Simultaneous Evaluation of Multiple Rotationally Excited States of H3+, H3O+, and CH5+ Using Diffusion Monte Carlo

Abstract

An extension to diffusion Monte Carlo (DMC) is proposed for simultaneous evaluation of multiple rotationally excited states of fluxional molecules. The method employs an expansion of the rotational dependence of the wave function in terms of the eigenstates of the symmetric top Hamiltonian. Within this DMC approach, each walker has a separate rotational state vector for each rotational state of interest. The values of the coefficients in the expansion of the rotational state vector associated with each walker, as well as the locations of the walkers, evolve in imaginary time under the action of a propagator based on the imaginary-time time-dependent Schrödinger equation. The approach is first applied to H3(+), H2D(+), and H3O(+) for which the calculated energies can be compared to benchmark values. For low to moderate values of J the DMC results are found to be accurate to within the evaluated statistical uncertainty. The rotational dependence of the vibrational part of the wave function is also investigated, and significant rotation–vibration interaction is observed. Based on the successful application of this approach to H3(+), H2D(+), and H3O(+), the method was applied to calculations of the rotational energies and wave functions for CH5(+) with v = 0 and J ≤ 10. Based on these calculations, the rotational energy progression is shown to be consistent with that for a nearly spherical top molecule, and little evidence of rotation–vibration interaction is found in the vibrational wave function.