Shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory

Area of Science:

• Chemical kinetics
• Quantum chemistry
• Theoretical chemistry

Background:

• Quantum transition-state theory (QTST) approximates reaction rates using quantum mechanical principles.
• The Wigner tunnelling correction factor, derived from QTST, is widely used but diverges in the shallow-tunnelling regime.
• Accurate rate calculations are crucial for understanding chemical reactions, especially those involving quantum tunnelling.

Purpose of the Study:

• To derive a novel shallow-tunnelling correction factor for Wigner-Eyring transition-state theory.
• To address and remove the divergence issue of the Wigner factor at the crossover temperature.
• To provide a more accurate method for calculating quantum rate coefficients in the shallow-tunnelling regime.

Main Methods:

• Starting with quantum transition-state theory (QTST) and ring-polymer approximations.
• Expanding the ring-polymer potential to second order.
• Numerically integrating over the two softest ring-polymer normal modes to remove divergence.
• Evaluating a one-dimensional integral along a straight line on the potential energy surface.

Main Results:

• A modified Wigner correction factor was derived, specifically for the shallow-tunnelling regime.
• The new factor successfully removes the divergence encountered by the standard Wigner factor.
• Numerical integration over soft ring-polymer modes proved effective in refining the correction factor.

Conclusions:

• The newly derived correction factor provides realistic estimates of quantum rate coefficients.
• This method enhances the applicability of Wigner-Eyring transition-state theory in the shallow-tunnelling regime.
• The study offers a significant improvement for theoretical calculations of chemical reaction rates involving quantum tunnelling.