Abstract: In this paper, we present a two-step variational procedure to solve the ro-vibrational problems for triatomic molecules using the transformed internal valence coordinates, which are just the symmetrized internal coordinates for an AB₂ molecule. The first step is the solution of a series of secular problems depending on K, which is the projection of the total angular momentum onto the body-fixed z-axis.The solution of these secular problems are technically the same process as solving a pure J=0 vibrational problem. In the second step, we use the Nlowest eigenfunctions obtained in the first step to construct the ro-vibrational Hamiltonian matrix and suggest an efficient diagonalization method to diagonalize this matrix. The ro-vibrational energy levels of H₂O molecule for J≤20 on the potential energy function fitted by Jensen are calculated and compared with the observed values and some theoretical results to test the procedure. It is shown from this application that the variational procedure described in this paper is efficient for the calculation of the higher ro-vibrational energy levels of a triatomic molecule, especially for an AB2 molecule.This variational procedure is very suitable for a series of Jcalculations.

Key words: Ro-vibrational excited states, Triatomic molecules, Variational procedure