The Application of Constricted Variational Density Functional Theory to Excitations Involving Electron Transitions from Occupied Lone-Pair Orbitals to Virtual π* Orbitals
Bibliographic record
Abstract
We have applied the constricted variational density functional method (CV(n)-DFT) to n → π* transitions in which an electron is moved from an occupied lone-pair orbital n to a virtual π* orbital. A total of 34 transitions involving 16 different compounds were considered using the local density approximation (LDA), Becke, three-parameter, Lee-Yang-Parr (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 density functional theory (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 0.86 and 0.69 eV, respectively, whereas B3LYP affords an excellent fit with BE at rmsd = 0.18 eV. Resorting next to CV(∞)-DFT, where energy terms to all orders in the variational parameters are included, results in all three functionals in too high excitation energies with rmsd = 1.69, 1.14, and 0.93 eV for LDA, B3LYP, and BHLYP, respectively. Adding in orbital relaxation considerably improves the results with rmsd = 0.54, 0.30, and 0.48 eV for LDA, B3LYP, and BHLYP, respectively. It is concluded that CV(∞)-DFT with orbital relaxation is a robust method for which the accuracy is less functionally dependent than that of CV(2)-DFT or adiabatic TDDFT.
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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 | 0.000 |
| 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".