Dofulator: A tool for calculating degrees of freedom of atoms in molecules with geometry constraints

Recently, we proposed a method for calculating per-atom and per-direction degrees of freedom (DoF) in the presence of geometric constraints, enabling fine-grained local kinetic temperature calculations. Here, we discuss relevant implementation details for various constraint geometries, including those which feature kinematic loops (e.g. benzene with rigid bond lengths). Furthermore, by analyzing the effects of deformation of semi-rigid molecules on the DoF of each constituent atom, we gain insight into conditions under which atomic DoF may vary significantly during a simulation. This provides some guidance towards cases where local DoF should be calculated dynamically to obtain reliable local temperature measurements, and cases where using the atomic DoF of the equilibrium geometry as a constant throughout the simulation would be sufficient. We have implemented the presented algorithms in an open-source C library, dofulator, which can be used on its own or through a Python interface that includes compatibility with the popular MDAnalysis package.