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

用于计算统计机械簇积分的迈尔采样方法：纳米技术和其他应用

• 批准号: 0414439
• 负责人: David Kofke
• 金额: $ 30万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-04-15 至 2008-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0414439&HistoricalAwards=false
• 关键词: Mayer; sampling; Methods; Calculation; Statistical

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.

Kofke，David A. / SUNY Buffalo“用于计算统计机械簇积分的迈耶采样方法：纳米技术和其他应用。”智力价值。该项目旨在开发和应用流体统计力学理论中出现的簇积分计算方法。在一般方法中，对等于积分阶数的分子进行蒙特卡罗采样，并根据被积函数的绝对值对构型进行加权。集合平均值产生相对于已知积分的簇积分值。初步研究表明该技术对于簇积分计算非常有效。这种通用方法称为 Mayer 采样，其基本形式与用于凝聚相自由能计算的伞采样方法相似。这项工作的一些目标是建立在这一基本思想的基础上，并检查该方法和其他基于自由能的方法用于计算一般簇积分（特别是维里系数）的效率和有效性。一个考虑因素包括制定在并行计算架构上进行计算的策略，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，这项工作的目标还包括应用这些方法来理解和预测流体特性。这些方法用于计算一系列模型势及其混合物的维里系数，从而首次检查现实模型系统的高阶系数。这项活动的目的之一是了解如何通过维里方程使用这些少分子模拟来估​​计关键特性。另一个目标是发现可以增进对复杂现象的理解的特征，例如疏水性以及对纳米技术和环境应用很重要的其他行为。更广泛的影响。进行了几种特殊形式的传播，以确保其他人很容易采用这项工作。首先，开发分子模拟模块用于教学环境，例如本科课程。每个都包含一个简单的交互式、面向图形的模拟，该模拟执行此处开发的类型的特定计算，并辅以描述其用途的支持材料，所有这些都通过基于网络的界面呈现。其次，开发面向图形的软件应用程序并通过网络提供。该软件旨在允许用户使用项目中开发的方法计算簇积分，并且可扩展，以便用户可以将其应用于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。该站点的访问者可以指定集群集的功能，并且将以适合其使用的形式返回满足给定标准的所有集群的列表（数量只有几个，或者可能是数千个，具体取决于规范）或她自己的计算机代码；或者，可以以图形方式呈现簇以供指导或思考。高阶团簇积分常规计算方法的开发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，例如环境友好型材料和工艺的开发。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，因此它们正在被强力分子模拟所取代。将分子模拟方法融入到这些治疗中将赋予它们新的实用性，并更新它们的应用和发展。这些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。