Evaluation of temperature in molecular dynamics simulation

Abstract

Among several finite-difference algorithms which are used in MD simulation three popular ones are: the leapfrog, the Verlet and the Beeman. All three algorithms produce exactly the same particle trajectories, but they differ in terms of definition of the velocity and hence give different values of kinetic energy or temperature for the system. Evaluation of the temperature of a simulated system can be based on the Taylor expansion of coordinates, velocities or kinetic energies; leading to expressions which we characterise as being of the Verlet type, Beeman type or corrected-leapfrog type. Twelve different expressions for evaluation of the kinetic energy of a system are discussed and compared by means of a one-dimensional two-particle system and a liquid simulation. The results, consistent in both tests, show that the Verlet expressions underestimate the kinetic energy while the Beeman expressions overstimate it. In terms of conservation of total energy the corrected-leapfrog expressions prove to be superior. We have also been able to suggest some improved expressions which give the correct average kinetic energy with even smaller fluctuations in total energy.