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

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

3. 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. 4 Why to study it? Basic sciencesInteraction photon/matter Coeherence/decoherence Nature of transition states Non-adiabatic phenomena BiologyLight and UV detection Photosynthesis Genetic code degradation Cellular proton pump Atmospheric sciencesUV induced chemistry Greenhouse effect AstrophysicsInterstellar molecular synthesis TechnologyControl of chemical reactions Molecular photo-switches

5. 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. 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. 7 Basic process I: Radiative decay (fluorescence) P ~ |  j|  |i  | 2  ~ ns

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

9. 9 1.How are the excited state surfaces? 2. For which geometries does the molecule have conical intersections? 3. Can the molecule reach them? The Static Problem

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

11. 11 Conical intersectionStructureExamples TwistedPolar substituted ethylenes (CH 2 NH 2 + ) PSB3, PSB4 HBT Twisted-pyramidalizedEthylene 6-membered rings (aminopyrimidine) 4MCF Stilbene Stretched- bipyramidalized Polar substituted ethylenes Formamide 5-membered rings (pyrrole, imidazole) H-migration/carbeneEthylidene Cyclohexene Out-of-plane OFormamide Rings with carbonyl groups (pyridone, cytosine, thymine) Bond breakingHeteroaromatic rings (pyrrole, adenine, thiophene, furan, imidazole) Proton transferWatson-Crick base pairs Primitive conical intersections

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

13. 13 Paths to conical intersections: Adenine

14. 14 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? The Dynamics Problem

15. 15 about methods & programs

16. 16 General methodology SubjectApproachMethods Vertical excitation spectra Conventional adiabatic quantum chemistry MRCI, CC2, TD-DFT Stationary points in excited states Conventional adiabatic quantum chemistry MRCI, CC2, TD-DFT Conical intersectionsNon-adiabatic quantum chemistry MRCI, MCSCF Reaction pathsConvent. adiabatic quantum chemistry (multireference) MRCI, CASPT2, MCSCF Lifetime and yieldsMixed quantum-classical dynamics methods MRCI, MCSCF (+ MM)

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

18. 18 MQCD methods: surface hopping Use the energy gradient to update the nuclear geometry according to the Newton`s Eq. 2 For the new nuclear geometry (only!), solve the SC-TDSE and correct classical solution by performing a hopping if necessary.3 Go back to step 1 and repeat the procedure until the end of the trajectory.4 Repeat procedure for a large number of trajectories to have the “classical wave packet”.5 For a fixed nuclear geometry, solve time- independent Schrödinger Eq. for electrons. Get the energy gradient and the couplings1 i) ii) iii)

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

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

21. 21 dynamics: adenine

22. 22 Photochemical process

23. 23 Photophysical process

24. 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. 25 This effect might have constituted an evolutionary advantage for the five nucleobases forming DNA and RNA.

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

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

28. 28

29. 29

30. 30 07501500 delay time / fs 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 S 1 [4] 2: 1 ps – relaxation into S 0 1: 100 fs – relaxation into S 0 (  *) [5] 2: 1 ps – relaxation into S 0 (n  *) 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) Experimental data on adenine

31. 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. 32 Conical intersections in adenine N-H 2E2E C 8 -C 9 E3E3 E8E8 2H32H3 4S34S3 4H34H3 B 3,6 6S16S1 LaLa  * 7T87T8  * imi n*n*

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

34. 34

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

36. 36 Adenine is trapped close to 2 E 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. 37 1 ps 30 ps 9H-Adenine 2-aminopurine

38. 38 conclusions

39. 39 Simple picture

40. 40 Beyond the simple picture

41. 41 Beyond the simple picture

42. 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. N EWTON -X is the first freely available program dedicated to this kind of simulations.

43. 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. 44 Zewail, J. Phys. Chem. A 104, 5660 (2000)

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