Relationship between the bond lengths in N-H...N,O-H...O,F-H...F,and Cl-H...Cl hydrogen bridges

The applicability of the equation $ e^{ - ((r_1 - r_0 )/b)^{5/3} } + e^{ - ((r_2 - r_0 )/b)^{5/3} } = 1 $ e^{ - ((r_1 - r_0 )/b)^{5/3} } + e^{ - ((r_2 - r_0 )/b)^{5/3} } = 1 has been studied. The equation defines the relationship between the experimental values of the covalent (r ₁) and hydrogen (r ₂) bond lengths in O-H...O bridges for describing the relation between the experimental interatomic distances in N-H...N bridges and the parameters of X-H...X fragments (X = O, N, F, Cl) calculated by the density functional method (B3LYP/6-31++G(d,p)) for neutral, positive, and negative molecular complexes. Here r ₀ is the mean value of the X-H bond length in free molecules; r _sym is the X...H distance in the symmetrical bridge; and b is the coefficient defined by the equation b = (r _sym − r ₀)/(ln2)^3/5. This equation allows us to adequately describe the relationships between bond lengths in nearly linear hydrogen bridges formed by oxygen, nitrogen, fluorine, and chlorine atoms. It is thus universal and can be used in studies of a wide range of substances.