Leveraging the Bias-Variance Tradeoff in Quantum Chemistry for Accurate Negative Singlet-Triplet Gap Predictions: A Case for Double-Hybrid DFT
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arXiv
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| Format: | Preprint |
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2025
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| author | Majumdar, Atreyee Ramakrishnan, Raghunathan |
| author_facet | Majumdar, Atreyee Ramakrishnan, Raghunathan |
| contents | Molecules that have been suggested to violate the Hund's rule, having a first excited singlet state (S$_1$) energetically below the triplet state (T$_1$), are rare. Yet, they hold the promise to be efficient light emitters. Their high-throughput identification demands exceptionally accurate excited-state modeling to minimize qualitatively wrong predictions. We benchmark twelve S$_1$-T$_1$ energy gaps to find that the local-correlated versions of ADC(2) and CC2 excited state methods deliver excellent accuracy and speed for screening medium-sized molecules. Notably, we find that double-hybrid DFT approximations (e.g., B2GP-PLYP and PBE-QIDH) exhibit high mean absolute errors ($>100$ meV) despite very low standard deviations ($\approx10$ meV). Exploring their parameter space reveals that a configuration with 75% exchange and 55% correlation, which reduces the mean absolute error to below 5 meV, but with an increased variance. Using this low-bias parameterization as an internal reference, we correct the systematic error while maintaining low variance, effectively combining the strengths of both low-bias and low-variance DFT parameterizations to enhance overall accuracy. Our findings suggest that low-variance DFT methods, often overlooked due to their high bias, can serve as reliable tools for predictive modeling in first-principles molecular design. The bias-correction data-fitting procedure can be applied to any general problem where two flavors of a method, one with low bias and another with low variance, have been identified a priori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Leveraging the Bias-Variance Tradeoff in Quantum Chemistry for Accurate Negative Singlet-Triplet Gap Predictions: A Case for Double-Hybrid DFT Majumdar, Atreyee Ramakrishnan, Raghunathan Chemical Physics Molecules that have been suggested to violate the Hund's rule, having a first excited singlet state (S$_1$) energetically below the triplet state (T$_1$), are rare. Yet, they hold the promise to be efficient light emitters. Their high-throughput identification demands exceptionally accurate excited-state modeling to minimize qualitatively wrong predictions. We benchmark twelve S$_1$-T$_1$ energy gaps to find that the local-correlated versions of ADC(2) and CC2 excited state methods deliver excellent accuracy and speed for screening medium-sized molecules. Notably, we find that double-hybrid DFT approximations (e.g., B2GP-PLYP and PBE-QIDH) exhibit high mean absolute errors ($>100$ meV) despite very low standard deviations ($\approx10$ meV). Exploring their parameter space reveals that a configuration with 75% exchange and 55% correlation, which reduces the mean absolute error to below 5 meV, but with an increased variance. Using this low-bias parameterization as an internal reference, we correct the systematic error while maintaining low variance, effectively combining the strengths of both low-bias and low-variance DFT parameterizations to enhance overall accuracy. Our findings suggest that low-variance DFT methods, often overlooked due to their high bias, can serve as reliable tools for predictive modeling in first-principles molecular design. The bias-correction data-fitting procedure can be applied to any general problem where two flavors of a method, one with low bias and another with low variance, have been identified a priori. |
| title | Leveraging the Bias-Variance Tradeoff in Quantum Chemistry for Accurate Negative Singlet-Triplet Gap Predictions: A Case for Double-Hybrid DFT |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2502.09330 |