Rotation–vibration motion of pyramidal XY₃molecules described in the Eckart frame: Theory and application to NH₃

Abstract

We present a new model for the rotation-vibration motion of pyramidal XY3 molecules, based on the Hougen–Bunker–Johns approach. Inversion is treated as a large-amplitude motion, while the small-amplitude vibrations are described by linearized stretching and bending coordinates. The rotation–vibration Schrödinger equation is solved variationally. We report three applications of the model to 14NH3 using an analytic potential function derived from high-level ab initio calculations. These applications address the J = 0 vibrational energies up to 6100 cm, the J≤2 energies for the vibrational ground state and the ν2, ν4, and 2ν2 excited vibrational states, and the J≤7 energies for the vibrational state. We demonstrate that also for four-atomic molecules, theoretical calculations of rotation–vibration energies can be helpful in the interpretation and assignment of experimental, high-resolution rotation–vibration spectra. Our approach incorporates an optimum inherent separation of different types of nuclear motion and thus remains applicable for rotation–vibration states with higher J values where alternative variational treatments are no longer feasible.