Optimization of B97-Type Density Functional Approximation, Global Hybrid, and Range-Separated Hybrid Energy Functionals with the D4 Dispersion Corrections in TAO-DFT

For multireference systems, Kohn-Sham density functional theory (KS-DFT) with the conventional exchange-correlation functionals can yield qualitative failures. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [Chai, J.-D. <i>J. Chem. Phys.</i> <b>2012</b>, 136, 154104] has been developed to address this challenge. In this work, to greatly improve the performance of the conventional density functional approximation (DFA), global hybrid (GH), and range-separated hybrid (RSH) functionals in TAO-DFT, we propose the reoptimized B97-type DFA, GH, and RSH functionals with the D4 dispersion corrections in TAO-DFT, yielding TAO-B97-D4, TAO-B97X-D4, and TAO-ωB97X-D4, respectively, wherein a newly proposed analytical parametrization of the optimal system-independent fictitious temperature θ is adopted. Also, with the constraint θ = 0 in parameter optimization, we propose the reoptimized B97-type RSH functional with the D4 dispersion corrections in KS-DFT, denoted as KS-ωB97X-D4. Besides, within TAO-DFT, we propose an efficient method, denoted as pTAO/TDA, to obtain excitation energies, without the issues of spurious excitations. The performance of the resulting functionals has been examined on a wide variety of test sets, including both single-reference systems (e.g., the GMTKN55 database and equilibrium geometries) and multireference systems (e.g., the iso-C₄₀ database and linear acenes). Moreover, we examine their performance on some challenging test sets, such as the dissociation of H₂⁺ and He₂⁺, dissociation of H₂ and N₂, and long-range charge-transfer excitations. Overall, KS-ωB97X-D4 yields high accuracy for the properties (e.g., thermochemistry, kinetics, and noncovalent interactions) of single-reference systems, while TAO-ωB97X-D4, which achieves reasonably good performance for both single-reference and multireference systems, is preferable for general applications.