Self-consistent Formulation of Constricted Variational Density Functional Theory with Orbital Relaxation. Implementation and Applications
Bibliographic record
Abstract
We introduce here a new version of the constricted nth order variational density functional method (CV(n)-DFT) in which the occupied excited state orbitals are allowed to relax in response to the change of both the Coulomb and exchange-correlation potential in going from the ground state to the excited state. The new scheme is termed the relaxed self-consistent field nth order constricted variational density functional (RSCF-CV(n)-DFT) method. We have applied the RSCF-CV(n)-DFT scheme to the nσ→π* transitions in which an electron is moved from an occupied lone-pair orbital nσ to a virtual π* orbital. A total of 34 transitions involving 16 different compounds were considered using the LDA, B3LYP, and BHLYP functionals. The DFT-based results were compared to the "best estimates" (BE) from high level ab initio calculations. With energy terms included to second order in the variational parameters (CV(2)-DFT), our theory is equivalent to the adiabatic version of time dependent DFT . We find that calculated excitation energies for CV(2)-DFT using LDA and BHLYP differ substantially from BE with root-mean-square-deviations (RMSD) of 0.87 and 0.65 eV, respectively, whereas B3LYP affords an excellent fit with BE at RMSD = 0.33 eV. Resorting next to CV(∞)-DFT where energy terms to all orders in the variational parameters are included results for all three functionals in too high excitation energies with RMSD = 1.62, 1.14, and 1.48 eV for LDA, B3LYP, and BHLYP, respectively. Allowing next for a relaxation of the orbitals (nσ,π*) that participate directly in the transition (SCF-CV(n)-DFT) leads to an improvement with RMSD = 0.49 eV (LDA), 0.50 eV (B3LYP), and 1.12 eV (BHLYP). The best results are obtained with full relaxation of all orbitals (RSCF-CV(n)) where now RMSD = 0.61 eV (LDA), 0.32 eV (B3LYP), and 0.52 eV (BHLYP). We discuss finally the relation between RSCF-CV(n) and Slater's ΔSCF method and demonstrate that the two schemes affords quite similar results in those cases where the excitation can be described by a single orbital displacement (nσ→π*).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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".