Eliminating Delocalization Error through Localized Orbital Scaling Correction with Orbital Relaxation from Linear Response

Abstract

Despite the great success Kohn-Sham density functional theory (KS-DFT) has achieved, the delocalization error remains a major challenge for commonly used density functional approximations (DFAs), resulting in systematic errors in ionization energies, electron affinities, band structures, and charge distributions. A recently developed localized orbital scaling correction (LOSC) method, namely linear response LOSC (lrLOSC), addresses these challenges by incorporating a functional correction that includes the screening effect and orbital localization within the LOSC framework. The method has been shown to provide accurate descriptions of bulk systems and core-level binding energies in small molecular systems. In this work, we extend the applicability of lrLOSC to a broader range of molecular systems, spanning various sizes, with a focus on the corrections to valence orbital energies and total energies. To enable the calculation of large chemical systems, we developed an efficient implementation of lrLOSC with computational costs comparable to standard KS-DFT calculations. Numerical results show that, while screening provides modest improvements for small molecules, it becomes critical for achieving high accuracy in larger molecules, from linear to three-dimensional systems. With the screening effect well captured in a unified way, lrLOSC provides accurate descriptions for a wide range of chemical systems, including organic molecular systems of varying sizes and transition-metal oxide complexes, establishing it as a powerful tool for enhancing the reliability of computational simulations of chemical systems.

Figures (4)

• Figure 1: The MAEs of IPs, measured in eV, for gas-phase molecules of varying sizes obtained through different methods. The test set comprises 61 small molecules (containing no more than 8 atoms), 31 large non-linear molecules (with more than 8 atoms), poly-acetylene H(HC=CH)_nH (where n ranges from 1 to 10), and transition metal oxides from the fourth period. Note that, in general, orbital energies from the parent GGA functional deviate by more than 4 eV.
• Figure 2: The MAEs of EAs, measured in eV, for gas-phase molecules of varying sizes obtained through different methods. The test set comprises 46 small molecules (containing no more than 8 atoms), 23 large non-linear molecules (with more than 8 atoms), and transition metal oxides from the fourth period. Note that, in general, orbital energies from the parent GGA functional deviate by nearly 3.5 eV.
• Figure 3: Error distribution of the first IP obtained form lrLOSC-PBE and GSC2-PBE for molecules with different sizes.
• Figure 4: lrLOSC total energy correction ($\Delta E_{\text{lrLOSC}}$) for (a) TCNE and its cation, and (b) benzonitrile and its cation. The vertical IPs are evaluated using three approaches: 1. The total energy difference between the cationic and neutral systems (indicated by green arrows), 2. The HOMO energy of the neutral system (bottom), and 3. The LUMO energy of the cationic system (top). The reference IP values are obtained from EOM-CCSD(T) calculations using the aug-cc-pVTZ basis set dunning_gaussian_1989. Errors relative to the EOM-CCSD(T) IP are reported beneath the total energy difference.