Properties of twenty five hydrogen-bonded complexes, namely, F-x(HF)n (n=1-6), RFx(HF)n (R=t-Bu, i-Pr, Et, Me; n = 1-3), XFx(HF)n (X = H, Br, Cl; n=1-2), and FF…HF with the hydrogen bond energy varying in a wide range have been calculated using ab initio methods at the MP2/6-31++G** level. For the first time, the energies, geometrical parameters and vibrational frequencies are obtained for the series of clusters, where the bonding character changes from covalent to van der Waals on the variation of proton-acceptor ability of the base, and the energies are in the range of 45 - 1 kcal/mol. The mutual influence of multiple hydrogen bonds of F…HF type in clusters, in which a fluorine anion or an atom participates in hydrogen bond formation as the acceptor, is systematically investigated. The relative changes in the values of the considered parameters on the sequential addition of an HF molecule (anticooperativity) were determined. It was shown that non-additivity of the interaction is most strongly pronounced in