Atomic Polarizations, Not Charges, Determine CH Out-of-Plane Bending Intensities of Benzene Molecules

Infrared gas phase intensities are reported for the first time for 23 CH out-of-plane bending vibrations of eight substituted benzene molecules and naphthalene by integration of bands from the Pacific Northwest National Laboratory (PNNL) spectral library. These experimental values are found to have an rms difference of 8.7 km mol^-1 with the B3LYP/6-311++G(d,p) values for intensities ranging from close to zero to 126.7 km mol^-1. These intensities are found to have transferable electronic structure parameters, and their square roots are proportional to the amplitudes of the hydrogen atom displacements perpendicular to the benzene ring. Quantum Theory of Atom in Molecules (QTAIM)-Charge-Charge Transfer-Dipolar Polarization models were determined from the B3LYP/6-311++G(d,p) electronic densities. By far, the largest electronic contribution to these intensities is the dipolar polarization of the carbon atom of the displaced CH bond, 0.214 e. Smaller contributions are found for the polarizations of the displaced hydrogen atoms (-0.043 e) and nearest neighbor carbon atoms (-0.052 e), both having directions opposite to that of the carbon atom polarization of the displaced CH bond. The movements of static equilibrium hydrogen charges make the smallest contribution canceling most of the hydrogen polarization changes. In fact, the carbon atomic polarizations alone account for 96.9% of the dipole moment derivative vector norm for the CH out-of-plane bends. The polarization model is also found to be valid for seven CH out-of-plane bending vibrations of N-fused benzene ring molecules (N = 3, 4, 5).