Comment on `Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry', by C. Argaez & M. Melgaard

TL;DR

This paper critically reviews a recent study on pseudo-relativistic multi-configuration methods in quantum chemistry, confirming the results but pointing out flaws and gaps in the proofs.

Contribution

It provides a critical commentary highlighting errors and incompleteness in the proofs of a recent influential paper on relativistic quantum chemistry methods.

Findings

The main results of the original paper are correct.

The proofs in the original paper are flawed and incomplete.

The commentary clarifies the validity of the results despite proof issues.

Abstract

In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.