Primary Role of Semi-Local and Exact-Exchange Difference in the Description of Correlation Effects in Hybrid Functionals

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Abstract
Hybrid density functional approximations are among the most widely used electronic-structure methods, yet the physical origin of their representation of correlation effects remains incompletely understood. In this work, we analyze correlation in hybrid functionals from the perspectives of Kohn–Sham exchange–correlation potentials, correlated densities, and energy-related observables. We show that the dominant qualitative features of correlation in hybrid DFAs do not arise primarily from the semilocal correlation functional itself, but instead from the difference between the semilocal exchange and exact-exchange contributions. This exchange-difference term is essential for restoring the physically correct structure of the correlation component of the exchange–correlation potential and the corresponding correlated density, whereas the semilocal correlation part acts mainly as a compensating contribution in the core and valence regions. Based on this analysis, we propose an interpretable construction principle for hybrid functionals in which the semilocal/exact-exchange difference is scaled in a controlled way. As a proof of concept, this methodology yields the simple global hybrid UMK26 functional. Despite its uncomplicated global-hybrid form, the functional produces correlation potentials and correlated densities in good agreement with CCSD(T) references, delivers accurate ionization potentials from orbital energies, and yields very good charge-transfer excitation energies, performing on a comparable footing with several recently proposed range-separated hybrids. Although UMK26 is not uniformly optimal across all thermochemical benchmarks, it performs particularly well for self-interaction-sensitive systems and provides a physically transparent route for the rational design of future hybrid density functionals.
Funding Information
  • Narodowe Centrum Nauki (2020/39/O/ST4/00005)
  • Narodowe Centrum Nauki (2021/42/E/ST4/00096)
  • Air Force Office of Scientific Research (FA9550-23-1-0118)

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