Equipartition Principle
for Internal Coordinate Molecular
Dynamics
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Abstract
The <i>principle of equipartition of (kinetic) energy</i> for all-atom Cartesian molecular dynamics states that each momentum
phase space coordinate on the average has <i>kT</i>/2 of
kinetic energy in a canonical ensemble. This principle is used in
molecular dynamics simulations to initialize velocities, and to calculate
statistical properties such as entropy. Internal coordinate molecular
dynamics (ICMD) models differ from Cartesian models in that the overall
kinetic energy depends on the generalized coordinates and includes
cross-terms. Due to this coupled structure, no such equipartition
principle holds for ICMD models. In this paper, we introduce noncanonical <i>modal coordinates</i> to recover some of the structural simplicity
of Cartesian models and develop a new equipartition principle for
ICMD models. We derive low-order recursive computational algorithms
for transforming between the modal and physical coordinates. The equipartition
principle in modal coordinates provides a rigorous method for initializing
velocities in ICMD simulations, thus replacing the <i>ad hoc</i> methods used until now. It also sets the basis for calculating conformational
entropy using internal coordinates