Mayer-sampling Methods for Calculation of Statistical - Mechanical Cluster Integrals: Nanotechnology and Other Applications

Kofke，大卫A. / SUNY布法罗“统计机械簇积分计算的迈耶抽样方法：纳米技术和其他应用。“智力优势。本项目旨在开发和应用计算流体统计力学理论中出现的簇积分的方法。在一般的方法中，Monte Carlo抽样进行的分子数量等于积分的顺序，和配置加权根据被积函数的绝对值。相对于已知的积分，包络平均值产生簇积分的值。初步研究表明，该技术是非常有效的集群积分计算。这种一般的方法被称为迈耶采样，其基本形式与用于凝聚相自由能计算的伞形采样方法相似。这项工作的一些目标是建立在这个基本思想，并检查效率和有效性，这和其他自由能为基础的方法计算集群积分一般，维里系数特别。一个考虑因素包括制定在并行计算架构上进行计算的战略，而另一个考虑因素则涉及开发用于生成某些计算所需的许多集群的设施。 除了这些开发活动之外，这项工作还旨在应用这些方法来理解和预测流体性质。该方法被用来计算维里系数的范围内的模型潜力和它们的混合物，允许第一次检查的高阶系数为现实的模型系统。这项活动的目的之一是了解如何以及这些少分子模拟可以使用，通过维里方程，以估计关键属性。另一个目标是发现可以提高理解复杂现象的特征，例如疏水性，其他对纳米技术和环境应用很重要的行为。执行几种特殊的传播形式，以确保其他人随时采用这项工作。首先，分子模拟模块被开发用于教学环境，如本科课程。每个都包括一个简单的交互式，面向图形的模拟，执行这里开发的类型的特定计算，并补充了描述其使用的支持材料，所有这些都通过基于Web的界面呈现。其次，开发面向图形的软件应用程序并通过网络提供。该软件的目的是允许用户计算集群积分使用的方法正在开发的项目，是可扩展的，使用户可以将其应用到任何感兴趣的模型系统。最后，开发了一个专门用于描述和生成集群的网站。网站的访问者可以指定一个簇集的特征，并将返回一个符合给定标准的所有簇的列表（编号只有几个，或者可能是数千个，取决于规格），以适合他或她自己的计算机代码使用的形式;或者，簇可以以图形方式呈现，以供指导或思考。高阶团簇积分常规计算方法的发展将对化学物理和应用热力学产生非常大的影响。这反过来又会影响广泛的应用，例如开发环境友好的材料和工艺。几十年来发展起来的优雅而强大的理论由于无法计算其中出现的一些关键量而受到阻碍，因此它们正在被蛮力分子模拟所取代。将分子模拟方法引入这些治疗方法中，将使其具有新的实用性，并使其应用和发展得到更新。这样的努力可以激发许多进步，包括处理多尺度系统和纳米技术应用建模的新方法。

Kofke, David A. / SUNY Buffalo"Mayer-Sampling Methods For Calculation Of Statistical-Mechanical Cluster Integrals:Nanotechnology And Other Applications."Intellectual merit. This project aims to develop and apply methods for calculating cluster integrals that appear in statistical mechanical theories of fluids. In the general approach, Monte Carlo sampling is performed on a number of molecules equal to the order of the integral, and configurations are weighted according to the absolute value of the integrand. Ensemble averages yield the value of the cluster integral in reference to a known integral. Preliminary studies have shown the technique to be very effective for cluster-integral calculations. This general approach is called Mayer sampling, and in its basic form it has similarities to the umbrella-sampling method for free-energy calculation of condensed phases. Some of the objectives of this work are to build upon this basic idea, and examine the efficiency and effectiveness of this and other free-energy based methods for the calculation of cluster integrals in general, and virial coefficients in particular. One consideration includes formulation of strategies for conducting the calculations on parallel computing architectures, while another is concerned with developing facilities for generating the many clusters needed in some of the calculations. In addition to these development activities, the work also has objectives to apply the methods to understand and predict fluid properties. The methods are used to calculate virial coefficients for a range of model potentials and their mixtures, allowing for the first time examination of high-order coefficients for realistic model systems. One aim of this activity is to understand how well these few-molecule simulations can be used, via the virial equation, to estimate critical properties. Another aim is to uncover features that can improve understanding complex phenomena, such as hydrophobicity other behaviors important to nanotechnology and environmental applications.Broader impact. Several special forms of dissemination are performed to ensure that others readily adopt this work. First, molecular simulation modules are developed for use in instructional settings, such as undergraduate courses. Each includes a simple interactive, graphically-oriented simulation that performs a particular calculation of the type developed here, supplemented with supporting material describing its use, all presented via a web-based interface. Second, a graphically-oriented software application is developed and made available via the web. This software is designed to permit the user to calculate cluster integrals using the methods being developed in the project, and is extensible so that the user can apply it to any model system of interest. Finally, a web site devoted to the description and generation of clusters is developed. A visitor to the site can specify features of a cluster set, and will have returned a listing of all clusters (numbering just a few, or perhaps thousands, depending on the specification) meeting the given criteria, in a form suitable for use by his or her own computer codes; alternatively the clusters can be presented pictorially for instruction or contemplation. Development of methods for routine calculation of high-order cluster integrals would have a very large impact on chemical physics and applied thermodynamics. This in turn can impact a broad range of applications, such as the development of environmentally benign materials and processes. Elegant and powerful theories developed over many decades have been hindered by an inability to calculate some of the key quantities appearing in them, and consequently they are being supplanted by brute-force molecular simulation. The infusion of molecular simulation methods into these treatments will imbue them a new practicality, and renew their application and development. Such efforts could inspire many advances, including new ways for handling multiscale systems and modeling for nanotechnological applications.