Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene

Benjamin Lasorne1, Fabrizio Sicilia, Michael J Bearpark

  • 1Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom.

Related Concept Videos

Photochemical Electrocyclic Reactions: Stereochemistry01:26

Photochemical Electrocyclic Reactions: Stereochemistry

The absorption of UV–visible light by conjugated systems causes the promotion of an electron from the ground state to the excited state. Consequently, photochemical electrocyclic reactions proceed via the excited-state HOMO rather than the ground-state HOMO. Since the ground- and excited-state HOMOs have different symmetries, the stereochemical outcome of electrocyclic reactions depends on the mode of activation; i.e., thermal or photochemical.
Selection Rules: Photochemical Activation
Cycloaddition Reactions: MO Requirements for Photochemical Activation01:12

Cycloaddition Reactions: MO Requirements for Photochemical Activation

Some cycloaddition reactions are activated by heat, while others are initiated by light. For example, a [2 + 2] cycloaddition between two ethylene molecules occurs only in the presence of light. It is photochemically allowed but thermally forbidden.
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
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).
ortho–para-Directing Activators: –CH3, –OH, –⁠NH2, –OCH301:11

orthopara-Directing Activators: –CH3, –OH, –⁠NH2, –OCH3

All ortho–para directors, excluding halogens, are activating groups. These groups donate electrons to the ring, making the ring carbons electron-rich. Consequently, the reactivity of the aromatic ring towards electrophilic substitution increases. For instance, the nitration of anisole is about 10,000 times faster than the nitration of benzene. The electron-donating effect of the methoxy group in anisole activates the ortho and para positions on the ring and stabilizes the corresponding...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...