Electron nuclear dynamics general reactions

Electron nuclear dynamics theory is a direct nonadiabatic dynamics approach to molecular processes and uses an electronic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the interparticle interactions. 

The Bom-Oppenheimer approximation is not always correct, especially with light nuclei and/or at finite temperature. Under these circumstances, the electronic distribution might be less well described by the solution of a Schroedinger equation. Non-adiabatic effects can be significant in dynamics and chemical reactions. Usually, however, non-adiabatic corrections are small for equilibrium systems at ordinary temperature. As a consequence, it is generally assumed that nuclear dynamics can be treated classically, with motions driven by Bom-Oppenheimer potential energy functions ... 

Since the development of ultrashort lasers, nudear wavepacket dynamics of various matters have attracted continuing attention [1,2]. The research targets extend from gas phase molecules [3, 4] to molecules in solution [5, 6], and solids [7]. In general, an excitation of matter by an ultrashort pulse with sufficient bandwidth leads to the creation of coherence between vibrational (or vibronic) eigenstates [1]. The induced nuclear wavepacket then starts to evolve on a certain potential energy surface and the dynamics is probed by a suitable pump-probe spectroscopy. The direct time-domain observation of the nudear motion provides us with valuable information on photochemical reaction dynamics, vibrational excitation/relaxation mechanisms, electron-vibration (phonon) coupling, and so on. 

We refer to this as the QTST estimate for the quantum electron transfer rate. Dynamical simulations allow us to test whether this formula applies to ET reactions in general. Here we have employed the electronic coordinate o-(t) to define the reaction coordinate and the centroid. An approach employing a nuclear reaction coordinate and centroid has been put forward in Ref. 37, leading to conclusions similar to those for the case of an electronic centroid. 

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