Nakatsuji Hiroshi, Nakashima Hiroyuki
Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan.
J Chem Theory Comput. 2024 Sep 3. doi: 10.1021/acs.jctc.4c00884.
The free complement (FC) theory for solving the scaled Schrödinger equation (SSE) was applied to the Li atom for calculating the exact wave functions, the energies, and the various properties of the ground doublet S and excited P states. The SSE is equivalent to the Schrödinger equation (SE) but does not have the divergence difficulty of the variational equation of the SE. Because the Li atom is a three-electron system, the variational exact FC calculations for solving the SSE are possible using the function = 1 - exp(-γ) as the "correct" scaling function of the SSE. The "reasonable" scaling function = was also used as comparative calculations. We performed variational calculations to the order eight of the FC theory and could obtain essentially exact solutions of the SSE or SE with the "correct" function of the FC theory. We report here the values of the exact energy, spin density, electron density, and electron-nuclear and electron-electron cusp values of the doublet S and P states. They agreed very well with the experimental values and the best theoretical values presented by Drake and collaborators. This is a simple example that the exact theory gives the exact solutions.
用于求解缩放薛定谔方程（SSE）的自由互补（FC）理论被应用于锂原子，以计算基态双重态S和激发态P态的精确波函数、能量以及各种性质。SSE等同于薛定谔方程（SE），但不存在SE变分方程的发散困难。由于锂原子是一个三电子系统，使用函数 = 1 - exp(-γ)作为SSE的“正确”缩放函数，就可以对求解SSE进行变分精确FC计算。“合理”的缩放函数 = 也被用作对比计算。我们对FC理论进行了八阶变分计算，并且使用FC理论的“正确”函数能够获得SSE或SE的基本精确解。我们在此报告双重态S和P态的精确能量、自旋密度、电子密度以及电子 - 核和电子 - 电子尖点值。它们与德雷克及其合作者给出的实验值和最佳理论值非常吻合。这是一个精确理论给出精确解的简单例子。
