Density Functional Theory of Electronic Structure

技术说明：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。这个理论的众多使用者使它成为所有物理学中被引用最多的理论。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，只需要求解自洽量子力学单电子方程。如果确切地知道交换相关能作为电子密度的函数，结果将是准确的。交换相关能的近似阶梯，越高的阶梯越复杂，越精确，可能导致新材料、化学品、药品、设备和工艺的可靠的计算机设计。这个阶梯的前三个梯级现在已经由第一性原理或完全非经验结构完成，这些结构满足密度泛函的已知精确约束：局部自旋密度近似（仅使用局部自旋密度作为局部成分），广义梯度近似或GGA（也使用密度梯度），以及元GGA（引入轨道动能密度）。这个建议解决了第四级或超gga（引入了精确的交换能量密度）和第五级或广义随机相位近似（引入了未占据的Kohn-Sham轨道）。在第4级，提出了一个局部混合泛函数，它保留了完全非经验的Tao-Perdew-Staroverov-Scuseria meta-GGA所满足的所有精确约束，同时增加了半经验的改进，应该进一步改善分子的描述。第四梯级的经验主义的必要性得到了解释。在第五级上，基于随机相位近似和高阶交换加上短期相关的meta-GGA校正，提出了一个完全非经验的RPAE+泛函。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是重要的。RPAE+还可用于构建实际的电子-离子赝势，从而加快计算速度。对于单电子密度，阶梯的前三或四阶并不精确（这是许多相关误差的根源）。Perdew和Zunger 1981的自相互作用修正解决了这个问题，但在空间的许多电子区域似乎矫正过了头。提出了一个包含轨道动能密度的阻尼因子来防止这种过校正。（修改后的自我互动修正是美国和匈牙利的一项研究合作。）化学反应通常在“过渡态”通过或越过能垒进行。为了预测反应速率，必须准确地计算势垒高度。在阶梯的前三个梯级上，障壁高度被严重低估，但在第四个梯级上或通过应用修正的自相互作用校正，可以有效地预测障壁高度。前三个梯级将进行一些残余结构和测试。优化后的有效孔深电位将在第三级及以上梯级上构建，以便与前两梯级的电位进行比较。将寻求动能的无轨道密度泛函，以加快大型系统的计算速度。本研究涉及研究生和本科生的教育以及博士后的专业发展。本理论研究将集中于进一步发展计算原子、分子和固体电子结构的方法。这项研究将在包括纳米科学在内的各个领域有广泛的应用。将与匈牙利的研究人员进行合作。学生和博士后也将得到支持。

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.