Density Functional Theory of Electronic Structure

材料研究部和化学部为该奖项提供资金，这将导致更准确的分子、化学物质和材料的计算机建模。为了做到这一点，PI将重点关注将一个原子与另一个原子结合在一起形成分子和材料的“胶水”，技术名称为交换相关能。能量越小，“胶水”的作用就越强，因为电子会避免接近其他带相同电荷的电子。电子的密度决定了交换相关能，但确切的公式尚不清楚。尽管如此，我们还是有可能利用计算机通过一个近似公式来预测哪些分子和材料能够存在，以及它们具有什么样的性质。PI已经开发出近似公式，与实际实验相比，这些公式可以很好地预测许多材料和分子的性质。在这项研究中，PI将为“胶水”开发更精确的近似，这些近似仍然有助于在计算机上有效地模拟分子和材料。PI最新的近似公式叫做SCAN。作为一个特征，它具有精确公式的所有属性，这些属性是从量子力学的基本原理中已知的，可以用于类似SCAN的近似。然而，这种类型的公式不可能是精确的；这种近似引入了电子与自身的虚假相互作用。该项目的一个主要目标是开发一种广泛有用的校正方法来克服SCAN的这种错误来源。对把原子粘合在一起的“胶水”的更精确近似的发展，导致了对化学物质、分子和材料性质的更好预测。这些预测可以导致发现具有理想性能的新材料，用于广泛的应用，从建筑和建筑，到复杂的电子设备，再到医疗应用的生物材料等等。这项研究能够更好地对材料基因组计划产生潜在影响的材料进行计算机建模。该奖项还有助于支持PI开发更好的方法来帮助教育更多的高中物理教师，并让本科生参与研究。材料研究部和化学部为该奖项提供资金，以支持Kohn-Sham密度泛函理论的研究，这是计算基态能量或能量差，平衡核位置以及原子，分子和固体中的电子密度的最广泛使用的方法。该理论在原则上是准确的，尽管在实践中，交换相关能的密度泛函必须近似。在之前的授权期间，Perdew研究小组开发了SCAN，这是一种“强约束和适当规范”的功能，对于不同键合系统比同等效率的近似更准确。SCAN元广义梯度近似满足半局部泛函所能满足的所有17个已知的精确约束条件，可以取代广泛使用的Perdew-Burke-Ernzerhof广义梯度近似。在目前的授标期内，将对SCAN和具有远程范德华校正的SCAN进行广泛的测试。这些测试将包括决定分子和固体相对稳定性的形成能、sp键和含过渡元素分子的大型参考数据集、聚乙炔链、固体的基态晶体结构（已被证明具有挑战性）、固体的基本带隙、金属的表面能和功函数，以及表面分子的吸附能。对SCAN进行精细的自相互作用校正将寻求保留弱相关系统平衡键的优秀SCAN描述，同时改进拉伸键，电荷转移和强相关系统的描述。将对完全非局部随机相位近似开发一种类似扫描的加性校正。对于任何自旋非极化密度的交换能的假设的紧下界，将寻求证明。最后，对选定系统的交换相关能差进行分析，从而更好地理解电子系统及其特性，以及SCAN的成功。交换相关函数更精确近似值的发展将导致对原子、分子和材料性质的更好预测，并可能导致发现具有所需性质的新材料，用于从建筑和建筑到复杂电子设备到医疗应用的生物材料等广泛应用。这项研究能够更好地对材料基因组计划产生潜在影响的材料进行计算机建模。该奖项还有助于支持PI开发更好的方法来帮助教育更多的高中物理教师，并让本科生参与研究。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Chemistry Division contribute funds to this award that will lead to more accurate computer modeling of molecules, chemicals, and materials. To do this the PI will focus on the "glue" that binds one atom to another to form molecules and materials which has the technical name exchange-correlation energy. Making this energy smaller strengthens the "glue" because electrons avoid close approaches to other electrons which have the same electric charge. The density of electrons determines the exchange-correlation energy, but the exact formula is not known. Nevertheless, it is possible to use a computer to predict what molecules and materials can exist, and with what properties, by using an approximate formula. The PI has developed approximate formulas that lead to good predictions of the properties of many materials and molecules as compared with actual experiments. In this research the PI will develop even more accurate approximations for the "glue" that still lend themselves to efficient simulation of molecules, and materials on a computer. The PI's most recent approximate formula is called SCAN. As a feature, it shares all the attributes of the exact formula that are known from fundamental principles of quantum mechanics that are possible for an approximation like SCAN. Nevertheless, no formula of this type can be exact; approximations of this type introduce a spurious interaction of an electron with itself. A major goal of this project will be to develop a widely-useful correction to overcome this source of error for SCAN.The development of more accurate approximations for the "glue" that holds atoms together leads to better predictions for the properties of chemicals, molecules, and materials. These predictions can lead to the discovery of new materials with desired properties for a wide range of applications from building and construction, to sophisticated electronic devices, to biomaterials for medical applications, and more. This research enables better computer modeling of materials with potential impact on the Materials Genome Initiative. This award also helps support the PI's efforts to develop better ways to help educate more high-school physics teachers,and to involve undergraduate students in the research.TECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division contribute funds to this award that supports research in Kohn-Sham density functional theory, the most widely-used method to calculate ground-state energies or energy differences, equilibrium nuclear positions, and electron densities in atoms, molecules, and solids. The theory is exact in principle, although in practice the density functional for the exchange-correlation energy must be approximated. In the preceding award period, the Perdew research group developed SCAN, a "strongly constrained and appropriately normed" functional that is more accurate for diversely-bonded systems than comparably-efficient approximations. Satisfying all 17 known exact constraints that a semilocal functional can, the SCAN meta-generalized gradient approximation could replace the widely-used Perdew-Burke-Ernzerhof generalized gradient approximation.In the current award period, extensive tests will be made for SCAN and for SCAN with a long-range van der Waals correction. These tests would include the formation energies which determine relative stabilities of molecules and solids from the elements in their standard states, large reference-data sets for sp-bonded and transition-element-containing molecules, the polyacetylene chain, the ground-state crystal structures of solids that have proven challenging to get correct for , fundamental band gaps of solids, surface energies and work functions of metals, and adsorption energies for molecules on surfaces, A refined self-interaction correction to SCAN would seek to preserve the excellent SCAN description of equilibrium bonds for weakly-correlated systems while improving the description of stretched bonds, charge transfers, and strongly-correlated systems. A SCAN-like additive correction to the fully-nonlocal random phase approximation would be developed. Proof would be sought for a hypothesized tight lower bound on the exchange energy of any spin-unpolarized density. Finally, exchange-correlation energy differences for selected systems would be analyzed in a way that could lead to a better understanding of electronic systems and their properties, and of the successes of SCAN. The development of more accurate approximations for exchange-correlation functions will result in better predictions for the properties of atoms, molecules, and materials and can lead to the discovery of new materials with desired properties for a wide range of applications from building and construction to sophisticated electronic devices to biomaterials for medical applications and more. This research enables better computer modeling of materials with potential impact on the Materials Genome Initiative. This award also helps support the PI's efforts to develop better ways to help educate more high-school physics teachers, and to involve undergraduate students in the research.