The Path-Integral Monte Carlo Method for Rotational Degrees of Freedom

  • M. H. Müser
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 82)


Very recent progress in the path-integral simulation of quantum mechanical rotational degrees of freedom (RDOF) is reviewed. Unlike translational degrees of freedom, where the free particle kernel can be obtained by a Gaussian integral, the kernel for RDOF is not analytically accessible. However, it can be obtained numerically to high precision on a fine grid so that all systematic errors can be kept controllably small. The formulae to generate the kernel for RDOF are given explicitly for one, two, and three-dimensional rotation. In particular, we discuss the consequences of confining the rotational state of a rigid body to one representation for the sign problem and the correlation time. A linear rotor in a Devonshire potential and solid methane are considered as examples.


Correlation Time Identity Representation Rotational State Monte Carlo Step Ground State Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Quantum Simulation of Condensed Matter Phenomena, Proceedings on an international Workshop, edited by J.D. Doll and J.E. Gubernatis (World Scientific, Singapore, 1990).Google Scholar
  2. [2]
    K.E. Schmidt and D.M. Ceperley, in Monte Carlo techniques for quantum fluids, solids and droplets, Topics in Appl. Phys. Vol. 71, edited by K. Binder (Springer, Berlin, 1992).Google Scholar
  3. [3]
    L.S. Schulman, Techniques and Applications of Path Integrations (John Wiley & Sons, New York, 1981).Google Scholar
  4. [4]
    M. H. Müser, Molecular Simulation, in press.Google Scholar
  5. [5]
    E.Y. Loh, Jr. and J.E. Gubernatis, R.T. Scalettar, S.R. White, D.J. Scalapino, and R.L. Sugar, Phys. Rev. B 41, 9301 (1990).ADSCrossRefGoogle Scholar
  6. [6]
    H. De Raedt and M. Frick, Phys. Rep. 231, 107 (1993).MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    R.A. Kuharski and P.J. Rossky, J. Chem. Phys. 82, 5164 (1985).ADSCrossRefGoogle Scholar
  8. [8]
    R.N. Zare, Angular Momentum (John Wiley & Sons, New York, 1988).Google Scholar
  9. [9]
    M.H. Müser and B.J. Berne, The path-integral Monte Carlo scheme for rigid tops, (preprint).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • M. H. Müser
    • 1
  1. 1.Department of ChemistryColumbia UniversityNew YorkUSA

Personalised recommendations