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Aromatic Hydrocarbon Anions: Structural Overview01:18

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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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In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as...
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Aromatic Hydrocarbon Cations: Structural Overview01:18

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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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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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Molecular Orbital Theory II03:51

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Molecular Orbital Energy Diagrams
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Electron Spin Densities and Density Functional Approximations: Open-Shell Polycyclic Aromatic Hydrocarbons as Case

Marika Savarese1, Éric Brémond2, Ilaria Ciofini3

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Density functional approximations (DFAs) show varied performance in predicting spin density for open-shell systems. Hybrid functionals generally improve accuracy over semilocal ones, but double hybrids present challenges for spin polarization studies.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Accurate prediction of spin density is crucial for understanding open-shell systems.
  • Density functional approximations (DFAs) are widely used but their performance varies.
  • Open-shell systems with extended conjugation, like π-radicals, are challenging test cases.

Purpose of the Study:

  • To investigate the performance of various density functional approximations (DFAs) in predicting spin density.
  • To evaluate how different DFAs handle electron delocalization and spin polarization in π-radicals.
  • To identify limitations of current DFAs for studying magnetic and electronic properties.

Main Methods:

  • Testing a large panel of DFAs on seven selected π-radicals.
  • Analyzing the prediction of spin density (difference between spin α and spin β electron densities).
  • Assessing the impact of functional types (semilocal, hybrid, double hybrid) on accuracy.

Main Results:

  • DFAs generally improve in predicting spin density from semilocal to hybrid functionals.
  • Double hybrid functionals show diminished performance due to the interplay of exact exchange and correlation.
  • Significant differences in spin delocalization and polarization patterns were observed across DFAs.

Conclusions:

  • The choice of DFA significantly impacts the accuracy of spin density predictions in π-radicals.
  • Current DFAs may not be universally applicable for studying spin-related phenomena like molecular magnetism.
  • Further development of DFAs is needed for reliable modeling of electron delocalization and spin polarization.