Electronic Structure of Metalloporphenes, Antiaromatic Analogues of Graphene

Zinc porphene is a two-dimensional material made of fully fused zinc porphyrins in a tetragonal lattice. It has a fully conjugated π-system, making it similar to graphene. Zinc porphene has recently been synthesized, and a combination of rough conductivity measurements and infrared and Raman spectroscopies all suggested that it is a semiconductor (Magnera, T.F. et al. Porphene and Porphite as Porphyrin Analogs of Graphene and Graphite, Nat. Commun.2023, 14, 6308). This is in contrast with all previous predictions of its electronic structure, which indicated metallic conductivity. We show that the gap-opening in zinc porphene is caused by a Peierls distortion of its unit cell from square to rectangular, thus giving the first account of its electronic structure in agreement with the experiment. Accounting for this distortion requires proper treatment of electron delocalization, which can be done using hybrid functionals with a substantial amount of exact exchange. Such a functional, PBE38, is then applied to predict the properties of many first transition row metalloporphenes, some of which have already been prepared. We find that changing the metal strongly affects the electronic structure of metalloporphenes, resulting in a rich variety of both metallic conductors and semiconductors, which may be of great interest to molecular electronics and spintronics. Properties of these materials are mostly governed by the extent of the Peierls distortion and the number of electrons in their π-system, analogous to changes in aromaticity observed in cyclic conjugated molecules upon oxidation or reduction. These results give an account of how the concept of antiaromaticity can be extended to periodic systems.


Functional choice
When choosing the functional to use, we considered the following properties: (a) good description of symmetry breaking (b) good account of the extent of electron (de)localization (c) numerical stability, few adjustable parameters, long-range corrections (a) Symmetry breaking.In order to accurately capture symmetry breaking in π-conjugated compounds, a functional should describe both σ-and π-bonding with comparable accuracy. 1s many contemporary functionals are geared towards the description of molecular properties,(e.g. 2) which are largely determined by the orbitals close to the Fermi energy, they are not guaranteed to give a good description of symmetry breaking.We looked at the % EE at which symmetry breaking occurs in archetypical cases such as cyclo[18]carbon 3 (1), tetratert-butyl-s-indacene 4 (2), and the hexacation of the butadiyne-linked six-porphyrin nanoring 5 (3).Our results (Table S2) show that at 37.5% EE, symmetry breaking occurs in all three cases, consistent with experimental results and previous studies.Naturally, symmetry breaking persists at higher (50%) amounts of EE, but using such high amounts of EE usually results in worse performance, which can be attributed to increased errors due to static correlation and worse description of dynamic correlation, 6 although highly tuned empirical functionals can remedy this (e.g.M06-2X, which has 54% exchange).Due to the presence of both aromatic and antiaromatic circuits in its structure, we investigated 2 in more detail.In their recent work, 4 Wu and Haley found that an accurate description of chemical shifts in 2 is very challenging for some DFT functionals.Following their protocol (which uses B97D-2 for chemical shift calculations), we find that a very good agreement with experiment (dRMSD = 0.61 ppm) is obtained if a PBE38 geometry is used, and that using geometries obtained with either more or less EE worsens the agreement of calculated chemical shifts with experiment.
(b) Electron delocalization.When looking at how to describe metalloporphenes, one source of inspiration were mixed-valence compounds.In these systems, the electronic coupling between different sites (i.e. the extent of electron/hole delocalization) can range from essentially zero (Robin-Day class I), to intermediate (Robin-Day class II), and very strong (Robin-Day class III). 73] (c) Stability.Unfortunately, calculations on metalloporphenes using BLYP35 were prone to numerical instabilities, precluding us from using it for large-scale calculations.However, calculations on a 2⨯2 ZnP fragment using BLYP35 and PBE38 give very similar results (HOMO-LUMO gap values EHL,BLYP35 = 1.65 eV; EHL,BLYP35 = 1.74 eV , and BLA values at the cyclooctatetraene ring BLABLYP35 = 0.048 Å and BLAPBE38 = 0.053 Å), indicating that PBE38 is a reasonable substitute.

