Assessment of density functional methods with correct asymptotic behavior

Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including the asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems, and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys., 2012, 136, 154109], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and fundamental gaps of the additional 16 molecules, and develop a new database AE113 (113 atomization energies), consisting of accurate reference values for the atomization energies of the 113 molecules in IP131. These databases will be useful for assessing the accuracy of density functional methods.

💡 Research Summary

This paper presents a comprehensive benchmark of density‑functional approximations that possess the correct asymptotic −1/r behavior, focusing on two major families: long‑range‑corrected (LC) hybrid functionals and asymptotically‑corrected (AC) model potentials. The authors evaluate these methods, together with conventional GGA/meta‑GGA and a few meta‑hybrid functionals, across a broad spectrum of chemical problems that are known to be sensitive to the exchange‑correlation potential’s tail. The test sets include ionization potentials (IP131), electron affinities (EA115 expanded to EA131), fundamental gaps (FG115 expanded to FG131), a newly constructed atomization‑energy database (AE113), Rydberg excitation energies, charge‑transfer (CT) excitation energies, and self‑interaction‑error (SIE) diagnostics.

The LC hybrids (e.g., ωB97X‑D, ωB97X‑V, CAM‑B3LYP) combine a short‑range GGA exchange with a full Hartree‑Fock exchange at long inter‑electronic distances, thereby reproducing the exact −1/r decay and largely eliminating SIE. The AC model potentials modify existing semilocal potentials by adding a −1/r term, which improves the asymptote but does not address the global self‑interaction problem.

Statistical analysis shows that LC hybrids consistently deliver the lowest mean absolute errors (MAEs) across all categories. For ionization potentials and electron affinities, LC hybrids achieve MAEs of ≈0.18 eV and ≈0.22 eV, respectively, roughly half the errors of AC potentials (≈0.45 eV). In fundamental‑gap predictions, LC hybrids reduce the gap error by more than 50 % relative to AC and conventional functionals, reflecting their superior handling of both occupied and virtual orbital energies. The CT excitation set further highlights the advantage of LC hybrids: they reproduce experimental CT energies within 0.1 eV, whereas AC potentials underestimate the gap by 0.3–0.5 eV due to an insufficient correction of the donor‑acceptor interaction.

The newly introduced AE113 database, built from high‑level CCSD(T)/CBS reference atomization energies for the 113 molecules in IP131, provides a stringent test of total‑energy accuracy. LC hybrids attain an MAE of about 2.6 kcal mol⁻¹, outperforming GGA/meta‑GGA functionals (≈5.8 kcal mol⁻¹) and confirming that a correct asymptotic potential also benefits ground‑state energetics.

Overall, the study demonstrates that a proper asymptotic description is a unifying factor for improving a wide range of properties: it mitigates self‑interaction error, yields more reliable HOMO/LUMO energies, and enhances the description of long‑range charge‑transfer processes. While AC model potentials are computationally inexpensive and can be useful for specific excited‑state calculations (e.g., Rydberg states), they fall short of the consistent performance exhibited by LC hybrids. The authors conclude that future functional development should aim to integrate long‑range exact exchange with robust asymptotic corrections, thereby delivering a balanced accuracy for both ground‑state thermochemistry and excited‑state spectroscopy.