A theory of Ehrenfest dynamics for open systems and its applications

Abstract

In conventional mixed electron-nuclear molecular dynamics simulations, the molecular systems are always treated as closed. Here starting from the exact quantum mechanical Lagrangian, a first principle electron-nuclear molecular dynamics theory for open systems has been developed at the Ehrenfest dynamics level. With this method, mixed electron-nuclear molecular dynamics simulations can be done for open systems which have both energy and particle exchanges with environments. The reduced single-particle density matrix in atomic orbital representation is used to extend the Ehrenfest dynamics theory for closed systems to deal with open systems. The electron translation factors for the atomic orbitals have been taken into account in the derivations. In the calculations of dissipation terms, Keldysh's nonequilibrium green's function method is used. The equations have been derived at both TD-DFT and TD-DFTB levels. The DFTB formulas of this method have been numerically implemented in the lodestar software.

To examine its validity, two examples have been simulated with this Ehfrenfest molecular dynamics method for open systems. First, a molecular electronic device consisting of hydrogen chain is used to investigate the effects of nuclear vibrations on the dynamics of electrons. It has been found that the nuclear motions can affect the quantum transport properties of molecular devices in two ways: the time-dependent effects and the static effects. The static effect, which can be reproduced with the conventional static simulations following molecular dynamics trajectories, is mainly resulted from the changes of the couplings between each atoms due to the configuration fluctuations. The time-dependent effects is mainly resulted from the changes of the potential field induced by the nuclei. Large oscillations may be induced in the transient electronic current due to the time-dependent effects, but it makes little contribution to current on long-time average. Similar results are obtained for meta-benzene system. In the second numerical example, current-induced dissociations of water molecule has been investigated with this EhMD-OS. Dissociation reactions have been seen when electrons go into the unoccupied orbitals of the water molecule. With different initial states, two kinds of products, hydrogen atom and H_2 molecule, have been obtained.