Coarse-Grained Free Energy Surface with Implicit Nuclear Quantum Effects: Benzene Clusters

João V M Pimentel1, Vladimir A Mandelshtam1

  • 1Department of Chemistry, University of California Irvine, Irvine, California 92697, United States.

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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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In 1865, August Kekule suggested the structure of benzene according to the structural theory of organic chemistry based on the three assertions—formula of benzene is C6H6, all the hydrogens of benzene are equivalent, and each carbon must have four bonds due to its tetravalency.
He proposed that benzene has a cyclic structure of six carbon atoms attached to one hydrogen atom each, with three alternating pi bonds.
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Simple unsubstituted benzene has six aromatic protons, all chemically equivalent. Therefore, benzene exhibits only a singlet peak at δ 7.3 ppm in the 1H NMR spectrum. The observed shift is far downfield because the aromatic ring current strongly deshields the protons. Any substitution on the benzene ring makes the aromatic protons nonequivalent, and the protons split each other. The peak is, therefore, no longer a singlet and the splitting pattern and their associated coupling constants depend...
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