Born-Oppenheimer approximation hydrogen molecule

Force constants, crude Born-Oppenheimer approximation, hydrogen molecule, minimum basis set calculation, 545-550 Forward peak scattering, electron nuclear... 

Initially the properties calculated were energetic in nature and related to IR spectroscopic measurements.64 Bishop s work was the first serious attempt to calculate the rovibronic energies of the hydrogen molecule and molecular ion without using the Born-Oppenheimer approximation (i.e., three- and four-body calculations). Many years later, this work is still cited and the relativistic... 

Various derivations of the Born-Oppenheimer approximation can be found in the literature. See Refs. (23-24) for typical reviews. The applicability of this approximation has been proven on several examples, cf. the seminal works of Kolos and Wolniewicz25-29 for various states of the hydrogen molecule. The results of Kolos and collaborators on H2 and of other authors for other systems were reviewed in several papers, cf., e.g. Refs. (24-32). Since intermolecular forces can only be discussed for fixed geometries of the interacting monomers, the Born-Oppenheimer approximation is a natural framework for the discussion of intermolecular interactions. Therefore, in this section we will briefly review all approximations leading to to the separation of the electronic and nuclear motions, and discuss situations in which this fundamental approximation fails. 

The equation is used to describe the behaviour of an atom or molecule in terms of its wave-like (or quantum) nature. By trying to solve the equation the energy levels of the system are calculated. However, the complex nature of multielectron/nuclei systems is simplified using the Born-Oppenheimer approximation. Unfortunately it is not possible to obtain an exact solution of the Schrddinger wave equation except for the simplest case, i.e. hydrogen. Theoretical chemists have therefore established approaches to find approximate solutions to the wave equation. One such approach uses the Hartree-Fock self-consistent field method, although other approaches are possible. Two important classes of calculation are based on ab initio or semi-empirical methods. Ah initio literally means from the beginning . The term is used in computational chemistry to describe computations which are not based upon any experimental data, but based purely on theoretical principles. This is not to say that this approach has no scientific basis - indeed the approach uses mathematical approximations to simplify, for example, a differential equation. In contrast, semi-empirical methods utilize some experimental data to simplify the calculations. As a consequence semi-empirical methods are more rapid than ab initio. 

Since the hydrogen molecule ion hJ contains only one electron, the Schrbdinger equation can be solved exactly (once we have accepted the Born-Oppenheimer approximation). In the... 

All the models are more complicated than before. One accounts for the breakdown of the Born-Oppenheimer approximation. Another shows the possibility of proton transfer by tunnel effect. We see that the role of the solvent cavity size and electron coupling was no longer negligible. It was shown that the water molecule ionisation and hydrogen bonding polarisation play an important role in the ionic equilibrium of water. 

The Schrodinger equation for the hydrogen molecule ion, hJ, can he solved in the Born-Oppenheimer approximation without additional approximations. The solutions are molecular orhitals that represent motion of the electron around both nuclei. 

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