Department of Chemistry and NANOLab Center of Excellence, University of Antwerp, Universiteitsplein 1, 2610 Antwerp, Belgium.
Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
J Chem Phys. 2020 Sep 21;153(11):114118. doi: 10.1063/5.0020240.
Atomistic simulation methods for the quantification of free energies are in wide use. These methods operate by sampling the probability density of a system along a small set of suitable collective variables (CVs), which is, in turn, expressed in the form of a free energy surface (FES). This definition of the FES can capture the relative stability of metastable states but not that of the transition state because the barrier height is not invariant to the choice of CVs. Free energy barriers therefore cannot be consistently computed from the FES. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Using our procedure, the standard FES as well as its gauge-corrected counterpart can be obtained by reweighing the same simulated trajectory at little additional cost. We apply the method to a number of systems-a particle solvated in a Lennard-Jones fluid, a Diels-Alder reaction, and crystallization of liquid sodium-to demonstrate its ability to produce consistent free energy barriers that correctly capture the kinetics of chemical or physical transformations, and discuss the additional demands it puts on the chosen CVs. Because the FES can be converged at relatively short (sub-ns) time scales, a free energy-based description of reaction kinetics is a particularly attractive option to study chemical processes at more expensive quantum mechanical levels of theory.
用于量化自由能的原子模拟方法得到了广泛应用。这些方法通过沿少量合适的集体变量 (CVs) 对系统的概率密度进行采样来操作，集体变量反过来又以自由能面 (FES) 的形式表示。这种 FES 的定义可以捕捉亚稳态的相对稳定性，但不能捕捉过渡态的稳定性，因为自由能面的高度对 CVs 的选择不具有不变性。因此，不能从 FES 一致地计算自由能势垒。在这里，我们提出了一种简单的方法来计算消除这种不一致性所需的量测修正。使用我们的程序，可以通过在几乎没有额外成本的情况下重新加权相同的模拟轨迹来获得标准 FES 及其量测修正对应物。我们将该方法应用于许多系统——溶解在 Lennard-Jones 流体中的粒子、Diels-Alder 反应和液态钠的结晶——以证明其能够产生一致的自由能势垒，正确捕捉化学或物理转化的动力学，并讨论它对所选 CVs 的额外要求。由于 FES 可以在相对较短的（亚纳秒）时间尺度上收敛，因此基于自由能的反应动力学描述是在更昂贵的量子力学理论水平上研究化学过程的一个特别有吸引力的选择。
