The importance of self-interaction and nonlocal exchange corrections to the density functional theory of intracavity electrons in Na-doped sodalites

Abstract

Electrons that are confined to zeolite cavities are modeled using a simplified pseudopotential scheme to represent the interaction of the electrons with both the sodalite framework and the Na+ ions. By comparing theory with recent experimental studies of G centers in Na-doped NaBr-SOD it is demonstrated that restricted forms of density functional theory, where two electrons are forced to pair in the same Kohn–Sham orbital, fail to correctly predict the true nature of the singlet, (spin unpolarized), G center. Electron confinement leads to generalized gradient corrections to the exchange of 0.74 eV and self-interaction corrections (SIC) of 0.7 eV over calculations performed in the local spin density approximation (LSDA). Only the self-interaction corrected generalized gradient approximation and the unrestricted Hartree–Fock approximation are in accord with experiment for the relative stability of the triplet (spin polarized) state. The unrestricted Hartree–Fock method is used to show that G-center absorptions will be blueshifted with respect to absorptions due to the isolated F centers. Constructing a Hubbard Hamiltonian we show that the exchange coupling ranges in values from 2.3 meV(UHF) to 3.6 meV(SIC-LSDA) corresponding to Neel temperatures that range from 27 to 41 K in agreement with experiment.