Density Functional Theory of Electronic Structure

技术总结化学部和材料研究部为该奖项提供资金。它支持理论和计算研究和教育，以推进第一性原理电子结构理论。在Kohn-Sham密度泛函理论中，要计算原子、分子、生物分子、固体、表面或纳米结构的基态核骨架、能量和电子自旋密度，只需求解自洽的量子力学单电子方程。如果所采用的交换相关能作为电子密度的泛函是精确的，则结果将是精确的。在实践中，精确泛函是不可计算的，但通过在交换相关能量密度中添加额外的半局部或非局部成分来满足更精确的约束，实际的泛函近似是可以改进的。亚广义梯度近似可以精确计算处于平衡状态或接近平衡状态的许多物质系统的性质。然而，令人惊讶的是，对于像硅和二氧化硅这样简单的固体，它们可能无法预测准确的结构能量差异和转变压力。PI将开发一种新的元广义梯度近似，该近似满足所有可能的精确约束，同时恢复更多的中程van der Waals相互作用，并针对这些和其他问题进行测试。对于电子共享的伸展键的描述，以及过渡金属氧化物和稀土元素的强关联，采用非局域精确交换成分的杂化泛函取得了令人惊讶的成功。然而，这些泛函通常依赖于一个或多个经验参数，并且可能无法满足即使是半局部泛函所满足的基本精确约束。PI将使用推测的长程极限来开发关联空穴的非经验混合模型，以用于精确交换。一个副产品将是对随机相近似的必要的非局域修正。对局域自旋密度近似的早期自作用修正对于强关联系统已经取得了一些成功，尽管它对更正常的分子和固体的平衡性质的描述令人失望，并且不会随着基础半局域泛函的改善而得到很大的改善。PI的目的是解决这些问题，通过使用复轨道消除自相互作用修正轨道密度的节点，并将自相互作用修正应用于PI改进的新的亚广义梯度近似，它将对紧凑单电子密度有更好的描述。最近的一项重大发展是将对软物质和生物物质很重要的长程范德华相互作用纳入密度泛函理论。PI计划以两种不同的方式将这些效应添加到省略它们的最佳半局部泛函和非局部泛函中。一是精确计算所有阶的范德华系数，求无穷级数和短程截止值之和；二是提取非局域范德华关联能量泛函的长程部分。Kohn-Sham密度泛函理论在化学和材料领域有着广泛的应用，在工程和地球物理中的应用也越来越广泛。这项研究所产生的改进的泛函将促进具有所需性质的新分子和材料的计算机设计。该奖项还支持培养从高中到研究生院的所有级别的博士后研究员和学生。非技术摘要：化学部和材料研究部为该奖项提供资金。它支持理论和计算研究和教育，以提高准确计算材料性质的能力。普通物质(原子、分子和固体)是由电子和原子核组成的。为了在计算机上预测其性质，并设计出具有所需性质的新材料，我们需要找到电子的能量和空间变化的密度，包括量子力学和静电斥力的影响。Kohn-Sham密度泛函理论是计算这些性质的广泛使用的方法。能量和密度可以通过最小化关于密度的能量的泛函或规则来得到。这种泛函的合理近似是已知的，并有效地描述了原子的形成和原子结合形成分子和固体。这个项目的目的是利用我们已有的关于精确泛函的知识来构造更准确但计算效率更高的近似。对结合原子形成分子和固体的“自然胶水”进行更好的近似，可以从组成原子的同一性和设计具有所需性质的材料的可能性来更准确地预测材料的性质。这项研究产生的新泛函可以在化学、生物化学、纳米科学、材料科学、凝聚态物理等领域得到良好的结果。该奖项还支持博士后研究员和从高中到研究生院的各级学生的教育。

TECHNICAL SUMMARYThe Chemistry Division and Division of Materials Research contribute funds to this award. It supports theoretical and computational research and education to advance first principles electronic structure theory. To calculate the ground-state nuclear framework, energy, and electron spin densities of an atom, molecule, biomolecule, solid, surface, or nanostructure within Kohn-Sham density functional theory, it is only necessary to solve self-consistent quantum mechanical one-electron equations. The results would be exact if the employed exchange-correlation energy as a functional of the electron density were exact. The exact functional is not computable in practice, but practical approximations to it are improvable by adding additional semilocal or nonlocal ingredients to the exchange-correlation energy density to satisfy more exact constraints. Meta-generalized gradient approximations can enable accurate calculation of the properties of many material systems at or near equilibrium. However, they can surprisingly fail to predict accurate structural energy differences and transition pressures for solids as simple as silicon and silicon dioxide. The PI will develop a new meta-generalized gradient approximation which satisfies all possible exact constraints while recovering more of the intermediate-range van der Waals interaction, and test it for these and other problems. For the description of stretched bonds over which electrons are shared, and thus of the 'strongly correlated' transition-metal oxides and lanthanides, hybrid functionals that employ a nonlocal exact-exchange ingredient have been surprisingly successful. However, these functionals typically rely on one or more empirical parameters, and can fail to satisfy basic exact constraints that even semilocal functionals satisfy. The PI will use a conjectured long-range limit to develop a nonempirical hybrid model for the correlation hole, for use with exact exchange. A byproduct will be a needed nonlocal correction to the random phase approximation.An early self-interaction correction to the local spin density approximation has had some success for strongly-correlated systems, although its description of the equilibrium properties of more normal molecules and solids is disappointing and does not much improve with improvement of the underlying semilocal functional. The PI aims to fix these problems by eliminating the nodes of the self-interaction correction orbital densities through the use of complex orbitals, and by applying the self-interaction correction to the PI's improved new meta-generalized gradient approximation, which will have an improved description of compact one-electron densities. A major recent development is the incorporation of long-range van der Waals interaction which is important for soft and biological matter, into density functional theory. The PI plans two different ways to add these effects to the best semi-local and nonlocal functionals that omit them. One involves the accurate calculation of van der Waals coefficients of all orders, with a summation of the infinite series and a short-range cutoff, and the other involves the extraction of the long-range part of a nonlocal van der Waals correlation energy functional. Kohn-Sham density functional theory is widely used in chemistry and materials, and is increasingly used in engineering and geophysics. The improved functionals that result from this research will facilitate the computer design of new molecules and materials with desired properties. This award also supports educating postdoctoral fellows and students at all levels from high-school through graduate school.NONTECHNICAL SUMMARY:The Chemistry Division and Division of Materials Research contribute funds to this award. It supports theoretical and computational research and education to advance the ability to compute the properties of materials accurately. Ordinary matter (atoms, molecules, and solids) is made up of electrons and nuclei. To predict its properties on the computer, and to design new materials with desired properties, we need to find the energy and spatially varying density of the electrons, including the effects of quantum mechanics and electrostatic repulsion. Kohn-Sham density functional theory is a widely used method to calculate these properties. The energy and density can be found by minimizing a functional or rule for the energy in terms of the density. Reasonable approximations to this functional are known, and usefully describe the formation of atoms and the binding of atoms to form molecules and solids. The aim of this project is to use the knowledge we have about the exact functional to construct approximations that are more accurate but still computationally efficient. Better approximations for "nature's glue" that binds atoms to form molecules and solids leads to more accurate predictions of materials properties from the identity of the constituent atoms and the potential to design materials with desired properties.New functionals that result from this research could be applied with good results in chemistry, biochemistry, nanoscience, materials science, condensed matter physics, and other fields. This award also supports education for postdoctoral fellows and students at all levels from high-school through graduate school.