(Supported by the Airforce Office of Scientific Research)

The previously unknown energetic form of nitrogen has been recently predicted theoretically and produced experimentally. This is a stable ring isomer of N_{3} (having the form of an isosceles triangle) called cyclic-N_{3} hereafter. Cyclic-N_{3} was first detected in the UV photolysis experiments:

ClN_{3}+ *hv* → Cl + N_{3}

Experimental data showed that in addition to the already known weakly bound linear-N_{3} isomer, there was another energetic form of N3, with energy about 1.35 eV above that of linear-N3. Thus, cyclic-N3 carries large amount of energy and is an interesting new candidate for technological applications in energy storage, high nitrogen explosives, and new propellants. It is worth mentioning that the nitrogen resources on our planet are practically limitless. Due to structural similarity the cyclic-N_{3} (a radical) can probably be used as a precursor for creating tetrahedral N_{4} (stable molecule) which then can be used as a powerful and clean monopropellant:

N_{4} → 2N_{2}

Since this reaction produces only nitrogen molecules, the main component of atmospheric air, the exhaust gases present no environmental hazards and are indistinguishable from the ambient air.

All available experimental information for cyclic-N_{3} is consistent with theoretical picture of this molecule; however, the final proof for the existence of cyclic-N_{3} is yet to be made by means of high-resolution spectroscopy. Cyclic-N_{3} is a Jahn-Teller molecule that exhibits a conical intersection between two of its potential energy surfaces at the *D*_{3h} (equilateral triangle) configuration. That conical intersection causes the equilibrium geometry to distort off the *D*_{3h} geometry. Further complication is due to the geometric phase effect, when the symmetry of electronic wave function changes six times as the vibrational wave function encircles the conical intersection.

In order to model the photoelectron spectrum of this molecule we have developed the PES for cationic species cyclic-N3+. We calculated all the vibrational states of cyclic-N3+ as well and finally derived the photo-electron spectrum of cyclic-N3 (see Fig. 4). This broad spectrum differs dramatically from that of the linear tri-nitrogen isomer, which has only one intense peak in this energy range due to similarity in the equilibrium structures of the neutral and ionized species. On the scale of Fig. 4 that single peak would appear at about 5680 cm-1. This difference should help to distinguish the two isomers simultaneously present in the experimental molecular beam.

We have developed an accurate *ab initio* the potential energy surface (PES) for cyclic-N_{3}, see Fig. 3, and carried out the state-of-the-art calculations of the vibrational energies and wave of functions cyclic-N_{3}. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-N_{3}: 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 other molecules. This unique example suggests a favorable path to experimental validation using infrared absorption spectroscopy.

**Figure 3: **A surface plot for stereographic projection of the cyclic-N3 PES. The value of the hyper-radius is fixed at 3.407 a.u. The conical intersection is seen at (*x* = 0, *y* = 0). The vertical axis gives energy in eV.

**Figure 4**: Theoretically predicted photoelectron spectra of cyclic-N_{3}.

a) Main band of transitions between the states of *E*-symmetry;

b) Hot bands of transitions between the states of *A*_{1}-symmetry (blue), *A*_{2}-symmetry (green), and *E*-symmetry (red). Final state labels in terms of polyads are given for several most intense peaks;

c) Vibrational wave function of one of cyclic-N_{3}^{+} states.

#### Relevant Publications

- D. Babikov, "Perturbation theory treatment of pseudo-rotation in cyclic-N
_{3}", J. Chem. Phys 134, 114305 (2011).
- D. Babikov, B.K. Kendrick, "The infrared spectrum of cyclic-N
_{3}: Theoretical prediction", J. Chem. Phys 133, 174310 (2010).
- D. Babikov, V. A. Mozhayskiy and A. I. Krylov, “The photoelectron spectrum of elusive cyclic-N3 and characterization of the potential energy surface and vibrational states of the ion”,
*J. Chem. Phys.* 125, 84306 (2006).
- V. A. Mozhayskiy, D. Babikov and A. I. Krylov, “Conical and glancing Jahn-Teller intersections in the cyclic trinitrogen cation”,
*J. Chem. Phys.* 124, 224309 (2006).
- D. Babikov, B. Kendrick, P. Zhang, and K. Morokuma, “Cyclic-N3: II. Large geometric phase effects in the vibrational spectra”,
*J. Chem. Phys.* 122, 44315 (2005).
- D. Babikov, P. Zhang, and K. Morokuma, “Cyclic-N3: I. An accurate potential energy surface for the ground doublet electronic state up to the energy of the 2A2/2B1 conical intersection”,
*J. Chem. Phys.* 121, 6743 (2004).