Open Access
March 2005 A Geometric Approach to Constrained Molecular Dynamics and Free Energy
Carsten Hartmann, Christof Schutte
Commun. Math. Sci. 3(1): 1-20 (March 2005).


We consider a molecule constrained to a hypersurface S in the conguration space Rm. In order to derive an expression for the mean force acting along the constrained coordinate we decompose the molecular vector field, and single out the direction of the respective coordinate utilising the structure of affine connections. By these means we reconsider the well-known results derived by Sprik et al. [1] and Darve et al. [2]; we gain concise geometrical insight into the different contributions to the force in terms of molecular potential, mean curvature, and the connection 1-form of the normal bundle over the submanifold S. Our approach gives rise to a Hybrid Monte-Carlo based algorithm that can be used to compute the averaged force acting on selected coordinates in the context of thermodynamic free energy statistics.


Download Citation

Carsten Hartmann. Christof Schutte. "A Geometric Approach to Constrained Molecular Dynamics and Free Energy." Commun. Math. Sci. 3 (1) 1 - 20, March 2005.


Published: March 2005
First available in Project Euclid: 17 March 2005

zbMATH: 1078.65009
MathSciNet: MR2132822

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 1 • March 2005
Back to Top