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There has been work done using constraints on the beads in the following papers: J. Chem. Phys. 112, 8910 (2000) and J. Chem. Phys. 123, 154504 (2005) but the theory had not been derived as you suggested.
Two recent papers have been published that justify the use of constraints on the beads to simulate quantum rigid bodies: J. Chem. Phys. 138, 184101 (2013) and J. Chem. Phys. 139, 184115 (2013).
The application of RATTLE/SHAKE correctly calculates the structural properties but requires a different energy estimator, but this can be calculated from the bead position and potential energy from the RPMD integrator.
I feel that this feature will be useful for many OpenMM users
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