Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation.

Area of Science:

• Quantum Chemistry
• Chemical Physics
• Computational Chemistry

Background:

• The quantum instanton approximation is a key method in quantum transition-state theory for calculating chemical reaction rates.
• It relies on the reactive flux correlation function and its initial time derivatives.
• Efficient calculation of these quantities is crucial for accurate reaction rate predictions.

Purpose of the Study:

• To present novel path-integral estimators for the initial decay profile of the reactive flux correlation function.
• To introduce a virial-type estimator offering computational advantages over traditional methods.
• To compare the variance and convergence properties of different estimators and flux operator treatments.

Main Methods:

• Development of several path-integral estimators for the reactive flux correlation function's initial derivatives.
• Derivation of a virial-type estimator using a coordinate scaling procedure.
• Comparison of local-path and global-path approaches for the flux operator, with the latter using second-order potential derivatives for reduced variance.

Main Results:

• The virial-type estimator demonstrates reduced variance compared to the thermodynamic estimator.
• The global-path approach for the flux operator achieves smaller variance than the local-path approach.
• Numerical tests on a 1D Eckart barrier and a proton transfer reaction validate the improved performance of the new estimators.

Conclusions:

• The presented path-integral estimators, particularly the virial-type estimator, enhance the efficiency and accuracy of quantum instanton calculations.
• The findings offer practical benefits for computational chemistry, enabling more reliable prediction of chemical reaction rates.
• This work contributes to the advancement of quantum transition-state theory methodologies.