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Like benzene, cyclobutadiene and cyclooctatetraene are cyclic compounds with alternate single and double bonds. However, their chemical behavior differs from benzene, as they are unstable and not aromatic. So, what are the structural characteristics of unsaturated compounds categorized as aromatic?  
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Neutral hydrocarbons like cyclopentadiene with an odd number of carbon atoms and one intervening CH2 group in the ring are not aromatic. Cyclopentadiene with 4 π electrons does not satisfy the 4n + 2 π electron rule. Additionally, the intervening CH2 group is sp3 hybridized and lacks a vacant p orbital, thereby interrupting the overlap of p orbitals in a continuous manner and preventing the delocalization of π electrons throughout the ring.
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The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
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Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
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Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Joan Grèbol-Tomàs1,2, Eduard Matito2,3, Pedro Salvador1

  • 1Departament de Química, Universitat de Girona, Campus de Montilivi, 17071, Girona, Spain.

Chemistry (Weinheim an Der Bergstrasse, Germany)
|May 22, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces new Hilbert-space partitions for atom-in-molecule (AIM) analysis, overcoming limitations in calculating aromaticity for large conjugated systems. The developed ESIpy code enables robust aromaticity assessment in complex molecules.

Keywords:
AromaticityAtomic PartitionComputational ChemistryElectron delocalizationExtended Systems

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Organic Chemistry

Background:

  • Aromaticity is key to molecular stability and reactivity, assessed via electron delocalization using atom-in-the-molecule (AIM) partitioning.
  • Real-space AIM methods face computational costs and numerical errors, limiting analysis to smaller molecules.
  • Existing Hilbert-space methods have reliability issues with large basis sets in modern computational chemistry.

Purpose of the Study:

  • To explore robust Hilbert-space partitions for atom-in-molecule (AIM) analysis in aromaticity studies.
  • To overcome limitations of real-space AIM methods for large conjugated systems.
  • To introduce a new computational tool for analyzing aromaticity in extended molecular structures.

Main Methods:

  • Investigated atom-in-molecule (AIM) partitioning using meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) in Hilbert space.
  • Developed and applied the ESIpy Python code for aromaticity analysis.
  • Calculated multicenter index (MCI) and Iring for large conjugated rings.

Main Results:

  • Meta-Löwdin, NAO, and IAO partitions effectively replace real-space AIMs, offering advantages without drawbacks.
  • Successfully computed multicenter index (MCI) and Iring values for large conjugated rings for the first time.
  • Introduced ESIpy, an open-source tool facilitating aromaticity analysis in extended systems.

Conclusions:

  • Hilbert-space partitions provide a computationally efficient and accurate alternative for AIM-based aromaticity calculations.
  • ESIpy enables the study of aromaticity in large, complex conjugated systems previously inaccessible.
  • This work advances the computational assessment of aromaticity in modern chemistry.