Stochastic manybody perturbation theory for anharmonic molecular vibrations
Abstract
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zeropoint energies and transition frequencies is developed, which combines the diagrammatic vibrational manybody perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus sizeconsistent first and secondorder anharmonic corrections to the energy and selfenergy are expressed as sums of a few m or 2mdimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of highorder force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higherorder force constants essentially up to an infinite order to be taken into account in a scalable, memoryefficient algorithm. The diagrammatic contributions to the frequencydependent selfenergies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the selfconsistent solutions to the Dyson equation to be obtained. Thismore »
 Authors:
 Department of Chemistry, University of Illinois at UrbanaChampaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States)
 (Japan)
 Publication Date:
 OSTI Identifier:
 22419820
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; DEGREES OF FREEDOM; EVALUATION; FREQUENCY DEPENDENCE; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; PERTURBATION THEORY; POTENTIAL ENERGY; SELFENERGY
Citation Formats
Hermes, Matthew R., Hirata, So, Email: sohirata@illinois.edu, and CREST, Japan Science and Technology Agency, 418 Honcho, Kawaguchi, Saitama 3320012. Stochastic manybody perturbation theory for anharmonic molecular vibrations. United States: N. p., 2014.
Web. doi:10.1063/1.4892614.
Hermes, Matthew R., Hirata, So, Email: sohirata@illinois.edu, & CREST, Japan Science and Technology Agency, 418 Honcho, Kawaguchi, Saitama 3320012. Stochastic manybody perturbation theory for anharmonic molecular vibrations. United States. doi:10.1063/1.4892614.
Hermes, Matthew R., Hirata, So, Email: sohirata@illinois.edu, and CREST, Japan Science and Technology Agency, 418 Honcho, Kawaguchi, Saitama 3320012. Thu .
"Stochastic manybody perturbation theory for anharmonic molecular vibrations". United States.
doi:10.1063/1.4892614.
@article{osti_22419820,
title = {Stochastic manybody perturbation theory for anharmonic molecular vibrations},
author = {Hermes, Matthew R. and Hirata, So, Email: sohirata@illinois.edu and CREST, Japan Science and Technology Agency, 418 Honcho, Kawaguchi, Saitama 3320012},
abstractNote = {A new quantum Monte Carlo (QMC) method for anharmonic vibrational zeropoint energies and transition frequencies is developed, which combines the diagrammatic vibrational manybody perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus sizeconsistent first and secondorder anharmonic corrections to the energy and selfenergy are expressed as sums of a few m or 2mdimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of highorder force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higherorder force constants essentially up to an infinite order to be taken into account in a scalable, memoryefficient algorithm. The diagrammatic contributions to the frequencydependent selfenergies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the selfconsistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixednode errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.},
doi = {10.1063/1.4892614},
journal = {Journal of Chemical Physics},
number = 8,
volume = 141,
place = {United States},
year = {Thu Aug 28 00:00:00 EDT 2014},
month = {Thu Aug 28 00:00:00 EDT 2014}
}

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