On Integral INICS Aromaticity of Pyridodiazepine Constitutional Isomers and Tautomers

The structure, energetics, and aromaticity of c.a. 100 constitutional isomers and tautomers of pyrido[m,n]diazepines (m = 1, 2; n = 2, 3, 4, 5; m ≠ n) were studied at the B3LYP/cc-pVTZ level. The pyrido[1,3]diazepines appear the most, while pyrido[2,4]diazepines are the least stable (ca. 26 kcal/mol). In the pyrido[1,n]diazepine group (n = 2-5), the [1,5] isomers are higher in energy by ca. 4.5 kcal/mol and the [1,4] ones by ca. 7 kcal/mol, and the pyrido[1,2]diazepines are the least stable (ca. 20 kcal/mol). All the most stable pyrido[1,n]diazepines have N-atoms near the ring's junction bond but on opposite sites. The most stable [2,n]-forms are also those with the pyridine ring N6-atom near the junction bond. Surprisingly, for the [1,2]-, [1,3]-, and [1,4]-isomer condensation types of pyridine and diazepine rings, the same N9 > N7 > N6 > N8 stability pattern obeys. The stability remains similar in a water medium simulated with the Polarizable Continuum Model of the solvent and is conserved when calculated using the CAM-B3LYP or BHandHlyp functionals. The ring's aromaticity in the pyridine[m,n]diazepines was established based on the integral INICS index resulting from the NICSzz-scan curves' integration. The integral INICS index is physically justified through its relation to the ringcurrent as demonstrated by Berger, R.J.F., et al. Phys. Chem. Chem. Phys. 2022, 24, 624. The six-membered pyrido rings have negative INICS_ZZ indices and can be aromatic only if they are not protonated at the N-atom. All protonated pyrido and seven-membered rings exhibit meaningful positive INICS_ZZ values and can be assigned as antiaromatic. However, some non-protonated pyrido rings also have substantial positive INICS_ZZ indices and are antiaromatic. A weak linear correlation (R² = 0.72) between the INICS_ZZ values of the pyridine I(6) and diazepine I(7) rings exists and is a consequence of the communication between the π-electron systems of the two rings. The juxtaposition of the INICS descriptor of the six- and seven-membered rings and diverse electron density parameters at the Ring Critical Points (RCP) revealed good correlations only with the Electrostatic Potentials from the electrons and nuclei (ESPe and ESPn). The relationships with other RCP parameters like electron density and its Laplacian, total energy, and the Hamiltonian form of kinetic energy density were split into two parts: one nearly constant for the six-membered rings and one linearly correlating for the seven-membered rings. Thus, most of the electron density parameters at the RCP of the six-membered rings of pyridodiazepines practically do not change with the diazepine type and the labile proton position. In contrast, those of the seven-membered rings display aromaticity changes in the antiaromatic diazepine with its ring structural modifications.