Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
J Chem Phys. 2010 Jun 7;132(21):214103. doi: 10.1063/1.3432255.
We examine the ability of two-stage free-energy perturbation methods to yield solid-phase free energies using a system of harmonically coupled particles as a reference. We consider two ways to construct a reference system, one based on derivatives of the intermolecular potential of the target system of interest (the conventional choice in lattice dynamics), and the other based on analysis of pairwise configurational correlations observed in simulations of the target system. For each case, we consider two perturbation techniques that compute the free energy difference between the target and reference systems while avoiding lengthy thermodynamic integration procedures. The methods are overlap sampling as optimized by Bennett, and umbrella sampling optimized in a similar fashion. Such methods require at most two simulations to yield a result, but they can fail if the target and reference do not share a sufficiently large set of relevant configurations. In particular, failure can be expected for large systems, and we examine the question of how large a system can be before this point is reached. Our test case is a face-centered cubic system of r(-12) soft spheres, and we find that for systems of up to 108 particles the methods are accurate for all temperatures up to melting; for systems of 256 particles the methods begin to break down at about half the melting temperature. Significantly, we observe that the correction to the harmonic reference is only weakly dependent on system size, suggesting an N-hybrid technique in which perturbation is applied to a small system and the result added to a large-system harmonic reference to obtain a good estimate of the correct large-system free energy. We also examine these approaches, along with thermodynamic integration in temperature, with respect to their computational efficiency. We find that Bennett's method using a derivative-based harmonic reference is the most efficient of all those examined, particularly when employed in the N-hybrid method.
我们以一个由谐和粒子组成的体系为参考，检验两阶段自由能微扰方法生成固相自由能的能力。我们考虑了两种构建参考体系的方法，一种基于目标体系分子间势能的导数（晶格动力学中的常规选择），另一种基于目标体系模拟中观察到的两两构型相关性的分析。对于每种情况，我们考虑了两种微扰技术，它们在避免冗长的热力学积分程序的情况下计算目标和参考体系之间的自由能差。这些方法是由 Bennett 优化的重叠采样和以类似方式优化的伞状采样。这些方法最多需要两次模拟即可得出结果，但如果目标和参考体系没有足够多的相关构型，它们可能会失败。特别是对于大型系统，我们会考察达到这一点之前可以处理的系统规模。我们的测试案例是面心立方(r(-12))软球体系，我们发现对于最多 108 个粒子的体系，这些方法在所有温度下直至熔化都是准确的；对于 256 个粒子的体系，这些方法在大约一半的熔化温度时开始失效。重要的是，我们观察到对谐和参考的修正仅与体系大小弱相关，这表明可以采用 N-混合技术，其中微扰应用于小体系，并将结果添加到大体系谐和参考中，以获得正确的大体系自由能的良好估计。我们还考察了这些方法，以及与温度相关的热力学积分，考察它们的计算效率。我们发现，基于导数的谐和参考的 Bennett 方法是所有考察方法中效率最高的，特别是在 N-混合方法中使用时。
