Leveraging the Bias‐Variance Tradeoff in Quantum Chemistry for Accurate Negative Singlet‐Triplet Gap Predictions: A Case for Double‐Hybrid DFT
Atreyee Majumdar, Raghunathan Ramakrishnan
Journal of Computational Chemistry·2025
<jats:title>ABSTRACT</jats:title><jats:p>Molecules that have been suggested to violate the Hund's rule, having a first excited singlet state () energetically below the triplet state (), 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 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 () despite very low standard deviations (). 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.</jats:p>