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

Source: J. Chem. Phys. 135, 244105 (2012); http://dx.doi.org/10.1063/1.3665391

Published 27 December 2011

KEYWORDS and PACS
Keywords
PACS
  • 31.15.ep
    Variational particle-number approach (density functional theory of atoms and molecules)
  • YEAR: 2011
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PUBLICATION DATA
ISSN:
1553-9628 (online)
Publisher:
AIP is a member of CrossRef AIP
Bryan K. Clark,1 Miguel A. Morales,2 Jeremy McMinis,3 Jeongnim Kim,4 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
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
History: Received 22 June 2011; accepted 9 November 2011; published 27 December 2011
Digital Object Identifier: http://dx.doi.org/10.1063/1.3665391

REFERENCES (20)

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  1. R. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, England, 2004).
  2. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover, New York, 1996).
  3. W. Foulkes, L. Mitas, R. Needs, and G. Rajagopal, Mod. Phys. 73, 33 (2001).
  4. P. Nukala and P. Kent, J. Chem. Phys. 130, 204105 (2009).
  5. See http://qmcpack.cmscc.org (2011) for the code and documentation.
  6. Matrix multiplication is known to scale theoretically better then O(n3) (i.e., at least O(n2.376)), but these asymptotically faster algorithms are rarely useful in practice.
  7. M. Casula, C. Attaccalite, and S. Sorella, J. Chem. Phys. 121, 7110 (2004).
  8. I. G. Gurtubay and R. J. Needs, J. Chem. Phys. 127, 124306 (2007).
  9. N. A. Benedek, I. K. Snook, M. D. Towler, and R. J. Needs, J. Chem. Phys. 125, 104302 (2006).
  10. A. Luchow and R. F. Fink, J. Chem. Phys. 113, 8457 (2000).
  11. J. Toulouse and C. J. Umrigar, J. Chem. Phys. 128, 174101 (2008).
  12. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery Jr., J. Comput. Chem. 14, 1347 (1993).
  13. P. Widmark, P. Malmqvist, and B. Roos, Theor. Chim. Acta 77, 291 (1990).
  14. K. Schuchardt, B. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, and T. Windus, J. Chem. Inf. Model. 47, 1045 (2007).
  15. D. J. Feller, J. Comput. Chem. 17, 1571 (1996).
  16. J. McMinis, M. A. Morales, B. K. Clark, J. Kim, and D. M. Ceperley, “Optimization and multi-determinant wave functions” (unpublished).
  17. H. Muller and W. Kutzelnigg, Mol. Phys. 92, 535 (1997).
  18. L. Bytautas and K. Ruedenberg, J. Chem. Phys. 124, 174304 (2006).
  19. D. Feller, C. M. Boyle, and E. R. Davidson, J. Chem. Phys. 86, 3424 (1986).
  20. Our implementation allows for line minimization to determine the optimal rescaling factor of the parameters found from the eigenvalue problem. This results in larger changes for the initial iterations and smaller changes during the final iterations. Depending on the details of the calculation, sample size, and type of wave function parameters, this can result in an efficiency gain. For large expansions we generally find that many more samples are needed when building the matrices used to solve for the parameter change direction than are needed for the line minimization.

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