Comment on “The consequences of neglecting permutation symmetry in the description of many-electrons systems”

FERNÁNDEZ, FRANCISCO M.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

JOHN WILEY & SONS INC

Año: 2019 vol. 119

0020-7608

In this article, we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their lack of proper permutation symmetry. This alternative building approach is based on products of a space times a spin function with opposite permutation symmetry. The main argument for devising such factors is that the eigenfunctions of the nonrelativistic Hamiltonian are either symmetric or antisymmetric with respect to the transposition of the variables of a pair of electrons. However, since the eigenfunctions of the nonrelativistic Hamiltonian are basis for the irreducible representations of the symmetric group, they are not necessarily symmetric or antisymmetric, except in the trivial case of two electrons. We carry out a simple and straightforward general analysis of the symmetry of the eigenfunctions of the nonrelativistic Hamiltonian and illustrate our conclusions by means of two exactly solvable models of N = 2 and N = 3 identical interacting particles. RELATED ARTICLE: Nascimento M. A. C. The consequences of neglecting permutation symmetry in the description of many-electrons systems. Int J Quantum Chem. 2019;119:e25765. https://doi.org/10.1002/qua.25765.