Collaborative Research: CMG: Quantum Monte Carlo Calculations of Deep Earth Materials

合作研究：CMG：地球深部材料的量子蒙特卡罗计算

• 批准号: 0703226
• 负责人: Richard Hennig
• 金额: $ 13.48万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-17 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0703226&HistoricalAwards=false
• 关键词: Collaborative; Research; CMG; Quantum; Monte

New mathematical methods in quantum Monte Carlo (QMC) simulation will be applied and developed to obtain more accurate properties of Earth materials than is possible using current electronic structure methods. QMC is one among the most precise known techniques to study realistic materials in physics and chemistry and provide a significant gain in precision compared traditional density functional theory (DFT) approaches. This will bring electronic structure quantum Monte Carlo methodology to a qualitatively higher level of applicability to complex materials and lead to increased accuracy. The new QMC techniques will be applied to forefront problems in the properties of Earth materials in order to obtain accurate equations of state, phase transitions, and elasticity of solid materials that are of high interest in geophysics. One significant limitation of today's QMC methods is the high computational demand, which currently makes applications to larger systems including solid solutions prohibitively expensive. A substantial portion of the QMC computation is spent on forming and evaluating a Slater determinant, which is constructed from one-particle orbitals. The team plans to develop and apply different localization transformations in order to obtain a sparse determinant. Two linear algebra methods will be developed for their efficient evaluation. First, Krylov's method for the iterative evaluation of a determinant will be incorporated into QMC. Secondly, the trace of the determinant will be calculated with Monte Carlo methods. Both techniques will further the goal of obtaining an order-N QMC techniques that are more efficient and applicable to a wider range of materials, well beyond the current possibilities.Computational mineral physics is part of the large effort to use computer simulations to predict and understand properties of the Earth. New mathematical techniques will be derived to make advance quantum Monte Carlo simulations more precise and significantly more efficient. The properties of important Earth materials at high pressure will be predicted with unprecedented accuracy. This work will also lead to a more precise description of a number of fundamental phase transitions in solid deep Earth. This project is a close collaboration between a mathematician, mathematical physicists, and geophysicists. It will bring new applied math methods into geoscience, with broad applicability to all Earth materials. The broader impact will include the development of new computational techniques applicable to many areas as well as the education of graduate students and post-docs in state-of-the-art materials simulations, teaching of new computational techniques in graduate level classes and during two workshops that will be organized.

量子蒙特卡罗（QMC）模拟中的新数学方法将被应用和开发，以获得比使用当前电子结构方法更准确的地球材料特性。QMC是研究物理和化学中现实材料的最精确的已知技术之一，与传统的密度泛函理论（DFT）方法相比，它在精度上有显著的提高。这将使电子结构量子蒙特卡罗方法对复杂材料的适用性达到更高的质量水平，并提高准确性。新的QMC技术将应用于地球材料性质的前沿问题，以获得精确的状态方程，相变和固体材料的弹性，这是地球物理学的高度兴趣。当今的QMC方法的一个显著限制是高计算需求，这使得目前应用于包括固溶体的较大系统的成本过高。QMC计算的很大一部分花费在形成和评估斯莱特行列式上，该行列式是由单粒子轨道构造的。该团队计划开发和应用不同的本地化变换，以获得稀疏行列式。两个线性代数方法将开发其有效的评估。首先，Krylov的方法迭代评估的行列式将被纳入QMC。其次，用蒙特卡罗方法计算行列式的迹。这两种技术都将进一步实现获得N阶QMC技术的目标，这些技术更有效，适用于更广泛的材料，远远超出了目前的可能性。计算矿物物理学是使用计算机模拟来预测和理解地球性质的巨大努力的一部分。新的数学技术将使先进的量子蒙特卡罗模拟更精确，更有效。重要地球物质在高压下的性质将以前所未有的准确性得到预测。这项工作还将导致更精确地描述固体深层地球中的一些基本相变。这个项目是数学家、数学物理学家和数学家之间的密切合作。它将为地球科学带来新的应用数学方法，广泛适用于所有地球材料。更广泛的影响将包括适用于许多领域的新计算技术的开发，以及研究生和博士后在最先进的材料模拟方面的教育，在研究生水平课程中以及将组织的两个研讨会期间教授新的计算技术。