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Related Concept Videos

Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

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).
Structure of Benzene: Kekulé Model01:07

Structure of Benzene: Kekulé Model

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.
NMR Spectroscopy of Benzene Derivatives01:37

NMR Spectroscopy of Benzene Derivatives

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...
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams
Nuclear Binding Energy02:13

Nuclear Binding Energy

The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons are bound together;...
π Molecular Orbitals of 1,3-Butadiene01:24

π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...

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Updated: Jun 19, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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.

The Journal of Physical Chemistry. A
|June 17, 2026
PubMed
Summary

This study introduces a new coarse-graining method to simulate nuclear quantum effects in molecular clusters. The approach quantifies these effects, including isotope impacts, in benzene clusters using a computationally efficient framework.

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Area of Science:

  • * Computational Chemistry
  • * Molecular Dynamics
  • * Quantum Mechanics

Background:

  • * Path-integral methods for nuclear quantum effects are computationally intensive.
  • * Existing methods struggle to efficiently incorporate quantum nuclear effects in molecular simulations.

Purpose of the Study:

  • * To develop a novel intramolecular coarse-graining framework for molecular cluster simulations.
  • * To incorporate nuclear quantum effects without relying on computationally expensive path-integral methods.
  • * To accurately calculate zero-point energies and vibrational free energy contributions.

Main Methods:

  • * Partitioning configuration space into slow intermolecular and fast intramolecular degrees of freedom.
  • * Quantum mechanical treatment of intramolecular modes using the local harmonic approximation.
  • * Classical Monte Carlo sampling of the temperature-dependent effective free energy surface.

Main Results:

  • * Successful incorporation of nuclear quantum effects into molecular cluster simulations.
  • * Quantification of nuclear quantum and isotope effects in a benzene cluster.
  • * Demonstration of a computationally efficient method for studying quantum effects.

Conclusions:

  • * The developed coarse-graining framework effectively includes nuclear quantum effects.
  • * The method allows for the quantification of subtle nuclear quantum and isotope effects.
  • * This approach offers a more efficient alternative to path-integral methods for specific systems.