|Posted on February 12, 2016 at 11:25 AM|
Porphyrins are ubiquitous pigments in nature, playing prominent roles in several biological processes. Expanded-porphyrins are also versatile compounds giving rise to a plethora of twisted Möbius aromatic structures that give rise to Hückel-to-Möbius topological switches. These molecules can be utilized in a number of applications, including molecular electronics, such as the preparation of photovoltaic cells (dye-sensitised solar cells), nonlinear optical materials or electroluminescene displays, biomimetic catalysis and medicine.
The salient features of porphyrins and expanded porphyrins are related to its long conjugated π-electron closed circuits that furnish these molecules with a certain aromatic character. The presence of conjugated circuits in these large molecular rings calls for aromaticity measures that can be unambiguously used in rings of arbitrary size and do not suffer from severe limitations.
The aromaticity is a key property of these species that can be used to guide the synthesis and the design of new molecules. There are very few aromaticity indices that can be applied to large macrocycles. Thus far, the studies dealing with these species analyzed the aromaticity using the harmonic-oscillator model of aromaticity (HOMA), the in-house aromatic fluctuation index (FLU) or the nuclear-independent chemical shifts (NICS). These indices suffer from serious drawbacks that could lead to erroneous conclusions: HOMA or FLU are reference-based indices and therefore lead to spurious results when applied to reactivity studies; whereas NICS is known to be size-dependent and it is highly affected by the currents of metals present in metalated porphyrins. A perfect candidate to characterize porphyrins are multicenter indices (MCI), which were shown as the most reliable ones according to a series of aromaticity tests we designed. Unfortunately, MCI suffers from a series of problems (mostly numerical precision and large computational cost) that prevents its application in large rings. The smallest porphyrin already requires 16-center MCI calculations, which are both computationally expensive and very inaccurate.
In a paper recently accepted in the special issue of Phys. Chem. Chem. Phys. devoted to Electron delocalization and aromaticity: "Celebrating the 150th Anniversary of the Kekulé Benzene Structure" I introduce a new electronic aromaticity index, AV1245. AV1245 consists of the average of the 4-center MCI values along the ring that keep a positional relationship of 1,2,4,5.
AV1245 measures the extent of transferability of the delocalized electrons between bonds 1-2 and 4-5, which is expected to be large in conjugated circuits and, therefore, in aromatic molecules. A new algorithm for the calculation of MCI for large rings is also introduced and used to produce the data for the calibration of the new aromaticity index. AV1245 does not rely on reference values, does not suffer from large numerical precision errors, and it does not present any limitation on the nature of atoms, the molecular geometry or the level of calculation. It is a size-extensive measure with a small computational cost that grows linearly with the number of ring members. Therefore, it is specially suited to study the aromaticity of large molecular rings as those occurring in porphyrins or belt-shaped Möbius structures (expanded porphyrins). The work includes the analysis of AV1245 in free-base and several bis-metalated Pd octaphyrins (1,0,1,0,1,0,1,0) shown in the picture above.