Femtochemistry: A theoretical overview

1. Femtochemistry: A theoretical overview II – Transient spectra and excited states Mario Barbatti mario.barbatti@univie.ac.at This lecture can be downloaded at http://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture2.ppt

2. Energy (eV) Singlet Triplet 10 VR Ph Fl PA 0 Nuclear coordinates Femtosecond phenomena 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

4. time-resolved experiments

5. absorption 0 Conventional UV absorption spectrum ade gua cyt thy Static spectrum: information is integrated over time

6. Ultra-short laser pulses Transient spectrum: information is time resolved

7. Time resolved spectra static transient

8. Transient (time-dependent) spectra: pump-probe Mestdagh et al. J. Chem. Phys. 113, 240 (2000)

9. Dt Dt + t w pump and probe

10. td ~2000 fs td < 200 fs td < 200 fs

11. Pump t = 60 fs l = 618 nm Probe t = 6 fs probe wavelength l = 560 - 710 nm Mathies et al. Science 240, 777 (1988)

12. absorption excited state absorption (ionization) 0 0 transmission transmission 1 1 spontaneous emission (fluorescence) stimulated emission 1 2

13. Transmission due to ground state depletion Ground state absorption Stimulated emission Excited state absorption

15. Bacteriorhodopsin

16. geometry optimization

17. Topography of the potential energy surface

18. Topography of the excited-state potential energy surface • We want determine: • minima • saddle points • minimum energy paths • conical intersections

19. Newton-Raphson A bit of basic mathematics: The Newton-Raphson’s Method f(x) Prove it! 0 x xR x3 x2 x1 Numerical way to get the root of a function

20. df/dx 0 x x2 x1 x3 xe Newton-Raphson To find the extreme of a function, apply Newton-Raphson’s Method to the first derivative f(x) 0 x xe

21. Gradient vector: Hessian matrix: Geometry optimization Taylor expansion: Szabo and Ostlund, Modern Quantum Chemistry, Appendix C

22. xe xk Geometry optimization At xe, g(xe) = 0 Prove it! If H-1 is exact: Newton-Raphson Method If H-1 is approximated: quasi-Newton Method When g = 0, an extreme is reached regardless of the accuracy of H-1, provided it is reasonable.

23. Numerical Expensive, unreliable, however available for any method for which excited-state energies can be computed 1 gradient = 2 x 3N energy calculations! • Problem 1: • Get the gradient g Analytical Fast, reliable, but not generally available Two ways to get the derivative of x2

24. Present situation of quantum chemistry methods Methods allowing for excited-state calculations:

25. Example: update in the BFGS method: • Problem 2: • Get the Hessian H (or H-1) Hessian has NxN = N2 elements Normally second derivatives are computed numerically Hessian matrix is too expensive! • Use approximate Hessian: • Compute H in inexpensive method (3-21G basis, e.g.) • Do not compute. Use guess-and-update schemes (MS, BFGS)

26. excited state relaxation

27. p p* The electronic configuration changes quickly after the photoexcitation

28. E • “Spectroscopic” minima are close to the FC region • Global minima often are counter-intuitive geometries X Minima in the excited states “Spectroscopic” minimum Global minimum

29. Minima in the excited states

30. Minima in the excited states Ground state minimum S1 “spectroscopic” minimum

31. Relaxation in the excited states Barbatti et al., in Radiation Induced Molecular Phenomena in Nucleic Acid ( 2008)

32. Surface can have different diabatic characters Merchan and Serrano-Andres, JACS 125, 8108 (2003)

33. E X Minima may have different diabatic characters Change of diabatic character np* Adiabatic surface p* pp* p* p p n n

34. Initial relaxation may involve several states E

35. Relaxation keeping the diabatic character Merchán et al. J. Phys. Chem. B 110, 26471 (2006)

36. Relaxation changing the diabatic character Barbatti et al. J.Chem.Phys. 125, 164323 (2006)

37. In general, multiple paths are available

38. pp*/cs np*/cs Energy np* np* Reaction path pp* n-1s p-3s* ps* p-1s pp*/cs Common reaction paths: efficiency

39. 2-pyridone The trapping effect 9H-adenine

40. Radiationless decay:thymine Zechmann and Barbatti, J. Phys. Chem. A 112, 8273 (2008)

41. Radiationless decay:lifetime

42. excited-state intramolecular proton transfer ESIPT

43. Proton Transfer in 2-(2'-Hydroxyphenyl)benzothiazole (HBT) Elsaesser and Kaiser, Chem. Phys. Lett. 128, 231 (1986)

44. ESIPT reaction schemes

45. Emission signal at the keto wave number appears after only 30 fs DT/T Lochbrunner, Wurzer, Riedle, J. Phys. Chem. A 107 10580 (2003)

47. Internal conversion should play a role

48. ESIPT lprobe = 570 nm Resolution: 30 fs Schriever et al., Chem. Phys. 347, 446 (2008) Barbatti et al., PCCP 11, 1406 (2009)

49. Next lecture • Adiabatic approximation • Non-adiabatic corrections Contact mario.barbatti@univie.ac.at This lecture can be downloaded at http://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture2.ppt