Ojeda-May Pedro, Pu Jingzhi
Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202, USA.
J Chem Phys. 2015 Nov 7;143(17):174111. doi: 10.1063/1.4934880.
The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r(-1) term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.
在阻尼移动力（DSF）形式体系[C. J. 芬内尔和J. D. 盖泽尔特，《化学物理杂志》124, 234104 (2006)]中，对沃尔夫求和方法[D. 沃尔夫等人，《化学物理杂志》110, 8254 (1999)]进行了扩展，用于在量子力学与分子力学相结合（QM/MM）的分子动力学模拟中处理静电作用。在此发展过程中，我们将QM/MM静电势能函数拆分为传统的库仑r⁻¹项和包含DSF贡献的一项。前者由基于截断的QM/MM模拟的标准机制处理，而后者作为福克矩阵校正纳入QM/MM相互作用哈密顿量。我们针对两个溶液相反应测试了所得的QM/MM-DSF方法，即铵离子和氯离子的缔合以及一个对称的SN2反应（其中一个甲基在两个氯离子之间交换）。通过将平均力势（PMF）曲线与QM/MM-埃瓦尔德方法和QM/MM-各向同性周期求和（IPS）方法的曲线进行比较，评估了QM/MM-DSF方法的性能，这两种方法都明确包含长程静电作用。对于离子缔合，QM/MM-DSF方法成功消除了在QM/MM-截断模拟中观察到的人为自由能漂移，与两种包含长程作用的方法结果显著一致。对于SN2反应，通过QM/MM-DSF方法获得的活化自由能与QM/MM-埃瓦尔德方法和QM/MM-IPS结果都吻合得很好。然而，对于PMF的适当收敛，后者所需的截断距离比QM/MM-DSF更大。避免了耗时的晶格求和，与QM/MM-埃瓦尔德方法相比，QM/MM-DSF方法的计算成本降低了55%。这些结果表明，除了QM/MM-IPS之外，QM/MM-DSF方法在化学反应凝聚相模拟中处理静电作用时，可能是QM/MM-埃瓦尔德方法的另一种高效且准确的替代方法。
