Molecular dynamics Born-Oppenheimer approximation

Type II quantum chaos is discussed in Section 4.2. It arises naturally in molecular physics in the form of the dynamic Born-Oppenheimer approximation (Bliimel and Esser (1994)). In the dynamic Born-Oppenheimer approximation chaos may occur in both the classical and the quantum subsystem, although neither the classical nor the quantum systems by themselves are chaotic. Type II quantum chaos was also identifled in a nuclear physics context (Bulgac (1991)). 

In the usual Born-Oppenheimer picture, the sum of A (Ai,A2,9) and V(q) is the adiabatic potential for the molecular coordinate q. For the computation of the adiabatic potential, q is treated as a fixed parameter. In the dynamic Born-Oppenheimer approximation discussed above, we interpret g as a classical dynamical variable, with the result that the molecular vibrations are described by the Hamiltonian function... 

In Section 11.1 we discuss recent advances in quantum chaology, i.e. the semiclassical basis for the analysis of atomic and molecular spectra in the classically chaotic regime. In Section 11.2 we discuss some recent results in type II quantum chaos within the framework of the dynamic Born-Oppenheimer approximation. Recent experimental and theoretical results of the hydrogen atom in strong microwave and magnetic fields are presented in Sections 11.3 and 11.4, respectively. We conclude this chapter with a brief review of the current status of research on chaos in the helium atom. 

Fig. 3. Vibrational population distributions of N2 formed in associative desorption of N-atoms from ruthenium, (a) Predictions of a classical trajectory based theory adhering to the Born-Oppenheimer approximation, (b) Predictions of a molecular dynamics with electron friction theory taking into account interactions of the reacting molecule with the electron bath, (c) Born—Oppenheimer potential energy surface, (d) Experimentally-observed distribution. The qualitative failure of the electronically adiabatic approach provides some of the best available evidence that chemical reactions at metal surfaces are subject to strong electronically nonadiabatic influences. (See Refs. 44 and 45.)...

Molecular Dynamics Beyond the Born-Oppenheimer Approximation. 

H. Koppel, W. Domcke, and L. S. Cederbaum, Multimode molecular dynamics beyond the Born-Oppenheimer approximation, Adv. Chem. Phys. 57, 59-246(1984). 

One has to emphasize that Eqs. (82) and (83) do not involve the Born-Oppenheimer approximation although the nuclear motion is treated classically. This is an important advantage over the quantum molecular dynamics approach [47-54] where the nuclear Newton equations (82) are solved simultaneously with a set of ground-state KS equations at the instantaneous nuclear positions. In spite of the obvious numerical advantages one has to keep in mind that the classical treatment of nuclear motion is justified only if the probability densities (R, t) remain narrow distributions during the whole process considered. The splitting of the nuclear wave packet found, e.g., in pump-probe experiments [55-58] cannot be properly accounted for by treating the nuclear motion classically. In this case, one has to face the complete system (67-72) of coupled TDKS equations for electrons and nuclei. 

Section 2 of this chapter notes will be devoted to the framework for separation of the ionic and electronic dynamics through the Born-Oppenheimer approximation. Atomic motion, with forces on the ions at each timestep evaluated through an electronic structure calculation, can then be propagated by Molecular Dynamics simulations, as proposed by first-principle Molecular Dynamics. This allows for a description of the electronic reorganisation following the atomic motion, e.g. bond rearrangements in chemical reactions. 

The simulation of a system of classical nuclei and electrons under the Born-Oppenheimer approximation can then be performed within a Molecular Dynamics framework as follows ... 

Theories of chemical reaction dynamics and molecular spectroscopy require a knowledge of the molecular potential energy surface (PES) [1,2]. This surface describes the variation in the total electronic energy of the molecule as a function of the nuclear coordinates, within the Born-Oppenheimer approximation, and hence it determines the forces on the atomic nuclei. 

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