The discrete variable representation of a triatomic Hamiltonian in bond length–bond angle coordinates

The discrete variable representation (DVR) is used to calculate vibrational energy levels of H2O and SO2. The Hamiltonian is written in terms of bond length–bond angle coordinates and their conjugate momenta. It is shown that although these coordinates are not orthogonal and the appropriate kinetic energy operator is complicated, the discrete variable representation is quite simple and facilitates the calculation of vibrational energy levels. The DVR enables one to use an internal coordinate Hamiltonian without expanding the coordinate dependence of the kinetic energy or evaluating matrix elements numerically. The accuracy of previous internal coordinate calculations is assessed.