Potential Function for the Inversion Process of Ammonia

Abstract

The process of inversion of ammonia has been considered as described by two totally symmetric internal coordinates. The potential function has been chosen by theoretical considerations and the values of the parameters which appear in it have been fixed by minimizing the differences between the calculated eigenvalues of the vibrational problem and the known values of the observed frequencies. Two versions of the vibrational problem have been considered; a simplified one (monodimensional), where only the bond angles are allowed to change, and a complete two‐dimensional one where the bond lengths were also allowed to change. The potential functions so obtained give a fairly good agreement between calculated and observed frequencies. The two‐dimensional potential function has the minimum at a bond length of 1.878 a.u. and at a bond angle of 105°36′ and gives a value of 0.00905 a.u. as the potential barrier to inversion. The bond length for the minimum of energy at the planar configuration is 1.837 a.u. This potential function and the resulting eigenfunctions of the vibrational Hamiltonian have been employed to calculate some spectroscopic constants, such as the quadratic and cubic force constants related to two totally symmetric coordinates, and the differences between the rotational constants of the odd and the even levels. The agreement with the available experimental data is satisfactory. Results of the above calculations are also given for ND₃.