A. Symmetry breaking in ZnP. Metalloporphenes such as ZnP are composed of both aromatic circuits (pyrrole and benzene, shown in blue in Figure ) with delocalized π bonds, and antiaromatic circuits (cylooctatetraene, orange) with distinctly localized bonds. This leads to mixed aromaticity (or concealed antiaromaticity 25 ), suggesting that both types of circuits need to be described with a similar level of accuracy to properly capture their electronic structure. All previous investigations of ZnP used pure density functional theory (DFT) to optimize its geometry, predicting a D4h (square) unit cell with a single minimum. Subsequent band structure calculations on this square minimum always yielded a gapless band structure, in contrast with experiment as well as with the observation that 2D materials with square lattices are exceedingly rare. This discrepancy between theory and experiment may be explained by recognizing that pure DFT overemphasizes delocalisation. In terms of the semiempirical Hubbard model, pure DFT underestimates U (the energy lost when two electrons occupy the same site) and overestimates the hopping integral t (the energy gained when an electron is free to move between sites). This leads to a too small U/t ratio, overemphasizing delocalization. Hybrid DFT can provide a better balance between localization (U) and delocalization (t) by including some percentage (usually 20-50%) of exact exchange (EE), which lowers the energy of all same-spin electron pairs. Therefore, the addition of EE promotes localization, or increases U/t, which comes at the expense of increased computation time and worse description of static correlation. By admixing different proportions of EE to the pure PBE (Perdew-Burke-Ernzerhof 31 ) functional, we found that at least 35% EE is necessary to break the square symmetry and open a band gap in ZnP (Figure ). Similar results were obtained in case of cyclo [18]carbon (an 18-membered all-carbon ring) and butadiyne-linked Zn porphyrin nanorings, which both require 30-35% EE to optimize to the experimentally found symmetrybroken geometries. For these reasons, all subsequent work presented here was done using the PBE38 (37.5% exact exchange) functional, which was also found to be the optimal proportion of EE in several benchmarks. ZnP and antiaromatic molecules. The symmetry breaking and gap-opening in ZnP may be rationalized by comparing it to antiaromatic (4n) annulenes, where n is the number of carbon atoms. In the absence of bond length alternation (BLA), 4n annulenes such as cyclobutadiene (n = 1) or planar cyclooctatetraene (n = 2) have a half-filled degenerate orbital pair related by a 90° rotation (i.e. sine and cosine solutions of the Hückel model; Figure ). This D4nh configuration is unstable; in fact, it is a transition structure connecting two equivalent broken symmetry D2nh minima, which have nonzero BLA. Introducing BLA breaks the degeneracy of the orbital pair, with one orbital (with density on shorter bonds) becoming occupied (i.e., the HOMO), and the other (with density on longer bonds) unoccupied (i.e., the LUMO; Figure ). As a result, the extent of BLA in 4n annulenes directly affects their HOMO-LUMO gap.