缩放式施罗丁格方程的精确缩放函数. 缩放式施罗丁格方程. II. II. II. II. II. II. II. II. II. II. II. II. II. II. II. II. II. II.
Hiroshi Nakatsuji1, Hiroyuki Nakashima1
1Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan.
Journal of chemical theory and computation
|April 29, 2024
概括
这项研究验证了缩放的施罗丁格方程 (SSE) 函数,用于准确的原子和分子计算. 这项研究表明,在使用特定的g函数来解决热原子的施罗丁格方程 (SE) 时,收度和精度有所提高.
科学领域:
- 量子化学 是一个量子化学.
- 理论原子和分子物理 理论原子和分子物理
背景情况:
- 缩放的施罗丁格方程 (SSE) 为解决解决标准施罗丁格方程 (SE) 时遇到的分歧问题提供了解决方案.
- 之前的工作为电子-电子 (e-e) 相互作用引入了分析g函数,但它们对电子-核 (e-n) 和e-e相互作用的应用需要进一步研究.
研究的目的:
- 在缩放的施罗丁格方程 (SSE) 框架内,评估先前提出的分析g函数对e-n和e-e相互作用的有效性.
- 为了评估这些g函数的性能,对热原子进行变量自由补充 (完整元素) (FC) 计算.
主要方法:
- 将变量自由补充 (FC) 理论应用于热原子,将新型g函数纳入e-n和e-e相互作用.
- 由于大多数测试g函数缺乏分析积分公式,用于变量FC计算使用了数值积分方案.
- 评估能量,波函数,H平方误差,能量下界和尖端属性.
主要成果:
- 具有特定g函数的变量FC计算证明了向原子的SE/SSE的精确解决方案的高效收.
- 在g函数r/(r + 1/γ),Ei和1 - exp(-γr) 中,效率以下降顺序呈现出优异的性能.
- 在将获得的FC波函数应用于最近提出的方法时,能量下界计算产生了良好的结果.
结论:
- 在缩放的施罗丁格方程 (SSE) 中使用适当的g函数显著提高了变量计算的趋同性和准确性.
- 测试的分析g函数,特别是r/(r + 1/γ),Ei和1 - exp(-γr,对于原子系统中的e-n和e-e相互作用都是有效的.
- 这种方法提供了一种可靠的方法来获得准确的波函数和能量,克服了标准SE的分歧问题.
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