Wavepackets ground state

Second-order effects include experiments designed to clock chemical reactions, pioneered by Zewail and coworkers [25]. The experiments are shown schematically in figure Al.6.10. An initial 100-150 fs pulse moves population from the bound ground state to the dissociative first excited state in ICN. A second pulse, time delayed from the first then moves population from the first excited state to the second excited state, which is also dissociative. By noting the frequency of light absorbed from tlie second pulse, Zewail can estimate the distance between the two excited-state surfaces and thus infer the motion of the initially prepared wavepacket on the first excited state (figure Al.6.10 ). 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

Figure Al.6.20. (Left) Level scheme and nomenclature used in (a) single time-delay CARS, (b) Two-time delay CARS ((TD) CARS). The wavepacket is excited by cOp, then transferred back to the ground state by with Raman shift oij. Its evolution is then monitored by tOp (after [44])- (Right) Relevant potential energy surfaces for the iodine molecule. The creation of the wavepacket in the excited state is done by oip. The transfer to the final state is shown by the dashed arrows according to the state one wants to populate (after [44]).

Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]).

Figure Al.6.26. Stereoscopic view of ground- and excited-state potential energy surfaces for a model collinear ABC system with the masses of HHD. The ground-state surface has a minimum, corresponding to the stable ABC molecule. This minimum is separated by saddle points from two distmct exit chaimels, one leading to AB + C the other to A + BC. The object is to use optical excitation and stimulated emission between the two surfaces to steer the wavepacket selectively out of one of the exit chaimels (reprinted from [54]).

Knopp G, Pinkas I and Prior Y 2000 Two-dimensional time-delayed coherent anti-Stokes Raman spectroscopy and wavepacket dynamics of high ground-state vibrations J. Raman Spectrosc. 31 51... 

Plenary 11. W Kiefer et al, e-mail address wolfgang.kiefer mail.imi-wue.de (TR CARS). Ultrafast impulsive preparation of ground state and excited state wavepackets by impulsive CARS with REMPI detection in potassium and iodine duners. 

So far we have exclusively discussed time-resolved absorption spectroscopy with visible femtosecond pulses. It has become recently feasible to perfomi time-resolved spectroscopy with femtosecond IR pulses. Flochstrasser and co-workers [M, 150. 151. 152. 153. 154. 155. 156 and 157] have worked out methods to employ IR pulses to monitor chemical reactions following electronic excitation by visible pump pulses these methods were applied in work on the light-initiated charge-transfer reactions that occur in the photosynthetic reaction centre [156. 157] and on the excited-state isomerization of tlie retinal pigment in bacteriorhodopsin [155]. Walker and co-workers [158] have recently used femtosecond IR spectroscopy to study vibrational dynamics associated with intramolecular charge transfer these studies are complementary to those perfomied by Barbara and co-workers [159. 160], in which ground-state RISRS wavepackets were monitored using a dynamic-absorption technique with visible pulses. 

The experiment is illustrated in figure B2.5.9. The initial pump pulse generates a localized wavepacket in the first excited state of Nal, which evolves with time. The potential well in the state is the result of an avoided crossing with the ground state. Every time the wavepacket passes this region, part of it crosses to the lower surface before the remainder is reflected at the outer wall of the potential. The crossing leads to... 

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

A) no VER and no dephasing. (B) VER is faster tiian a vibrationai period. Once tire vibrationai ground state is reached, tire wavepacket begins to osciiiate coherentiy. (C) The VER rate is comparabie to a vibrationai period so some coherence is seen in botii excited and ground states. (D) Dephasing is faster tiian VER. 

As in previous sections, the zeros of l (x, t) in the complex t plane at fixed x are of interest. This appears a hopeless task, but the situation is not that bleak. Thus, let us consider a wavepacket initially localized in the ground state in the sense that in Eq. (50), for some given x. 

Figure 3, Wavepacket dynamics of the photodissociation of NOCl, shown as snapshots of the density (wavepacket amplitude squared) at various times, The coordinates, in au, are described in Figure b, and the wavepacket is initially the ground-state vibronic wave function vertically excited onto the 5i state. Increasing corresponds to chlorine dissociation. The density has been integrated over the angular coordinate. The 5i PES is ploted for the geometry, 9 = 127, the ground-state equilibrium value,...

Figure 39. Pump-dump control of NaK molecule by using two quadratically chirped pulses. The initial state taken as the ground vibrational eigenstate of the ground state X is excited by a quadratically chirped pulse to the excited state A. This excited wavepacket is dumped at the outer turning point at t 230 fs by the second quadratically chirped pulse. The laser parameters used are = 2.75(1.972) X 10-2 eVfs- 1.441(1.031) eV, and / = 0.15(0.10)TWcm-2 for the first (second) pulse. The two pulses are centered at t = 14.5 fs and t2 = 235.8 fs, respectively. Both of them have a temporal width i = 20 fs. (See color insert.) Taken from Ref. [37].

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].

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

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