Cyclic-$N3.$ II. Significant geometric phase effects in the vibrational spectra

An accurate theoretical prediction of the vibrational spectra for a pure nitrogen ring (cyclic-$N3)$ molecule is obtained up to the energy of the $A22/B12$ conical intersection. A coupled-channel approach using the hyperspherical coordinates and the recently published ab initio potential energy surface [D. Babikov, P. Zhang, and K. Morokuma, J. Chem. Phys. 121, 6743 (2004)] is employed. Two independent sets of calculations are reported: In the first set, the standard Born–Oppenheimer approximation is used and the geometric phase effects are totally neglected. In the second set, the generalized Born–Oppenhimer approximation is used and the geometric phase effects due to the $D3h$ conical intersection are accurately treated. All vibrational states are analyzed and assigned in terms of the normal vibration mode quantum numbers. The magnitude of the geometric phase effect is determined for each state. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-$N3:$ it is ∼100 cm⁻¹ for the low-lying vibrational states and exceeds 600 cm⁻¹ for several upper states. On average, this is almost two orders of magnitude larger than in the previously reported studies. This unique example suggests a favorable path to experimental validation.