标题： 一种用于最小化伦纳德-琼斯能量的变分方法 显示英文标题

标题： A Variational Approach for Minimizing Lennard-Jones Energies

摘要： 一种用于计算具有单体-单体相互作用的Lennard-Jones势的分子构象性质的变分方法被提出。 该方法专门用于处理角度自由度，{\it 转子}，其包括在温度退火的情况下迭代求解一组确定性方程。 为了获得稳定的收敛性，Lennard-Jones势的短距离奇异行为是绝热开启的。 作为该方法的测试平台，使用了两种不同的分子系综，它们分别由大致密集堆积或更伸长的基态特征。 对于后者，问题是从氨基酸的自然出现频率和现象学确定的势参数生成的；它们似乎比以前在合成蛋白质研究中假设的无序程度要低。 特别是对于密集堆积的问题，变分算法在最小能量方面明显优于梯度下降方法。 尽管它无法与仔细的模拟退火算法竞争，但变分方法只需要极小的计算机时间。 当在有限温度下将该方法应用于聚电解质时的问题和结果也进行了简要讨论。 显示英文摘要

摘要： A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and consists in the iterative solution of a set of deterministic equations with annealing in temperature. The singular short-distance behaviour of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed ore a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.