DNRF Centre "Glass and Time," IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2013 Dec 14;139(22):224106. doi: 10.1063/1.4836615.
For discrete classical Molecular Dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment h there exists (for sufficiently small h) a shadow Hamiltonian H̃ with energy Ẽ(h), for which the discrete particle positions lie on the analytic trajectories for H̃. The first order estimate of Ẽ(h) is employed to determine the relation with the corresponding energy, E, for the analytic dynamics with h = 0 and the zero-order estimate E0(h) of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics for the (NVT̃(h)) ensemble and determine the relations between the energies and temperatures for the different ensembles, including the (NVE0(h)) and (NVT0(h)) ensembles. The differences in the energies and temperatures are proportional with h(2) and they are of the order of a few tenths of a percent for a traditional value of h. The relations between (NVẼ(h)) and (NVE), and (NVT̃(h)) and (NVT) are easily determined for a given density and temperature, and allow for using larger time increments in MD. The accurate determinations of the energies are used to determine the kinetic degrees of freedom in a system of N particles. It is 3N - 3 for a three dimensional system. The knowledge of the degrees of freedom is necessary when simulating small system, e.g., at nucleation.
对于通过“Verlet”算法（VA）获得的离散经典分子动力学（MD），在时间增量 h 下存在（对于足够小的 h）具有能量Ẽ(h)的阴影哈密顿量 H̃，对于该离散粒子位置位于 H̃的分析轨迹上。使用Ẽ(h)的一阶估计来确定与分析动力学的相应能量 E 的关系，h = 0，以及文献中出现的用于 VA 的 MD 的离散动力学的零阶估计 E0(h)。我们为（NVT̃(h))系综推导了一个相应的正则动力学的时间可逆 VA 算法，并确定了不同系综之间的能量和温度之间的关系，包括（NVE0(h))和（NVT0(h))系综。对于传统的 h 值，能量和温度的差异与 h(2)成正比，并且它们的量级为百分之几。对于给定的密度和温度，（NVẼ(h))和（NVE）以及（NVT̃(h))和（NVT）之间的关系很容易确定，并且允许在 MD 中使用更大的时间增量。准确确定能量可用于确定 N 个粒子系统中的动力学自由度。对于三维系统，自由度为 3N - 3。在模拟小系统（例如成核）时，需要了解自由度。
