Wavepacket motion

Figure B2.1.8 Dynamic absorption trace obtained with the dye IR144 in methanol, showing oscillations arising from coherent wavepacket motion (a) transient observed at 775 mn (b) frequency analysis of the oscillations obtained using a linear prediction, smgular-value-decomposition method.

Marquardt R and Quack M 1991 The wavepacket motion and intramolecular vibrational redistribution... 

In light of tire tlieory presented above one can understand tliat tire rate of energy delivery to an acceptor site will be modified tlirough tire influence of nuclear motions on tire mutual orientations and distances between donors and acceptors. One aspect is tire fact tliat ultrafast excitation of tire donor pool can lead to collective motion in tire excited donor wavepacket on tire potential surface of tire excited electronic state. Anotlier type of collective nuclear motion, which can also contribute to such observations, relates to tire low-frequency vibrations of tire matrix stmcture in which tire chromophores are embedded, as for example a protein backbone. In tire latter case tire matrix vibration effectively causes a collective motion of tire chromophores togetlier, witliout direct involvement on tire wavepacket motions of individual cliromophores. For all such reasons, nuclear motions cannot in general be neglected. In tliis connection it is notable tliat observations in protein complexes of low-frequency modes in tlie... 

Figure 55. Two-dimensional coupled potential energy surfaces and the wavepacket motion, (a) Si — S2 surfaces and (b) Si — So surfaces. The black, gray, and white circles and dotted lines indicate the locations of the FC region. Si - S2 conical intersection minimum, 5MR Si — So conical intersection minimum, and seam lines, respectively. The solid arrows indicate the schematic wavepacket pathway in the case of natural photoisomerization starting from the vibrational ground state. Taken from Ref. [49].

Takeuchi T, Tahara T (2005) Coherent nuclear wavepacket motions in ultrafast excited-state intramolecular proton transfer sub-30-fs resolved pump-probe absorption spectroscopy of 10-hydroxybenzo[h]quinoline in solution. J Phys Chem A 109 10199-10207... 

S. P. Shah and S. A. Rice. Controlling quantum wavepacket motion in reduced-dimensional spaces reaction path analysis in optimal control of HCN isomerization. Faraday Trans., 113 319-331(1999). 

DOWNHILL V- Z WAVEPACKET MOTION IN TDMAE Ar CLUSTERS, EXCITED AT 266 nm AND PROBED AT 800 nm... 

Symmetry breaking wavepacket motion and absence of deuterium isotope effect in ultrafast excited state proton transfer... 

The double proton transfer of [2,2 -Bipyridyl]-3,3 -diol is investigated by UV-visible pump-probe spectroscopy with 30 fs time resolution. We find characteristic wavepacket motions for both the concerted double proton transfer and the sequential proton transfer that occur in parallel. The coherent excitation of an optically inactive, antisymmetric bending vibration is observed demonstrating that the reactive process itself and not only the optical excitation drives the vibrational motions. We show by the absence of a deuterium isotope effect that the ESIPT dynamics is entirely determined by the skeletal modes and that it should not be described by tunneling of the proton. 

Unlike the case of simple diatomic molecules, the reaction coordinate in polyatomic molecules does not simply correspond to the change of a particular chemical bond. Therefore, it is not yet clear for polyatomic molecules how the observed wavepacket motion is related to the reaction coordinate. Study of such a coherent vibration in ultrafast reacting system is expected to give us a clue to reveal its significance in chemical reactions. In this study, we employed two-color pump-probe spectroscopy with ultrashort pulses in the 10-fs regime, and investigated the coherent nuclear motion of solution-phase molecules that undergo photodissociation and intramolecular proton transfer in the excited state. 

Fig. 2. Nuclear motion of the ground-state vibration at 386 cm 1 that corresponds to the excited-state wavepacket motion observed in the dissociative S2 State.

