2018/02/02 by Bhavsar, Rutvij Vihang, Ramakrishnan, Raghunathan
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1802.00873
In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function (W) thanks to a universal functional transformation (F), whose formal existence is akin to that of the exchange-correlation functional in density functional theory. While the exact dependence of F on W is unknown, a few approximate parametric models have been proposed in the past. Here, for a dataset of 923 one-dimensional external potentials with two interacting electrons, we apply machine learning to model F within the kernel Ansatz. We deal with over-fitting of the kernel to a specific region of phase-space by a one-step regularization not depending on any hyperparameters. Reference correlation energies have been computed by performing exact and Hartree--Fock calculations using discrete variable representation. The resulting models require W calculated at the Hartree--Fock level as input while yielding monotonous decay in the predicted correlation energies of new molecules reaching sub-chemical accuracy with training.