Levy–Lieb Principle Meets Quantum Monte Carlo

Abstract

We review an approach where the energy functional of Density-Functional Theory (DFT) can be determined without empiricism via a Quantum Monte Carlo (QMC) procedure. The idea consists of a nested iterative loop where the configurational space of the electrons in the QMC procedure is determined by a trial one-particle electron density; this allows then for the determination of a first guess for the energy functional, which is then in turn used for a DFT minimization process. This latter delivers a new electron density and the loop is repeated iteratively until convergence is reached and thus the electronic structure of the system determined. In essence, from the applied point of view, such an approach is a compromise between the large computational cost but high accuracy of QMC and the reasonable computational cost but lower accuracy of DFT. The proposed approach goes beyond the standard Kohn–Sham method, which is the standard in DFT, and requires neither orbitals nor the a priori specification of the exchange and correlation functional. From the conceptual point of view, the relevant aspect is that the 3N-dimensional wavefunction is derived as a function(al) of the three-dimensional electron density, which is the key principle of DFT.