IR intensities for out-of-plane vibrations at planar transition state structures: The NX3 series

The ground state pyramidal geometries of NX₃ (X = H, F, Cl, Br) molecules might undergo a process called “pyramidal inversion”, with a planar transition state structure connecting two identical but oppositely oriented pyramids. In view of recent findings regarding infrared intensities of planar molecules as well as IR intensities of transition states structures, which have demonstrated how the atomic dipoles cannot be ignored when describing the molecular dipole moment, we now combine these two approaches in evaluating the IR intensities of the planar transition state structures of the pyramidal inversions of NX₃. We also applied a numerical method to decompose the force constant of the out-of-plane imaginary normal mode. Our findings show that Coulomb forces are the main factor that shapes the inversion barrier of those molecules. Also, the Charge–Charge Transfer–Dipolar Polarization (CCTDP) decomposition of the imaginary reveals that, while the CT term is null due to symmetry constraints, the DP contribution follows the same direction of the inversion and the atomic polarization X in response to the nitrogen movement in the imaginary normal mode depends on the relative volume of N and X. The out-of-plane normal modes of molecules such as PF₅ are slight different from those of NX₃, since their normal modes may not be subject to the same symmetry constrains, indicating a mathematical distinction between planar and non-planar molecules.