Abstract
The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H2 molecule. Specifically, we are interested in the term describing the electronic interaction of the charge distribution of one of the hydrogen atoms with the proton of the second atom. Quantum mechanics provides the charge distribution; hence, the evaluation of this term is a semi-classic quantum physics issue. For states other than the ground state the charge distributions are not spherically symmetric; they are functions of the radial and the angular coordinates. For the excited states we develop exact analytic expressions conducive to the potential energies. Because of the functional complexities of the wave functions, the evaluation of the core integrals is carried out utilizing symbolic capabilities of Mathematica [1]. Plots of these energies vs. the distance between the two protons reveal global features.
Highlights
Literature search reveals that quantum chemists customarily prefer adapting the shell method of charge distribution of the electron calculating the coulombic related potential energy issues of an H2 molecule
We show for the diffused ground state the volume and the shell charge distribution methods are equivalent
Motivation of proposing our investigation is to augment the current scope of energy issues of an H2 molecule
Summary
Literature search reveals that quantum chemists customarily prefer adapting the shell method of charge distribution of the electron calculating the coulombic related potential energy issues of an H2 molecule. In this method one assumes that the charge distribution is composed of concentric spherical shells of finite thicknesses about the proton. Our third objective is to utilize our derived formulation and for a handful of selected excited states explicitly evaluate their associated potentials Plots of these results as a function of the inner-atomic distance between the two protons reveal certain characteristics; this is discussed in text. We close our investigation outlining our related continual search
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