Calculation of the Energy of H3 and of H3+. III

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Abstract
In previous communications, the energy of the triatomic hydrogen molecule and of the triatomic positive ion was calculated by the variational method for the symmetrical linear configurations. In this paper, these energies are obtained for two unsymmetrical linear configurations using the most general eigenfunction which can be formed out of 1s hydrogen‐like atomic orbitals. Two of the four difficult exchange integrals which involve the coordinates of three nuclei are obtained in closed form. For the Wang plus polar states approximation, the activated state for the reaction H+H2 is found to be linear symmetrical whereas the semi‐empirical calculations give an unsymmetrical activated state. The complete potential energy surface for three hydrogen atoms on a line is constructed, for this Wang plus polar states approximation. The energy of the triatomic positive ion is likewise lowest for the linear symmetrical. The complete energy surface of H2+H+ in a line is constructed and the vibration frequencies computed. The frequency of the linear symmetrical vibration for H3 + is 1.4×1014 wave no. per sec. and the frequency of the linear unsymmetrical vibration is 1.2×1014.

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