Density Functional Theory of Electronic Structure

技术解释 Kohn和Sham的密度泛函理论是目前凝聚态物理和量子化学中最广泛使用的电子结构计算方法。这个理论的众多使用者使它成为所有物理学的引用领袖。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，只需要求解自洽的量子力学单电子方程。 如果交换相关能作为电子密度的函数被精确地知道，结果将是精确的。交换相关能的近似阶梯，在更高的梯级上更复杂和更精确，可能导致新材料，化学品，药物，设备和过程的可靠计算机设计。这个阶梯的前三个梯级现在已经由第一原理或完全非经验的构造完成，这些构造满足密度泛函的已知精确约束：局域自旋密度近似（仅采用局部自旋密度作为局部成分），广义梯度近似或GGA（也采用密度梯度），和超GGA（引入轨道动能密度）。该建议涉及第四个梯级或超GGA（其引入精确的交换能量密度）和第五阶或广义无规相位近似（其引入未占据的Kohn-Sham轨道）。在第四个梯级上，提出了一个局部混合泛函，它保留了完全非经验的Tao-Perdew-Staroverov-Scuseria元GGA所满足的所有精确约束，同时添加了半经验的改进，应该进一步改善分子的描述。对第四阶梯的需要进行了解释。在第五层，提出了一个完全非经验的RPAE+泛函，基于高阶交换的随机相位近似加上短程相关的元GGA校正。RPAE+基本上满足所有已知的精确约束。它包括完全精确交换，以及长程货车范德华相互作用，这对软凝聚态物质和生物分子很重要。RPAE+还可以用来构造真实的电子-离子赝势，以加快计算速度。阶梯的前三或四个梯级对于单电子密度来说并不精确（这是许多相关错误的根源）。Perdew和Zunger 1981的自相互作用修正解决了这个问题，但在空间的多电子区域似乎过度修正。一个阻尼因子，涉及轨道动能密度，提出了防止这种过度校正。(The修正后的自我相互作用校正是美国/匈牙利研究合作。化学反应通常在“过渡态”通过或越过能量势垒进行。 为了预测反应速率，必须精确计算势垒高度。障碍高度被严重低估的阶梯的前三个梯级，但可能是有用的预测第四梯级或应用修订后的自相互作用校正。 一些剩余的结构和测试将在前三个梯级上进行。将在第三和更高的梯级上构造优化的有效或Kohn-Sham势，用于与前两个梯级上的势进行比较。一个轨道自由密度泛函的动能将寻求，以加快计算大型system.This研究涉及研究生和本科生的教育和博士后研究员的专业发展。非技术性解释这项理论研究将集中在进一步发展计算原子、分子和固体的电子结构的方法上。 这项研究将在包括纳米科学在内的各种领域中具有广泛的应用。 将与匈牙利的研究人员开展合作。 学生和博士后同事也将得到支持。

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.