Wavepacket theory computation

Exciting new developments, not discussed in the review are the extension of time-dependent wavepacket reactive scattering theory to full dimensional four-atom systems [137,199-201], the adaptation of the codes to use the power of parallel computers [202], and the development of new computational techniques for acting with the Hamiltonian operator on the wavepacket [138]. 

The first class of approaches could be labelled as exact . A complete diagonalization of the full static electrons + ions hamiltonian in principle allows to access any dynamical process. It should thus provide a fully detailed description of the dynamics of the system. However, up to now, such calculations have focused on structural properties rather than on dynamical ones. Furthemore, even today s computer capabilities barely allow such calculations for clusters of more than very few atoms [14]. Cluster s size limitations are comparable for molecular physics s technics, based on the time propagation of quantal wavepackets [15]. These exact approaches hence mainly provide benchmarks for the other theories, but do not really allow a full exploration of the various facets of the physics involved. 

It is actually very difficult to solve the entire scheme down to Eq. (6.5) for systems of chemical interest, even if a very good set of >/) is available. (Note that electronic structure theory (quantum chemistry) can handle far larger molecular systems within the Born-Oppenheimer approximation) than the nuclear dynamics based on Eq. (6.5) can do.) This is because the short wavelength natme of nuclear matter wave blocks accurate computation and brings classical nature into the nuclear dynamics, in which path (trajectory) representation is quite often convenient and useful than sticking to the wave representation. Then what do the paths of nuclear dynamics look like on the occasion of nonadiabatic transitions, for which it is known that the nuclear wavepackets bifurcate, reflecting purely quantum nature. 

With increasing system size, the implementation of ab initio electron wavepacket dynamics, such as the semiclassical Ehrenfest theory, using nuclear derivative coupling tends to be computationally more demanding because of the necessity of solving coupled perturbed equations. We therefore propose a useful treatment of nonadiabatic coupling, in which one can avoid the tedious coupled perturbed equations for the nuclear derivative of molecular orbitals and CSFs. 

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