Gaussian wavepacket vibrational

Because the initial vibrational state for absorption spectra often is v = 0, the vibrational nonstationary state typically produced initially is an only slightly distorted Gaussian wavepacket centered at R"g. Conservation of momentum requires that this approximately minimum-uncertainty wavepacket be launched at the turning point on the upper surface, R e = R"g, which lies vertically above R"g. [This is a consequence of the stationary phase condition, see Sections 5.1.1 and 7.6 and Tellinghuisen s (1984) discussion of the classical Franck-Condon... 

Figure 9. Potential energy curves V(R) for the HF and HI molecule, as indicated. The collision process is described by an incoming Gaussian wavepacket (dashed lines). For the HF molecule the objective is to decrease the energy of the scattered particles in order that bound states are populated (vibrational energies Ev are indicated by the horizontal lines). For HI, the objective is to selectively populate the v = 19 state.

Figure C3.5.7. Possible modes of vibrational wavepacket (smootli Gaussian curve) motion for a highly vibrationally excited diatomic molecule produced by photodissociation of a linear triatomic such as Hglj, from [8].

Fig. 7.12. Comparison of the measured and the calculated absorption spectra for the So — Si transition in CH3ONO. The quantum number n denotes vibrational excitation of the NO moiety in the complex. The theoretical spectrum is obtained in a three-dimensional wavepacket calculation including the ONO bending angle in addition to the two N-0 stretching coordinates. The spectrum is convoluted with a Gaussian function with width AEres = 0.02 eV in order roughly to mimic thermal broadening and is artificially shifted along the energy axis. Reproduced from Untch, Weide, and Schinke (1991a).

In most vibrational wavepacket experiments, the time-evolving S (t) generally contains more than two vibrational eigenstates. The vibrational quantum numbers and t = to amplitudes of these vibrational eigenstates in k(t) are determined by the nature of the pluck that creates l (t) at f0. If the excitation-pulse is a simple, smooth, and short-time Gaussian, the result is a Franck-Condon pluck... 

Starting from the groimd vibrational state on the ground (X) electronic state, we form a wavepacket on the first excited (A) state with a 2-axis polarized prnnp pulse of the form of Eq. (3.84) with intensity = 4 X 10 W cm, tvjjz = 3.63 eV, and a Gaussian envelope of FWHM r, = 8 fs. 

For the model system a 3-fs (FWHM) Gaussian pulse, resonant to the S0-S2 transition with moderate maximum electric field (100 GV/cm ) is used as pump pulse. The pump pulse should be resonant and its time duration short compared to the systems nuclear dynamics to produce a narrow and localized vibrational wavepacket on the excited state, which later can be efficiently coupled to the state. The MIR-control-field (3.0 p,m, 12 fs FWHM (100 GV/cm ), CEP = 0.1 n) has to follow at the right delay, here within 40 fs. 

The excitation pulse used in Fig. 11.17 was assumed to include a broad band of energies relative to the vibrational energy spacing ho. In this rather special situation, X u,t) has a Gaussian shape that remains constant indefinitely as the wavepacket oscillates. Such wavepackets provide a useful description of the radiation emitted from a continuous-wave laser. In this picture, the spatial oscillations of the wavepacket resemble the oscillating electric field associated with a continuous stream of photons with constant energy [118]. 

The dense line structure and the irregularity of the spectral envelope of the C spectrum reflect internal-conversion processes taking place on a time scale of the order of a vibrational period, i.e., several femtoseconds. This is made explicit by directly monitoring the C state electronic population using wavepacket dynamical methods (see Section 3.2). A Gaussian is located initially on the C state surface in the center of the Franck-Condon zone. As discussed above, this corresponds to a broadband excitation of all A2u vibronic levels in the photoelectron spectrum. Seven degrees of freedom and approximately 900 000 basis functions have been included in the expansion, equation (54). The result of the wave-packet... 

Figure 5 Population dynamics of the coupled X, B, and C electronic states of the benzene radical cation. The initial wavepacket is a Gaussian, located on the C state surface in the center of the Franck-Condon zone, (a) Time evolution of the C state population under the influence of the C-B vibronic coupling, excluding the interaction with the X state, (b) Electronic population of the C state (full line), B state (dotted line), and X state (dashed line) as resulting from a quantum-dynamical three-state four-mode treatment, (c) Same as panel (b), but with inclusion of a fifth vibrational mode (C-C stretching mode)...

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