Combining classical reactive scattering and the time-energy uncertainty relation.

Area of Science:

• Chemical Dynamics
• Computational Chemistry
• Physical Chemistry

Background:

• Gaussian binning, used since the early 2000s, refines classical dynamical simulations for predicting state-resolved cross sections in molecular beam experiments.
• The method assigns Gaussian statistical weights to classical trajectories, prioritizing product energies near quantized values.

Purpose of the Study:

• To extend Gaussian binning to activated complexes in chemical reactions.
• To incorporate both stationary and time-dependent states of the activated complex.
• To improve the accuracy of reaction probability calculations.

Main Methods:

• Treating the activated complex as a stationary state with narrow Gaussian weights.
• Treating the activated complex as a time-dependent state with broadened Gaussian weights, consistent with the time-energy uncertainty relation.
• Coupling the time-dependent approach with calculations of tunneling through parabolic adiabatic barriers.

Main Results:

• The extended Gaussian binning methods were applied to calculate reaction probabilities for model processes with long-lived and short-lived activated complexes.
• The calculated reaction probabilities showed very good agreement with quantum probabilities.
• Analysis of quantum probability shapes was performed using classical dynamics and the time-energy uncertainty relation.

Conclusions:

• The extended Gaussian binning method provides accurate predictions of reaction probabilities.
• The study offers insights into the relationship between classical dynamics, the time-energy uncertainty relation, and quantum probabilities.
• The research examines potential violations of zero-point energy at the transition state.