Path integral Monte Carlo calculation of electronic forces

Fenghua Zong, D. M. Ceperley

Research output: Contribution to journalArticlepeer-review


We describe a method to evaluate electronic forces by path integral Monte Carlo (PIMC) calculation. Electronic correlations, as well as thermal effects, are included naturally in this method. For fermions, a restricted approach is used to avoid the "sign" problem. The PIMC force estimator is local and has a finite variance. We applied this method to determine the bond length of H2 and the chemical reaction barrier of H + H2→H2 + H. At low temperature, good agreement is obtained with ground-state calculations. We studied the proton-proton interaction in an electron gas as a simple model for hydrogen impurities in metals. We calculated the force between the two protons at two electronic densities corresponding to Na (rs = 3.93) and Al (rs = 2.07) using a supercell with 38 electrons. The result is compared to previous calculations. We also studied the effect of temperature on the proton-proton interaction. At very high temperature, our result agrees with the Debye screening of electrons. As temperature decreases, the Debye theory fails both because of the strong degeneracy of electrons and most importantly, the formation of electronic bound states around the protons.

Original languageEnglish (US)
Pages (from-to)5123-5130
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
StatePublished - 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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