TY - JOUR

T1 - Using discrete variable representation path integral Monte Carlo with metropolis sampling to compute ground state wavefunctions

AU - Xiao, Yingsheng

AU - Poirier, Bill

N1 - Funding Information:
This work is supported by the office of Advanced Scientific Computing Research, Mathematical, Information and Computational Sciences Divison of the US Department of Energy, under contract DE-FG03-02ERZ5-534, and by a grant from the Welch Foundation (D-1523).

PY - 2007/6

Y1 - 2007/6

N2 - The discrete variable representation (DVR) matrix dynamics formulation of the path integral Monte Carlo (PIMC) method, implemented numerically in a way that enables Metropolis sampling to be employed, 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 predefined grid points. The new method is applied here to compute the ground state wavefunction of a model one degree-of-freedom (1DOF) Morse oscillator system. A one-to-two order-of-magnitude reduction in CPU effort is observed, in comparison with a conventional PIMC simulation. The generalization for many DOFs is straightforward, and expected to result in even greater performance enhancement.

AB - The discrete variable representation (DVR) matrix dynamics formulation of the path integral Monte Carlo (PIMC) method, implemented numerically in a way that enables Metropolis sampling to be employed, 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 predefined grid points. The new method is applied here to compute the ground state wavefunction of a model one degree-of-freedom (1DOF) Morse oscillator system. A one-to-two order-of-magnitude reduction in CPU effort is observed, in comparison with a conventional PIMC simulation. The generalization for many DOFs is straightforward, and expected to result in even greater performance enhancement.

KW - Green's function

KW - Imaginary time

KW - Morse oscillator

UR - http://www.scopus.com/inward/record.url?scp=34547307339&partnerID=8YFLogxK

U2 - 10.1142/S021963360700299X

DO - 10.1142/S021963360700299X

M3 - Article

AN - SCOPUS:34547307339

SN - 0219-6336

VL - 6

SP - 309

EP - 321

JO - Journal of Theoretical and Computational Chemistry

JF - Journal of Theoretical and Computational Chemistry

IS - 2

ER -