Development in Functional Approximations and in Theory for Excited States

The accuracy of DFT predictions depends on the quality of density functional approximations. Despite advancements, significant delocalization errors persist, leading to underestimating energy gaps in molecules and materials, incorrectly predicting the dissociation limits of chemical bonds, overdelocalizing charge distributions, and misaligning energy levels at interfaces. These errors stem from the violation of exact conditions on fractional charges, which are consequences of quantum mechanical degeneracy manifested in the classical variable of electron density. Our recent development of the localized orbital scaling correction (LOSC) addresses these errors and elevates DFT to a new level of robustness and accuracy, both for molecules and bulk systems.

The orbital energies from our LOSC calculations reveals hidden excited state information from ground calculations, guiding us to the theory for excited states. Similarly in terms of total energies, since the 1970s, Kohn-Sham functionals have been employed for ∆SCF calculations of excited state energies, achieving accuracy comparable to that for ground state results, despite a lack of theoretical justification. Our recent research has established the theoretical foundation for ∆SCF calculations of excited states, showing that it is necessary to go beyond electron density and use the first-order density matrix of the noninteracting reference system to define the energy functional. The minimum of this functional corresponds to the ground state energy, consistent with ground state DFT, while the stationary solutions yield excited-state energies and electron densities, consistent with ∆SCF calculations. We also established the linear conditions for fractional charges in the excited-state theory and introduced the concepts of excited state chemical potentials. This in turn leads to the clear physical meaning of occupied and virtual orbitals energies as excited-state chemical potentials, and novel approaches to calculating excited states.