Collision dynamics Born approximation

Since HF has a closed-shell electronic structure and no low-lying excited electronic states. HF-HF collisions may be treated quite adequately within the framework of the Born-Oppenheimer electronic adiabatic approximation. In this treatment (4) the electronic and coulombic energies for fixed nuclei provide a potential energy V for internuclear motion, and the collision dynamics is equivalent to a four-body problem. After removal of the center-of-mass coordinates, the Schroedinger equation becomes nine-dimensional. This nine-dimensional partial differential... 

A full theoretical treatment of Pgl within the Born-Oppenheimer approximation involves two stages. First, the potentials V (R), V+(R), and the width T(f ) of the initial state must be calculated in electronic-structure calculations at different values of the internuclear distance R—within the range relevant for an actual collision at a certain collision energy—and then, in the second stage the quantities observable in an experiment (e.g., cross sections, energy and angular distributions of electrons) must be calculated from the functions V+(R), V+(R), and T(f ), taking into account the dynamics of the heavy-particle collisions. 

From a theoretical point of view, in the study of atom-atom or atom-molecule collisions one needs to solve the Schrodinger equation, both for nuclear and electronic motions. When the nuclei move at much lower velocities than those of the electrons inside the atoms or molecules, both motions (nuclear and electronic) can be separated via the Born-Oppenheimer approximation. This approach leads to a wave function for each electronic state, which describes the nuclear motion and enables us to calculate the electronic energy as a function of the intemuclear distance, i.e. the potential energy V r). Therefore, V r) can be obtained by solving the electronic Schrodinger equation for each inter-nuclear distance. As a result, the nuclear motion, which we shall see is the way chemical reactions take place, is a dynamical problem that can be solved by using either quantum or classical mechanics. 

Chemical dynamics is the link between the potential energy surface (PES) (or surfaces) and an observable chemical phenomena. In principle the PES comes from an ab initio quantum chemistry calculation (within the Born-Oppenheimer approximation) though in practice it is often constructed by some more approximate model, e.g., semiempirical quantum chemistry or totally empirical force field models. First a brief overview of the present state of the methodology and scope of applications in this area is given. We will concentrate on chemical dynamics in the gas phase, though much of the methodology of this field has carried over to the study of dynamical processes in condensed phases, gas-surface collision processes, and also dynamics in biomolecular systems. 

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