Can halogen bond energy be reliably estimated from electron density properties at bond critical point? The case of the (A)nZ-Y•••X- (X, Y = F, Cl, Br) interactions

Relationships between the Y center dot center dot center dot X bond critical point (BCP) properties or the Y center dot center dot center dot X distance and the halogen bond interaction energy were analyzed in detail by theoretical methods for the series of structures [(A)(n)Z-Y center dot center dot center dot X](-) (X,Y = F, Cl, Br; totally 441 structures). No relationship was found for the whole set of structures or for the series [(A)(n)Z-F center dot center dot center dot X](-), [(A)(n)Z-Cl center dot center dot center dot X](-), and [(A)(n)Z-Br center dot center dot center dot X](-). The interaction energies may be roughly estimated from the BCP properties for the series [(A)(n)Z-Y center dot center dot center dot F](-), [(A)(n)Z-Y center dot center dot center dot Cl](-), and [(A)(n)Z-Y center dot center dot center dot Br](-) as well as for [(A)(n)Z-Y center dot center dot center dot X](-) (when (A)(n)Z is variable, X and Y are constant) with the mean absolute deviation values 2.04-4.38 kcal/mol. The corresponding recommended relationships are provided and they are significantly different from the popular dependencies deduced previously for other types of noncovalent interactions. Tremendous effect of the computational method and basis set on the relationships under analysis was discovered. Computational results clearly indicate that, for practical purposes, the E-int(BCP property) dependencies should be established not simply for each global type of interactions (hydrogen bond, halogen bond, chalcogen bond, etc.) but for each combination of the first and second order atoms taking into account also the computational method and basis set.