Constrained molecular dynamics: Difference between revisions

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Constrained molecular dynamics is performed using the SHAKE algorithm.<ref name="Ryckaert77"/>.
Constrained molecular dynamics is performed using the SHAKE{{cite|ryckaertt:jcp:1977}} algorithm.
In this algorithm, the Lagrangian for the system <math>\mathcal{L}</math> is extended as follows:
In this algorithm, the Lagrangian for the system <math>\mathcal{L}</math> is extended as follows:
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== References ==
== References ==
<references>
   
<ref name="Ryckaert77">[http://dx.doi.org/10.1016/0021-9991(77)90098-5 J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).]</ref>
[[Category:Advanced molecular-dynamics sampling]][[Category:Theory]]
</references>
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[[Category:Molecular Dynamics]][[Category:Theory]][[Category:Howto]]

Latest revision as of 09:59, 15 October 2024

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