Applications of<i>B</i>-splines in atomic and molecular physics

TLDR

B‑splines, introduced over 50 years ago in applied mathematics, have become a cornerstone of computational atomic and molecular physics, with their use exploding since the 1990s when powerful computers became available. This review aims to present the main properties of B‑splines and explain why they are useful for solving diverse problems in atomic and molecular physics. We compile an extensive reference list of theoretical works employing B‑splines up to 2000 and highlight applications that revealed new phenomena, illustrating the reasons for the method’s success. The review shows that B‑spline applications have led to the discovery of novel phenomena and that their flexibility, completeness, and numerical stability underpin this success.

Abstract

One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.