Department of Chemistry, Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan.
J Chem Phys. 2019 Mar 21;150(11):114109. doi: 10.1063/1.5089199.
In an extended QM/MM (quantum mechanical/molecular mechanical) description of a solution, the solvent molecules surrounding the solute are incorporated into the QM region besides the solute. In a recent development, we introduced a simple and efficient method, referred to as boundary constraint with correction (BCC), to prevent the diffusion of the QM solvent into the bulk. The major purpose of the present work is to develop a method to compute the solvation free energy of a QM solute in an extended QM/MM simulation by means of the BCC method. The strategy of our development is to utilize the QM/MM-ER method which combines the QM/MM simulation and the theory of solutions termed energy representation (ER) to expedite the free energy calculation. A theory is, then, formulated to couple QM/MM-ER and the BCC method on the basis of the statistical mechanics. A notable feature of our method is that the effect of the constraint potentials on the free energy completely vanishes when the force field of the QM solvent coincides with that of the MM solvent. The method is applied to the calculations of the solvation free energies of a water molecule and a hydronium ion in water solutions. It turns out that the present method can offer a significant improvement in describing the free energy Δν of the hydronium ion, in particular, as compared with the conventional QM/MM approach. Explicitly, Δν is obtained as -98.0 kcal/mol showing a good agreement with an experimental value of -103.5 kcal/mol, while -86.1 kcal/mol by the conventional method.
在溶液的扩展 QM/MM（量子力学/分子力学）描述中，除溶质外，溶剂分子也被包含在 QM 区域中。在最近的一项发展中，我们引入了一种简单有效的方法，称为带修正的边界约束（BCC），以防止 QM 溶剂扩散到本体中。本工作的主要目的是开发一种方法，通过 BCC 方法计算扩展 QM/MM 模拟中 QM 溶质的溶剂化自由能。我们的开发策略是利用 QM/MM-ER 方法，该方法结合了 QM/MM 模拟和称为能量表示（ER）的溶液理论，以加快自由能计算。然后，基于统计力学，我们制定了一种理论，将 QM/MM-ER 和 BCC 方法耦合起来。我们方法的一个显著特点是，当 QM 溶剂的力场与 MM 溶剂的力场相同时，约束势对自由能的影响完全消失。该方法应用于水分子和水合氢离子在水溶液中的溶剂化自由能计算。结果表明，与传统的 QM/MM 方法相比，本方法在描述水合氢离子的自由能Δν方面可以显著提高。具体来说，得到的Δν为-98.0 kcal/mol，与实验值-103.5 kcal/mol非常吻合，而传统方法得到的Δν为-86.1 kcal/mol。
