Density Functional Theory of Electronic Structure

Kohn和Sham的密度泛函理论是目前凝聚态物理和量子化学中应用最广泛的电子结构计算方法。这一理论的众多使用者使其成为所有物理学的引文领先者。要计算原子、分子、生物分子、固体、表面或纳米结构的核骨架、基态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。如果交换关联能作为电子密度的泛函已知，则结果将是精确的。交换关联能的梯形近似，其更高的阶梯更复杂且更精确，可能导致新材料、化学品、药品、器件和工艺的可靠的计算机设计。这一阶梯的前三阶现在已经由满足密度泛函的已知精确约束的第一性原理或完全非经验构造完成：局域自旋密度近似(仅使用局域自旋密度作为局域成分)、广义梯度近似或GGA(也使用密度梯度)和亚GGA(引入轨道动能密度)。这一建议涉及第四级或超GGA(引入精确交换能量密度)和第五级或广义随机相近似(引入未占据的Kohn-Sham轨道)。在第四阶，提出了一种局部混合泛函，该泛函保留了完全非经验的Tao-Perdew-Staroverov-Scus eria Meta-GGA所满足的所有精确约束，同时增加了半经验的改进，从而进一步改善了对分子的描述。第四级解释了经验主义的必要性。在第五阶，提出了一个完全非经验的RPAE+泛函，该泛函基于高阶交换的随机位相近似和用于短程关联的Meta-GGA校正。RPAE+基本上满足所有已知的精确约束。它包括完全精确的交换，以及远程范德华相互作用，这对软凝聚态物质和生物分子可能是重要的。RPAE+还可以用来构建真实的电子-离子赝势，从而加快计算速度。梯子的前三到四级对于单电子密度并不是准确的(这是许多相关错误的根源)。Perdew和Zunger 1981的自相互作用修正修正了这个问题，但似乎在空间的许多电子区域修正过度了。提出了一个包含轨道动能密度的阻尼因子来防止这种过度修正。(修正后的自相互作用修正是美国和匈牙利的一项研究合作。)化学反应通常会穿过或越过“过渡态”的能量屏障。为了预测反应速度，必须准确地计算势垒高度。在阶梯的前三个阶梯上，屏障高度被严重低估，但在第四个阶梯上或通过应用修订的自我相互作用修正，可以有效地预测屏障高度。将在前三个梯级上进行一些剩余施工和测试。优化的有效势或Kohn-Sham势将被构造在第三级和更高级上，以与前两级上的势进行比较。为了加快大系统的计算速度，将寻求动能的无轨道密度泛函。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。非技术解释他的理论研究将集中在进一步发展计算原子、分子和固体电子结构的方法上。这项研究将在包括纳米科学在内的各个领域有广泛的应用。将与匈牙利的研究人员开展合作。学生和博士后助理也将得到支持。

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.