Department of Chemistry (SGM418), University of Southern California, 3620 McClintock Avenue, Los Angeles, California 90089, United States.
J Phys Chem B. 2011 Jun 23;115(24):7950-62. doi: 10.1021/jp201217b. Epub 2011 May 27.
Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.
近年来，人们在开发方法方面付出了巨大努力，以期获得凝聚相反应的量子力学/分子力学（QM/MM）自由能。然而，仍然存在重大挑战需要解决，特别是在进行适当构象采样方面涉及的高计算成本，特别是在获得从头算 QM/MM（QM(ai)/MM）自由能表面方面。一种似乎在这方面提供理想进展方式的越来越流行的方法是优雅的元动力学（MTD）方法。然而，在当前工作中，我们指出了与该方法相关的微妙效率问题，并说明了我们手头有一种更强大的方法。更具体地说，我们展示了我们原始想法的更新版本的有效性，该想法使用经典参考势能进行 QM(ai)/MM 计算[J. Phys. Chem. 1995, 99, 17516]，我们称之为准动力学（PD）。这种方法基于使用经验价键（EVB）参考势能，该势能已经类似于真实的从头算势能。参考势能通过迭代和高度自动化的细化过程拟合到从头算势能。然后使用细化的 EVB 势构建相应的自由能曲线，并使用线性响应近似（LRA）评估 QM(ai)/MM 活化自由能势垒。EVB 表面的自动细化（从而减少参考和从头算势能之间的差异）是加速 LRA 方法收敛的关键因素。我们将我们的 PD 方法应用于一个测试反应，即氯离子和甲基氯之间的 S(N)2 反应，并证明，目前，这种方法比元动力学方法（至少在其当前实现中）更强大和更具成本效益。我们还讨论了 PD 方法在探索复杂系统方面的一般特征，并澄清它不是一种仅限于通过适当采样加速 QM(ai)/MM 计算的专门方法，而是可以在各种应用中使用。事实上，我们指出，使用参考（CG）势能并结合其 PD 细化以及我们的正则化方法，提供了非常通用和强大的策略，可以非常有效地用于探索已经通过 MTD 方法研究过的任何性质。
