International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Effective potentials to minimise the total energy functional in DFT and RDMFTNikitas Gidopoulos
Durham University, Durham, United Kingdom
Coauthor(s) : Nektarios Lathiotakis
 National Hellenic Research Foundation, Athens, Greece
Effective local potential theories in electronic structure underlie most single-particle schemes including the Kohn Sham theory and local reduced density matrix functional theory [1-3]. These theories share a common mathematical problem: quite different effective local potentials can lead to similar ground state densities and wave functions. This problem is in addition to well known pathologies of the equations determining the effective potential when the latter and the orbitals are expanded in finite basis sets. Finally, self interaction errors in approximate XC functionals in DFT manifest in the wrong asymptotics of the XC potential. A few years ago, to deal with all these issues, we restricted the admissible set of effective potentials by writing the Hartree-exchange and correlation potential, in any approximation in DFT or local RDMFT, as the electrostatic potential of an effective charge density that is non-negative and for an N-electron system it integrates to N-1 electrons. These constraints guarantee that two N-electron densities that are close to each other arise from effective potentials that are close to each other too and also they enforce the correct asymptotic behaviour of the XC potential at large distances away from the electronic system [5,6], curing the effects of self interactions that are present in the approximate XC energy as a functional of the density or the density matrix. In this talk, I shall give an overview of our approach to determine the effective potential, which is common in applications of our method using DFT or RDMFT approximations.
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