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Development and implementation of atomic/molecular simulation methods based on nested sampling.

机译：基于嵌套采样的原子/分子模拟方法的开发与实现。

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摘要

Atomic/molecular simulation continues to grow as a supplement to, and in some cases a replacement for, experimental studies. As such, there is an increasing need to develop new simulation methods that can overcome the deficiencies of existing methods, including an ever increasing demand for more robust and efficient simulation methods.;This dissertation focuses on developing and implementing new atomic/molecular simulation methods based on the Nested Sampling framework. The methods based on Nested Sampling perform well in the vicinity of phase transitions, and in many cases can outperform existing methods in both efficiency and robustness.;We begin by developing an isobaric Nested Sampling scheme. This athermal scheme makes a single top down sweep of the isobaric phase space, from which the isothermal-isobaric partition function can be computed for essentially any temperature. We show that the method effectively handles isobaric phase transitions and is more efficient than parallel tempering for the test cases examined. We then continue to explore the use of the Nested Sampling framework for free energy calculations. The Nested Sampling Monte Carlo method we have developed can be used to compute the relative free energy between systems governed by different Hamiltonian functions. We show that the method outperforms Widom's test particle insertion method at high density, while avoiding problems of the end point catastrophe on the reference side. We also show that this method effectively handles phase transitions, and can used to compute system properties as a function of a Hamiltonian-scaling factor. Lastly, we explore a Nested Sampling Monte Carlo framework for grand canonical ensemble calculations. We develop the theory for an athermal and a thermal approach. The athermal approach is similar to the isobaric Nested Sampling scheme, and can be used to compute the Grand Canonical partition function. However, we show that the athermal approach is theoretically flawed. Initial test cases demonstrate that the error may be small, and suggest that additional modifications may restore the validity of the approach. The thermal approach to Nested Sampling in the grand canonical case is based on our relative free energy Nested Sampling scheme, and could be used to compute the relative grand canonical free energy. The thermal approach could also be used to compute system properties as a function of chemical potential. Although we believe this approach is theoretically sound, we have yet to test the approach, and we suspect there may be some practical issues surrounding the sampling.
机译：原子/分子模拟继续发展，作为对实验研究的补充，在某些情况下替代了实验研究。因此，迫切需要开发新的模拟方法来克服现有方法的不足，包括对更健壮和有效的模拟方法的不断增长的需求。本论文着重于开发和实现基于原子/分子模拟的新方法。在嵌套采样框架上。基于嵌套采样的方法在相变附近表现良好，并且在许多情况下都可以在效率和鲁棒性方面优于现有方法。我们首先开发了一种等压嵌套采样方案。这种无热方案对等压相空间进行了一次自上而下的扫描，从中可以基本上针对任何温度计算出等温-等压分配函数。我们表明，该方法可以有效地处理等压相变，并且比平行回火对测试案例的效率更高。然后，我们继续探索使用嵌套抽样框架进行自由能计算。我们开发的嵌套采样蒙特卡洛方法可用于计算受不同哈密顿函数控制的系统之间的相对自由能。我们证明了该方法在高密度下优于Widom的测试粒子插入方法，同时避免了参考侧端点灾难的问题。我们还表明，该方法可以有效地处理相变，并且可以根据汉密尔顿比例因子来计算系统属性。最后，我们探索了嵌套抽样蒙特卡洛框架，用于大正则合奏计算。我们开发了一种无热和热方法的理论。无热方法类似于等压嵌套采样方案，可用于计算Grand Canonical分区函数。但是，我们证明了无热方法在理论上是有缺陷的。最初的测试案例表明该错误可能很小，并建议进行其他修改可以恢复该方法的有效性。大正则情况下的嵌套采样的热方法基于我们的相对自由能嵌套采样方案，可用于计算相对大正则自由能。热学方法也可以用于计算系统性质与化学势的函数。尽管我们认为该方法在理论上是正确的，但我们尚未对该方法进行测试，并且我们怀疑抽样可能存在一些实际问题。

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  • 作者

    Wilson, Blake A.;

  • 作者单位

    The University of Texas at Dallas.;

  • 授予单位 The University of Texas at Dallas.;
  • 学科 Physical chemistry.;Statistics.;Molecular physics.
  • 学位 Ph.D.
  • 年度 2016
  • 页码 108 p.
  • 总页数 108
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 康复医学;
  • 关键词

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