The uncharted space of non-Hermitian solutions to the Hartree-Fock and Kohn-Sham equations

TL;DR

This paper explores the novel space of non-Hermitian solutions to Hartree-Fock and Kohn-Sham equations, revealing new physically interpretable states that extend the applicability of these methods to open-system scenarios.

Contribution

It introduces and characterizes a new class of non-Hermitian solutions to HF and KS equations, highlighting their physical relevance and implications for open-system quantum chemistry.

Findings

New non-Hermitian solutions are always encountered in open-system calculations.

These solutions can be physically interpreted, extending the applicability of HF and KS.

The work uncovers an uncharted space of solutions in quantum chemistry methods.

Abstract

Many problems in physical chemistry involve systems that are coupled to an environment, such as a molecule interacting with an adjacent surface, possibly resulting in meta-stable molecular states where electron density is transferred to the surface. Such systems can be described by non-Hermitian quantum mechanics (NHQM), where the Hamiltonian includes dissipative terms. Within NHQM, one can also formulate the Hartree-Fock (HF) and Kohn-Sham (KS) methods and, as in the conventional theory, an effective independent-particle picture is employed. The crucial observation of the present work is that even for systems that are not coupled to an environment, in the HF or KS equation a single electron is coupled to a bath of the remaining electrons which can act as an environment, opening up the possibility for the exchange of current density between the one-electron and the remaining N-1 electron system. The corresponding self-consistent states represent a new uncharted space of solutions to the HF and KS equations. We show that the additional solutions can have a physical interpretation and thus extend the range of problems HF and KS can be applied to. If open-system HF and KS calculations are performed, the new class of solutions is always encountered but this has also not been noted previously.