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Radical reactions can occur either intermolecularly or intramolecularly. In an intermolecular radical reaction, a nucleophilic radical adds to an electrophilic alkene or vice versa. In such reactions, the radical and generally the alkene, which is also called the radical trap, are two different molecules. Additionally, for such intermolecular reactions to occur, the radical trap must be active, present in an excess concentration, and the radical starting material must have a weak...
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Ring-opening metathesis polymerization or ROMP involves strained cycloalkenes as starting materials. The mechanism of ROMP proceeds by reacting cycloalkene with Grubbs catalyst to give metallacyclobutane intermediate which undergoes a ring-opening reaction to form new carbene. The new carbene reacts with another molecule of cycloalkene. Repetition of these steps leads to the formation of an unsaturated open-chain polymer product. All these steps are reversible, however, relieving the ring...
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Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
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Pericyclic Reactions: Introduction01:17

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Electrocyclic reactions are reversible reactions. They involve an intramolecular cyclization or ring-opening of a conjugated polyene. Shown below are two examples of electrocyclic reactions. In the first reaction, the formation of the cyclic product is favored. In contrast, in the second reaction, ring-opening is favored due to the high ring strain associated with cyclobutene formation.
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Updated: Dec 25, 2025

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Multistate ring polymer instantons and nonadiabatic reaction rates.

Srinath Ranya1, Nandini Ananth1

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA.

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|March 23, 2020
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Summary

We developed two new methods, Mean-Field (MF)-RPI and Mapping Variable (MV)-RPI, to study quantum dynamics in multistate systems. The MF-RPI accurately calculates rate constants for adiabatic and nonadiabatic processes.

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Area of Science:

  • Quantum chemistry
  • Chemical dynamics
  • Statistical mechanics

Background:

  • Accurate calculation of quantum canonical partition functions is crucial for understanding chemical dynamics.
  • Multistate systems present challenges due to complex electronic and nuclear interactions.

Purpose of the Study:

  • To introduce and validate two novel multistate ring polymer instanton (RPI) formulations: Mean-Field (MF)-RPI and Mapping Variable (MV)-RPI.
  • To assess their performance in calculating rate constants for systems exhibiting adiabatic and nonadiabatic dynamics.

Main Methods:

  • Derivation of two RPI formulations from an exact path integral representation.
  • Application to model two-state systems coupled to a single nuclear mode.
  • Numerical computation and analysis of instanton paths and electronic state populations.

Main Results:

  • MF-RPI shows good agreement with literature for symmetric systems and robust performance with driving forces.
  • MV-RPI provides unique insights into electronic state population changes along the instanton path.
  • Both methods confirm the existence of a zero-mode and identify true instanton solutions.
  • MF-RPI accurately calculates rate constants across a wide range of coupling strengths.

Conclusions:

  • The developed MF-RPI and MV-RPI methods offer accurate and robust approaches for studying quantum dynamics in multistate systems.
  • These methods are particularly effective for both adiabatic and nonadiabatic regimes.
  • The MF-RPI provides a reliable tool for calculating reaction rate constants.