The optical properties of the F center in BaF2 are of importance because the F center is a product of radiation damage when the material is used as a luminescent radiation detector. Its optical excitation energy is 2.03 eV, experimentally. We have applied computational modeling to study this process. Our method is based on a quantum molecular cluster containing the defect, embedded in a shell-model crystal. When the excess electron of the F center is kept localized in the molecular cluster, an excitation energy of 3.33 eV is found. When the F-center electron is allowed to become much more diffuse, the ground state remains within the vacancy, but the excited state delocalizes, and the excitation energy drops to about 2.56 eV, but the model is inaccurate because quantum-mechanical features of distant ions are omitted. A polaronic representation of the single diffuse electron is then carefully incorporated with the embedded quantum cluster treatment of the system. The polaron in BaF2 is found to be beyond the intermediate-coupling regime. Feynman's path-integral results for Fröhlich's polaron model give an effective mass of 3.12, in units of band mass. The resultant estimate of F-center excitation energy is 2.04 eV. The successful combination of a quantum molecular cluster modeling element with bulk crystal modeling elements (band mass and polaron correction) warrants further study along these lines. Quantitative and physical limitations of the method and results are discussed.