重要性采样方法与自由能计算

Importance Sampling Methods and Free Energy Calculations

分子动力学模拟与自由能计算已经在化学、生物学与材料学等领域得到广泛的应用。然而,由于在传统分子动力学模拟的时间尺度内,体系很难跨越较高的自由能能垒,在相空间内的采样大大受限,采样困难使自由能计算难以收敛。增强采样是解决这一问题的有效途径,重要性采样方法就是其中一类。本文综述了四种广泛应用的重要性采样方法——伞状采样方法、metadynamics方法、自适应偏置力方法和温度加速分子动力学方法的原理和进展,其中重点概述了自适应偏置力方法的最新发展——扩展自适应偏置力方法和扩展广义自适应偏置力方法,并对这四种重要性采样方法的优缺点进行了比较。最后,讨论和展望了重要性采样与自由能计算方法面临的挑战和前景,并提出了对自适应偏置力方法可能的改进,如与加速分子动力学(aMD)或弦方法结合以提高在高维度空间中的采样效率。

Molecular dynamics（ MD） simulations with free energy calculations have been widely applied to chemistry,biology and material science. However,within the timescale of conventional MD simulations,ergodic sampling in phase space is limited due to high free-energy barriers. Insufficient sampling may,in turn,lead to poor convergence of the free energy calculations based on conventional MD simulations. Enhanced sampling is a powerful technique to overcome this difficulty,among which importance sampling method is the most representative one. In this paper,the principles and progress of four prevalent importance sampling methods, namely, umbrella sampling（ US）, metadynamics（ MtD）, adaptive biasing force（ ABF） and temperature accelerated molecular dynamics（ TAMD）,are described and reviewed. In particular,the recent developments of ABF,such as the extended ABF（ eABF） considered as the second generation of ABF,and the extended generalized ABF（ egABF） methods designed for high dimensional sampling,are comprehensively summarized. The advantages and disadvantages of US,MtD,TAMD and ABF with their variants are presented and compared. Furthermore,challenges and outlooks for free energy calculation with importance sampling methods are discussed and prospected. Specifically,possible further improvements to current ABF methods,such as combination with accelerated molecular dynamics（ aMD） simulations or string methods to enhance sampling efficiency in high-dimensional spaces are put forward.