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A separable shadow Hamiltonian hybrid Monte Carlo method

J. Chem. Phys. 131, 174106 (2009); doi:10.1063/1.3253687

Published 3 November 2009

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Christopher R. Sweet,1 Scott S. Hampton,2 Robert D. Skeel,3 and Jesús A. Izaguirre1
1Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
2Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 USA
3Department of Computer Science, Purdue University, West Lafayette, Indiana 47907, USA
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc). ©2009 American Institute of Physics
History: Received 5 May 2009; accepted 2 October 2009; published 3 November 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/174106/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.xv
    Molecular dynamics and other numerical methods in atomic and molecular physics
  • 02.70.Uu
    Applications of Monte Carlo methods
  • YEAR: 2009

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