Instanton rate constant calculations close to and above the crossover temperature

Area of Science:

• Chemical Physics
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Canonical instanton theory accurately predicts reaction rate constants but overestimates them near a crossover temperature.
• This theory becomes inapplicable at temperatures above the crossover point.
• Semi-classical rate expressions offer potential improvements for accuracy.

Purpose of the Study:

• To compare the accuracy of recent semi-classical rate expressions with canonical instanton theory.
• To address the limitations of existing methods at low and high temperatures.
• To develop a correction for canonical instanton theory to improve rate constant predictions.

Main Methods:

• Solving the stability matrix for the action in degrees of freedom orthogonal to the instanton path.
• Developing two novel methods to overcome limitations at low temperatures.
• Deriving a simple correction to canonical instanton theory.

Main Results:

• Semi-classical methods and the derived correction accurately reproduce rate constants over the entire temperature range.
• The spurious overestimation near the crossover temperature is alleviated.
• Rate constants were calculated and compared for three distinct reactions, including H in the Müller-Brown potential and H2 + OH reaction.

Conclusions:

• The developed semi-classical methods and correction enhance the accuracy of rate constant calculations.
• Canonical instanton theory's limitations near crossover temperatures can be effectively addressed.
• The findings provide a more reliable approach for predicting reaction rates in chemical systems.