We report a systematic investigation of the temperature-dependent infrared vibrational spectra of a family of chemically related coordination polymer magnets based upon bridging bifluoride (HF2-) and terminal fluoride (F-) ligands in copper pyrazine complexes including Cu(HF2)(pyz)(2)BF4, Cu(HF2)(pyz)(2)ClO4, and CuF2(H2O)(2)(pyz). We compare our results with several one- and two-dimensional prototype materials including Cu(pyz)(NO3)(2) and Cu(pyz)(2)(ClO4)(2). Unusual low-temperature hydrogen bonding, local structural transitions associated with stronger low-temperature hydrogen bonding, and striking multiphonon effects that derive from coupling of an infrared-active fundamental with strong Raman-active modes of the pyrazine building-block molecule are observed. On the basis of the spectroscopic evidence, these interactions are ubiquitous to this family of coordination polymers and may work to stabilize long-range magnetic ordering at low temperature. Similar interactions are likely to be present in other molecule-based magnets.