Time-dependent dynamics of electrons and nuclei

Abstract

Using the time-dependent variational principle with a group theoretical coherent state defining the wave functions for electrons and nuclei, a system of coupled, first-order, nonlinear differential equations is obtained for a general molecular system. The equations form a classical Hamiltonian system within a generalized phase space that allows a systematic time-dependent study of molecular processes. The approach is general and provides a computational framework for a variety of properties such as transition and excitation probabilities in atomic and molecular collisions, and molecular spectra such as vibrational spectra with anharmonicities. The basic approximation corresponding to the choice of a single determinantal wave function for the electrons and classical nuclei is analyzed. Illustrative applications to the p+H collision process and to vibrations of the H2O molecule exhibit good agreement with experiment and with other theoretical work.

Isotope effect for associative detachment:H(D)−+H(D)→H2(Miller1, Bruhns2, Čı́žek3 et al. 2012Phys. Rev. A292240View full textAdd to dashboardCite

“…This method uses a time dependent variational principle to derive an approximation to the time-dependent Schrödinger equation (see [23,24] for further details). The simulations indicate that 97% of the scattered H + 2 and 99% of the scattered D + 2 are contained within the CEM half-angle cone of 0.4 • .…”

A direct dynamics study of protonated alcohol dehydration and the Diels-Alder reaction

“…From ca. 200 trajectories calculated at each of four different temperatures, the selectivity given by the ratio of ET to Sub(C) products varied from 1.02 to 1.43 at 148 to 598 K. 8 Beyond the Born-Oppenheimer approximation, it has been shown that the coupling between the electrons and the nuclei with electron-nuclear dynamics (END) formalism 2,21 is fundamental to obtain a qualitative and quantitative description of the electron transfer in the reaction H + + H → H + H + . 22 Thus, it might be expected that the inclusion of the electron-nuclear coupling would affect the ET:Sub(C) selectivity.…”

Multiple time scale Hartree–Fock molecular dynamics

“…In recent years, several approaches have been developed, differing mostly in the way the electronic wave function is treated. For example, Landman and co-workers [l] propagate the wave function quantum mechanically using density functional theory (DFT); Micha and co-workers [2] employ timedependent Hartree-Fock (TDHF) theory; and there are even attempts to join nuclear and electronic motion without invoking the Born-Oppenheimer approximation [3]. In this paper, however, our focus is on the group of algorithms often termed Car-Parrinello propagations .…”