Performance of parameterized double-hybrid DFT for positive singlet–triplet gaps and charge-transfer excitations

Determine the predictive performance of the parameterized double-hybrid density functionals B2GP-PLYP and PBE-QIDH with exchange and correlation mixing coefficients a_x = 0.75 and a_c = 0.55 when applied to molecules with positive singlet–triplet gaps and to excited states with charge-transfer character, assessing whether these parameterizations maintain reliability in these regimes.

Background

This work investigates prediction of inverted (negative) singlet–triplet gaps using a range of methods and highlights a bias–variance tradeoff within double-hybrid DFT, particularly for B2GP-PLYP and PBE-QIDH. The authors scan exchange–correlation mixing parameters and identify a low-bias setting at a_x = 0.75 and a_c = 0.55 for both functionals, which substantially reduces mean error though typically at the cost of increased variance.

They propose an internally referenced scaling scheme that corrects systematic bias of low-variance parameterizations using the low-bias (75,55) variants as internal references, achieving excellent accuracy on a benchmark of triangular molecules. However, they explicitly note that it remains unresolved how these parameterized models perform for positive singlet–triplet gaps and for charge-transfer excitations, a challenging regime where even CC2 can show deficiencies.