Local Temperature\nMeasurement in Molecular Dynamics\nSimulations with Rigid Constraints

Constraining\nmolecules in simulations (such as with constant\nbond\nlengths and/or angles) reduces their degrees of freedom (DoF), which\nin turn affects temperature calculations in those simulations. When\nlocal temperatures are measured, e.g., from a set of atoms in a subvolume\nor from velocities in one Cartesian direction, the result can appear\nto unphysically violate equipartition of the kinetic energy if the\nlocal DoF are not correctly calculated. Here, we determine how to\ncorrectly calculate local temperatures from arbitrary Cartesian component\nkinetic energies, accounting for general geometric constraints, by\nself-consistently evaluating the DoF of atoms subjected to those constraints.\nThe method is validated on a variety of test systems, including systems\nsubject to a temperature gradient and those confined between walls.\nIt is also shown to provide a sensitive test for the breakdown of\nkinetic energy equipartition caused by the approximate nature of numerical\nintegration or insufficient equilibration times. As a practical demonstration,\nwe show that kinetic energy equipartition between C and H atoms connected\nby rigid bonds can be violated even at the commonly used time step\nof 2 fs and that this equipartition violation appears to usefully\nindicate configurational overheating.