The strange history of B functions or how theoretical chemists and mathematicians do (not) interact

TL;DR

This paper explores the historical development of B functions, emphasizing their mathematical properties and potential to improve molecular integral calculations, highlighting the need for better collaboration between chemistry and mathematics.

Contribution

It provides a historical perspective on B functions and argues for increased interdisciplinary collaboration to advance theoretical chemistry.

Findings

B functions have simple Fourier transforms facilitating molecular integrals.

Historically, chemistry and mathematics have had limited interaction.

Future progress relies on stronger interdisciplinary collaboration.

Abstract

$B$ functions are a class of relatively complicated exponentially decaying basis functions. Since the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why $B$ functions should offer any advantages. However, $B$ functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of $B$ functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.