Planta Piloto de Ingeniería Química, PLAPIQUI, Universidad Nacional del Sur, Camino La Carrindanga Km 7-CC: 717, Bahía Blanca, Argentina.
Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil.
J Chem Phys. 2019 Mar 21;150(11):114110. doi: 10.1063/1.5085441.
Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs.
动能均分是许多旨在对正则系综进行采样的确定性和随机分子动力学方法的前提。虽然这对于实际系统是预期的，但数值积分引入的离散化误差可能导致均分偏离。幸运的是，反向误差分析允许我们获得实际受均分影响的量的高阶估计。这与一个影子哈密顿量有关，只有当时间步长接近零时，它才会收敛到指定的哈密顿量。本文以直接的方式处理离散化效应。通过少量的计算开销，我们得到了改进的动能和势能版本，它们的和是影子哈密顿量的合适估计量。然后，我们通过使用改进的动能而不是传统的动能来调整恒温器过程。该过程显示出与改进系统兼容的正则系综，而不是与原始系统兼容的正则系综，但可以通过重新加权轻松恢复后者的正则平均值。水被建模为刚体，是我们建议的一个极好的测试案例，因为它的数值稳定性可以扩展到足够大的时间步长，从而在 Verlet 型积分器中产生明显的离散化误差。通过应用我们的新方法，我们能够减轻液体水的平衡性质的离散化效应，时间步长高达 5 fs。
