Theory of Electron-Pair Density Functions and Its Quantum Chemical Applications

电子对在原子和分子中的运动由电子对胞内(相对运动)和胞外(质心运动)密度函数来描述。对于原子系统，这些电子对密度用它们的球面平均值来表征。电子对密度是理解原子和分子中电子-电子相互作用的重要概率密度函数，但到目前为止，我们对其理论结构和在量子化学问题中的实际应用还缺乏足够的了解，本研究的目的是阐明电子对密度函数的理论结构，并将新的结果应用于各种化学和物理问题。本课题两年来的研究成果总结如下：(1)引入了广义电子对密度函数。胞内密度和胞外密度是密度函数的两个特例。…此外，我们还证明了电子对密度的二阶矩满足严格的求和规则，它连接了原子和分子的单电子和双电子性质。(2)我们发现原点的电子对密度值由电子-电子结合函数和平衡函数确定，并阐明了这些函数的数学结构。报道了102个基态原子的数值结果。(3)我们报道了胞内和胞外密度的二阶矩与各种物理性质的严格联系，到目前为止，这些都是独立研究的。这些性质包括电子和核动能、振子强度和、核质量修正能、反磁极化率和偶极极化率。(4)分子内和分子外密度的二阶矩也阐明了原子和分子中电子的统计关联。在Hartree-Fock近似下，原子中的电子要么是负相关的，要么是不相关的。(5)我们引入了描述电子空间角分布的电子间角密度函数，并给出了原子的数值结果。(6)对于处于基态的He、Li和Be原子，研究了电子相关对电子对性质的影响。研究结果指出并纠正了文献价值中的不一致之处。较少

The motions of electron-pairs in atoms and molecules are described by the electron-pair intracule (relative motion) and extracule (center-of-mass motion) density functions. For atomic systems, these electron-pair densities are characterized by their spherical averages. The electron-pair densities are important probability density functions to understand the electron-electron interactions in atoms and molecules, but up to now we have neither sufficient knowledge about their theoretical structures nor practical applications to quantum chemical problems.The purpose of this research project has been to clarify the theoretical structure of the electron-pair density functions and to apply new results to various chemical and physical problems. The results of this research project during the two years are summarized as follows:(1) We introduced a generalized electron-pair density function. The intracule and extracule densities have been shown to be two particular cases of the density function. … More We have also shown that the second moments of the electron-pair densities satisfy a rigorous sum rule, which connects one- and two-electron properties of atoms and molecules.(2) We found that the electron-pair density values at the origin is specified by the electron-electron coalescence and counterbalance functions, and clarified the mathematical structures of these functions. Numerical results were reported for 102 atoms in their ground states.(3) We reported that the second moments of the intracule and extracule densities are rigorously connected to various physical properties, which were hitherto studies independently. The properties include electronic and nuclear kinetic energies, oscillator strength sums, nuclear mass correction energies, diamagnetic susceptibilities, and dipole polarizabilities.(4) The second moments of the intracule and extracule densities also clarify the statistical correlation of electrons in atoms and molecules. In the Hartree-Fock approximation, electrons in atoms are either negatively correlated or uncorrelated.(5) We have newly introduced the interelectronic angle density function which characterizes the spatial angular distribution of electrons and reported numerical results for atoms.(6) For the He, Li, and Be atoms in their ground states, the electron correlation effect on the electron-pair properties were examined. The results point out and correct the inconsistency in the literature values. Less