Abstract
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 sphf, dbsr-hf, and spmchf 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.
Highlights
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
In an early B-spline study, Froese Fischer and Parpia [16] studied the accuracy of the application of B-splines to the Dirac equation for He with a grid over the range (0, 40), comparing a grid for ρ = r1/4 with a grid for ρ = log(r )
B-spline Slater integrals included in the summation
Summary
Oleg improved and extended the library, which became the basis for the BSR code he published in 2006 [2] for both non-relativistic and the Breit–Pauli R-matrix theory This paper reviews the development of spline methods for variational approaches to solutions of the wave equation for atoms with the assumption that the reader is familiar with the basic properties of splines as presented by Bachau et al [10]. Unlike the latter, the emphasis here is more on the computational methods and the programs that have emerged rather than their application
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
