Torsion dynamics of molecular systems

Based on the concept of free energy, we derive a Hamiltonian formulation for molecular dynamics in torsion space. The appropriate reaction coordinates for the free energy calculations are defined in terms of soft constraints as introduced by Brooks, Zhou, and Reich (unpublished) in the context of molecular dynamics. We consider a few simplifications that allow one to calculate the free energy analytically and to write the corresponding equations of motion as a constraint Hamiltonian system that can conveniently be discretized by the well known SHAKE algorithm. The additional computational costs, compared to using the orginal force field and constraining bond lengths and bond angles to their equilibrium value (hard constraints), amount, in general, to less than a complete force evaluation. We show, for a single butane molecule, that our Hamiltonian formulation yields the correct Boltzmann distribution in the torsion angle while the original Hamiltonian, together with hard constraints on the bond lengths and bond angles, results in a much reduced transition rate between the trans and cis configuration.