Gaussian wavepacket calculations semiclassical calculation

In this semiclassical calculation, we use only one wavepacket (the classical path limit), that is, a Gaussian wavepacket, rather than the general expansion of the total wave function. Equation (39) then takes the following form ... 

From a practical point of view the classical method using directly the probability density function is not convenient, and it is computationally preferable to use an approach that involves trajectory calculations. A derivation of such formulation can be made by starting from the quantum-mechanical TDSCF, and using semiclassical (gaussian) wavepackets. Here we merely quote the final result. In analogy to (62), the single-mode classical SCF potentials are given by... 

All the initial electronic state populations are set to be localized at the energetically highest adiabatic state to be compatible with the calculation for PSANB and the semiclassical Ehrenfest theory. The momentum of the wavepacket is varied by changing the initial wave number as k =16.05, 32.11, 48.16, 64.22, 80.28, 96.33, 112.39, 128.44, 144.50 and 160.56 a.u., which specifies the initial Gaussian wavepacket of minimum uncertainty... 

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