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Journal of Chemical Physics / Volume 132 / Issue 15 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 132, 154113 (2010); http://dx.doi.org/10.1063/1.3380831 (9 pages)

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited

Michele Casula1, Saverio Moroni2,3, Sandro Sorella2,3, and Claudia Filippi4

1Centre de Physique Théorique, CNRS, École Polytechnique, 91128 Palaiseau Cedex, France
2International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy
3CNR-IOM Democritos National Simulation Center, Via Beirut 2-4, 34014 Trieste, Italy
4Faculty of Science and Technology and MESA+Research Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

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(Received 1 February 2010; accepted 13 March 2010; published online 21 April 2010)

We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat nonlocal pseudopotential in a variational way. We show that such scheme—when applied to large enough systems—maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing: (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. DMC AND NONLOCAL PSEUDOPOTENTIALS
    1. Beyond the LA
  3. SIZE-CONSISTENCY
    1. Size-consistent variational formulations: SVDMC Version 1
    2. Size-consistent variational formulations: SVDMC Version 2
  4. LRDMC AND NONLOCAL PSEUDOPOTENTIALS
    1. Small a2 correction for good trial function
    2. Well defined lattice regularization
  5. PERFORMANCE OF THE PROPOSED METHODS
    1. Time-step error
    2. Relative efficiency
  6. CONCLUSIONS

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KEYWORDS and PACS

Keywords

diffusion, many-body problems, Monte Carlo methods, pseudopotential methods, variational techniques

PACS

  • 71.15.Dx

    Computational methodology (Brillouin zone sampling, iterative diagonalization, pseudopotential construction)

  • 31.15.xt

    Variational techniques

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3380831

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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