Vibrational energy levels of ammonia-type molecules from first principles calculations

The vibrational spectra of ammonia and the hydronium ion, including both their symmetric and asymmetric isotopomers, are calculated variationally using potential energy surfaces obtained with the latest methods of electronic structure calculation. The centrally bound ammonia-type molecules are interesting systems to study, due to the combination of the large-amplitude inversion motion and five high-frequency modes. This facilitates the study of capabilities and feasibility of the latest theories in molecular physics and quantum chemistry and their numerical application. I have developed a six-dimensional variational program for the calculation of vibrational energy levels in ammonia-type molecules. The program employs an exact kinetic energy operator, successive basis sets contractions, and full symmetry of the systems. The six-dimensional potential energy surface is accurately represented by a special Taylor-type series expansion, where the inversion mode and the symmetric stretching mode are handled separately from the asymmetric motions. Coupled-cluster electronic energies, used for the potential energy function, are either extrapolated to the complete basis set limit or the corresponding results are obtained with explicitly correlated methods. Corevalence correlation, relativistic effects, higher excitations in coupled-cluster series, and correction to the Born–Oppenheimer approximation are included. All these factors are essential in order to achieve 1 cm−1 accuracy for the vibrational energies of ammonia-type molecules.