Informing Empirically\nFitted Density Functionals about\nthe Physics of Interelectronic Interactions

Further progress in constructing highly accurate density\nfunctionals\nby enforcing known laws of interelectron interactions is slow, so\nfitting techniques are usually employed nowadays. These approaches\nwere shown to lead to overfitting when a functional becomes unreliable\nfor properties on which it was not trained on. An approach to maintain\nthe correct physical behavior of a functional during its training\nis required to build more complex and accurate functionals, including\nthose based on neural networks. We devise such an approach and apply\nit to reparameterize the heavily fitted and popular M06-2X functional\non its original training set. The resulting physics-informed functionals\npiM06-2X and piM06-2X-DL approached the accuracy of M06-2X in thermochemical\ntasks and the accuracy of PBE0 in electron densities, taking the best\nout of both worlds. Surprisingly, we find that a very similar performance\ncan be achieved directly by using the PBE-2X functional without any\nfitting. The proposed approach should be indispensable for training\nfuture neural-network-based functionals.