State Key Laboratory of Precision Spectroscopy, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.
Phys Chem Chem Phys. 2019 Oct 9;21(39):21942-21959. doi: 10.1039/c9cp04113c.
The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.
量子力学（QM）/分子力学（MM）自由能面的间接方法为 QM 水平的自由能模拟提供了更经济的选择。间接方法的特点是使用计算效率更高但准确性较低的哈密顿量（即低水平哈密顿量）直接计算自由能分布，并进行低水平到高水平的校正。在热力学循环中，通过阿尔克法（alchemical method）对沿物理上有意义的反应坐标的直接低水平计算进行校正，该方法通常通过基于微扰的技术来实现。在我们之前的工作中，提出了一种多维非平衡拉拔框架，用于间接构建 QM/MM 自由能面。之前，我们专注于通过直接 MM 模拟和 MM 到 SQM 校正从间接获得半经验 QM（SQM）结果。在这项工作中，我们通过结合直接 SQM 结果和 SQM 到 QM 校正，将该方法应用于获得从头算 QM 哈密顿量下的结果。一系列 SQM 和 QM 哈密顿量进行了基准测试。结果表明，在低水平哈密顿量中，PM6 表现最佳。因此，我们建议在间接自由能模拟中使用 PM6 作为低水平理论。考虑到它与高水平哈密顿量的更高相似度，用键电荷校正修正后的 PM6 可能比现有的 AM1-BCC 模型更准确。当前工作的另一个核心结果是在僵硬弹簧极限下的非平衡自由能模拟中选择约束强度和适当时间步长的基本方案。我们提供了理论推导，强调使用足够大的力常数和选择适当的时间步长的重要性。值得注意的是，根据我们的推导，选择时间步长的一般经验法则是，只要使用僵硬弹簧近似，即使在涉及氢键的约束模拟中，也应使用 1 fs 或更小的时间步长。
