BSHF: A program to solve the Hartree–Fock equations for arbitrary central potentials using a B-spline basis

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.

BSHF程序可在B样条（B-spline）基组下，求解原子、带负电离子以及任意中心势场中N电子体系的哈特里-福克（Hartree–Fock）方程。在B样条基组框架下，哈特里-福克积分微分方程可被简化为计算复杂度更低的本征值问题。该程序不仅可自洽求解基态电子结构，还能在冻结靶标的N电子基态势场中，计算额外电子或正电子的离散与连续激发态。由此，该程序可生成一套近乎完备的正交归一基组，可用于高阶多体理论计算。自洽迭代过程中的稳健高效收敛可通过多种策略实现，其中包括将电子电荷从缩减值逐步缩放至真实值，以此增强电子-电子相互作用的强度。该程序的功能与操作方式将通过教程式示例进行说明。