Energetics and chemical bonding of the 1,3,5-tridehydrobenzene triradical and its protonated form

Quantum chemical calculations were applied to investigate the electronic structure of the parent 1,3,5-tridehydrobenzene triradical (C6H3, TDB) and its anion (C6H3-), cation (C6H3+) and protonated form (C6H4+). Our results obtained using the state-averaged complete active space self-consistent-field (CASSCF) followed by second-order multi-state multi-configuration perturbation theory, MS-CASPT2, and MRMP2 in conjunction with the large ANO-L and 6-311++G(3df,2p) basis set, confirm and reveal the followings: (i) TDB has a doublet 2A1 ground state with a 4B2-2A1 energy gap of 29 kcal/mol, (ii) the ground state of the C6H3- anion in the triplet 3B2 being 4 kcal/mol below the 1A1 state. (iii) the electron affinity (EA), ionization energy (IE) and proton affinity (PA) are computed to be: EA = 1.6 eV, IE = 7.2 eV, PA = 227 kcal/mol using UB3LYP/6-311++G(3df,2p) + ZPE; standard heat of formation ΔHf(298 K, 1 atm)(TDB) = 179 ± 2 kcal/mol was calculated with CBS-QB3 method. An atoms-in-molecules (AIM) analysis of the structure reveals that the topology of the electron density is similar in all compounds: hydrogens connect to a six-membered ring, except for the case of the 2A2 state of C6H4+ (MBZ+) which is bicyclic with fused five- and three-membered rings. Properties of the chemical bonds were characterized with Electron Localization Function (ELF) analysis, as well as Wiberg indices, Laplacian and spin density maps. We found that the radicals form separate monosynaptic basins on the ELF space, however its pair character remains high. In the 2A1 state of TDB, the radical center is mainly localized on the C1 atom, while in the 2B2 state it is equally distributed between the C3 and C5 atoms and, due to the symmetry, in the 4B2 state the C1, C2 and C3 atoms have the same radical character. There is no C3-C5 bond in the 2A1 state of TDB, but the interaction between these atoms is strong. The ground state of cation C6H3+ (DHP), 1A1, is not a diradical and has a doubly aromatic character. Aromaticity of the different compounds was studied within the ELF framework and the standard deviation of the bond lengths and bond orders. The Jahn-Teller distorted 2A1 and 2B2(C2v) states of TDB were found to exhibit an aromaticity comparable to that of benzene. Overall protonation of the TDB reinforces the stability of the low-spin doublet states, the classical Hund's rule is not obeyed. In a view, these species could better be regarded as radicals than triradicals.