A numerical-tensorial “hybrid” nuclear motion Hamiltonian and dipole moment operator for spectra calculation of polyatomic nonrigid molecules

Abstract

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen–Bunker–Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from ab initio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems.

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet (X~3B1) methylene

“…The difference between the energy levels obtained from the two computer codes is around 10 À5 cm À1 up to 10,000 cm À1 (see Ref. 21), but contrary to DVR3D, we are able to provide quite easily the vibrational and rotational quantum numbers.…”

“…The nuclear-motion Hamiltonian described in Ref. 21 will be also briefly discussed. In Section 4, the calculated rovibrational energy levels will be compared to both available experimental data and previous ab initio results.…”

“…This model is described in detail in Ref. 21. The kinetic energy and potential parts were both Taylor expanded in terms of two normal mode coordinates describing the "small" vibrations (associated here with ν 1 and ν 3 ) for each point of a numerical grid for the nonrigid coordinate ρ describing the large Note: All these values were determined from a fit of the ab initio PES.…”