Figure 13. Femtosecond dynamics of dissociation (Nal) reaction. Bottom Experimental observations of wavepacket motion, made by detection of the activated complexes [Nal] or the free Na atoms. Top Potential energy curves (left) and the exact quantum calculations (right) showing the wavepacket as it changes in time and space. The corresponding changes in bond character are also noted covalent (at 160 fs), covalent/ionic (at 500 fs), ionic (at 700 fs), and back to covalent (at 1.3 ps).

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

When the pump-probe delay is varied slowly and continuously (i.e., both parameters are varied simultaneously), the high-frequency oscillations due to the optical phase of the wavepacket can be resolved in the transient signal, as shown by Blanchet et al. [27], who monitored the wavepacket motion and... 

Figure 8. Frequency-filtered Na2+ pump-probe signal in comparison to the averaged signal of Fig, 4. The filtered signal measures by how much the Na2+ signal is modulated with the laser frequency. Such modulations occur when there is interference between excitation by the probe pulse and the wavepackets formed by the pump laser pulse. This interference effect causes both the A EJ and the 2 1 Ilg state wavepacket motion to be observable in the signal.

On the other hand, additional spectroscopic information can be obtained by making use of this technique The Fourier transform of the frequency-filtered transient (inset in Fig. 8) shows that the time-dependent modulations occur with the vibrational frequencies of the A E and the 2 IIg state. In the averaged Na2+ transient there was only a vanishingly small contribution from the 2 IIg state, because in the absence of interference at the inner turning point ionization out of the 2 IIg state is independent of intemuclear distance, and this wavepacket motion was more difficult to detect. In addition, by filtering the Na2+ signal obtained for a slowly varying pump-probe delay with different multiples of the laser frequency, excitation processes of different order may be resolved. This application is, however, outside the scope of this contribution and will be published elsewhere. 

Figure 18. Transient Na3+ signal for strongly attenuated 80-fs pump-probe laser pulses of 620 nm. The frequencies observed in the Fourier transform are due to vibrational wavepacket motion on the B state potential.

The question is then, first, how often has such a complete match between experiment and theoretical simulation been achieved Second, are there good examples where complete simulations have been carried out but lead to two or more equally acceptable models to interpret the experimental results I refer to this question of ambiguity also in relation to a very similar problem arising in the interpretation of nontime-resolved high-resolution spectroscopy data [1,2], which provided in fact, the first experimental results on nontrivial three-dimensional wavepacket motion on the femtosecond time scale [3]. 

Figure 4. Schematic of the potential energy curves of the relevant electronic states The pump pulse prepares a coherent superposition of vibrational states in the electronic A 1 EJ state at the inner turning point. Around v = 13 this state is spin-orbit coupled with the dark b 3n state, causing perturbations. A two-photon probe process transfers the wavepacket motion into the ionization continuum via the (2) llg state [7].

Figure 5. Wavepacket motion of the 39,39 K2 A state interrogated by (a) a two-photon probe pulse via the (2) 1 IIg state and (i>) a one-photon probe process into the ionization continuum (c, d) corresponding Fourier transforms, indicating a stronger second harmonic for the one-photon probe process [7].

Wavepacket motion is now routinely observed in systems ranging from the very simple to the very complex. In the latter category, we note that coherent vibrational motion on functionally significant time scales has been observed in the photosynthetic reaction center [15], bacteriorhodopsin [16], rhodopsin [17], and light-harvesting antenna of purple bacteria (LH1) [18-20]. Particularly striking are the results of Zadoyan et al. [21] on the... 

The peak shift data in Fig. 17 show oscillatory character, as is our first two examples (I2 and LH1). This arises from vibrational wavepacket motion. In addition, the very fast drop in peak shift to about 65% of the initial value in -20 fs results from the interference between the wavepackets created in different intramoleculear modes. This conclusion follows directly from obtaining the frequencies and relative coupling strengths of the intramolecular modes from transient grating studies of IR144, carried out in the same solvents (data not shown). Thus, by visual inspection of Fig. 17, an answer to a long-standing question—What fraction of the spectral width arises from intra- and intermolecular motion —is immediately apparent. 

---