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Jörg Tatchen and Eli Pollak
The initial value representation (IVR) of semiclassical propagators in combination with Monte-Carlo integration techniques is considered as a very promising means to overcome the dimensionality bottleneck encountered in full quantum dynamics. In this work, we try to take advantage of a second, similarly important feature of IVR schemes: In principle, they do not need precomputed potential energy surfaces which in fact are hardly available for complex systems in molecular physics and chemical reaction dynamics. IVR schemes may be realized in the spirit of on-the-fly molecular dynamics approaches which employ an interfaced quantum chemical program to obtain the potential energy surface data needed for propagating the trajectories. We study the vibrational structure of the S0 → S1 Herzberg-Teller allowed transition in formaldehyde by means of a frozen Gaussian semiclassical IVR approach. The S1 state potential energy surface of formaldehyde (H2CO) is well known to display two symmetry-equivalent minima (corresponding to bent configurations) which are connected by a very shallow barrier of ca. 240 cm-1.[1] The S1 state of formaldehyde thus represents a realistic example of a multidimensional system for which anharmonicities and tunneling effects are important. The main difficulty in practical semiclassical IVR computations is caused by the highly oscillatory, complex-valued integrand of the semiclassical propagator which makes it expensive to converge the Monte-Carlo integrations over phase space. The feasibility of on-the-fly techniques for semiclassical IVR critically depends, however, on whether the number of trajectories can be kept within narrow limits or not. We study the dependence of the resulting spectrum on the sample size. Possible ways of improved importance sampling for the Monte-Carlo integration will be discussed. [1] M. Merchan and B. O. Roos, Theoret. Chim. Acta 92, 227 (1995). |
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