In a recent paper [F. Aviat et al., J. Chem. Theory Comput. 13, 180–190 (2017)], we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in truncating the conjugate gradient algorithm at a fixed predetermined order leading to a fixed computational cost and can thus be considered “non-iterative.” This gives the possibility to derive analytical forces avoiding the usual energy conservation (i.e., drifts) issues occurring with iterative approaches. A key point concerns the evaluation of the analytical gradients, which is more complex than that with a usual solver. In this paper, after reviewing the present state of the art of polarization solvers, we detail a viable strategy for the efficient implementation of the TCG calculation. The complete cost of the approach is then measured as it is tested using a multi-time step scheme and compared to timings using usual iterative approaches. We show that the TCG methods are more efficient than traditional techniques, making it a method of choice for future long molecular dynamics simulations using polarizable force fields where energy conservation matters. We detail the various steps required for the implementation of the complete method by software developers.

中文翻译：

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截断共轭梯度（TCG），一种用于计算分子动力学极化的非迭代/固定成本策略：快速评估分析力

在最近的一篇论文中[F. Aviat等。，J. Chem。理论计算。13，180–190（2017）]，我们提出了截断共轭梯度（TCG）方法来计算极化分子模拟中的极化能量和作用力。该方法包括以固定的预定顺序截断共轭梯度算法，从而导致固定的计算成本，因此可以被认为是“非迭代的”。这提供了导出分析力的可能性，从而避免了迭代方法中常见的能量守恒（即漂移）问题。关键在于解析梯度的评估，该解析梯度比常规求解器的解析梯度更为复杂。在本文中，在回顾了极化解算器的最新技术之后，我们详细介绍了有效实施TCG计算的可行策略。然后，在使用多时间步长方案进行测试时，测量该方法的完整成本，并与使用常规迭代方法的计时进行比较。我们表明，TCG方法比传统技术更有效，使其成为将来在能量守恒很重要的情况下使用可极化力场进行长分子动力学模拟的一种选择方法。我们详细介绍了软件开发人员实施完整方法所需的各个步骤。