论文标题
基于静电势拟合原子电荷与MM子系统尺寸线性缩放的静电电势拟合原子电荷，静电嵌入QM/mm的分析能量，梯度和Hessian
Analytic energy, gradient, and hessian of electrostatic embedding QM/MM based on electrostatic potential fitted atomic charges scaling linearly with the MM subsystem size
论文作者
论文摘要
静电势拟合方法（ESPF）是定义由量子密度矩阵得出的原子电荷的强大方法，该矩阵在存在外部静电电势的情况下，用于在存在外部量子机械电荷分布。这些可以在哈密顿量中用于定义强大，有效的静电嵌入QM/mm方法。 ESPF QM/mm的原始公式包含两个主要近似值，即忽略网格衍生物和对总QM电荷的不保守。在这里，我们提出了一个新的ESPF原子电荷运营商，该操作员几乎没有额外的计算成本来解决这些缺点。新的电荷运算符采用以原子为中心的网格，并在用密度矩阵追踪时保存总电荷。我们为能量，梯度和Hessian提供了一种有效且易于实现的分析形式，该形式与MM子系统大小线性缩放。我们表明，网格衍生物和电荷保护是至关重要的，以保留能量及其衍生物的翻译不变性特性以及原子电荷衍生物所满足的精确条件。作为概念验证，我们计算了导致加密块状反应过程中导致过氧化氢形成的过渡状态。最后，我们表明，完整的QM/MM Hessian的构建与MM子系统大小线性缩放。
Electrostatic potential fitting method (ESPF) is a powerful way of defining atomic charges derived from quantum density matrices fitted to reproduce a quantum mechanical charge distribution in the presence of an external electrostatic potential. These can be used in the Hamiltonian to define a robust and efficient electrostatic embedding QM/MM method. The original formulation of ESPF QM/MM contained two main approximations, namely, the neglect of grid derivatives and the non-conservation of the total QM charge. Here, we present a new ESPF atomic charge operator which solves these drawbacks at virtually no extra computational cost. The new charge operators employ atom-centered grids and conserve the total charge when traced with the density matrix. We present an efficient and easy-to-implement analytic form for the energy, gradient, and hessian that scale linearly with the MM subsystem size. We show that grid derivatives and charge conservation are fundamental to preserve the translational invariance properties of energies and its derivatives and exact conditions to be satisfied by the atomic charge derivatives. As proof of concept, we compute the transition state that leads to the formation of hydrogen peroxide during cryptochrome's reoxidation reaction. Last, we show that the construction of the full QM/MM hessian scales linearly with the MM subsystem size.
