Quantum Systems: A Mathematical Journey from Few to Many Particles

Kantorovich dual solution for strictly correlated electrons in atoms and molecules

Lin Lin

Lawrence Berkeley National Laboratory


Kohn-Sham density functional theory (KSDFT) is the most widely used electronic structure theory for condensed matter systems. If the exact exchange-correlation functional (xc) is given, KSDFT provides the exact total energy for the ground-state of a many-body problem with the cost of a mean-field calculation. Tremendous progress has been made in the past three decades in constructing approximate exchange correlation functionals based on the known information from the uniform electron gas. However, such approximate exchange-correlation functionals are known to fail for strongly correlated systems. The many-body Coulomb repulsive energy of strictly correlated electrons (SCE) provides direct information on the exact exchange-correlation functional in the strong interaction limit. Mathematically such limit can be obtained by solving a N-body optimal transport problem with Coulomb cost. Until now the treatment of strictly correlated electrons has been based on the calculation of comotion functions with the help of semianalytic formulations. This procedure is system-specific and has been limited to spherically symmetric atoms and strictly one-dimensional systems. We develop a nested optimization method which solves the Kantorovich dual problem directly, and thus facilitates a general treatment of strictly correlated electrons for systems including atoms and small molecules. (Joint work with Christian Mendl)