We have measured several IR bands of FCH2CN-BF3 and ClCH2CN-BF3 in solid nitrogen, argon, and neon. These bands include the B-F asymmetric stretch (nu(a)(BF)), the B-F symmetric stretch (nu(s)(BF)), the BF3 symmetric deformation or "umbrella" mode (delta(s)(BF)), and the CN stretch (nu(CN)). For both complexes, the frequencies of these modes shift across the various media, particularly the B-F asymmetric stretching band, and thus they indicate that the inert gas matrix environments significantly alter the structural properties of FCH2CN-BF3 and ClCH2CN-BF3. Furthermore, the frequencies shift in a manner that parallels the dielectric constant of these media, which suggests a progressive contraction of the B-N distances in these systems and also that it parallels the ability of the medium to stabilize the increase in polarity that accompanies the bond contraction. We have also mapped the B-N distance potentials for FCH2CN-BF3 and ClCH2CN-BF3 using several density functional and post-Hartree-Fock methods, all of which reveal a flat, shelflike region that extends from the gas-phase minimum (near 2.4 angstrom) toward the inner wall (to about 1.7 angstrom). Furthermore, we were able to rationalize the medium effects on the structure by constructing hybrid bond potentials composed of the electrostatic component of the solvation free energy and the gas-phase electronic energy. These curves indicate that the solvation energies are greatest at short B-N distances (at which the complex is more polar), and ultimately, the potential minima shift inward as the dielectric constant of the medium increases.