Direct Unconstrained Optimization of Excited States in Density Functional Theory
Bibliographic record
Abstract
Orbital-optimized density functional theory (DFT) has emerged as an alternative to time-dependent (TD) DFT, capable of describing difficult excited states with significant electron density redistribution, such as charge-transfer, Rydberg, and double-electron excitations. Here, a simple method is developed to solve the main problem of excited-state optimization─the variational collapse of excited states onto the ground state. In this method, called variable-metric time-independent DFT (VM TIDFT), the electronic states are allowed to be nonorthogonal during the optimization, but their orthogonality is gradually enforced with a continuous penalty function. With nonorthogonal electronic states, VM TIDFT can use molecular orbital coefficients as independent variables, which results in a closed-form analytical expression for the gradient and allows to employ any of the multiple unconstrained optimization algorithms that guarantee convergence of the excited-state optimization. Numerical tests on multiple molecular systems show that the variable-metric optimization of excited states performed with a preconditioned conjugate gradient algorithm is robust and produces accurate energies for well-behaved excitations and, unlike TDDFT, for more challenging charge-transfer and double-electron excitations.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".