Anharmonic contributions to the inversion vibration in 2-aminopyrimidine

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Abstract
The out‐of‐plane vibrations of the amino group in 2‐aminopyrimidine have large amplitudes, and cannot be properly described within the harmonic approximation. The normal modeanalysis carried out at this level of approximation at the restricted Hartree–Fock level and at the second‐order Mo/ller–Plesset perturbation theory level failed to match the experimental transition frequency of ν≊200 cm−1 of the inversion vibration in this compound. In an effort to better understand this vibration motion, we went beyond the harmonic approximation. The inversion vibration was treated as being uncoupled from all other nuclear degrees of freedom. An internal coordinate (ω) was chosen whose displacement mimicked the out‐of‐plane distortion of the amino group during the inversion vibration. Electronic energy was calculated at the second‐order Mo/ller–Plesset perturbation theory level at selected values of ω to form a double‐well curve describing a model potential within which the nuclei move during the vibration. This potential was incorporated into a one‐dimensional Hamiltonian, and vibrational energy expectation values were variationally determined by utilizing the harmonic wavefunctions as the basis set. Two sets of calculations were performed: one in which the mirror plane of symmetry was preserved throughout the vibrational deformation limiting the internal coordinates to 17, and another in which the symmetry was unconstrained permitting description by 3N−6=30 internal coordinates. These calculations resulted in prediction of the v=0→v=1 transition energy of ν=130.1 cm−1 and ν=206.7 cm−1, respectively, reasonably matching the experimental value of ≊200 cm−1.