Towards B-Spline Atomic Structure Calculations

• Main Author: Charlotte Froese Fischer
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Atoms
• Subjects: atomic structure; B-splines; eigenvalue methods; Newton–Raphson method; variational theory
• Online Access: https://www.mdpi.com/2218-2004/9/3/50

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related <span style="font-variant: small-caps;">sphf, dbsr-hf</span>, and <span style="font-variant: small-caps;">spmchf</span> programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.