A heterogeneous conductorlike solvation model (conductorlike screening model/conductorlike polarizable continuum model) that uses different local effective dielectrics for different portions of the solute cavity surface is implemented for quantum chemical Hartree-Fock and Kohn-Sham methods. A variational treatment is used to form the heterogeneous solvation operator, so a simple analytic expression of the energy gradients, which are vital for geometry optimization and molecular dynamics simulation, is derived and implemented. Using the new Fixed Points with Variable Areas surface tessellation scheme, continuous and smooth potential energy surfaces as well as analytic gradients are obtained for this heterogeneous model. Application of the heterogeneous solvation model to a realistic quantum model consisting of 101 atoms for the type-1 Cu center in rusticyanin shows that the desolvation due to protein burial can likely raise the reduction potential by approximately 200 mV and, including the heterogeneity in geometry optimization, can likely affect the results by approximately 2 kcal/mol or approximately 70 mV.