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Bond orders in metalloporphyrins Marcel Swart1,2  Received: 5 June 2020 / Accepted: 29 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract A new concept of bond order density of shared electron pairs is introduced to study the electronic structure in molecules. This BODSEP analysis is applied to the distortion of benzene toward its building blocks (acetylenes), metalloporphyrins and two recent examples from the literature. The S12g/TZ2P results show the gradual disappearance of the bonds while distorting benzene and strengthening the bonds in acetylene to reach a final triple bond value. A large range of bond orders are observed for the metalloporphyrins, which are consistent with aromaticity indices from the literature [Can. J. Chem. 2009, 87, 1063]; with an ideal value of 1.5 for aromatic molecules (because of resonance), it suggests that (BODSEP) bond orders might be used for aromaticity measures. Finally, the delocalized bonds in porphyrins are localizing in the corrphycenes, and bond order strengths for different spin states of dipyrrolonaphthyridinedione have been assigned, which differ from the original description. Keywords  Chemical bonding · Porphyrins · Benzene · Bond orders

1 Introduction The creativity of chemists is fostered by thinking of molecules in terms of building blocks [1], similar to Lego, which has led to the construction [2] of nanosized supramolecules [3–5], biomolecules [6, 7] or transition metal complexes [8, 9] with great precision. The similarity of pieces within families of these building blocks has been known for decades and is used extensively in synthetic routes; within quantum chemistry, this similarity can be targeted (as Carbó-Dorca has demonstrated in great detail) through quantitative structure–activity relationships (QSAR) [10–12] or quantitative Dedicated to Ramon Carbó-Dorca on the occasion of his 80th birthday. Published as part of the special collection of articles derived from the Chemical Concepts from Theory and Computation. Electronic supplementary material  The online version of this article (https​://doi.org/10.1007/s0021​4-020-02667​-z) contains supplementary material, which is available to authorized users. * Marcel Swart [email protected] 1



ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain



IQCC and Department of Chemistry, University of Girona, c/M.A. Capmany 69, 17003 Girona, Spain

2

structure–property relationships (QSPR) [13–15]. However, molecules such as fullerenes or porphyrins can display a wide variety of properties which depend strongly on the total number of electrons [16], presence or absence of encapsulated clusters [17, 18], the type of metal to which the molecule is bound [19, 20] or the conformations/distortions of, e.g., porphyrin rings [21–24]. In 2009 [19], I reported how the chemical bonding in metalloporphyrins changes as function of the size of the transition metal, its spin state and its ability to form ionic or covalent bonds. Together with Feixas and Solà, we also investiga