The zeolite sodalite is a crystalline compound consisting of cages. The windows connecting the cages are large enough to allow small molecules to be absorbed. The material studied here, called sodium electro-sodalite (SES), is prepared by absorbing one Na atom in each cage. Because of the large electric fields inside the cages, each alkali atom is ionized and the donated electron is shared among several ions. A noninteracting electron model, used in earlier work, calculated the absorption spectrum and the temperature dependence of the Al and Si NMR shifts and found good agreement with experiment. The model predicted that the material is a metal. However, recently published low-temperature magnetic susceptibility measurements show that the ground electronic state is antiferromagnetic. This is incompatible with a noninteracting electron model. In this paper we study the electronic properties of this material by using various levels of spin-density functional (local density approximation, local spin-density approximation, generalized gradient spin-density approximation, and self-interaction corrected generalized gradient spin-density approximation) and unrestricted Hartree-Fock calculations. While all calculations show SES to be a narrow band material, only the unrestricted Hartree-Fock (UHF) and self-interaction corrected (SIC) density functional calculations lead to an autoferromagnetic ground state. The resulting Wannier functions are used to calculate the exchange constant for the antiferromagnetic Heisenberg spin-Hamiltonian. The Neel temperature predicted by UHF is 47 K while the self-interaction-corrected generalized gradient spin-density approximation gives a Neel temperature of 42 K.