Theoretical Photochemistry SoSe 2015

Transcription

1 Theoretical Photochemistry SoSe 2015 Lecture 8 Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Theoretical Photochemistry 1

2 Topics 1. Photophysical Processes 2. The Born-Oppenheimer approximation 3. Wavepackets 4. Beyond Born-Oppenheimer non-adiabatic transitions 5. The Franck-Condon picture of electronic transitions 6. Interaction with light & what do we measure experimentally? 7. Conical intersections 8. Examples: Ethene, Protonated Schiff Bases (Retinal), Azobenzene 9. Some electronic structure aspects 10. Dynamics: trajectories or wavefunctions? 11. Wavefunction propagation techniques 2

3 12. Trajectory surface hopping techniques 13. Non-linear optical spectroscopy: calculation of spectroscopic signals 14. Extended systems: Excitons, light-harvesting, etc. 15. Solvent/environmental effects 3

4 Some examples 1. Transient absorption, pump-probe spectra, time-resolved fluorescence 2. Photon echoes 3. More than one dimension: 2D photon echoes 4. 2D infrared experiments 4

5 1. Excited-state absorption / pump-probe spectroscopy We need the 3rd-order contribution P (3) (t) = ψ (1) (t) ˆµ ψ (2) (t) + c.c. ( ) = ψ (1) S1 (t ; τ ) ˆµ exp iĥ S2 (t t ) ˆµ ψ (1) S1 (t ; τ ) E(t )dt two pulses (pump/probe) with a delay τ The experiment probes the excited-state population ψ S1 (t; τ ) 2 as a function of the delay time τ between the pump/probe pulse 5

6 Transient absorption web.vu.lt/ff/m.vengris/images/trspectroscopy02.pdf time-resolved two-pulse (pump-probe) spectroscopy 6

7 Transient absorption for a photochemical switch from: Ultrafast isomerization and vibrational coherence of biomimetic photoswitches: Experimental investigation by femtosecond transient absorption spectroscopy, by Julien Briand, Ph.D. thesis Université de Strasbourg (2009). 7

8 NaI: one of the first fs pump-probe experiments NaI Na + I (Zewail & co (1989)) many oscillations between covalent and ionic states 8

9 Time-Resolved Fluorescence often provides complementary information to transient absorption suitable to monitor FRET (Fluorescence Resonance Energy Transfer) 9

10 Intramolecular charge transfer (ICT): DMABN (dimethylaminobenzonitrile) Serrano-Andrés et al., J. Chem. Phys. 117, 3189 (1995) Observe dual fluorescence: LE (locally excited) state + CT (charge transfer) state 10

11 ICT mechanism Fuss et al., Faraday Discuss. 127, 23 (2004) typical time scales (measured in femtosecond time-resolved experiments): τ 1 = 5-10 fs τ 2 = fs τ 3 = 500 fs - 1 ps The reaction coordinate mainly involves the twist, but also other modes and the solvent reaction coordinate Also, there s a conical intersection! 11

12 Do fluorescence and transient absorption probe the same intramolecular charge transfer state of 4-(dimethylamino)benzonitrile? Gustavsson et al. J. Chem. Phys. 131, (a) DMABNinAcn LE (b) (c) (d) ICT FIG. 1. The femtosecond timeresolved fluorescence upconversion spectra: a two-dimensional image plot and b its corresponding timeevoluted spectra of DMABN in acetonitrile Acn at room temperature. The spectral region around 400 nm was masked thoroughly to protect a detector in the excitation wavelength of 267 nm. The fluorescence decay curves of c the LE emission at 350 nm and d the ICT emission at 550 nm for DMABN in Acn. Common decay time constants were evaluated including other upconversion sets not shown here by a nonlinear leastsquares global fit with a deconvolution procedure. The numbers in the parentheses indicate a standard deviation 1. Fluorescence Gustavsson et al., J. Chem. Phys. 131, (2009) 12

