Common Molecular Dynamics Algorithms Revisited: Accuracy and Optimal Time Steps of Störmer–Leapfrog Integrators
✍ Scribed by Alexy K. Mazur
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 432 KB
- Volume
- 136
- Category
- Article
- ISSN
- 0021-9991
No coin nor oath required. For personal study only.
✦ Synopsis
tween the order of the finite difference equation and its analytical analog [2], to their time reversibility [2,9,10],
The Sto ¨rmer-Verlet-leapfrog group of integrators commonly used in molecular dynamics simulations has long become a text-to oscillating fundamental solutions [11] and to their symbook subject and seems to have been studied exhaustively. There plectic property [9, 12,13]. A hallmark of these method are, however, a few striking effects in performance of algorithms is a square power growth of global errors with the step which are well known but have not received adequate attention in size, which is invariably observed with different testing the literature. A closer view of these unclear observations results
techniques and can even be used for debugging computer in unexpected conclusions. It is shown here that contrary to the conventional point of view, the leapfrog scheme is distinguished codes [5]. Because of the low apparent order of approximain this group both in terms of the order of truncation errors and the tion they usually appear less accurate than other methods conservation of the total energy. In this case the characteristic in comparative studies, but, with large step sizes, when square growth of fluctuations of the total energy with the step size, other algorithms loose stability, the leapfrog scheme and commonly measured in numerical tests, results from additional its analogs still produce trajectories with very low total interpolation errors with no relation to the accuracy of the computed trajectory. An alternative procedure is described for checking energy energy drift and correct average static and dynamic properconservation of leapfrog-like algorithms which is free from interpoties [14-16]. These observations are known and exploited lation errors. Preliminary tests on a representative model system for such a long time that it seems to have been forgotten
suggest that standard step size values used at present are lower that actually they are quite unusual and that this behavior than necessary for accurate sampling.