Shell M Scott, Debenedetti Pablo G, Panagiotopoulos Athanassios Z
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 2):056703. doi: 10.1103/PhysRevE.66.056703. Epub 2002 Nov 22.
We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom-in which all potential energies, volumes, and numbers of particles are equally probable-we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.
我们给出了一种针对所谓“随机游走”算法非格点实现的严格推导，该算法是王和兰道最近提出的[《物理评论快报》86, 2050 (2001)]。该算法最初是为离散系统开发的，它使用蒙特卡罗移动根据态密度的倒数对构型进行采样；在每个模拟步骤中对态密度的估计都会得到改进，并最终用于计算热力学性质。我们基于对态密度的动力学贡献和构型贡献进行严格分离，给出了一种针对原子系统的实现方法。通过为构型自由度构建一个“均匀”系综——其中所有势能、体积和粒子数具有同等概率——我们建立了一个在连续介质情况下正确实施模拟接受标准和计算热力学平均值的框架。为了证明我们方法的通用性，我们使用两种实现变体对 Lennard-Jones 流体进行了示例计算，并且在两种情况下都发现与关于气液共存轨迹的已发表文献值有很好的一致性。
