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

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 a complex potential. 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 study is that even for systems that are not coupled to an environment, in the non-Hermitian HF or KS equation, a single electron is interacting with the remaining electrons, which act as an environment, allowing 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, therefore, 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.