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Femtochemistry: A theoretical overview Mario Barbatti II – Transient spectra and excited states This lecture can be downloaded.

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Presentation on theme: "Femtochemistry: A theoretical overview Mario Barbatti II – Transient spectra and excited states This lecture can be downloaded."— Presentation transcript:

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

2 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 Femtosecond phenomena

3

4 4 time-resolved experiments

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

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

7 7 Time resolved spectra static transient

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

9   tt + tt pump and probe

10  d ~2000 fs  d < 200 fs

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

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

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

14 14

15 15 Bacteriorhodopsin

16 16 geometry optimization

17 17 Topography of the potential energy surface

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

19 19 Newton-Raphson A bit of basic mathematics: The Newton-Raphson’s Method 0 xRxR x f(x)f(x) x1x1 x2x2 x3x3 Numerical way to get the root of a function Prove it!

20 20 To find the extreme of a function, apply Newton-Raphson’s Method to the first derivative 0 xexe f(x)f(x) 0 x df/dx x xexe x1x1 x2x2 x3x3 Newton-Raphson

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

22 22 Geometry optimization At x e, g(x e ) = 0 Prove it! xexe xkxk 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 23 Problem 1: Get the gradient g Numerical Expensive, unreliable, however available for any method for which excited-state energies can be computed 1 gradient = 2 x 3N energy calculations! Analytical Fast, reliable, but not generally available Two ways to get the derivative of x 2

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

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

26 26 excited state relaxation

27 27   The electronic configuration changes quickly after the photoexcitation

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

29 29 Minima in the excited states

30 30 Minima in the excited states Ground state minimumS 1 “spectroscopic” minimum

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

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

33 33 Minima may have different diabatic characters E X nn   Change of diabatic character Adiabatic surface n   n  

34 34 Initial relaxation may involve several states E

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

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

37 37 In general, multiple paths are available

38 38 Common reaction paths: efficiency  */cs n  n  */cs Energy n  Reaction path  */cs   -1s   -3s  n-1s

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

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

41 41 Radiationless decay: lifetime

42 42 excited-state intramolecular proton transfer ESIPT

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

44 44 ESIPT reaction schemes

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

46 46

47 47 Internal conversion should play a role

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

49 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


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