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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.07048 |
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| _version_ | 1866917132162301952 |
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| author | Ernzerhof, Matthias Loutis, Mohamed Roy, Pierre-Olivier Mayou, Didier |
| author_facet | Ernzerhof, Matthias Loutis, Mohamed Roy, Pierre-Olivier Mayou, Didier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The uncharted space of non-Hermitian solutions to the Hartree-Fock and Kohn-Sham equations Ernzerhof, Matthias Loutis, Mohamed Roy, Pierre-Olivier Mayou, Didier Quantum Physics 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. |
| title | The uncharted space of non-Hermitian solutions to the Hartree-Fock and Kohn-Sham equations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.07048 |