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.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

“…The zero-point energy is evaluated by taking the time-averaged value of V ref (τ) in eq . In the expression for V ref , V̅ is the average potential energy of the ensemble, α is 0.5/Δτ, , and N w (τ) is the number of walkers at imaginary time τ. Once equilibrated, the density of the walkers near the molecular configuration represented by the coordinates, x , is proportional to the value of the ground state wave function at that geometry.…”

Quasistructural molecules

“…The development of accurate potential energy and electric dipole moment hypersurfaces 182,183 for CH + 5 allowed the quantum-chemical characterization of the rovibrational dynamics of CH + 5 . Earlier studies 178,[184][185][186][187][188][189][190][191][192][193][194][195] yielded rovibrational energy-level patterns that even qualitatively differ from the results of variational nuclear-motion computations. 55,[196][197][198] The variational results also revealed that the rovibrational energy-level pattern of CH + 5 defies any interpretation attempts based on the standard RRHO model.…”

Rotation/Torsion Coupling in H5+, D5+, H4D+, and HD4+ Using Diffusion Monte Carlo

“…A more complete description of the theory and our implementation can be found in earlier publications. 18,22,24,25,27 Briefly, the algorithm that we use is based on the studies of Anderson. 23, 27 The approach derives from the parallel structure of the diffusion equation, which includes a coordinate-dependent rate process…”

“…The details of the simulation approach have been described previously. 22 The most significant change is the introduction of a potential energy term in eq 15. For this study, V(ϕ) is evaluated at the position of each walker at each time step.…”