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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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Stochastic evaluation of second-order Dyson self-energies

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Title
Stochastic evaluation of second-order Dyson self-energies
Author
Willow, Soohaeng YooKim, Kwang S.Hirata, So
Keywords
Computational costs; Efficient importance samplings; Metropolis algorithms; Monte Carlo integration; Perturbation correction; Quasiparticle energy; Stochastic evaluations; Stochastic methods
Issue Date
201304
Publisher
AMER INST PHYSICS
Citation
JOURNAL OF CHEMICAL PHYSICS, v.138, no.16, pp. -
Abstract
A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Greens function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 108 Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.
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DOI
http://dx.doi.org/10.1063/1.4801862
ISSN
0021-9606
Appears in Collections:
SNS_Journal Papers
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