Laboratoire Francis Perrin, CNRS-URA 2453, CEA, IRAMIS, Service des Photons Atomes et Molécules, F-91191 Gif-sur-Yvette Cedex, France.
J Chem Phys. 2011 Oct 14;135(14):144109. doi: 10.1063/1.3647333.
A novel Monte Carlo flat histogram algorithm is proposed to get the classical density of states in terms of the potential energy, g(E(p)), for systems with continuous variables such as atomic clusters. It aims at avoiding the long iterative process of the Wang-Landau method and controlling carefully the convergence, but keeping the ability to overcome energy barriers. Our algorithm is based on a preliminary mapping in a series of points (called a σ-mapping), obtained by a two-parameter local probing of g(E(p)), and it converges in only two subsequent reweighting iterations on large intervals. The method is illustrated on the model system of a 432 atom cluster bound by a Rydberg type potential. Convergence properties are first examined in detail, particularly in the phase transition zone. We get g(E(p)) varying by a factor 10(3700) over the energy range [0.01 < E(p) < 6000 eV], covered by only eight overlapping intervals. Canonical quantities are derived, such as the internal energy U(T) and the heat capacity C(V)(T). This reveals the solid to liquid phase transition, lying in our conditions at the triple point. This phase transition is further studied by computing a Lindemann-Berry index, the atomic cluster density n(r), and the pressure, demonstrating the progressive surface melting at this triple point. Some limited results are also given for 1224 and 4044 atom clusters.
提出了一种新的蒙特卡罗平坦直方图算法，以获得具有连续变量（如原子团簇）的系统的经典势能态密度 g(E(p))。它旨在避免 Wang-Landau 方法的冗长迭代过程，并仔细控制收敛，但保持克服能量障碍的能力。我们的算法基于 g(E(p)) 的双参数局部探测得到的一系列点（称为 σ 映射）的初步映射，并且仅在两个后续的重新加权迭代中在大间隔上收敛。该方法在由类里德堡型势束缚的 432 原子团簇模型系统上进行了说明。首先详细检查了收敛特性，特别是在相变区。我们在 [0.01 < E(p) < 6000 eV] 的能量范围内获得了 g(E(p)) 的变化，变化幅度为 10(3700)，仅使用了八个重叠间隔。得出了一些正则量，如内能 U(T)和热容 C(V)(T)。这揭示了我们条件下的固-液相变，位于三相点。通过计算 Lindemann-Berry 指数、原子团簇密度 n(r)和压力，进一步研究了这个相变，证明了三相点处的表面逐渐熔化。还给出了 1224 和 4044 原子团簇的一些有限结果。
