Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

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  • J. César Cruz
    Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa 1 , San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, Ciudad de México C.P. 09340, Mexico
  • Jorge Garza
    Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa 1 , San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, Ciudad de México C.P. 09340, Mexico
  • Takeshi Yanai
    Department of Chemistry, Graduate School of Science, Nagoya University 2 , Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
  • So Hirata
    Department of Chemistry, University of Illinois at Urbana-Champaign 4 , 600 South Mathews Avenue, Urbana, Illinois 61801, USA

説明

<jats:p>A second-order many-body perturbation correction to the relativistic Dirac–Hartree–Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-cumulative distribution function method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with 92% strong scalability going from 64 to 4096 processors.</jats:p>

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