Generalized form of the conserved quantity in constant-temperature molecular dynamics

Abstract

A generalized form of the conserved quantity in the constant-temperature molecular dynamics (MD) simulation is proposed as a measure of accuracy of MD simulations. This quantity is defined as the deviation of the distribution functions, or the Jacobian determinant, generated by the MD trajectory, from the ideal canonical value. For the Nosé–Hoover equations, this has the same form as the Hamiltonian of Nosé’s extended system. We calculated the conserved quantities for a series of constant-temperature simulations of a small protein, crambin, in water, and used them to evaluate the accuracy of the simulations under various conditions; i.e., with the Gaussian isokinetic or Nosé–Hoover equations, with flexible or rigid-body water, and with a single- or multiple-time-step algorithm. New integrators, based on the decomposition of the exponential Liouville operators, were developed for the simulation with rigid-body water. The comparison of the conserved quantities showed that the Gaussian isokinetic equations produced almost the same degree of accuracy as the Nosé–Hoover equations, and that the rigid-body treatment of water and the multiple-time-step algorithm greatly improved the accuracy.