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

电子对密度函数理论及其量子化学应用

基本信息

批准号：
13640495
负责人：
KOGA Toshikatsu
金额：
$ 2.24万
依托单位：
MURORAN INSTITUTE OF TECHNOLOGY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

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

电子对在原子和分子中的运动可以用电子对的相对运动和质心运动密度函数来描述。对于原子系统，这些电子对密度的特征是它们的球形平均值。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，但迄今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没有足够的了解。本研究项目的目的是澄清电子对密度函数的理论结构，并将新结果应用于各种化学和物理问题。本文将近两年的研究成果总结如下：(1)引入了广义电子对密度函数。小泡内密度和小泡外密度已被证明是密度函数的两种特殊情况。我们还证明了电子对密度的第二矩满足一个严格的和规则，它连接了原子和分子的单电子和双电子性质。(2)我们发现原点处的电子对密度值是由电子-电子聚结和平衡函数指定的，并阐明了这些函数的数学结构。报道了102个原子基态的数值结果。(3)我们报道了小泡内和小泡外密度的二阶矩与各种物理性质密切相关，这些物理性质迄今为止都是独立研究的。这些性质包括电子和核动能、振子强度和、核质量修正能、抗磁化率和偶极极化率。(4)微粒内和微粒外密度的二阶矩也阐明了原子和分子中电子的统计相关性。在Hartree-Fock近似中，原子中的电子要么负相关，要么不相关。(5)引入表征电子空间角分布的电子间角密度函数，并报道了原子的数值结果。(6)对He、Li和Be原子基态，考察了电子相关对电子对性质的影响。结果指出并纠正了文献价值的不一致。少