Building new non-empirical hybrid and double-hybrid density functionals from the TCA family of GGA expressions.

The Tognetti-Cortona-Adamo (TCA) correlation functional, and their subsequent variants, constitutes an important family of nonempirical generalized gradient approximations that have found successful applications in molecular and solid-state electronic structure calculations. In this work, we present a systematic assessment of the original TCA functional together with the revTCA, gracTCA, and transTCA variants within nonempirical hybrid (TCA0) and double-hybrid (TCA-QIDH) frameworks. Their performance is evaluated using the comprehensive GMTKN55 benchmark database, including more detailed analysis of the challenging MB16-43 and SIE4x4 subsets, as well as three different global performance metrics: WTMAD-2A, WTMAD-2B, and the recently proposed WTMAD-4. The results reveal a consistent improvement in accuracy upon ascending "Jacob's ladder," with the nonempirical double-hybrid models reducing the global errors by approximately a factor of 2-3 relative to their GGA counterparts. Among the semilocal functionals, the original TCA correlation provides the most balanced overall performance, while the differences among the various TCA-based models become much less pronounced at the double-hybrid level. Importantly, the relative ranking of the functionals is essentially unaffected by the choice of the WTMAD metric, demonstrating the robustness of the conclusions with respect to the weighting scheme adopted for the GMTKN55 database. The remaining deficiencies are associated with dispersion-dominated intermolecular interactions, highlighting the potential use of some long-range correlation corrections. Overall, this study confirms that the TCA functional, particularly when adopted in a double-hybrid scheme, constitutes a reliable and transferable framework for the development of accurate density functional approximations applicable to a broad range of chemical problems.