lifetime of nucleobases Canuel et al. J. Chem. Phys. 122, 074316 (2005)

27. 1 ps 30 ps 2-aminopurine 9H-Adenine

30. 0 750 1500 delay time / fs Experimental data on adenine Lifetime: Something between 750 fs [1] and 1.1 ps [2] Mechanism: Single-exponential decay [3] Double-exponential decay [2] 1: 100 fs – relaxation into S1 [4] 2: 1 ps – relaxation into S0 1: 100 fs – relaxation into S0 (pp*) [5] 2: 1 ps – relaxation into S0 (np*) Triple-exponential decay! [1] [1] Ullrich et al. JACS 126, 2262 (2004) [2] Canuel et al. J. Chem. Phys. 122, 074316 (2005) [3] Kang et al. JACS 124, 12958 (2002) [4] Perun et al. JACS 127, 6257 (2005) [5] Serrano-Andrés et al. PNAS 103, 8691 (2006)

31. Theoretical methods • Static calculations • MR-CIS(6,5)/SA3-CAS(12,10)/6-31G* (optimizations) • CASPT2/CASSCF(16,12)/6-31G* (single points) • Dynamics simulations • 60 trajectories of 600 fs with 0.5 fs time step (~1 month each) • Surface hopping with four electronic states • MR-CIS(6,4)/SA4-CAS(12,10)/[6-31G*,3-21G]

32. pp*imi ps* La np* ps* Conical intersections in adenine 7T8 2H3 4H3 4S3 E8 E3 B3,6 N-H 6S1 C8-C9 2E

33. How does deactivation ocurr? Barbatti and Lischka, JACS 130, 6831 (2008)

35. 2-pyridone Barbatti et al., Chem. Phys. 349, 278 (2008) Excited state dynamics: what do we have learned? 9H-adenine

36. Adenine is trapped close to 2E conformation and because of this it has time enough to tune the coordinates of the conical intersection. Adenine is a non-fluorescent species. Pyridone does not stay close to any specific conformation long enough in order to have time to tune the coordinates of the conical intersections. Pyridone is a fluorescent species.

37. 2-aminopurine 9H-Adenine 1 ps 30 ps

38. conclusions

39. Simple picture

40. Beyond the simple picture

41. Beyond the simple picture

42. About the methods • MQCD simulations at ab initio multireference level start to be feasible for molecules with about 10 heavy atoms (+MM) with the current computational capabilities. • They are still a new field being explored by few groups around the world. • NEWTON-X is the first freely available program dedicated to this kind of simulations.

43. About the methods • MQCD simulations are not a substitute for the conventional quantum-chemistry calculations, but a complementary tool to be used carefully given their high computational costs. • They can be specially useful to test specific hypothesis raised either by experimental analysis or conventional calculations.

44. Zewail, J. Phys. Chem. A 104, 5660 (2000)

45. Next lecture • Transient spectrum • Excited state surfaces Contact mario.barbatti@univie.ac.at This lecture can be downloaded at http://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture1.ppt