Influence of pseudo-Jahn-Teller activity on the singlet-triplet gap of azaphenalenes

We analyze the possibility of symmetry-lowering induced by pseudo-Jahn-Teller interactions in six previously studied azaphenalenes that are known to have their first excited singlet state (S1) lower in energy than the triplet state (T1). The primary aim of this study is to explore whether Hund's rule violation is observed in these molecules when their structures are distorted from C2v or D3h point group symmetries by vibronic coupling. Along two interatomic distances connecting these point groups to their subgroups Cs or C3h, we relaxed the other internal degrees of freedom and calculated two-dimensional potential energy subsurfaces. The many-body perturbation theory (MP2) suggests that the high-symmetry structures are the energy minima for all six systems. However, single-point energy calculations using the coupled-cluster method (CCSD(T)) indicate symmetry lowering in four cases. The singlet-triplet energy gap plotted on the potential energy surface also shows variations when deviating from high-symmetry structures. A full geometry optimization at the CCSD(T) level with the cc-pVTZ basis set reveals that the D3h structure of cyclazine (1AP) is a saddle point, connecting two equivalent minima of C3h symmetry undergoing rapid automerization. The combined effects of symmetry lowering and high-level corrections result in a nearly zero singlet-triplet gap for the C3h structure of cyclazine. Azaphenalenes containing nitrogen atoms at electron-deficient sites - 2AP, 3AP, and 4AP - exhibit more pronounced in-plane structural distortion; the effect is captured by the long-range exchange-interaction corrected DFT method, omega B97XD. Excited state calculations of these systems indicate that in their low-symmetry energy minima, T1 is indeed lower in energy than S1, upholding the validity of Hund's rule. Jahn-Teller analysis predicts the symmetries of the in-plane distortion vibrational modes as or B2: C2v -> Cs agreeing with the vibrational frequencies of the saddle-points. Geometry optimization at post-MP2 quantum chemistry levels capture symmetry lowering of cyclazine and its polyaza analogues with nitrogen at electron-deficient sites.