All the bound vibrational states of H3+: A reappraisal

The 3D discrete variable representation (DVR) calculations of Henderson and Tennyson [Chem. Phys. Lett. 173, 133 (1990)] are reanalyzed to find the source of the nonvariational behavior highlighted by Carter and Meyer [J. Chem. Phys. 96, 2424 (1992)]. The discrepancy is found to be caused not by the use of incorrect boundary conditions, but by a failure of the quadrature approximation commonly used in DVR calculations. Corrected DVR calculations show variational but slow convergence. Calculations using the same intermediate vectors as the nonvariational calculations and a corrected final Hamiltonian show greatly enhanced convergence. The vibrational band origins computed with this method are converged to within 2 cm−1 up to 35 000 cm−1. A complete list of these is presented and comparisons made with previous predictions.