Inversion Vibrational Energy Levels of PH3+(X̃2A2″) Calculated by a New Two-dimension Variational Method

Abstract

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration (υ1) and the symmetric umbrella vibration (inversion vibration) (υ2) of PH3+(X̃2A2″) that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used 1-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assumption of reduced mass, and the interactions between the υ1 and υ2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH3+ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm−1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH3. The application to NH3 is less successful, which shows some limitations of the method compared with a full dimension computation.