A unified framework for semiclassical reaction rate theory.

Area of Science:

• Chemical Kinetics
• Quantum Mechanics
• Theoretical Chemistry

Background:

• Existing semiclassical methods like instanton theory and SCTST have limitations.
• A unified theoretical framework is needed for accurate reaction rate calculations.

Purpose of the Study:

• Develop a general semiclassical theory for reaction rate constants.
• Encompass and generalize existing semiclassical methods.
• Explore new avenues for modeling chemical reaction kinetics.

Main Methods:

• Formalism based on cumulative reaction probability and instanton contributions.
• Generalization of Gutzwiller's trace formula.
• Exact WKB/quantum Hamilton-Jacobi theory for one-dimensional systems.
• Exploration of connections to VPT2 and thermal instanton theory.

Main Results:

• Unified framework encompassing instanton theory and SCTST.
• Generalization to microcanonical scattering rates and all orders in ℏ.
• Explicit expressions for generalized reduced action up to O(ℏ4).
• Derivation of thermal instanton rate theory and perturbative corrections.
• First-order corrections for sphaleron rates above crossover temperature.

Conclusions:

• The developed theory provides a robust framework for semiclassical reaction rate calculations.
• It unifies and generalizes existing methods, offering improved accuracy.
• Potential for developing novel semiclassical methods for chemical kinetics modeling.