ℏ 4 quantum corrections to semiclassical transmission probabilities

Area of Science:

• Physical Chemistry
• Quantum Mechanics
• Chemical Kinetics

Background:

• Current methods for calculating thermal reaction rates combine vibrational perturbation theory with semiclassical approximations.
• Existing theories are systematically developed only up to second order, limiting accuracy at low temperatures where tunneling is crucial.
• The accuracy of second-order theories in the tunneling regime remains unclear.

Purpose of the Study:

• To develop a fourth-order vibrational perturbation theory for calculating thermal reaction rates.
• To assess the accuracy of the extended theory, particularly in the low-temperature tunneling regime.
• To provide a quantitative measure for evaluating the reliability of second-order approximations.

Main Methods:

• Systematic development of quantum perturbation theory up to sixth order.
• Extension of the uniform semiclassical approximation using an imaginary action.
• Modification of the second-order theory to fourth order, introducing an \u201c\u20182 modified potential\u201d\u2019.

Main Results:

• The fourth-order theory correctly reproduces the \u201c\u20184 term in the expansion of the exact thermal rate.
• The relative correction from the fourth order provides an objective indicator of second-order theory accuracy.
• The modified fourth-order theory demonstrates remarkable accuracy for asymmetric Eckart potentials.

Conclusions:

• The developed fourth-order theory offers improved accuracy for thermal reaction rate calculations, especially in the quantum tunneling regime.
• This work establishes a benchmark for assessing the validity of lower-order approximations.
• The modified fourth-order approach shows significant promise for accurate rate predictions in complex chemical systems.