On the Theoretical Calculation of Vibrational Frequencies and Intensities of Polyatomic Molecules; H3+, H2D+, HD2+, and D3+

A straightforward method is described for calculating the fundamental vibrational frequencies and intensities for a polyatomic molecule starting with a theoretically obtained potential energy surface and associated electronic state wavefunction. Given the latter two quantities, this method is much easier to carry out than the common reverse problem of predicting force constants from observed frequencies and molecular dipole moment derivatives from absolute intensities. The proposed method can be programmed easily and generally to handle any polyatomic system for which a theoretical energy surface and electronic-state wave-function are available. An application to H3+ and its isotopic counterparts is described.