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The past decade has seen an increasing interest in designing sophisticated density functional approximations (DFAs) by integrating the power of machine learning (ML) techniques. However, application of the ML-based DFAs is often confined to simple model systems. In this work, we construct an ML correction to the widely used Perdew-Burke-Ernzerhof (PBE) functional by establishing a semilocal mapping from the electron density and reduced gradient to the exchange-correlation energy density. The resulting ML-corrected PBE is immediately applicable to any real molecule, and yields significantly improved heats of formation while preserving the accuracy for other thermochemical and kinetic properties. This work highlights the prospect of combining the power of data-driven ML methods with physics-inspired derivations for reaching the heaven of chemical accuracy.

Electron affinity (EA) is the energy released when an additional electron is attached to an atom or a molecule. EA is a fundamental thermochemical property, and it is closely pertinent to other imp...

Delocalization error associated with the presently used density functional approximations is one of the main sources of errors which plague density functional theory calculations. In this paper, we give a comprehensive review on scaling correction (SC) approaches developed recently for reducing the delocalization error. The global and local SC approaches impose the rigorous Perdew-Parr-Levy-Balduz condition that the total electronic energy should scale linearly between integer electron numbers, on systems involving global and local fractional electron distributions, respectively. After presenting the theoretical background and mathematical formulation of scaling corrections, we demonstrate that they lead to universal alleviation of delocalization error. This is exemplified by the substantial improvement for the prediction of a wide range of electronic properties, including Kohn-Sham frontier orbital energies and band gaps, dissociation behavior of molecules, reaction barriers, electric polarizabilities, and charge-transfer species. The encouraging performances of SC approaches highlight their practicality and usefulness, and also affirm that an explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error. The existing limitations, the remaining challenges, and the future perspectives of SC are also discussed. Moreover, the SC approaches are compared with some existing methods attempting to remove the self-interaction error, such as the Perdew-Zunger self-interaction correction, the local hybrid hyper-generalized gradient approximations, and the rangeseparated density functional approximations. The unique advantages of SC suggest that it could open a novel and potentially paradigm-changing route for advancing density functional theory methods towards chemical accuracy.

We explore effects of orbital relaxation on Kohn–Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn–Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn–Sham frontier orbital energies by Hartree–Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scaling correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.