A real-space time-domain calculation of the frequency-dependent dielectric constant of nonmetallic crystals is outlined and the integrals required for this calculation are computed. The outline is based on time dependent current density functional theory and is partially implemented in the ab initio density functional theory FIREBALL program. The addition of a vector potential to the Hamiltonian of the system is discussed as well as the need to include the current density in addition to the particle density. The derivation of gradient integrals within a localized atomic-like orbital basis is presented for use in constructing the current density. Due to the generality of the derivation we also give the derivation of the kinetic energy, dipole, and overlap interactions.