  During the past decades, approximate Kohn-Sham density-functional theory
schemes garnered many successes in computational chemistry and physics; yet the
performance in the prediction of spin state energetics is often unsatisfactory.
By means of a machine-learning approach, an enhanced exchange and correlation
functional is developed to describe adiabatic energy differences in transition
metal complexes. The functional is based on the computationally efficient
revision of the regularized strongly constrained and appropriately normed
(R2SCAN) functional and improved by an artificial neural-network correction
trained over a small dataset of electronic densities, atomization energies
and/or spin state energetics. The training process, performed using a
bio-inspired non gradient-based approach adapted for this work from Particle
Swarm Optimization, is discussed in detail. The meta-GGA functional is finally
shown to outperform most known density functionals in the prediction of
adiabatic energy differences for both the validation test and the generality
test.
