Can the FCI energies/properties be predicted with HF/DFT densities?

We use the elongated hydrogen chain as an illustration to affirmatively answer the question, “Can the FCI energies/properties be predicted with Hartree–Fock (HF) or density function theory (DFT) densities?” as proposed by the late Bob Parr. We employ some simple physics-inspired density-based quantities from the information-theoretic approach (ITA) to linearly correlate with the full configuration interaction (FCI) energies with the approximate DMRG (density matrix renormalization group) method as a solver. We have showcased that the deviations between the calculated and predicted ground-state energies are only about a few milliHartree. Moreover, with the “gold standard” CCSD(T) (coupled cluster with singles and doubles, and perturbative triples) polarizabilities as a reference, we have found a way to systematically reduce the severe overestimation of the molecular polarizabilities as calculated by the approximate DFT functionals. Accordingly, we have applied this strategy to simultaneously predict the energies and molecular properties of strongly correlated systems only with the ground-state electron densities as an input, which should be a good starting point for more complex systems.Graphical abstract