Non-covalent interactions
A hydrogen bond (H-bond), is a specific type of interaction that involves dipole-dipole attraction between a partially positive hydrogen atom and a highly electronegative, partially negative oxygen, nitrogen, sulfur, or fluorine atom (not covalently bound to said hydrogen atom). It is not a covalent bond, but instead is classified as a strong non-covalent interaction. It is responsible for why water is a liquid at room temperature and not a gas (given water's low molecular weight). Most commonly, the strength of hydrogen bonds lies between 0 - 4 kcal/mol, but can sometimes be as strong as 40 kcal/mol In solvents such as chloroform or carbontetrachloride one observes e.g. for the interaction between amides additive values of about 5 kJ/mol. According to L. Pauling the strength of a hydrogen bond is essentially determined by the electrostatic charges. Measurements of thousands complexes in chloroform or carbontetrachloride have led to additive free energy increments for all kind of donor-acceptor combinations.
Metal ions in aqueous solution
The strength of the metal-oxygen bond can be estimated in various ways. The hydration enthalpy, though based indirectly on experimental measurements, is the most reliable measure. The scale of values is based on an arbitrarily chosen zero, but this does not affect differences between the values for two metals. Other measures include the M–O vibration frequency and the M–O bond length. The strength of the M-O bond tends to increase with the charge and decrease as the size of the metal ion increases. In fact there is a very good linear correlation between hydration enthalpy and the ratio of charge squared to ionic radius, z/r. For ions in solution Shannon's "effective ionic radius" is the measure most often used.