13 Do fluorescence and transient absorption probe the same intramolecular charge transfer state of 4-(dimethylamino)benzonitrile? (a) DMABN in Acn (c) (b) (d) FIG. 2. The femtosecond timeresolved transient absorption spectra s22 to 25 ps with an interval of 0.1 psd at sad shorter- and sbd longerwavelength region for DMABN in Acn at room temperature. The arrows indicate the time evolution of the spectra, and assignments for the transients are also shown. Kinetics at scd the 420 nm transient stictd and sdd 680 nm transient sthe psp-state absorptiond, which were extracted with a band integration from the timeresolved spectra fsad and sbdg. Leaders show the fitted decay times with a standard deviation in the parentheses. Downloaded 02 Dec 2010 to Redistribution subject to AIP license or copyright; see Absorption Gustavsson et al., J. Chem. Phys. 131, (2009) 13

14 2. Photon echoes purpose: measure the homogeneous linewidth but not the inhomogeneous linewidth! use an echo technique to eliminate the inhomogeneous dephasing 14

15 Emergence of inhomogeneous broadening ) χ(t) = exp ( 2 t 2 ( ) J(t) = exp iω eg t Γt (inhomogeneous) (homogeneous) Gaussian lineshape Lorentzian lineshape 15

16 Analogy to spin echoes Hahn, Phys. Rev. 80, 580 (1950) S = slow F = fast dephasing rephasing coherent spin evolution: σ x (t) = σ 12 exp( iωt) + σ 21 exp(iωt) σ y (t) = i(σ 12 exp( iωt) σ 21 exp(iωt)) 16

17 Optical photon echo experiment Kernit, Abella, Hartmann, Phys. Rev. Lett. 13, 567 (1964) monitor electronic coherence ρ eg as a function of the time delay τ note: various types of echo experiments: two-pulse, three-pulse etc. 17

18 Coherence some general remarks wavefunction picture: coherent superposition states ( Ψ(t) = c 1 (t) φ 1 exp ī ) ( h E 1t + c 2 (t) φ 2 exp ī ) h E 2t this translates as follows to the density operator picture: ˆρ = Ψ(t) Ψ(t) = i,j=1,2 i,j=1,2 ρ ij (t) φ i φ j i = j: populations, i j: coherences c i (t)c j ( (t)exp ī ) h (E i E j )t φ i φ j now include ensemble average: ˆρ = n p n Ψ n (t) Ψ n (t) dephasing of coherence ( T 2, decoherence,... ) 18

19 E.g., photon echoes for I 2 Cornstock, Lozovoy, Dantus J. Chem. Phys. 119, 6546 (2003) monitor the coherence decay, i.e., ρ XB (t), in the presence of He, Ar, N 2, O 2, C 3 H 8 etc. 19

20 Photon echoes for I 2, cont d obtain homogeneous dephasing rates as a function of perturber density similar experiments in solution phase where inhomogeneous dehasing is predominant 20

21 Photon echoes as a probe of solvation dynamics Passino, Nagasawa, Fleming, J. Chem. Phys. 107, 6094 (1997) peak shift measurements (from 3PE = 3-pulse stimulated photon echo) report directly on solvation dynamics shortest time scale (< 100 fs) reflects inertial solvation ps scale scale directly related to solvation correlation function ω(t) ω(0) / ω 2 21

22 Complementary approach: hole burning idea: laser excitation of a sub-ensemble of species within inhomogeneously broadened envelope 22

23 3. More than one dimension: 2D photon echoes pulse sequence: pulse 1 t 1 pulse 2 T pulse 3 t 3 2D Fourier transform S echo (ω 1, T, ω 3 ) cross peaks appear, indicating a transfer process (coherence or population transfer) 23

24 Excitation transfer in multi-chromophoric systems Two basic configurations: φ 1 = e (1) g (2) φ 2 = g (1) e (2) general exciton state = superposition of these configurations: Ψ exciton (t) = c 1 (t) φ 1 + c 2 (t) φ 2 the configurations are coupled via the Coulomb interaction: V Coulomb 12 = dr 3 D dr3 A ρ (eg) D (r D)ρ (ge) A (r A) r D r A Note: dipole-dipole approximation Förster theory 24

