Marsalek Ondrej, Chen Pei-Yang, Dupuis Romain, Benoit Magali, Méheut Merlin, Bačić Zlatko, Tuckerman Mark E
Department of Chemistry, New York University , New York, New York 10003, United States.
Géosciences Environnement Toulouse, OMP-Université Paul Sabatier , 14 avenue Edouard Belin, 31400 Toulouse, France.
J Chem Theory Comput. 2014 Apr 8;10(4):1440-53. doi: 10.1021/ct400911m. Epub 2014 Mar 5.
The problem of computing free energy differences due to isotopic substitution in chemical systems is discussed. The shift in the equilibrium properties of a system upon isotopic substitution is a purely quantum mechanical effect that can be quantified using the Feynman path integral approach. In this paper, we explore two developments that lead to a highly efficient path integral scheme. First, we employ a mass switching function inspired by the work of Ceriotti and Markland [ J. Chem. Phys. 2013, 138, 014112] that is based on the inverse square root of the mass and which leads to a perfectly constant free energy derivative with respect to the switching parameter in the harmonic limit. We show that even for anharmonic systems, this scheme allows a single-point thermodynamic integration approach to be used in the construction of free energy differences. In order to improve the efficiency of the calculations even further, however, we derive a set of free energy derivative estimators based on the fourth-order scheme of Takahashi and Imada [ J. Phys. Soc. Jpn. 1984, 53, 3765]. The Takahashi-Imada procedure generates a primitive fourth-order estimator that allows the number of imaginary time slices in the path-integral approach to be reduced substantially. However, as with all primitive estimators, its convergence is plagued by numerical noise. In order to alleviate this problem, we derive a fourth-order virial estimator based on a transferring of the difference between second- and fourth-order primitive estimators, which remains relatively constant as a function of the number of configuration samples, to the second-order virial estimator. We show that this new estimator converges as smoothly as the second-order virial estimator but requires significantly fewer imaginary time points.
讨论了化学系统中由于同位素取代而计算自由能差的问题。同位素取代时系统平衡性质的变化是一种纯粹的量子力学效应，可以使用费曼路径积分方法进行量化。在本文中，我们探索了两种发展，它们导致了一种高效的路径积分方案。首先，我们采用了一种受Ceriotti和Markland [《化学物理杂志》2013年，138卷，014112]工作启发的质量切换函数，该函数基于质量的平方根倒数，并且在谐波极限下相对于切换参数导致完全恒定的自由能导数。我们表明，即使对于非谐波系统，该方案也允许在构建自由能差时使用单点热力学积分方法。然而，为了进一步提高计算效率，我们基于高桥和今田[《日本物理学会杂志》1984年，53卷，3765]的四阶方案推导了一组自由能导数估计器。高桥 - 今田方法生成了一个原始的四阶估计器，它允许在路径积分方法中大幅减少虚时间切片的数量。然而，与所有原始估计器一样，其收敛受到数值噪声的困扰。为了缓解这个问题，我们基于将二阶和四阶原始估计器之间的差异（作为配置样本数量的函数相对保持恒定）转移到二阶维里估计器，推导了一个四阶维里估计器。我们表明，这个新估计器的收敛与二阶维里估计器一样平滑，但需要的虚时间点明显更少。
