Chapter

Mathematical Approaches to Biomolecular Structure and Dynamics

Volume 82 of the series The IMA Volumes in Mathematics and its Applications pp 161-185

Integration Methods for Molecular Dynamics

  • Benedict J. LeimkuhlerAffiliated withDepartment of Mathematics, University of Kansas
  • , Sebastian ReichAffiliated withKonrad-Zuse Zentrum
  • , Robert D. SkeelAffiliated withDepartment of Computer Science, University of Illinois

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Abstract

Classical molecular dynamics simulation of a macromolecule requires the use of an efficient time-stepping scheme that can faithfully approximate the dynamics over many thousands of timesteps. Because these problems are highly nonlinear, accurate approximation of a particular solution trajectory on meaningful time intervals is neither obtainable nor desired, but some restrictions, such as symplecticness, can be imposed on the discretization which tend to imply good long term behavior. The presence of a variety of types and strengths of interatom potentials in standard molecular models places severe restrictions on the timestep for numerical integration used in explicit integration schemes, so much recent research has concentrated on the search for alternatives that possess (1) proper dynamical properties, and (2) a relative insensitivity to the fastest components of the dynamics. We survey several recent approaches.

Key words

leapfrog method Verlet method symplectic method multiple-timestep methods symplectic integrator molecular dynamics simulation constrained dynamics SHAKE multiple time scales long-time integration