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The Hydrogen Molecular Ion Revisited

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Jean-Philippe Grivet

Centre de Biophysique Moléculaire, C.N.R.S., and Département de Physique, Université d''Orléans, Orléans, France

J. Chem. Educ., 2002, 79 (1), p 127

DOI: 10.1021/ed079p127

Publication Date (Web): January 1, 2002

Abstract

The numerical solution of the hydrogen molecular cation problem is described. The Schrödinger equation is set up in confocal ellipsoidal coordinates. After separation of variables, two ordinary eigenvalue equations are obtained. They are related to the angular and to the radial part of the wave function and involve two separation constants. Both are solved in detail, using the shooting algorithm running on a personal computer. The electronic energy is computed as a function of the internuclear distance for the two lowest molecular states--the symmetric, bonding level and the antisymmetric, antibonding level. Plots of the corresponding electron densities are displayed.