On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation

Area of Science:

• Quantum Chemistry
• Chemical Physics
• Computational Chemistry

Background:

• The semiclassical instanton approach has quantitative deficiencies in calculating thermal rate constants.
• Accurate calculation of thermal rate constants is crucial for understanding chemical reaction dynamics.

Purpose of the Study:

• To present an efficient path integral approach for evaluating thermal rate constants within the quantum instanton (QI) approximation.
• To overcome the limitations of previous semiclassical methods for rate constant calculations.

Main Methods:

• Utilizing imaginary time path integrals to evaluate the quantum instanton (QI) rate constant based on Boltzmann operator properties.
• Developing statistical estimators for quantities evaluable with nonlinear reaction coordinates and general Hamiltonians.
• Introducing a two-dimensional quantum free energy surface and adaptive umbrella sampling for optimizing dividing surfaces.

Main Results:

• The QI rate constant can be efficiently evaluated using established imaginary time path integral techniques.
• The proposed statistical estimators are applicable to complex chemical systems with general Hamiltonians.
• The method demonstrated excellent agreement with quantum scattering calculations for a gas-phase hydrogen exchange reaction.

Conclusions:

• The presented path integral approach offers an efficient and accurate method for calculating thermal rate constants.
• The quantum instanton (QI) approximation, combined with imaginary time path integrals, provides a robust framework for chemical reaction rate studies.
• This work facilitates the accurate computation of reaction rates for complex chemical processes.