Defects
The positions of investigated defects a, b, and c in a 2⨯2 supercell of ZnP are shown in Figure S1.As geometry optimisations of 2⨯2 supercells of ZnP with C1 symmetry are prohibitively costly, we optimised smaller model systems and then manually built our defect geometries.
For defect a (Figure S2a), one Zn atom was replaced with two hydrogens, which were placed on opposing nitrogens with a bond length of 0.99 Å.Such a defect may be formed if the reinsertion of Zn following the polymerization is incomplete, and experimental evidence suggests that the density of such free-base macrocycles is no larger than 1 in 400. 14The direct band gap of this system was found to be ~0.49eV, about half of the value in pure ZnP.

From porphyrin to porphene
To understand how the electronic structure of Zn porphyrin is transformed into Zn porphene, we performed molecular calculations of Zn porphyrin and 2⨯2 and 3⨯3 Zn porphene fragments using PBE38 (Figure S3).We note that 3⨯3 fragment calculation fails when a functional with a low proportion of EE is used (e.g.B3LYP or PBE0), but proceeds without issue if a high-EE functional such as PBE38 or M06-2X (or a range-separated functional such as ωB97X-D) is used.In all cases when the calculation is successful, the geometry optimises to a minimum with alternating bond lengths in the cyclooctatetraene moiety.
Our results show that both the HOMO-LUMO gap and the average amount of bond-length alternation (BLA) in the cyclooctatetraene moieties reach values comparable to those in a polymer for a 3⨯3 fragment of ZnP (Figure S3c,d).Direct comparison is difficult, as a small Gaussian basis was used for molecular calculations, and a larger plane wave-based basis (and pseuodopotentials) were used for the polymer.
The electronic structure and antiaromaticity of ZnP may be compared to its 2⨯2 fragment (Figure S3e), where one BLA pattern of orbitals in the cycylooctatetraene moiety is associated with HOMO -1 and HOMO -11, and the other to HOMO and LUMO, leading to a paratropic coupling between HOMO -1 and LUMO and driving the bond-length alternation.

Defects b and
c (FigureS2b,c) correspond to the interruption in the π-conjugation.They were built by taking two neighboring meso (b) or beta (c) carbons out of the porphene plane by roughly ±0.15 Å for b (±0.20 Å in the case of c) Å and adding hydrogens to them (1.10 Å) in the axial position, which resulted in C-C-H angles of 105° for b (106° in the case of c).Defect b interrupts only the aromatic circuits and results in a strong shrinkage of the band gap (0.12 eV).Defect c affects both aromatic and antiaromatic circuits and has a relatively smaller effect on the band gap (0.54 eV).

Figure S1 .Figure S2 .
Figure S1.Defects in ZnP.(a) corresponds to the replacement of one zinc with two hydrogens, while (b) and (c) describe structures with the highlighted bond hydrogenated.

Figure S3 .
Figure S3.The HOMO-LUMO gap (EHL, or band gap Eg in case of the polymer) and average amount of bond-length alternation in the cyclooctatetraene unit(s) (BLACOT) in (a) Zn porphyrin, (b) a 2⨯2 or (c) a 2⨯2 fragment of ZnP, and (d) in ZnP.(e) 2⨯2 fragment orbitals with significant π-density on the cyclooctatetraene unit.

Table S1 .
Sensitivity of metalloporphene properties to the amount of exact exchange (% EE) included in the DFT functional.
a conductivity b direct band gap
a Energy difference between the D4h and D2h minima (eV).b work function (eV); c conductivity (MS/m)
a Indirect (Eg,i) and direct (Eg,d) band gap.b Energy difference between the D4h and D2h minima (eV).c work function (eV); d valence (mVB) and conduction (mCB) eff.mass