The rovibrational levels of ammonia

Abstract

In this paper we report variational rovibrational studies on ammonia and its isotopomers. We use six internal coordinates (one of which describes the umbrella motion). The expansion functions are products of one-dimensional functions of these internal coordinates, multiplied by appropriate functions of the Euler angles to describe the rotational motion. We use a previously published high accuracy six-dimensional potential energy surface [LEONARD, C., HANDY, N. C., CARTER, S., and BOWMAN, J. M., 2002, Spectrachim. Acta, 58, 825]. We derive the full kinetic energy operator for the rovibrational motion in these coordinates. This operator has been completely checked to give a hermitian secular matrix. All matrix elements are evaluated numerically by quadrature. The symmetry of the expansion functions is fully described in D3h, C2v and Cs. It is not possible to perform the calculations in D3h, but complete degeneracy in the appropriate levels is obtained with the C2v program. The algebraic complexity of this program has been far greater than for any other variational study we have undertaken for a tetra-atomic molecule. We present J = 0, 1, 2 energy levels for the experimentally observed band origins of NH3, and J = 0, 1 energy levels for the ground state and fundamentals of NH2D, ND2H and ND3. For the asymmetric isotopomers, identical results are obtained for both C2v and Cs, thus confirming the validity of the method. The levels we obtain are completely converged. Agreement with observation is of the order of 0.5% (of course being dependent upon the accuracy of the potential energy surface); therefore the ordering of the rotational levels and their splitting is completely predicted and understood.