Perturbatively corrected ring-polymer instanton rate theory rigorously captures anharmonicity and deep tunneling

Area of Science:

• Quantum Chemistry
• Chemical Kinetics
• Theoretical Chemistry

Background:

• Instanton theory is a semiclassical method for calculating reaction rates.
• Standard instanton theory (RPI) neglects perpendicular anharmonicity, limiting accuracy.
• Accurate rate calculations are crucial for understanding chemical reactions.

Purpose of the Study:

• To develop a more accurate instanton rate theory.
• To incorporate anharmonic effects into instanton calculations.
• To provide a method applicable with ab initio electronic-structure calculations.

Main Methods:

• Derivation of perturbatively corrected instanton rate theory (RPI+PC).
• Utilizing third and fourth derivatives of the potential energy surface.
• Application of flux-correlation formalism and asymptotic analysis.
• Analysis of semiclassical limit properties.

Main Results:

• RPI+PC significantly enhances the accuracy of instanton theory.
• The method captures perpendicular anharmonic effects.
• RPI+PC is independent of the dividing surface choice.
• Demonstrated improved performance on model systems like H + H2.

Conclusions:

• RPI+PC offers a systematic improvement over standard RPI.
• The method is computationally efficient and applicable with ab initio methods.
• RPI+PC provides a more rigorous approach to quantum tunneling rate calculations.