DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2011 Sep 14;135(10):104101. doi: 10.1063/1.3623585.
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.
导出了一种算法，用于模拟 N 个经典粒子系统的恒势能超曲面上的测地线。首先，通过离散测地线稳定性条件并通过标准拉格朗日乘子实现恒势能约束，导出了基本的时间可逆测地线算法。通过对 Lennard-Jones 液体的单精度计算机模拟测试了基本的 NVU 算法。如果力截止平滑并且两个初始构型在机器精度内具有相同的势能，则可以获得出色的数值稳定性。然而，就像 NVE 算法一样，为了补偿最终导致势能向更高值“熵漂移”的数值误差的积累，非常长的运行需要稳定剂。引入了对基本 NVU 算法的修改，以确保势能和步长守恒；还消除了质心漂移。通过模拟验证的分析论证表明，修改后的 NVU 算法是绝对稳定的。最后，我们展示了模拟结果，表明 NVU 算法和标准的跳跃 NVE 算法对于 Lennard-Jones 液体具有相同的径向分布函数。
