A Calculation of Atomic Structures. By D. R. Hartree Pp. xiii, 181. 40s. 1957. (Wiley, New York)

Self-consistent-field (SCF) and multiconfiguration (MC) Hartree-Fock (HF) methods in atomic calculations: Numerical integration approaches

High‐order B‐splines provide effective basis functions for constructing solutions to the Schrodinger equation. For high‐lying levels of the Morse potential septic splines yield an accuracy comparable to harmonic oscillators. They can also approximate hydrogenic wavefunctions; typically one‐third of the N eigenvalues of an N×N matrix are more accurate than 0.01%. Matrix eigenvectors can also represent scattering states. The approximation is uniformly valid spatially when basis functions terminate sharply.

B-spline expansion bases for excited states and discretized scattering states

A simple process is proposed to solve the one-electron two-fixed-centre problem-shielded or not-when written as a pair of three-term recurrence relations, by use of a recent method from Killingbeck associated with Miller's algorithm. The method, which provides accurate eigenvalues and corresponding eigenfunctions, is also very efficient to obtain accurate values of their derivatives with respect to the internuclear distance. As an illustrative example, detailed calculations are presented for the well known X2 Sigma g+ state of H2+ at R=2 au.

https://iopscience.iop.org/article/10.1088/0953-4075/22/5/003/pdf

J.K. Cayford

Papers

A finite-difference Newton-Raphson solution of the two-center electronic Schrödinger equation

A finite difference Newton-Raphson solution of the atomic Hartree-Fock problem