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Journal of Chemical Physics / Volume 135 / Issue 24 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 135, 244105 (2011); http://dx.doi.org/10.1063/1.3665391 (9 pages)

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm

Bryan K. Clark1, Miguel A. Morales2, Jeremy McMinis3, Jeongnim Kim4, and Gustavo E. Scuseria5

1Princeton Center For Theoretical Science, Princeton University, Princeton, New Jersey 08544 and Department of Physics, Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA
2Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, USA
3Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
4National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
5Department of Chemistry and Department of Physics & Astronomy, Rice University, Houston, Texas 77005-1892, USA

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(Received 22 June 2011; accepted 9 November 2011; published online 27 December 2011)

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BACKGROUND
  3. EVALUATING WAVE FUNCTION RATIOS
  4. GRADIENTS AND LAPLACIANS
    1. Updating the gradients first
    2. Updating each determinant first
    3. Direct application of the generalized matrix determinant lemma
  5. ADDITIONAL CONSIDERATIONS
  6. WATER MOLECULE
  7. CONCLUSIONS

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KEYWORDS and PACS

Keywords

ground states, molecular electronic states, Monte Carlo methods, STO calculations, variational techniques, water, wave functions

PACS

  • 31.15.ep

    Variational particle-number approach

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3665391

PUBLICATION DATA

ISSN

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

Publisher

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

For access to fully linked references, you need to log in.
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