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Kim, Kwang S.
Center for Superfunctional Materials (CSM)
Research Interests
  • Theoretical/experimental nanosciences, molecular electronics spectroscopy, energy materials

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Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers

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Title
Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers
Author
Willow, Soohaeng YooHermes, Matthew R.Kim, Kwang S.Hirata, So
Keywords
COUPLED-CLUSTER; MP2 ENERGY; SYSTEMS; IONIZATION; MORPHOLOGY; MOLECULES; GRADIENT; CARBON; STATE
Issue Date
201310
Publisher
AMER CHEMICAL SOC
Citation
JOURNAL OF CHEMICAL THEORY AND COMPUTATION, v.9, no.10, pp.4396 - 4402
Abstract
A Monte Carlo (MC) integration of the second-order many-body perturbation (MP2) corrections to energies and self-energies eliminates the usual computational bottleneck of the MP2 algorithm (i.e., the basis transformation of two-electron integrals), thereby achieving near-linear size dependence of its operation cost, a negligible core and disk memory cost, and a naturally parallel computational kernel. In this method, the correlation correction expressions are recast into high-dimensional integrals, which are approximated as the sums of integrands evaluated at coordinates of four electron random walkers guided by a Metropolis algorithm for importance sampling. The gravest drawback of this method, however, is the inevitable statistical uncertainties in its results, which decay slowly as the inverse square-root of the number of MC steps. We propose an algorithm that can increase the number of MC sampling points in each MC step by many orders of magnitude by having 2m electron walkers (m > 2) and then using m(m - 1)/2 permutations of their coordinates in evaluating the integrands. Hence, this algorithm brings an O(m(2))-fold increase in the number of MC sampling points at a mere O(m) additional cost of propagating redundant walkers, which is a net O(m)-fold enhancement in sampling efficiency. We have demonstrated a large performance increase in the Monte Carlo MP2 calculations for the correlation energies of benzene and benzene dimer as well as for the correlation corrections to the energy, ionization potential, and electron affinity of C-60. The calculation for C-60 has been performed with a parallel implementation of this method running on up to 400 processors of a supercomputer, yielding an accurate prediction of its large electron affinity, which makes its derivative useful as an electron acceptor in bulk heterojunction organic solar cells.
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DOI
http://dx.doi.org/10.1021/ct400557z
ISSN
1549-9618
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