We present an efficient formalism for property evaluation using the Hartree-Fock-density-functional-theory method. The formalism uses the relaxed density concept for first-order properties which allows us to compute many different components of a property as well as many different properties once we have solved a single set of linear equations spanning the particle-hole space of the system. The density matrix representation of the method indicates that the method accounts for the correlation correction to Hartree-Fock only through particle-hole space. We also show why conventional density functionals based upon a local density and its gradient fail to account for electromagnetic effects. For second-order properties, we show that no extra linear equations need to be solved, once the regular coupled perturbed Hartree-Fock equations are solved.