25 Exciton transfer can be coherent and ultrafast quantum dynamics simulation: site population site 1: initial excitation site population/coherence site 1: initial excitation coherence time [fs] time [fs] site-site excitation energy transfer φ n φ n+1 transfer is mediated by coherences φ n φ n+1 but the environment could rapidly induce decoherence can one observe any coherent transfer experimentally? 25

26 Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems Fleming & collaborators, Nature 446, 782 (2007) LETTERS NATURE Vol April fs Arcsinh 280 fs Coherence wavelength (nm) fs Arcsinh fs Coherence wavelength (nm) Rephasing wavelength (nm) 788 Arcsinh Figure 1 Two-dimensional electronic spectra of FMO. Selected two-dimensional electronic spectra of FMO are shown at population times from T 5 0 to 600 fs demonstrating the emergence of the exciton 1 3 cross-peak (white arrows), amplitude oscillation of the exciton 1 diagonal peak (black arrows), the change in lowestenergy exciton peak shape and the oscillation of the 1 3 cross-peak amplitude. The data are shown with an arcsinh coloration to highlight smaller features: amplitude increases from blue to white (for a three-dimensional representation of the coloration see Fig. 3a). Rephasing wavelength (nm) 788 Arcsinh

27 Exciton transfer in the FMO complex Brixner & collaborators, Nature 434, 625 (2005) 1 2, 4 7 3, , 6 1 FMO = Fenna-Matthews-Olson bacteriochlorophyll a (BChl) protein of green sulphur bacteria antenna system that collects light and channels excitation to a reaction center where charge transfer takes place 27

28 Coherence dynamics in photosynthesis: protein protection of excitonic coherence Lee, Cheng, Fleming, Science 316, 1462 (2007) Fig. 1. The 2CECPE experiment. (A) The 77 K 2CECPE = two-color electronic coherence photon echo experiment 28

29 Photon echo experiment G. Engel and collaborators, New J. Phys. 12 (2010)

30 4. 2D infrared experiments measure correlations between instantaneous vibrational frequencies signal depends on anharmonicity the vibration can act as a probe for a fluctuating environment Pump Frequency [cm -1 ] Absorbance (a) ACN (b) Benzoylchloride (c) NMA Absorbance Change [mod] Probe Frequency [cm -1 ] Probe Frequency [cm -1 ] Probe Frequency [cm -1 ] C=O bond region of IR and 2D-IR spectra of different peptides Hamm, J. Biol. Phys. 35, 17 (2009) 30

31 Vibrational coupling in α-helical proteins A. S. Davydov, Phys. Scr. 20, 387 (1979) H = n [ ] E 0 a n a n J(a n a n+1 + a n+1 a n) + p2 n 2M +W 2 (q n+1 q n ) 2 + χa n a n(q n+1 q n ) a n, a n: raising/lowering op s for amide (CO) vibration at site n q n, p n : phonon op s for H-bonded lattice mode at site n Hamm & Edler, Phys. Rev. B 73, (2006) 31

32 Moving towards 3D? Garret-Roe and Hamm, Acc. Chem. Res., 42, 1412 (2009) FIGURE 1. Principle of 2D-IR and 3D-IR spectroscopy: (a, c) pulse sequences; (b, d) model spectra; (e) an example ω-trajectory. 32

33 Moving towards 3D / cont d Garret-Roe and Hamm, Acc. Chem. Res., 42, 1412 (2009) Experimental (a) and simulated (b) 3D-IR spectra of the asymmetric stretch vibration of CO 2 dissolved in water general idea of 3D-IR: information on higher-order correlations with respect to low-frequency solvent modes whose effect is monitored by high-frequency spectator modes 33

34 Recommended reading Ahmed Zewail s Nobel lecture: prizes/chemistry/laureates/1999/zewail-lecture.html David Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective, new edition: University Science Books (2007). see also: Abraham Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer, And Reactions in Condensed Molecular Systems, Oxford University Press (2006). Shaul Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press (1999). 34