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Connecting and combining rules of aromaticity. Towards a unified theory of aromaticity

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Most of the archetypal aromatic compounds present high symmetry and have degenerate highest‐occupied molecular orbitals. These orbitals can be fully occupied resulting in a closed‐shell structure or can be same‐spin half‐filled. This closed‐shell or same‐spin half‐filled electronic structure provides an extra stabilization and it is the origin of several rules of aromaticity such as the Hückel 4N + 2 rule, the lowest‐lying triplet excited state 4N Baird rule, the 4N rule in Möbius‐type conformation, the 4N + 2 Wade–Mingos rule in closo boranes or the 2(N + 1)2 Hirsch rule in spherical aromatic species. Combinations of some of these rules of aromaticity can be found in some particular species. Examples of these combinations will be discussed and the validity of some of these rules will be assessed. Moreover, it is possible to establish connections with some of these rules of (anti)aromaticity and, therefore, they can be partially generalized, which represents a step forward to a future unified theory of aromaticity. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Software > Quantum Chemistry
In blue the most stable structure of molecules I and II in their closed‐shell singlet state. In red, alternative structures of these molecules that do not follow the Glidewell–Lloyd rule
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Benzannulated cyclobutadiene linear and kinked isomers
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The molecular orbitals of the valence electrons of 5Ta3
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Covalent, diradical, and polar mesomeric structures relevant to explain the electronic structure of compound TMTQ. (Reprinted with permission from Reference . Copyright 2016 Wiley)
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Analogy between boron hydrides and hydrocarbons based on Hückel's rule. Below each figure NICS(0) value (in italics, in ppm) is included. (Reprinted with permission from Reference . Copyright 2016 Wiley)
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Electronic confined space analogy applied to benzene leads to closo borane B7H72− by using BH+4 as sacrificial atom (sA). The total number of 36 valence electrons remains constant throughout the process
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A series of compounds derived from the application of electronic confined space analogy to acetylene. In the first row, we have acetylene (I) and two structures obtained from I by electronic transmutation and second row correspond to structures generated by the addition of up to three H+ as sacrificial atoms (red atoms) to compound III with a triple BB bond
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Extended Ottosson's cube summarizing several combinations of rules of (anti)aromaticity for annulenes
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(a) Two out of the five Kekulé resonance structures of phenanthrene and their corresponding Clar aromatic π‐sextets indicated with a circle. The structure with the largest number of aromatic π‐sextets is the so‐called Clar's structure and (b) application of the Glidewell–Lloyd rule to two polycyclic conjugated hydrocarbons
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Distribution of molecular orbitals in spherical systems. Numbers in red correspond to closed‐shell structures (Hirsch's rule) and numbers in blue to the open‐shell half‐filled with same spin electrons structures (2N2 + 2N + 1 rule)
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Distribution of molecular orbitals and electrons in (a) Hückel aromatic compounds, (b) Baird lowest lying triplet state aromatic compounds, and (c) Möbius aromatic compounds. The orbital in red can be present or not depending on the number of C atoms of the annulene
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Software > Quantum Chemistry
Electronic Structure Theory > Density Functional Theory
Electronic Structure Theory > Ab Initio Electronic Structure Methods

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