Bond energies of molecules using optimal transport theory for the strictly-correlated-electron (SCE) limit of Density-Functional-Theory

Standard Kohn-Sham DFT starts from a mean-field approximation: the kinetic energy is modeled exactly, while the electron-electron interactions are modeled through a split into a mean-field term, and corrections from the exchange-correlation term. The SCE limit starts from the opposite limit: the electron-electron interactions are assumed to dominate over the kinetic energy, and hence it is a semi-classical limit. It is hence well suited to study strongly-correlated situations, e.g. bond breaking. While the SCE limit includes many-body interactions, it can be identified as a problem from Optimal Transport theory with Coulomb cost function. Hence it can be solved by a nested optimization in its dual (Kantorovich) formulation. We incorporate the Kantorovich solution within the KS-DFT framework and solve it using the finite element method. Bond-energy curve is obtained using this method for hydrogen molecule, and is compared against other exchange-correlation models to show the improved results. We then investigate bond-breaking in ethane and other small molecules using the SCE limit.