A Simple Model for the Mean and Difference of NH-Stretching Frequencies for NH₂ Groups, and Its Application to Results of Some ab initio Vibrational-Frequency Calculations

Abstract

The expression for the sum of the eigenvalues of the 2×2 GF matrix for two interacting NH bonds suggests that the mean NH-stretching frequency for an NH₂ group should be closely proportional to ( Σf )^½, where Σf is the sum of the two corresponding force constants. Ab initio results for the NH₂ groups in various conformations of ethanamine , hydrazine and 1,1-dimethylhydrazine confirm such constancy to within 0.1%.

The corresponding expression for the difference of the eigenvalues suggests, counterintuitively, that the difference of NH-stretching frequencies for an NH₂ group in a given molecular system should also be largely proportional to ( Σf )^½ and, except for the gauche conformation of 1,1-dimethylhydrazine, ab initio results for the above molecules support this suggestion to within ±14 cm^-1. In the exceptional case, the difference of NH-stretching force constants makes a much larger than usual contribution.

Relative values of the force constants for various molecular species may be interpreted in terms of the relative geometries and effects of donation of lone-pair electrons at an adjacent centre into antibonding N-H orbitals at the given centre.