Abstract BSHF solves the Hartree–Fock equations in a B-spline basis for atoms, negatively charged ions, and systems of N electrons in arbitrary central potentials. In the B-spline basis the Hartree–Fock integro-differential equations are reduced to a computationally simpler eigenvalue problem. As well as solving this for the ground-state electronic structure self-consistently, the program can calculate discrete and/or continuum excited states of an additional electron or positron in the field of the frozen-target N -electron ground state. It thus provides an effectively complete orthonormal basis that can be used for higher-order many-body theory calculations. Robust and efficient convergence in the self-consistent iterations is achieved by a number of strategies, including by gradually increasing the strength of the electron–electron interaction by scaling the electron charge from a reduced value to its true value. The functionality and operation of the program is described in a tutorial style example. Program summary Program Title: BSHF Program Files doi: http://dx.doi.org/10.17632/fj3y6c58dy.1 Code Ocean Capsule: https://doi.org/10.24433/CO.1226817.v2 Licensing provisions: GPLv3 Programming language: Fortran 90. External routines/libraries: LAPACK. Nature of problem: Self-consistent solution of electronic structure for atoms and electrons in arbitrary central potentials in the Hartree–Fock approximation. Solution method: A B-spline basis is employed that transforms the Hartree–Fock integro-differential equations to a computationally simpler eigenvalue problem. The eigenvalue problem is solved iteratively until self-consistency is achieved. Unusual or notable features: 1. Robust and efficient convergence in the self-consistent iterations is achieved by gradually increasing the value of the electron charge from a reduced value to its true value, i.e., increasing the strength of the electron–electron interaction. In this way all orbitals are calculated simultaneously at every iteration of the self-consistency loop, i.e., without the need to successively fill the occupied shells from the core to valence (as most other Hartree–Fock codes require for convergence). 2. In addition to atoms and negative ions, the program solves the Hartree–Fock equations for systems of N electrons confined in an arbitrary central potential specified by the user: thus the program can be used to e.g., calculate the structure of electrons confined in harmonic potentials, which are known to approximate the electron gas. 3. In addition to calculating the ground state of the N -electron system, the program calculates the discrete and/or continuum excited states for an additional electron or positron in the field of the ‘frozen’ N -electron target. It thus provides an orthonormal basis that can be used as input for many-body theory calculations. Restrictions: The program solves non-relativistic Hartree–Fock equations for spherically symmetric systems only (in modelling systems other than atoms, e.g., harmonically confined electron gas or jellium-type models of clusters, relativistic effects can often be negligible and a non-relativistic treatment is perfectly suitable). For open-shell atoms the central-field approximation is used, i.e., the potential is angularly averaged.

中文翻译：

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BSHF：使用 B 样条基础求解任意中心势的 Hartree-Fock 方程的程序

摘要 BSHF 在 B 样条基中求解原子、带负电离子和任意中心电位的 N 电子系统的 Hartree-Fock 方程。在 B 样条基础中，Hartree-Fock 积分微分方程简化为计算上更简单的特征值问题。除了自洽地解决基态电子结构的这个问题外，该程序还可以计算冻结目标 N 电子基态场中附加电子或正电子的离散和/或连续激发态。因此，它提供了一个有效完整的正交基，可用于高阶多体理论计算。在自洽迭代中稳健而有效的收敛是通过多种策略实现的，包括通过将电子电荷从减小的值缩放到其真实值来逐渐增加电子-电子相互作用的强度。该程序的功能和操作在教程样式示例中进行了描述。程序概要 程序名称：BSHF Program Files doi：http://dx.doi.org/10.17632/fj3y6c58dy.1 代码海洋胶囊：https://doi.org/10.24433/CO.1226817.v2 许可条款：GPLv3 编程语言：Fortran 90。外部例程/库：LAPACK。问题的性质：Hartree-Fock 近似中任意中心势中原子和电子的电子结构的自洽解。求解方法：采用 B 样条基将 Hartree-Fock 积分微分方程转换为计算上更简单的特征值问题。迭代求解特征值问题，直到实现自洽。不寻常或显着的特征： 1. 通过将电子电荷的值从减小的值逐渐增加到其真实值，即增加电子 - 电子相互作用的强度，可以实现自洽迭代中稳健而有效的收敛。通过这种方式，所有轨道在自洽循环的每次迭代中同时计算，即不需要从核心到化合价连续填充占据的壳层（因为大多数其他 Hartree-Fock 代码需要收敛）。2. 除了原子和负离子之外，该程序还解决了限制在用户指定的任意中心势中的 N 电子系统的 Hartree-Fock 方程：因此该程序可用于，例如，计算被限制在谐波势中的电子的结构，这是已知的近似电子气。3. 除了计算 N 电子系统的基态外，该程序还计算“冻结”N 电子靶场中附加电子或正电子的离散和/或连续激发态。因此，它提供了一个正交基，可用作多体理论计算的输入。限制：该程序仅求解球对称系统的非相对论 Hartree-Fock 方程（在原子以外的建模系统中，例如调和约束电子气或团簇的果冻型模型，相对论效应通常可以忽略不计，非相对论治疗是完全合适的）。对于开壳原子，使用中心场近似，即，