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 (HF(2)-) and terminal fluoride (F-) ligands in copper pyrazine complexes including Cu(HF(2))(pyz)(2)BF(4), Cu(HF(2))(pyz)(2)ClO(4), and CuF(2)(H(2)O)(2)(pyz). We compare our results with several one- and two-dimensional prototype materials including Cu(pyz)(NO(3))(2) and Cu(pyz)(2)(ClO(4))(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.