Unexplored solutions in Hartree–Fock and Kohn–Sham equations
Bibliographic record
Abstract
Many problems in physical chemistry involve systems that are coupled to an environment, such as a molecule interacting with a nearby surface. In these cases, electron density may flow between the system and its surroundings, leading to metastable states and other open-system phenomena that cannot be captured by conventional Hermitian quantum mechanics. Non-Hermitian quantum mechanics (NHQM) [1] provides a natural framework for the description of open systems. Hartree-Fock (HF) and Kohn-Sham (KS) methods can be extended to the non-Hermitian domain [2–7]. Here, we show that even for nominally isolated systems, within HF and KS, each electron can be viewed as coupled to the remaining electrons, which serve as an environment. This viewpoint reveals that an electron can leave or rejoin the system, producing self-consistent complex potentials. These unconventional solutions are absent in the conventional closed-system HF and KS approach. We show that these additional solutions can be physically meaningful. Our results highlight the importance of incorporating non-Hermitian perspectives into electronic structure calculations, offering new insights and extending the range of problems HF and KS can be applied to. [1] Moiseyev, N. Non-Hermitian Quantum Mechanics, Cambridge University Press (2011). [2] Zhou, Y., Ernzerhof, M. J. Chem. Phys. 136, 094105 (2012). [3] Ernzerhof, M. J. Chem. Phys. 125, 124104 (2006). [4] Zhou, Y., Ernzerhof, M. J. Phys. Chem. Lett. 3, 1916–1920 (2012). [5] Burton, H. G. A., Thom, A. J. W. J. Chem. Theory Comput. 12, 167–173 (2016). [6] Burton, H. G. A., Gross, M., Thom, A. J. W. J. Chem. Theory Comput. 14, 607–618 (2018). [7] Burton, H. G. A., Thom, A. J. W., Loos, P.-F. J. Chem. Theory Comput. 15, 4374–4385 (2019).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".