Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: application to liquid argon and water.
Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: application to liquid argon and water.
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DOI：
10.1063/1.1814355
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发表时间：
2004-11
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通讯作者：
Ronald P White;H. Meirovitch
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文献类型：
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作者：
Ronald P White;H. Meirovitch
假设扫描(HS)方法是通过分析蒙特卡罗或分子动力学技术获得的玻尔兹曼样品来计算绝对熵、S和自由能F的一般方法。将HS应用于流体，通过使用转移概率(TPS)逐渐将分子放置在它们在I处的位置来重建样品的每个构型I。在这个过程的每一步，系统被分成两个部分，已经处理的分子(“过去”)，它们是固定的，以及尚未确定的(移动的)“未来”分子。准确地获得Tp需要在冻结的过去存在的情况下计算未来分子的所有位置上的配分函数，因此习惯上调用各种近似来最好地表示这些量。在最近的一份出版物中[Proc.娜塔莉。阿卡德。SCI。美国101,9235(2004)]我们开发了一个称为完全HSMC的HS版本，其中每个TP都是通过涉及所有未来分子(完全未来)的MC模拟来计算的；该方法非常成功地应用于Lennard-Jones体系(液体Ar)和一盒TIP3P水分子。在其基本实现中，该方法提供了F的下界和上界，其中后者只能对相对较小的系统进行评估。在这里，我们引入了一个新的上界表达式，它可以用于更大的系统。我们还提出了F的一个新的精确表达式，并验证了它的有效性。这些自由能泛函大大提高了精确度(应用于上述液体系统)，这与我们的热力学积分结果相当。我们形式化并讨论了HSMC的理论方面，这些方面在以前的研究中没有得到解决。此外，还开发了几个泛函，并通过对单一构型的分析，证明了它们提供了自由能。
The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy S and free energy F by analyzing Boltzmann samples obtained by Monte Carlo or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). At each step of the process the system is divided into two parts, the already treated molecules (the "past"), which are fixed, and the as yet unspecified (mobile) "future" molecules. Obtaining the TP exactly requires calculating partition functions over all positions of the future molecules in the presence of the frozen past, thus it is customary to invoke various approximations to best represent these quantities. In a recent publication [Proc. Natl. Acad. Sci. USA 101, 9235 (2004)] we developed a version of HS called complete HSMC, where each TP is calculated from an MC simulation involving all of the future molecules (the complete future); the method was applied very successfully to Lennard-Jones systems (liquid argon) and a box of TIP3P water molecules. In its basic implementation the method provides lower and upper bounds for F, where the latter can be evaluated only for relatively small systems. Here we introduce a new expression for an upper bound, which can be evaluated for larger systems. We also propose a new exact expression for F and verify its effectiveness. These free energy functionals lead to significantly improved accuracy (as applied to the liquid systems above) which is comparable to our thermodynamic integration results. We formalize and discuss theoretical aspects of HSMC that have not been addressed in previous studies. Additionally, several functionals are developed and shown to provide the free energy through the analysis of a single configuration.