Efficient full quantum calculations for small molecules using novel phase space optimized discrete variable representation path integral Monte Carlo Methods



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Texas Tech University


Solving the nuclei motion Schrodinger equation with only Born-Oppenhiemer approximation remains a great challenge, due to the exponential scaling of the computation. A full-dimensional basis set method utilizing phase space optimized (PSO) discrete variable representations (DVRs), designed to efficiently compute the rovibrational states of triatomic systems with long-range interactions, has been applied to the benchmark Li-(H2) ion-molecule system and the He(H2) van der Waals complex system. These applications are very challenging due to the long range nature of the interaction and the narrow level spacings near dissociation. All of the rovibrational bound states and a number of resonance states are computed to very high accuracy (one ten-thousandth of a wavenumber or better). For Li-(H2) several new bound levels are reported. The resonances exhibit a clear-cut separation into shape and Feshbach varieties, with the latter characterized by extremely long lifetimes (microseconds or longer). For He(H2) three different isotopologues are considered, all of which are found to have a single bound state with a very low binding energy. Several extremely long-lived Feshbach resonances are also reported.

In order to beat the exponential scaling of basis set methods, a DVR matrix dynamics formulation of the path integral Monte Carlo (PIMC) method is proposed as a means of computing ground state quantum wavefunctions. A key advantage of the DVR-PIMC approach is that customized marginal potentials may be employed, leading to significantly larger PIMC time step sizes, and substantial reductions in computational (CPU) effort. An additional key advantage of the present implementation is that the DVR provides a natural set of interpolant functions that can be used for accurate interpolation and extrapolation of function and tensor quantities away from the predefined grid points. This new method is applied to H2O, Ne3 and Ne4, which showed nearly linear scaling for both CPU and memory usage. Owing to the direct simulation of wavefunctions, statistical error of PIMC for energy calculations is reduced greatly, and extrapolation can be used to further speed PIMC convergence.



Quantum calculations