The Structure of H3, H3+, and of H3—. IV

Abstract

In this paper, a direct calculation is made of the force constant for bending the nuclei in the triatomic hydrogen molecule, H₃, and in the ion, H₃⁺, from a straight line. The neutral molecule has lower energy when the atoms are in a line rather than in neighboring triangular configurations. The opposite is true for the positive ion. The quantum‐mechanical variational method is used together with the most general eigenfunctions which can be compounded from 1s hydrogen‐like orbitals. The polar‐homopolar composition of these eigenfunctions and the effective nuclear charge are varied simultaneously to give the lowest energy. For H₃, we obtain the force constant for bending, 15.88 kcal./radian², and the corresponding vibration frequency for bending, 3.26×10¹³ sec.^—1. These values agree well with those obtained by the semi‐empirical scheme. The force constant for bending H₃⁺ from a straight line is — 15.41 kcal./radian². This negative value for the force constant indicates that the positive ion has lowest energy for triangular configurations, as predicted by Coulson. The energy of H₃^— is calculated for a linear symmetrical configuration. It is found that for reasonably small separations, H₃^— is unstable with respect to H₂+H^—. At large separations H^— is attracted to H₂ to form a loose cluster but a rough calculation of the equilibrium constant indicates that Concentration H₃^—/Concentration H^—=0.2×pressure H₂ in atmospheres. Thus at the low pressures which are used in the mass spectrograph, H₃^— could not be detected.