有限元法作为研究受限原子电子结构的替代方法
Juan-José García-Miranda1, Rubicelia Vargas1, Jorge Garza1
1Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C.P. 09340, México City, México.
Physical review. E
|October 18, 2023
概括
有限元素方法 (FEM) 提供了一种可靠的,无基础集的方法来解决有限原子的量子化学方程. 这种数值方法提供了准确的结果,作为未来对原子电子结构研究的基准.
科学领域:
- 计算量子化学 计算量子化学
- 原子物理 原子物理
- 材料科学 材料科学 材料科学
背景情况:
- 传统的量子化学计算通常依赖于基础集,需要对特定的原子系统和限制潜力进行广泛的优化.
- 基本集的限制可能会引入不准确性,特别是对于被限制的原子,其中电子相互作用被显著改变.
研究的目的:
- 引入和验证一种新的有限元素方法 (FEM) 方法,用于解决受限原子的Hartree-Fock和Kohn-Sham方程.
- 为了证明FEM的可靠性和效率相比传统的依赖基准的方法,如Roothaan的方法.
- 为未来关于受限原子的研究建立一个基准,特别是在Kohn-Sham框架内.
主要方法:
- 在不规则网格上应用有限元法 (FEM) 来解决Hartree-Fock和Kohn-Sham方程.
- 使用零碎或定义良好的导数函数来定义有限和无限的限制潜力.
- 将FEM结果与使用总和轨道能量的Roothaan方法进行比较.
主要成果:
- FEM方法在解决局限,和原子的量子力学方程方面表现出可靠性.
- 哈特里-福克计算的FEM结果与现有数据有很好的一致性,验证了数值方法.
- 这项研究为Kohn-Sham限制原子计算提供了新的基准数据,解决了已发表文献中的差距.
结论:
- FEM是一种强大而准确的数值技术,用于研究有限的原子,独立于基础集.
- 这项工作为开发一种多功能量子化学代码铺平了道路,该代码能够处理许多电子原子的任意封闭潜力.
- 建立的基准数据将促进未来的研究和验证,在封闭的原子系统领域.
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