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Constrained molecular dynamics is performed using the SHAKE algorithm .
In this algorithm, the Lagrangian for the system is extended as follows:
where the summation is over geometric constraints,
is the Lagrangian for the
extended system, and is a Lagrange multiplier
associated with a geometric constraint :
being a geometric parameter and is the
fixed during the
In the SHAKE algorithm, Lagrange multipliers
in the iterative procedure:
- perform a standard MD step (leap-frog algorithm):
- use the new positions
to compute Lagrange multipliers for all constraints:
- update the velocities and positions by adding a contribution due to restoring forces (proportional
- repeat steps 2-4 until all
than a predefined tolerance.
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