Density functional theory (DFT) provides a formally exact way of reducing the intractable many-electron problem to an effective single electron problem, where the quantum many-electron interactions are encapsulated into a mean-field, called the exchange-correlation (xc). Although known to be unique functionals of the ground-state electronic charge density, rho(r), the exact form of these functionals - expressed either as energy (E_{xc}[rho(r)]) or potential (v_xc[rho(r)]) - are unknown, necessitating the use of approximate functionals. The existing xc functionals, despite their success in predicting a wide range of materials properties, exhibit certain notable failures - underpredicted bandgaps, incorrect bond-dissociation curves, wrong charge-transfer excitations, to name a few. Typically, these approximations are constructed through semi-empirical parameter fitting in model systems, thereby making systematic improvement and conformity to certain known exact conditions difficult. We attempt to address this through data-driven modeling of xc functionals. This involves, generating a training data set comprising of rho(r) to v_xc(r) map, and then, use of machine learning algorithms to learn the functional form of vxc[ρ(r)] (and Exc[ρ(r)]), conforming to the exact conditions.
In this talk, I will present the details regarding generating the rho(r) to v_xc(r) map and then sketch out the basic idea behind a machine-learned xc functionals. Speaker(s): Bikash Kanungo (University of Michigan)