量子力学中的 Roothaan-Hartree-Fock (R-H-F) 近似计算在原子、分子和材料电子结构计算中具有重要的意义, 是其他高精度电子结构计算方法的基础. 本工作根据开源网站Basis Set Exchange 中丰富的基组资源, 利用高斯型基组矩阵元具有解析表达式的特性, 自行编写 Roothaan-Hartree-Fock 计算程序, 可以较为方便的达到高精度的计算结果. 同时本工作用不同大小的基组计算了多种原子和离子的基态能量, 研究了 He、Be、C2+ 等原子和离子在不同基组下的收敛特性. 此外, 基于自行编写的 R-H-F 程序计算得到 He、Be、Ne 的第一电离能, 与实验对比最大误差不超过 6.84%.

The Roothaan-Hartree-Fock (R-H-F) approximation in quantum mechanics plays an important role in the calculation of the electronic structure of atoms, molecules and materials, and is the basis for other high-precision electronic structure calculation methods. Based on the rich basis set resources in the open-source website Basis Set Exchange, this paper uses the characteristics of the analytic expression of the Gaussian basis set matrix elements, and the in-house Roothaan-Hartree-Fock computer program, to easily achieve high-precision calculation results. The ground state energies of various atoms and ions are calculated with basis sets of different sizes, and it is found that with the increase of the number of basis functions, different types of basis sets exhibit different convergence properties. Furthermore, using the self-written R-H-F program, this work calculated the first ionization energies of He, Be, and Ne, with a maximum error of 6.84 percent compared to the experiment.