F center in sodium electrosodalite as a physical manifestation of a non-nuclear attractor in the electron density

The structure of sodium electrosodalite (SES), ${\mathrm{Na}}_8({\mathrm{AlSiO}}_4{)}_6,$ has been determined at 20 K using synchrotron powder diffraction. Subsequently the electron density was calculated through a periodic unrestricted Hartree-Fock approach and analyzed by topological methods. The F center is found to manifest itself as a maximum in the electron density at a non-nuclear position. Thus it possesses a separate identity and behaves quantum mechanically as an open system, bounded by a surface of local zero flux in the gradient vector field of the electron density. Different basis sets have been considered, and the introduction of a basis set capable of describing the F center leads to a large drop in the total energy. The F center contains almost solely unpaired electron density which is loosely bound and exhibits a very low kinetic energy density. Calculations on both a ferromagnetic and an antiferromagnetic phase have been performed and the total electron densities in the two phases are found to be very similar, with the alternating ordering of the spin density being the only difference between the two phases. The electron localization function has been introduced for an open-shell system and has been used to illustrate the magnetic phase transition.