School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA.
J Chem Phys. 2022 May 7;156(17):174105. doi: 10.1063/5.0087386.
We present a density functional theory (DFT)-based, quantum mechanics/molecular mechanics (QM/MM) implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle-mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF) ionic liquid were considered as "simple" and "complex" solvents, respectively, with water and p-phenylenediamine (PPD) solute molecules treated at the QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible errors for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF for which real-space truncation produces severe errors even at 2-3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms with our presented algorithm providing a general and robust approach.
我们提出了一种基于密度泛函理论（DFT）的量子力学/分子力学（QM/MM）方法，通过直接实空间积分粒子网格 Ewald（PME）计算的静电势实现长程静电嵌入。关键的转换是将静电势从 PME 网格插值到 DFT 求积网格，从那里可以利用标准的 DFT 机制轻松评估积分。我们提供了网格大小和实空间校正选择的数值准确性基准，并证明在引入名义计算开销的同时实现了良好的收敛性。此外，该方法只需对现有软件包进行微小修改，如我们在 OpenMM 和 Psi4 软件中的实现所示。在介绍收敛性基准后，我们评估了在三个用 QM/MM 建模的溶质/溶剂系统中长程静电嵌入的重要性。水和 1-丁基-3-甲基咪唑四氟硼酸盐（BMIM/BF）离子液体分别被视为“简单”和“复杂”溶剂，水和对苯二胺（PPD）溶质分子在 QM 理论水平上进行处理。虽然对于简单系统（如水溶剂中的水溶质），使用标准实空间截断的静电嵌入可能引入可忽略的误差，但当 QM/MM 应用于复杂溶剂（如离子液体）时，误差会变得更加显著。一个极端的例子是氧化 PPD 在 BMIM/BF 中的静电嵌入能，对于这种情况，即使在 2-3nm 的截断距离下，实空间截断也会产生严重的误差。后一个例子说明了，在浓电解质/离子介质中计算氧化还原电势时，需要仔细选择长程静电嵌入算法，我们提出的算法提供了一种通用且稳健的方法。
