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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
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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
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4 time-resolved experiments
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5 Static spectrum: information is integrated over time Conventional UV absorption spectrum 0 absorption ade gua thy cyt
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Ultra-short laser pulses Transient spectrum: information is time resolved
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7 Time resolved spectra static transient
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Transient (time-dependent) spectra: pump-probe Mestdagh et al. J. Chem. Phys. 113, 240 (2000)
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tt + tt pump and probe
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d ~2000 fs d < 200 fs
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Mathies et al. Science 240, 777 (1988) probe wavelength = 618 nm = 60 fs = 560 - 710 nm = 6 fs Pump Probe
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0 absorption 1 transmission 2 stimulated emission 0 excited state absorption (ionization) 1 transmission 1 spontaneous emission (fluorescence)
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Transmission due to ground state depletion Excited state absorption Stimulated emission Ground state absorption
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15 Bacteriorhodopsin
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16 geometry optimization
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17 Topography of the potential energy surface
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18 Topography of the excited-state potential energy surface We want determine: minima saddle points minimum energy paths conical intersections
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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!
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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
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21 Taylor expansion: Hessian matrix: Gradient vector: Geometry optimization Szabo and Ostlund, Modern Quantum Chemistry, Appendix C
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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.
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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
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24 Present situation of quantum chemistry methods Methods allowing for excited-state calculations:
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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:
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26 excited state relaxation
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27 The electronic configuration changes quickly after the photoexcitation
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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
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29 Minima in the excited states
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30 Minima in the excited states Ground state minimumS 1 “spectroscopic” minimum
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31 Relaxation in the excited states Barbatti et al., in Radiation Induced Molecular Phenomena in Nucleic Acid ( 2008)
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32 Merchan and Serrano-Andres, JACS 125, 8108 (2003) Surface can have different diabatic characters
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33 Minima may have different diabatic characters E X nn Change of diabatic character Adiabatic surface n n
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34 Initial relaxation may involve several states E
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35 Relaxation keeping the diabatic character Merchán et al. J. Phys. Chem. B 110, 26471 (2006)
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36 Relaxation changing the diabatic character Barbatti et al. J.Chem.Phys. 125, 164323 (2006)
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37 In general, multiple paths are available
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38 Common reaction paths: efficiency */cs n n */cs Energy n Reaction path */cs -1s -3s n-1s
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39 The trapping effect 9H-adenine 2-pyridone
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40 Radiationless decay: thymine Zechmann and Barbatti, J. Phys. Chem. A 112, 8273 (2008)
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41 Radiationless decay: lifetime
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42 excited-state intramolecular proton transfer ESIPT
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43 Proton Transfer in 2-(2'-Hydroxyphenyl)benzothiazole (HBT) Elsaesser and Kaiser, Chem. Phys. Lett. 128, 231 (1986)
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44 ESIPT reaction schemes
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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
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47 Internal conversion should play a role
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48 ESIPT probe = 570 nm Resolution: 30 fs Schriever et al., Chem. Phys. 347, 446 (2008) Barbatti et al., PCCP 11, 1406 (2009)
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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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