Computational Methods for Electronic Structure

本研究的长期目标是发展理论和计算方法来准确预测多电子系统的性质，然后将这些方法应用于重要的凝聚态物质系统。本研究的重点主要是量子蒙特卡罗（QMC）方法的发展和应用。然而，部分研究试图将这些方法与其他理论问题联系起来，例如金属和绝缘体之间在多体电子波函数方面的根本区别。QMC可以为电子系统提供非常准确的结果：最着名的例子是均匀电子气，其中QMC提供了基于大多数密度泛函（DFT）计算的基准。基于DFT的方法是目前唯一可行的方法，用于精确的大规模模拟现实系统，然而，即使是改进的泛函有众所周知的缺陷。在过去的几年里，在有限温度下的离子模拟与电子的QMC模拟（CEIMC方法）的耦合方面取得了实质性的进展。除了更准确之外，在必须执行其他平均的情况下，QMC方法可以与基于DFT的方法一样有效。目前，氢在扩展系统中的应用正在生产中。在不久的将来，QMC方法将得到发展，重点是更精确的波函数，改进的边界条件，以及能够有效地使用更大计算设备的新方法。这项研究将使具有核心电子的元素的应用能够使用更精确的赝势。计算电子力的方法将使离子系统的动力学计算成为可能。该方法的应用将包括氢的整个过程。温度和压力的全相图。虽然有许多以前的QMC和DFT模拟，CEIMC方法消除了他们的大部分限制。在目前的研究中，绝缘体-金属相变、原子-分子相变以及温度和零点效应之间的联系仍然是缺乏的，特别是在实验不存在或不可靠的情况下，模拟应该澄清这种情况。另一个挑战是从第一原理出发对水进行微观模拟，这是许多科学问题的基础，似乎也是QMC模拟所能达到的。这种方法的力量可以应用于其他问题，例如，模拟真实的纳米结构器件中电子及其自旋状态的新方法，可能比现有的基于网格的方法更准确和更有效。整个器件可以通过耦合两个随机步来模拟--一个是求解复杂结构中的静电方程，另一个是求解电子的Nbody量子方程.模拟物质基本方程的计算复杂性（在经典而非量子计算机上）是一个非常重要和基本的问题。挑战在于精确地解决许多相互作用粒子的问题，包括强相互作用系统和协同现象。QMC方法使得计算玻色系统的热力学性质，包括超流性成为可能。然而，费米子符号问题是限制目前工作的一个关键问题，并且解决或最小化符号问题的步骤是计算科学中的突出挑战之一。此外，新的计算方法的发展经常导致新的理论理解以及在其他学科中有用的算法。这些计算量子方法的发展将对许多科学领域的课程产生质的影响，包括物理学，材料科学，化学甚至生物学，通过使更准确，更快，这些计算将解决有关氢在高温高压下的性质的问题，这是木星行星形成模型的基础;水和溶液的微观性质;以及纳米系统的性质。这项研究主要是由研究生和博士后进行的，他们往往后来进入工业界，从而转移了最新的计算方法。作为研究结果开发的计算机和软件将通过材料计算中心提供给一般的研究社区，并用于伊利诺伊大学和其他地方的本科课程，研究生课程和暑期学校。

The long-range goal of this research is to develop theoretical and computational methods to predict accuratelythe properties of many-electron systems and then to apply the methods to important condensed mattersystems. The focus of this research is primarily on the development and application of quantumMonte Carlo (QMC) methods. However, part of the research attempts to tie these approaches to othertheoretical issues such as the fundamental distinction between metals and insulators in terms of the manybodyelectron wave function.QMC can provide very accurate results for electronic systems: the most well-known example is the homogenous electron gas where QMC has provided the benchmark upon which are based most density functional (DFT) calculations. DFT-based methods are the only current method feasible for accurate large-scale simulations of realistic systems; however, even the improved functionals have well-known defects. The past few years have seen substantial progress in coupling the simulation of ions at a finite temperature with QMC simulation of the electrons (the CEIMC method). In addition to being more accurate, in cases where other averaging must be performed, the QMC approach can be as efficient as DFT-based approaches. Applications to extended systems of hydrogen are now in production. In the near futurethere will be development of QMC methods, with emphasis upon more accurate wave functions, improvedboundary conditions, and new methods able to use much larger computational facilities efficiently.The research will enable applications to elements with core electrons using more accurate pseudopotentials.Methods to calculate electronic forces will enable dynamical calculations of ionic systems.Applications of the methods will include hydrogen throughout the whole phase diagram of temperatureand pressure. Although there have been numerous previous QMC and DFT simulations, the CEIMCmethod removes most of their limitations. The connection between the insulator-metallic transition, theatomic molecular-transition and temperature and zero point effects is still lacking in current approaches.The simulations should clarify the situation, especially under conditions where experiment is non-existentor unreliable. A further challenge is the microscopic simulation of water from first principles, which isabsolutely fundamental to many scientific questions and which appears to be within reach of QMC simulation.The power of this approach can be applied to other problems, for example, new methods to simulateelectrons and their spin states in real nanostructure devices, potentially more accurately and efficientlythan with existing grid-based approaches. The entire device can be simulated by coupling tworandom walks-one to solve the electrostatic equations in a complicated structure and another for the Nbodyquantum equation for the electrons.The computational complexity of the simulation of the basic equations of matter (onclassical not quantum computers) is a very important and fundamental issue. The challenge is to solveaccurately problems with many interacting particles, including strongly interacting systems and cooperativephenomena. QMC methods have made it possible to compute the thermodynamic properties of bosonicsystems, including superfuidity. However, the fermion sign problem is a critical issue limitingpresent work, and steps toward solving or minimizing the sign problem are among the outstanding challengesin computational science. In addition, development of new computational approaches frequentlyleads to new theoretical understanding as well as algorithms useful in other disciplines.The development of these computational quantum methods will have a qualitative impactupon the course of many fields of science including physics, materials science, chemistry and evenbiology, by enabling much more accurate, and potentially faster, simulation of a broad range of systems.The calculations will resolve questions about the properties of hydrogen at high temperatures and pressures,the basis of models for the formation of Jovian planets; the microscopic properties of water andsolutions; and properties of nanoscale systems. The research is carried out primarily by graduate studentsand postdocs who often go later to industry, thus transferring the latest computational methods. Algorithmsand software developed as a result of the research will be made available to the general researchcommunity through the Materials Computation Center and used in undergraduate courses, graduatecourses, and summer schools at the University of Illinois and elsewhere.