Vibrational configuration interaction using a tiered multimode scheme and tests of approximate treatments of vibrational angular momentum coupling: A case study for methane

We present vibrational configuration interaction calculations employing the Watson Hamiltonian and a multimode expansion. Results for the lowest 36 eigenvalues of the zero total angular momentum rovibrational spectrum of methane agree with the accurate benchmarks of Wang and Carrington to within a mean unsigned deviation of 0.68, 0.033, and 0.014 cm^-1 for 4-mode, 5-mode, and 6-mode representations, respectively. We note that in the case of the 5-mode results, this is a factor of 10 better agreement than for 5-mode calculations reported earlier by Wu, Huang, Carter, and Bowman for the same set of eigenvalues, which indicates that the multimode expansion is even more rapidly convergent than previously demonstrated. Our largest calculations employ a tiered approach with matrix elements treated using a variable-order multimode expansion with orders ranging from 4-mode to 7-mode; strategies for assigning matrix elements to particular multimode tiers are discussed. Improvements of 7-mode coupling over 6-mode coupling are small (averaging 0.002 cm^-1 for the first 36 eigenvalues) suggesting that 7-mode coupling is sufficient to fully converge the results. A number of approximate treatments of the computationally expensive vibrational angular momentum terms are explored. The use of optimized vibrational quadratures allows rapid integration of the matrix elements, especially the vibrational angular momentum terms, which require significantly fewer quadrature points than are required to integrate the potential. We assign the lowest 243 states and compare our results to those of Wang and Carrington, who provided assignments for the same set of states. Excellent agreement is observed for most states, but our results are lower for some of the higher-energy states by as much as 20 cm^-1, with the largest deviations being for the states with six quanta of excitation in the F₂ bends, suggesting that the earlier results were not fully converged with respect to the basis set. We also provide corrections to several of the state assignments published previously.