Machine-Learned Energy Functionals for Multiconfigurational Wave Functions

We introduce multiconfiguration data-driven functional methods (MC-DDFMs), a group of methods which aim to correct the total or classical energy of a qualitatively accurate multiconfigurational wave function using a machine-learned functional of some featurization of the wave function such as its density, on-top density, or both. On a data set of carbene singlet-triplet energy splittings, we show that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a robust degree of active-space independence. Beyond demonstrating that the density and on-top density hold the information necessary to correct the singlet-triplet energy splittings of multiconfigurational wave functions, this approach shows great promise for the development of functionals for MC-PDFT because corrections to the classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies such as those yielded by CASSCF or NEVPT2.