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Ultrafast processes in molecules

Ultrafast processes in molecules. II – Transient spectra and excited states. Mario Barbatti barbatti@kofo.mpg.de. Energy (eV). Singlet. Triplet. 10. VR. Ph. Fl. PA. 0. Nuclear coordinates. Femtosecond phenomena. conical intersection 10-10 2 fs.

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Ultrafast processes in molecules

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  1. Ultrafast processes in molecules II – Transient spectra and excited states Mario Barbatti barbatti@kofo.mpg.de

  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 PA – photoabsorption 1 fs VR – vibrational relaxation 102-105 fs Fl – fluorescence 106-108 fs Ph – phosforescence 1012-1017 fs

  3. time-resolved experiments

  4. absorption 0 ade gua cyt thy Static spectrum: information is integrated over time

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

  6. Time resolved spectra static transient

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

  8. Dt Dt + t w pump and probe

  9. td ~2000 fs td < 200 fs td < 200 fs

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

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

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

  13. Bacteriorhodopsin

  14. geometry optimization

  15. Topography of the potential energy surface

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

  17. 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

  18. 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

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

  20. 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.

  21. 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

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

  23. 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)

  24. excited state relaxation

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

  26. 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

  27. Minima in the excited states

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

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

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

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

  32. Initial relaxation may involve several states E

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

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

  35. In general, multiple paths are available

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

  37. 2-pyridone The trapping effect 9H-adenine

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

  39. Radiationless decay:lifetime

  40. excited-state intramolecular proton transfer ESIPT

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

  42. ESIPT reactionschemes

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

  44. Internal conversion should play a role

  45. ESIPT: environment effects lprobe = 570 nm Resolution: 30 fs • Barbatti, Aquino, Lischka, Schriever, Lochbrunner, Riedle, PCCP 11, 1406 (2009)

  46. ESIPT: QM/MM simulations • Ruckenbauer, Barbatti, Lischka, unpublished

  47. Next lecture • Adiabatic approximation • Non-adiabatic corrections Contact barbatti@kofo.mpg.de

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