A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field II: Quantum Chemistry Calculations with Gauge Invariant Atomic Orbitals
Bibliographic record
Abstract
In a companion paper, we have developed a phase-space electronic structure theory of molecules in magnetic fields, whereby the electronic energy levels arise from diagonalizing a phase-space Hamiltonian Ĥ PS ( X, P, G, B ) that depends parametrically on nuclear position and momentum. The resulting eigenvalues are translationally invariant; moreover, if the magnetic field is in the z -direction, then the eigenvalues are also invariant to rotations around the z -direction. However, like all Hamiltonians in a magnetic field, the theory has a gauge degree of freedom (corresponding to the position of the magnetic origin in the vector potential), and requires either (i) formally, a complete set of electronic states or (ii) in practice, gauge-invariant atomic orbitals (GIAOs) in order to realize such translational and rotational invariance. Here we describe how to implement a phase-space electronic Hamiltonian using GIAOs within a practical electronic structure package (in our case, Q-Chem). We further show that novel phenomena can be observed with finite B -fields, including minimum energy structures with Π min ≠ 0, indicating nonzero electronic motion in the ground-state.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".