Using fixed-node diffusion Monte Carlo to investigate the effects of rotation-vibration coupling in highly fluxional asymmetric top molecules: Application to H2D+

Abstract

A fixed-node diffusion Monte Carlo approach for obtaining the energies and wave functions of the rotationally excited states of asymmetric top molecules that undergo large amplitude, zero-point vibrational motions is reported. The nodal surfaces required to introduce rotational excitation into the diffusion Monte Carlo calculations are obtained from the roots of the asymmetric top rigid rotor wave functions calculated using the system's zero-point, vibrationally averaged rotational constants. Using H(2)D(+) as a model system, the overall accuracy of the methodology is tested by comparing to the results of converged variational calculations. The ability of the fixed-node diffusion Monte Carlo approach to provide insights into the nature and strength of the rotation-vibration coupling present in the rotationally excited states of highly fluxional asymmetric tops is discussed. Finally, the sensitivity of the methodology to the details of its implementation, such as the choice of embedding scheme, is explored.

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

“…Typically, this mass is given by 1/G d,d , where G d,d is the Wilson G-matrix element associated with d n (τ). As such, 21,23 τ τ δτ μ τ μ τ δτ…”

“…In our previous study of excited states of asymmetric top molecules, we developed an algorithm for addressing this issue. 21 Although the approach was effective, it was not straightforward to implement.…”

“…21. The values of the parameters used for these calculations and the form of the potential are provided in the Supporting Information.…”

Nodal variational principle for excited states

“…The QMC method is now being commonly used for excited states as well as ground states. In fact, the nodal variational principle for excited states presented in this paper is being implied without a proof for a number of QMC applications, such as the computations of optical gaps in nanostructures [12] and solids [13], diffusive properties of the vacancy defects in diamond [14], diamonoid excitation energies and Stokes shifts [15], excitation spectra of localized Wigner states [16], quasiparticle excitations of the electron gas [17], and electronic [18] and rovibrational excitations [19] of molecules. As the QMC experience demonstrates, even approximations to the correct nodal surfaces typically result in accurate excited-state values.…”

Diffusion Monte Carlo in Internal Coordinates

“…Finally, the results of five statistically independent DMC calculations were averaged for the ground state as well as for each nodal region of the excited states. 16,17 The set of internal coordinates used in this study for H 3 + and its isotopologues are two bond lengths, r 12 and r 23 , as well as the bond angle between them, θ 123 . For the mixed isotopologues, these coordinates are defined such that atom 2 is the unique isotope.…”