径向Hartree-Fock-Slater方程的新的数值解法

本文提出径向Hartree-Fock-Slater(HFS)方程的一种新的数值解法。使用二阶或四阶有限差分法,把HFS方程离散化,构成一组拟线性代数本征值问题。其系数矩阵与解有关,需用迭代方法求近似解。本工作对数值方法做了改进,使得数值处理比较完整和统一。已编成计算机程序,对Cu⁺和Mn²⁺进行了计算。所得结果与文献1,2]的结果一致,表明此法的稳定性和精确性良好。还对一系列原子和离子问题进行过计算,证明此法能成功地用于中性原子和正离子的计算。

A NEW NUMERICAL METHOD FOR THE SOLUTION OF RADIAL HARTREE-FOCK-SLATER EQUATION

In this paper, a new numerical method for the solution of radial Hartree-Fock-Slater equation is proposed. The discretized form of the HFSequation, using second-order or 4th-order finite differences, results in a set of quasi-linear algebraic eigenvalue problems. The coefficient-matrices are dependent on the solutions. After linearizing the coefficient-matrices, we can solve the eigenvalue problems by the Newton's method to obtain the eigenvalues and the corresponding eigenvectors simultaneously. We solve he linear system therein by the double sweep method. Then we can correct the coefficient-matrices by the simple weighting iterate method or by the Newton's method. This numerical method has been programmed for computer. The results of trial calculations of Cu⁺ and Mn²⁺ are consistent with those in published literature. Actual calculation shows that the stability of this numerical method is good.