Toxvaerd Søren
Department of Science and Environment, Roskilde University, Post Box 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2025 Jan 14;162(2). doi: 10.1063/5.0251514.
A recent article in J. Chem. Phys. argues that the two algorithms, the velocity-Verlet and position-Verlet integrators, commonly used in Molecular Dynamics (MD) simulations, are different [L. Ni and Z. Hu, J. Chem. Phys. 161, 226101 (2024)]. However, not only are the two algorithms just different formulations of the same discrete algorithm, but also are other simple discrete algorithms used in MD simulations in the natural sciences. They are all reformulations of the discrete algorithm derived by Newton in 1687 in Proposition I in the very first part of his book Principia. The different reformulations of Newton's algorithm for discrete dynamics lead to identical discrete dynamics with the same invariances, momentum, angular momentum, and energy as Newton's analytical dynamics. Hundreds of thousands of MD simulations with Newton's discrete dynamics have appeared but unfortunately with many recorded errors for energies, potential energies, temperatures, and heat capacities. The public software for MD should be corrected.
《化学物理杂志》最近的一篇文章认为，分子动力学（MD）模拟中常用的两种算法，即速度Verlet积分器和位置Verlet积分器，是不同的[L. Ni和Z. Hu，《化学物理杂志》161, 226101 (2024)]。然而，这两种算法不仅只是同一离散算法的不同形式，而且自然科学中MD模拟使用的其他简单离散算法也是如此。它们都是牛顿在1687年其《原理》第一部分命题I中推导的离散算法的重新表述。牛顿离散动力学算法的不同重新表述导致了相同的离散动力学，具有与牛顿解析动力学相同的不变性、动量、角动量和能量。已经出现了数十万次使用牛顿离散动力学的MD模拟，但不幸的是，在能量、势能、温度和热容量方面有许多记录错误。MD的公共软件应该得到修正。
