A constrained hybrid Monte-Carlo algorithm and the problem of calculating the free energy in several variables. (English) Zbl 1185.82051
Summary: We consider the problem of computing molecular free energy profiles along several orthogonal reaction coordinates by means of constrained simulations. The reaction coordinates define families of submanifolds, and the mean force along the reaction coordinates is the averaged force acting vertically to the submanifold. We give a rigorous justification for the calculation of the mean force along the constrained coordinates, and provide a concise geometrical interpretation of the different contributions to the mean force in terms of the extrinsic geometry of the submanifold. From this we are able derive a hybrid Monte-Carlo-based algorithm that can be used to compute expectation values from constrained simulations such as the mean force in the context of thermodynamic free energy statistics.
MSC:
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 37A60 | Dynamical aspects of statistical mechanics |
| 37J05 | Relations of dynamical systems with symplectic geometry and topology (MSC2010) |
| 65C05 | Monte Carlo methods |
| 70F20 | Holonomic systems related to the dynamics of a system of particles |
| 70H45 | Constrained dynamics, Dirac’s theory of constraints |
Keywords:
molecular dynamics; holonomic constraints; free energy; affine connections; hybrid Monte-CarloReferences:
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