Density Functional Theory of Electronic Structure

电子结构密度泛函理论

• 批准号: 0501588
• 负责人: John Perdew
• 金额: --
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-15 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0501588&HistoricalAwards=false
• 关键词: Density; Functional; Theory; Electronic; Structure

TECHNICAL EXPLANATION The density functional theory of Kohn and Sham is now the most widely-used method of electronic structure calculation in both condensed matter physics and quantum chemistry. The many users of this theory make it the citation leader of all physics. To calculate the nuclear framework, ground state energy, and electron spin densities of an atom, molecule, bio-molecule, solid, surface, or nanostructure, it is only necessary to solve self-consistent quantum mechanical one-electron equations. The results would be exact if the exchange-correlation energy as a functional of the electron density were known exactly.A ladder of approximations to the exchange-correlation energy, on which higher rungs are more complex and more accurate, may lead up to the reliable computer design of new materials, chemicals, pharmaceuticals, devices, and processes. The first three rungs of this ladder have now been completed by first-principles or fully non-empirical constructions that satisfy known exact constraints on the density functional: the local spin density approximation (employing only the local spin densities as local ingredients), the generalized gradient approximation or GGA (employing also the density gradients), and the meta-GGA (which introduces the orbital kinetic energy density).This proposal addresses the fourth rung or hyper-GGA (which introduces the exact exchange energy density), and the fifth rung or generalized random phase approximation (which introduces the unoccupied Kohn-Sham orbitals). On the fourth rung, a local hybrid functional is proposed which preserves all the exact constraints satisfied by the fully non-empirical Tao-Perdew-Staroverov-Scuseria meta-GGA, while adding semi-empirical refinements that should further improve the description of molecules. The need for empiricism on the fourth rung is explained. On the fifth rung, a fully non-empirical RPAE+ functional is proposed, based on the random phase approximation with higher-order exchange plus a meta-GGA correction for short-range correlation. RPAE+satisfies essentially all known exact constraints. It includes full exact exchange, as well as the long-range van der Waals interaction which can be important for soft condensed matter and for bio-molecules. RPAE+ can also be used to construct realistic electron-ion pseudopotentials that speed up calculations.The first three or four rungs of the ladder fail to be exact for one-electron densities (and that is the root of many related errors). The self-interaction correction of Perdew and Zunger 1981 fixes this problem, but seems to overcorrect in many-electron regions of space. A damping factor, involving the orbital kinetic energy density, is proposed to prevent this overcorrection. (The revised self-interaction correction is a U.S./Hungary research collaboration.)A chemical reaction typically proceeds through or over an energy barrier at a "transition state". To predict the rate of the reaction, the barrier height must be calculated accurately. Barrier heights are seriously underestimated on the first three rungs of the ladder, but might be predicted usefully on the fourth rung or by application of the revised self-interaction correction. Some residual constructions and tests will be made on the first three rungs. The optimized effective or Kohn-Sham potential will be constructed on the third and higher rungs, for comparison with the potential on the first two rungs. An orbital-free density functional for the kinetic energy will be sought, to speed up calculations for large systems.This research involves the education of graduate and undergraduate students and the professional development of postdoctoral fellows. NON-TECHNICAL EXPLANATIONThis theoretical research will focus on further developing methods to calculate the electronic structure of atoms, molecules and solids. The research will have wide applications in a variety of fields including nanoscience. Collaborations will be carried out with researchers in Hungary. Students and postdoctoral associates will also be supported.

技术解释KOHN和SHAM的密度功能理论现在是凝结物理学和量子化学中最广泛使用的电子结构计算方法。该理论的许多用户使其成为所有物理学的引文领导者。为了计算原子，分子，生物分子，固体，表面或纳米结构的核框架，基态能量和电子自旋密度，仅需要求解自谐量子机械单电子方程。 如果交换相关能量作为电子密度的函数完全知道，结果将确切。现在，该梯子的前三个梯级已经通过第一原则或完全非经验结构来完成，这些结构满足了密度的已知​​确切约束：局部旋转密度近似（仅采用局部旋转密度作为局部成分），作为广义梯度近似或GGA（也使用了密度梯度），并介绍了密度梯度和META-GIGAS和META-GGA（即或META-GGA）（即构成或Meta-Gga）（即构成或gga）（均为Meta-gga）（即构成或gga）（均为gga）（即构成）nucea-gga（the Meta-gga）（即构成元素）。提案介绍了第四次或Hyper-GGA（引入确切的交换能量密度），以及第五次或广义的随机相位近似（这引入了空置的Kohn-Sham轨道）。在第四次登录中，提出了局部杂交功能，该功能保留了完全非经验的Tao-perdew-perdew-perdew-perdew-scuseria meta-gga所满足的所有确切约束，同时添加了半经验的细化，应进一步改善分子的描述。解释了第四次经验主义的需求。在第五次rung上，提出了完全非经验的RPAE+功能，基于具有高阶交换的随机近似以及用于短距离相关性的元ggga校正。 RPAE+基本上满足所有已知的确切约束。它包括完整的精确交换以及远程范德华的相互作用，这对于软凝结物质和生物分子可能很重要。 RPAE+也可用于构建速度加速计算的现实电子伪电势。梯子的前三个或四个梯级对于一电子密度而言无法精确（这是许多相关误差的根源）。 Perdew and Zunger 1981的自我交流校正解决了这个问题，但在许多电子空间区域似乎过度正确。提出了涉及轨道动能密度的阻尼因子，以防止这种过度校正。 （修订后的自我交织校正是美国/匈牙利研究的合作。）化学反应通常在“过渡状态”的能源屏障中进行。 为了预测反应的速率，必须准确计算屏障高度。梯子的前三个梯级被严重低估，但可能会在第四次梯级上有用或通过修订后的自我相互作用校正来实用。 一些剩余的结构和测试将在前三个梯级上进行。优化的有效或Kohn-Sham电位将在第三个和更高的梯级上构建，以与前两个梯级的电势进行比较。将寻求无轨道的密度功能，以加快大型系统的计算。这项研究涉及研究生和本科生的教育以及博士后研究员的专业发展。非技术解释这项理论研究将集中于进一步开发计算原子，分子和固体的电子结构的方法。 这项研究将在包括纳米科学在内的各个领域中应用。 合作将与匈牙利的研究人员进行。 学生和博士后同事也将得到支持。