Computational & Applied Math Seminar

Optimization Models and Approaches for Strictly Correlated Electrons

  • Speaker: Xin Liu(Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

  • Time: Apr 29, 2024, 16:00-17:00

  • Location: M4009, College of Science Building


In electronic structure calculations, Kohn-Sham equations rank among the most widely adopted mathematical models. However, due to the deficiency of available approximations for exchange-correlation energy, Kohn-Sham equations cannot well describe strictly correlated electrons at present. To this end, some models based on the strong-interaction limit of density functional theory have been developed in recent decades. The associated energy minimizations can be formulated as multi-marginal optimal transport problems with Coulomb cost (MMOT). Since the curse of dimensionality resides in MMOT, its low-dimensional reformulations are indispensable. In this talk, we consider the reformulation based on a Monge-like ansatz. We discuss the difficulties in the corresponding optimization problems, and also propose a global optimization approach for numerical resolution.