Diffusion frequency factors in some simple examples of transition-state rate theory

Area of Science:

• Chemical kinetics
• Physical chemistry
• Theoretical chemistry

Background:

• The Eyring rate theory is a fundamental model in chemical kinetics.
• It expresses rate constants using a frequency factor (kT/h) and partition functions.
• Extending this theory to diffusion-controlled processes is an active area of research.

Purpose of the Study:

• To extend the Eyring formalism to diffusion-controlled and hybrid reaction dynamics.
• To introduce a new frequency factor, D/Rλ, for diffusion-controlled processes.
• To demonstrate the applicability of the modified Eyring formalism using simple examples.

Main Methods:

• Substitution of the standard frequency factor (kT/h) with a diffusion-based factor (D/Rλ).
• Application of the modified Eyring formalism to diffusion-controlled and hybrid kinetic models.
• Utilizing simple model systems to illustrate the theoretical extensions.

Main Results:

• The Eyring formalism can be successfully extended to include diffusion-controlled processes.
• A new frequency factor, D/Rλ (where D is the diffusion coefficient, λ is the thermal de Broglie wavelength, and R is a characteristic distance), is proposed.
• The modified formalism is also applicable to hybrid cases, bridging diffusion and dynamics.

Conclusions:

• The Eyring formalism provides a versatile framework for calculating rate constants in various reaction regimes.
• Modified frequency factors, while not universal, are useful for approximating rate constants in complex systems by combining simple and complicated models.
• This work offers conceptual insights and practical approximations for understanding reaction dynamics.