Vibrational energies for $NH3$ based on high level ab initio potential energy surfaces

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple substitutions [CCSD(T)] have been carried out to generate six-dimensional (6D) potential energy surfaces (PES) and dipole moment surfaces (DMS) for the electronic ground state of ammonia. Full 6D-PES and 6D-DMS (14400 points) were computed with the augmented correlation-consistent triple-zeta basis (aug-cc-pVTZ). For a selected number of points (420 in $C3v$ symmetry and 1260 in lower symmetry), more accurate energies (CBS+) were obtained by extrapolating the CCSD(T) results for the $aug-cc-pVXZ$ $(X=T,Q,5)$ basis sets to the complete basis set limit and adding corrections for core-valence correlation and relativistic effects. Two procedures were investigated to enhance the quality of the 6D-PES from CCSD(T)/aug-cc-pVTZ by including the CBS+ data points. The resulting 6D-PES were represented by analytical functions involving Morse variables for the stretches, symmetry-adapted bending coordinates, and a specially designed inversion coordinate (up to 76 fitted parameters, rms deviations of about 5 cm⁻¹ for 14 400 ab initio data points). For these analytical surfaces, vibrational energies were calculated with a newly developed computer program using a variational model that employs an Eckart-frame kinetic energy operator. Results are presented and compared to experiment for the vibrational band centers of $NH3$ and its isotopomers up to around 15 000 cm⁻¹. For our best 6D-PES, the term values of the fundamentals are reproduced with rms deviations of 4.4 cm⁻¹ $(NH3)$ and 2.6 cm⁻¹ (all isotopomers), the maximum deviation being 7.9 cm⁻¹.