Out-of-plane vibrations of NH₂ in 2-aminopyrimidine and formamide

The out-of-plane vibrations of the amino group in primary amines involve its inversion and rotation relative to the rest of the molecule. These two vibrations in 2-aminopyrimidine (see Fig. 1) were investigated with the combined use of matrix-isolation IR spectroscopy and ab initio quantum mechanical methodology. The ab initio methodology was also applied to another primary amine, formamide, for which a gas-phase IR spectra have been previously assigned. Ab initio potential energy surfaces were calculated in internal coordinates, ω and τ, whose displacements mimicked the inversion and internal rotation normal-mode distortions of the amino group, respectively. Vibrations along these two coordinates were considered uncoupled from all other nuclear motions. Total energy was calculated at the second-order Møller-Plesset perturbation theory level at selected values of ω and τ to allow a least-squares fitting of an analytical function depicting the potential energy curves and surface. A numerical procedure for determining the values of the kinetic energy operator in internal coordinates was also implemented to which an analytical function was fit. Vibrational energy expectation values were variationally determined by utilizing products of Gaussian and sinusoidal functions as the basis set. The resultant calculated fundamental transition energies for the coupled inversion and internal rotation vibrations of 2-aminopyrimidine are v_inv=140.6 cm^-1 and v_rot=440.3 cm^-1, respectively. These theoretical values reasonably match the experimental quantities of v≈200 cm^-1 and v≈500 cm^-1, and allow firm assignment of these two experimental infrared spectral bands to the inversion and internal rotation vibrations of the amino group in 2-aminopyrimidine, respectively. For formamide (see Fig. 2), the calculated transition energies for the inversion and internal rotation vibrations, v_inv=249 cm^-1 and v_rot=602, match the experimental frequencies of ≈289 cm^-1 and ≈602 cm^-1, and confirm the accuracy of the theoretical method.