Propagation, Gaussian wave packets

Determination of the time-dependent nuclear wave function now becomes a straightforward exercise in the locally quadratic theory. We need to propagate Gaussian wave packets of the form... 

Heather R and Metiu H 1985 Some remarks concerning the propagation of a Gaussian wave packet trapped in a Morse potential Chem. Phys. Lett. 118 558-63... 

The wave packets <()( ) and x(0 to be propagated forward and backward, respectively, are expanded in terms of the frozen Gaussian wave packets as (see also Section II.B)... 

A description, which is somewhat intermediate between a full quantum model and a classical propagation scheme is the Gaussian wave packet approach for the classical-like mode. This picture was first introduced by Heller [44] and adapted by Billing [18,45,46] to the mixed classical quantum system. Therein one mode is described as a time dependent Gaussian wave packet [18,15]... 

Figure 7 The time auto correlation function and the corresponding spectrum for a Gaussian wave packet propagating on an excited harmonic potential energy surface, (a) The short time decay of C(/) (cf. Eq. (17)) and the broad spectrum (= the Franck Condon envelope (cf. (18)). (b)The longer time dependence of C(r) and the corresponding, vibrationally resolved, spectrum.

In order to generate the exact electronic wave function at each nuclear configuration, the time relaxation method can be used [22]. An arbitrarily chosen Gaussian wave packet is propagated in imaginary time by using the following eqnation ... 

Ohrn and co-workers have developed a direct dynamics approach which incorporates both the electrons and nuclei dynamics (END).""" The complete electron-nuclear coupling terms are retained in the calculation and, as a result, the dynamics is not constrained to a single Born-Oppenheimer potential energy surface i.e., electronic non-adiabaticity is explicitly included. A complication in this approach is the computational demand in propagating an electronic wavefunction which is an accurate representation of the ground electronic state as well as multiple excited electronic states. This approach will become more widely used as computation becomes more powerful. In its initial development,""" Deumens et al. used END and treated the dynamics of the nuclei purely classical as in the above classical direct dynamics. More recently, a semiclassical description of the nuclear motion has been implemented by incorporating Heller s""" "" Gaussian wave packet dynamics."" ... 

Gaussian wavepackets multiple spawning, 402 propagation, 380-381 molecular systems, component amplitude analysis, wave packet construction, 229-230... 

We have found, by direct numerical propagation under H, that initially Gaussian pseudorotating wave packets often remain fairly well localized over several periods of motion. Even a wave packet excited into the trough of a sym-triazine-like system with k 2 executes more than a... 

Figure 4. Gaussian width parameters for the initially undistorted excited state wave packet as a function of propagation time.

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