A simple functional representation of angular-dependent hydrogen-bonded systems. 1. Amide, carboxylic acid, and amide-carboxylic acid pairs

For describing the angular dependence of the energy of hydrogen bonds, especially for amide, carboxylic acid, and amide-carboxylic acid molecular pairs, four interatomic distances are used instead of the conventional internal coordinates (the hydrogen bond distance, two bond angles, and one dihedral angle). With the new representation, the angular dependence of the energy of hydrogen bonds can be well described with only 6-12 type potential functions without additional functions involving bond or dihedral angles. In the new model, the repulsion between 1-3 atomic pairs proved to be the most important for describing the angular dependence of the energy of hydrogen bonds. The parameters of these empirical hydrogen bond potential functions were optimized with the 6-31G** ab initio potential energy surfaces of 11 hydrogen-bonded molecular pairs. The empirical potential functions reproduce the ab initio potential surfaces very well.