Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, MN 55455-0431, USA.
Phys Chem Chem Phys. 2011 Jun 14;13(22):10556-64. doi: 10.1039/c0cp02850a. Epub 2011 Mar 14.
We performed geometry optimizations using the tuned and balanced redistributed charge algorithms to treat the QM-MM boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. In the tuned and balanced redistributed charge (TBRC) scheme, the QM boundary atom is terminated by a tuned F link atom, and the charge of the MM boundary atom is properly adjusted to conserve the total charge of the entire QM/MM system; then the adjusted MM boundary charge is moved evenly to the midpoints of the bonds between the MM boundary atom and its neighboring MM atoms. In the tuned and balanced redistributed charge-2 (TBRC2) scheme, the adjusted MM boundary charge is moved evenly to all MM atoms that are attached to the MM boundary atom. A new option, namely charge smearing, has been added to the TBRC scheme, yielding the tuned and balanced smeared redistributed charge (TBSRC) scheme. In the new scheme, the redistributed charges near the QM-MM boundary are smeared to make the electrostatic interactions between the QM region and the redistributed charges more realistic. The TBRC2 scheme and new TBSRC scheme have been tested for various kinds of bonds at a QM-MM boundary, including C-C, C-N, C-O, O-C, N-C, C-S, S-S, S-C, C-Si, and O-N bonds. Charge smearing is necessary if the redistributed charges are close to the QM region, as in the TBSRC scheme, but not if the redistributed charge is farther from the QM region, as in the TBRC2 scheme. We found that QM/MM results using either the TBRC2 scheme or the TBSRC scheme agree well with full QM results; the mean unsigned error (MUE) of the QM/MM deprotonation energy is 1.6 kcal/mol in both cases, and the MUE of QM/MM optimized bond lengths over the three bonds closest to the QM-MM boundary, with errors averaged over the protonated forms and unprotonated forms, is 0.015 Å for TBRC2 and 0.021 Å for TBSRC. The improvements in the new scheme are essential for QM-MM boundaries that pass through a polar bond, but even for boundaries that pass through C-C bonds, the improvement can be quite significant.
我们使用经过调谐和平衡重分布电荷算法进行几何优化，以处理组合量子力学和分子力学（QM/MM）方法中的QM-MM 边界。在调谐和平衡重分布电荷（TBRC）方案中，QM 边界原子由调谐 F 键原子终止，并且 MM 边界原子的电荷被适当调整以保持整个 QM/MM 系统的总电荷守恒；然后，调整后的 MM 边界电荷均匀移动到 MM 边界原子与其相邻 MM 原子之间的键的中点。在调谐和平衡重分布电荷-2（TBRC2）方案中，调整后的 MM 边界电荷均匀移动到连接到 MM 边界原子的所有 MM 原子上。新的选项，即电荷弥散，已添加到 TBRC 方案中，产生了调谐和平衡弥散重分布电荷（TBSRC）方案。在新方案中，QM-MM 边界附近的重分布电荷被弥散，以使 QM 区域和重分布电荷之间的静电相互作用更加真实。TBRC2 方案和新的 TBSRC 方案已在 QM-MM 边界的各种键上进行了测试，包括 C-C、C-N、C-O、O-C、N-C、C-S、S-S、S-C、C-Si 和 O-N 键。如果重分布电荷靠近 QM 区域，如在 TBSRC 方案中，则需要电荷弥散，但如果重分布电荷离 QM 区域更远，如在 TBRC2 方案中，则不需要电荷弥散。我们发现，使用 TBRC2 方案或 TBSRC 方案的 QM/MM 结果与全 QM 结果吻合得很好；在这两种情况下，QM/MM 去质子化能的平均无偏差（MUE）为 1.6 kcal/mol，并且最靠近 QM-MM 边界的三个键的 QM/MM 优化键长的 MUE，质子化形式和非质子化形式的误差平均化，对于 TBRC2 为 0.015 Å，对于 TBSRC 为 0.021 Å。对于穿过极性键的 QM-MM 边界，新方案的改进是必不可少的，但即使对于穿过 C-C 键的边界，改进也可能非常显著。
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