Barnes C Daniel, Kofke David A
Department of Chemical Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260-4200, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2B):036709. doi: 10.1103/PhysRevE.65.036709. Epub 2002 Mar 6.
We propose a Monte Carlo simulation method for the evaluation of free energies in crystalline systems. In principle, the method involves evaluating the free-energy difference between systems of N molecules and 2N molecules. This difference, coupled with the assumption that the free energy is extensive and thus proportional to N, provides sufficient information to obtain the absolute free energy of the crystal. The approach to doubling the system size does not involve insertion or removal of molecules in the system. Instead, the configurations of the molecules are expressed in terms of the normal-mode coordinates of a harmonic lattice. By decoupling certain of these coordinates from the molecule configurations, we obtain a transformation that in effect yields the system-size doubling. The method is examined via application to a system of hard rods in one dimension. This simple model is considered principally because of the availability of an analytic solution for its free energy, which permits accurate testing of the performance and correctness of the proposed method. In using the hard-rod model we also avoid other complications related to treatment of the temperature, and application of normal-mode coordinate decoupling in higher dimensions. The proposed method is shown to be able to provide good results for the free-energy calculation, but further development will be needed before it can be considered practical for general-purpose use.
我们提出了一种用于评估晶体系统中自由能的蒙特卡罗模拟方法。原则上，该方法涉及评估(N)个分子的系统与(2N)个分子的系统之间的自由能差。这种差异，再加上自由能是广延量且因此与(N)成正比的假设，提供了足够的信息来获得晶体的绝对自由能。将系统大小加倍的方法不涉及在系统中插入或移除分子。相反，分子的构型用简谐振子晶格的正则模坐标来表示。通过将这些坐标中的某些坐标与分子构型解耦，我们得到了一种变换，实际上实现了系统大小的加倍。通过将该方法应用于一维硬棒系统来进行检验。考虑这个简单模型主要是因为其自由能有解析解，这使得能够准确测试所提出方法的性能和正确性。在使用硬棒模型时，我们还避免了与温度处理以及在更高维度应用正则模坐标解耦相关的其他复杂问题。结果表明，所提出的方法能够为自由能计算提供良好的结果，但在被认为可实际用于通用目的之前，还需要进一步发展。
