Density Functional Theory of Electronic Structure

该奖项支持理论研究和教育，部分原因是希望提高凝聚态物理和量子化学中实践的密度泛函理论的准确性。PI描述了交换关联泛函的“阶梯”近似，其中第一级是局部自旋密度近似，第二级是广义梯度近似(GGA)。这些标准近似不能使电子结构计算具有化学上的准确性。特别是，它们不能准确地描述强关联或强空间不均匀密度、长链分子的极化率或高激发态。PI建议通过几个项目的工作来解决这些问题：(1)开发和测试与近似的第三和第四阶梯相对应的交换相关泛函的近似。Meta-GGA将被开发为缓慢变化的密度限制和等轨道密度限制之间的受控内插。Hyper-GGA使用精确的交换能量密度来实现无自相互作用误差和正确的非均匀标度行为。(2)用改进的电子-电子自洽相互作用对密度泛函方法研究了均匀电子气。精确的高密度和低密度极限之间的能量内插将被用来探索自旋极化的电子气。结果将与计算成本高得多的扩散蒙特卡罗计算进行比较。(3)扩散蒙特卡罗、密度泛函理论和RPA方法将并行进行胶体表面能的计算，以解决扩散蒙特卡罗和其他方法计算的表面能之间的明显差异。(4)对真实固体的计算将检验一个新的解析状态方程，并将为轨道相关的准GGA和超GGA能量泛函构造Kohn-Sham势。(5)非经验性地建立了轨道动能的拉普拉斯水平的亚GGA。该项目还直接有助于本科生和研究生的教育，以及博士后研究人员的专业发展。该奖项支持基础理论研究，旨在提高基于密度泛函的材料理论的准确性。将使用解析和数值方法。密度泛函理论被广泛用于预测各种材料的性质，如晶体结构、电子自旋密度和声子模。PI研究的另一个组成部分将研究与电子气相关的基本问题，以及改进的动能近似。均匀电子气在密度泛函理论的实际应用中起着基础性的作用。该奖项还支持本科生、研究生和博士后教育。

This award supports theoretical research and education motivated in part by the desire to improve the accuracy of density functional theory as practiced in condensed matter physics and quantum chemistry. The PI describes a "ladder" of approximations for the exchange-correlation functional in which the first rung is the local spin density approximation and the second rung is the generalized gradient approximation (GGA). These standard approximations do not enable electronic structure calculations with chemical accuracy. In particular, they do not accurately describe strongly correlated or strongly spatially inhomogeneous densities, polarizabilities of long-chain molecules, or highly excited states. The PI proposes to address these problems through work on several projects: (1) Develop and test approximations for the exchange-correlation functional that correspond to the third and fourth rungs of the "ladder" of approximations. The meta-GGA would be developed as a controlled interpolation between the slowly varying and iso-orbital density limits. The hyper-GGA uses the exact exchange energy density to achieve freedom from self-interaction error and a correct non-uniform scaling behavior. (2) The uniform electron gas will be explored using a modified pair density functional method with a self-consistent electron-electron interaction. An energy interpolation between exact high- and low-density limits will be used to explore the spin-polarized electron gas. The results will be compared with much more computationally expensive diffusion Monte Carlo calculations. (3) Diffusion Monte Carlo, density-functional theory, and RPA studies of the jellium surface energy will be carried out in parallel to resolve the apparent discrepancy between surface energies calculated using diffusion Monte Carlo and other methods. (4) Calculations for real solids will test a new analytic equation of state and will construct a Kohn-Sham potential for the orbital-dependent meta-GGA and hyper-GGA energy functionals. (5) A Laplacian-level meta-GGA will be constructed non-empirically for the orbital kinetic energy. This project also contributes directly to the education of undergraduate and graduate students, and to the professional development of postdoctoral researchers.This award supports fundamental theoretical research with an aim to improve the accuracy of density-functional based theories of materials. Analytical and numerical methods will be used. Density functional theory is widely used to predict a variety of materials properties, such as crystal structures, electron spin densities, and phonon modes. Another component of the PI's research would study fundamental problems associated with the electron gas and improved approximations for the kinetic energy. The homogeneous electron gas plays a fundamental role in the practical application of density functional theory. This award also supports education at the undergraduate, graduate, and postdoctoral levels.