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

In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, Argaez and Melgaard have studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case [M. Lewin, Solutions of the multiconfiguration equations in quantum chemistry, Arch. Ration. Mech. Anal. 171 (1) (2004) 83114. doi:10.1007/s00205003-0281-6]. The main results of the paper of Argaez and Melgaard are correct, but the proofs are both wrong and incomplete.