Dependence of the length of the hydrogen bond on the covalent and cationic radii of hydrogen, and additivity of bonding distances

The lengths of the hydrogen bond, d(–H) in inorganic and biochemical groups have been evaluated from the observed donor (X) to acceptor (Y) distances, d(XH…Y)obs using the covalent and ϕ-based ionic radii of X and Y, where ϕ is the Golden ratio. It is found that d(−H) = nd(H+) + md(H), where d(H) and d(H+) = 2d(H)/ϕ2 = 0.28 Å are, respectively, the covalent and cationic radii, n = 1 or 2 and m = mX + mY = 0, 1, 2 or 3. In all cases, d(XH…Y)obs = d(XH…Y)cal = d(X) + d(H) + d(–H) + d(Y).