Open Collections

UBC Faculty Research and Publications

Towards B-Spline Atomic Structure Calculations Froese Fischer, Charlotte, 1929-

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.

Item Metadata

Title
Towards B-Spline Atomic Structure Calculations
Creator
Froese Fischer, Charlotte, 1929-
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2021-07-31
Description
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.
Subject
atomic structure; B-splines; eigenvalue methods; Newton–Raphson method; variational theory
Genre
Article
Type
Text
Language
eng
Date Available
2021-10-12
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0402492
URI
http://hdl.handle.net/2429/79945
Affiliation
Science, Faculty of; Computer Science, Department of
Citation
Atoms 9 (3): 50 (2021)
Publisher DOI
10.3390/atoms9030050
Peer Review Status
Reviewed
Scholarly Level
Faculty
Rights URI
https://creativecommons.org/licenses/by/4.0/
Aggregated Source Repository
DSpace

Item Media

Item Citations and Data

Rights

CC BY 4.0