Comment about the use of Monte-Carlo methodology for the representation of atomic electronic densities

TL;DR

This paper discusses the correct application of Monte-Carlo methods for representing atomic electronic densities, emphasizing the importance of coordinate choice and providing guidance for educational purposes.

Contribution

It offers a critical analysis and guidelines for proper use of Monte-Carlo approaches in atomic orbital representations, addressing common misconceptions.

Findings

Monte-Carlo methods can be inaccurate with non-Cartesian coordinates

Proper coordinate selection is crucial for accurate atomic density representation

Guidelines improve educational understanding of Monte-Carlo applications

Abstract

Representations of atomic orbitals based on Monte-Carlo (MC) approaches are not always correct when using various sets of orthogonal coordinates other than Cartesian coordinates. The analysis proposed here gives elements for a proper use of MC methodology. It can be very useful for students and for teachers.