Constrained molecular dynamics

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Constrained molecular dynamics is performed using the SHAKE algorithm.[1]. In this algorithm, the Lagrangian for the system is extended as follows:

where the summation is over r geometric constraints, is the Lagrangian for the extended system, and λi is a Lagrange multiplier associated with a geometric constraint σi:

with ξi(q) being a geometric parameter and ξi is the value of ξi(q) fixed during the simulation.

In the SHAKE algorithm, the Lagrange multipliers λi are determined in the iterative procedure:

  1. Perform a standard MD step (leap-frog algorithm):
  2. Use the new positions q(tt) to compute Lagrange multipliers for all constraints:
  3. Update the velocities and positions by adding a contribution due to restoring forces (proportional to λk):
  4. repeat steps 2-4 until either |σi(q)| are smaller than a predefined tolerance (determined by SHAKETOL), or the number of iterations exceeds SHAKEMAXITER.

Anderson thermostat

  • For a constrained molecular dynamics run with Andersen thermostat, one has to:
  1. Set the standard MD-related tags: IBRION=0, TEBEG, POTIM, and NSW.
  2. Set MDALGO=1, and choose an appropriate setting for ANDERSEN_PROB.
  3. Define geometric constraints in the ICONST-file, and set the STATUS parameter for the constrained coordinates to 0.
  4. When the free-energy gradient is to be computed, set LBLUEOUT=.TRUE.

References