Constrained molecular dynamics

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Constrained molecular dynamics is performed using the SHAKE[1] algorithm.[2]. 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.



References

  1. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).
  2. Cite error: Invalid <ref> tag; no text was provided for refs named Ryckaert77