A semilocal machine-learning correction to density functional approximations

Machine learning (ML) has demonstrated its potential usefulness for the development of density functional theory methods. In this work, we construct an ML model to correct the density functional approximations, which adopts semilocal descriptors of electron density and density derivative and is trained by accurate reference data of relative and absolute energies. The resulting ML-corrected functional is tested on a comprehensive dataset including various types of energetic properties. Particularly, the ML-corrected Becke's three parameters and the Lee-Yang-Parr correlation (B3LYP) functional achieves a substantial improvement over the original B3LYP on the prediction of total energies of atoms and molecules and atomization energies, and a marginal improvement on the prediction of ionization potentials, electron affinities, and bond dissociation energies; whereas, it preserves the same level of accuracy for isomerization energies and reaction barrier heights. The ML-corrected functional allows for fully self-consistent-field calculation with similar efficiency to the parent functional. This study highlights the progress of building an ML correction toward achieving a functional that performs uniformly better than B3LYP.