Density functional calculations for full structures of dimers of Cu(II) complexes linked via O-H...O hydrogen bonds provide exchange-coupling constants that are in excellent agreement with experimentally reported values. Magneto-structural correlations between the exchange-coupling constant and the O...O distance or the separation between the coordination planes of the two monomers are analyzed. The calculations support the orbital models usually employed in qualitative interpretations of magneto-structural correlations, showing excellent correlations between the calculated coupling constants and the square of the orbital gap or of the overlap between the two magnetic orbitals. The orbital gap responsible for the antiferromagnetic coupling is seen to result from direct through-space overlap between the oxygen atoms of the two monomers, whereas the hydrogen bonds play an essentially structural role by holding these oxygen atoms in close proximity.