Vibrational energy levels for symmetric and asymmetric isotopomers of ammonia with an exact kinetic energy operator and new potential energy surfaces

Abstract

A new vibrational Hamiltonian operator for ammonia is presented. The potential energy part is expressed in terms of symmetrized bond-angle valence coordinates and an inversion coordinate, which is a function of the bond angles. In the exact kinetic energy operator, the stretching part is instead given in terms of unsymmetrized bond displacement coordinates. Six-dimensional ammonia potential energy surfaces are calculated using high-level ab initio tools, the CCSD(T) method with aug-cc-pVQZ and aug-cc-pVTZ basis sets. The potential energy functions are constructed in two, two-dimensional steps. The surfaces are expressed as a Taylor-type series with respect to the doubly degenerate asymmetric stretching and bending coordinates. This representation is given along a two-dimensional surface of the totally symmetric stretching and inversion coordinates of ammonia. Vibrational energies are calculated variationally in a finite basis representation. Employing successive basis set contractions, it is possible to optimize some potential energy parameters simultaneously for seven symmetric and asymmetric isotopomers very effectively. The symmetric part of the surface is fitted to experimentally observed vibrational band centers up to 6000 cm−1. This reduces the mean absolute error from 7.84 cm−1 with a pure ab initio potential to 0.44 cm−1 compared to the experimental values for NH314. In addition, vibrational energy levels of NH314 have been calculated up to about 15 000 cm−1 using the pure ab initio surface obtained with the aug-cc-pVTZ basis set. The nuclear motion calculation converges all levels up to about 10 000 cm−1 to within 0.05 cm−1.