Norcorrole as a Delocalized, Antiaromatic System

Nickel norcorrole provides an unusual example of a molecule that is strongly antiaromatic according to the magnetic criterion, but which exhibits, according to high-quality DFT calculations, a symmetric, delocalized structure with no difference in bond length between adjacent Cmeso-Cα bonds. A fragment molecular orbital analysis suggests that these discordant observations are a manifestation of the high stability of the dipyrrin fragments, which retain their electronic and structural integrity even as part of the norcorrole ring system.

www.nature.com/scientificreports www.nature.com/scientificreports/ To investigate the question of magnetic antiaromaticity of NiNc, we visualized the magnetically induced current density profile (as previously done for a variety of porphyrin, hydroporphyrin 18 , carbaporphyrin 19 , corrole, and isocorrole 20 derivatives) and also calculated the bond magnetizabilities 21,22 at the B3LYP/def2-TZVP 23 level (Fig. 3). Furthermore, we decomposed both the current intensities and the bond magnetizabilities into σ and π components ( Table 2). According to the quantum theory of atoms in molecules (QTAIM) 24 , the total magnetizability of a closed-shell molecule can be decomposed into atomic and bond magnetizabilities, with the latter providing an indirect measure of the total current density flux through the interatomic surface between two neighboring atoms 25 . Keith and Bader showed that, unlike for aliphatic chains, the atomic and bond magnetizabilities of benzene are significantly anisotropic; the out-of-plane components of the magnetizabilities were found to be about three times larger than the in-plane components 26,27 . In a series of papers, one of us demonstrated that the out-of-plane bond magnetizability provides a safe index for assessing aromaticity even in complicated cases 21,22,28,29 , where simple probes such as nucleus independent chemical shift (NICS) and its variants fail 30 . Table 2 shows that the π-framework of NiNc sustains a strong paratropic electronic current (which is associated with positive bond magnetizabilities) that offsets a much smaller diatropic current along the σ-framework. The strong paratropic current is a clear indication of magnetic antiaromaticity of NiNc.
As noted above, nothing in chemical theory actually rules out a delocalized structure for an antiaromatic system. Whether bond localization will occur in a given case depends on the relative importance of π and σ distortivities of the system [31][32][33] . Typically, for antiaromatic systems, the former wins out [2][3][4] . The exceptional nature of NiNc in this regard is perhaps best appreciated in terms of the great stability of the two dipyrrin anion (dipy)      Table 2. Out-of-plane bond magnetizabilities ( χ b zz , cgs-ppm) and magnetically induced current intensities (MICI, nA/T) for NiNc. See diagram in the leftmost column for definition of bonds a-h.
fragments that make up the molecule. Such an interpretation is fully in line with a fragment molcular orbital (MO) analysis, which we carried out for the planar D 2h complex MgNc. As shown in Fig. 4, all 12 occupied π MOs of MgNc may be regarded as bonding and antibonding combinations of the 6 occupied π MOs of the Mg(dipy)F fragments. This statement is actually not a trivial one, the key implication being that none of the occupied π MOs of MgNc owes its origin to any of the unoccupied π MOs of the Mg(dipy)F fragments. The two dipyrrin halves thus largely maintain their electronic integrity as part of the norcorrole macrocycle. Notably, such an interpretation is consistent with elementary notions of organic functional groups: as vinylogous amidinates, dipyrrin anions are indeed expected to resist structural distortions such as double bond localization.

Conclusion
Our knowledge of antiaromatic porphyrinoid systems has deepened greatly in recent years. Thus, a variety of spectroscopic features have now been recognized as hallmarks of such systems 34 . As low-bandgap materials, antiaromatic porphyrinoids in general and norcorrole derivatives in particular are potentially of great interest as components of molecular electronic circuits 35 . Against this exciting backdrop, we have confirmed that simple norcorrole derivatives afford unique examples of symmetric, delocalized, antiaromatic systems. Fragment MO analysis suggests that these seemingly contradictory attributes reflect the great stability of the two dipyrrin halves of the molecule. In other words, the energetic imperative of delocalized bonding within the dipyrrin fragments overrules that of antiaromaticity-related bond length alternation.

Methods
Geometry optimization studies and the fragment MO analysis were carried out with the ADF2017 36,37 program system using methods described above. All optimized structures (see Supplementary information for coordinates) were confirmed as local minima via frequency analyses. To obtain current density plots and current intensities, geometry optimizations and GIAO NMR calculations were performed at the B3LYP/def2-TZVP level with Gaussian 09 rev. D1 38 . The NMR computations were further analyzed with the AIMAll (version 16.05.18) suite of programs 39 . Current densities were obtained within the context of quantum theory of atoms in molecules as developed by Keith and Bader [40][41][42][43][44] .