Splitting probabilities as optimal controllers of rare reactive events

Area of Science:

• Chemical Kinetics
• Statistical Mechanics
• Computational Chemistry

Background:

• The committor is key for understanding rare reactive events in chemical kinetics.
• It defines the ideal reaction coordinate but generating trajectories from it is challenging.

Purpose of the Study:

• To demonstrate the generative utility of the committor function.
• To show that the committor can produce statistically exact reactive trajectory ensembles.
• To connect the committor to optimal control and splitting probability for trajectory generation.

Main Methods:

• Relating a time-dependent committor analog to splitting probability.
• Solving a generalized bridge problem and a boundary value problem.
• Applying stochastic optimal control and spectral theory.

Main Results:

• Derived a general form for the optimal controller of a bridge process.
• Showed that committor gradients encode force fields that guarantee reactivity.
• Generated reactive trajectories with numerically exact statistics.

Conclusions:

• The committor function offers a generative approach to chemical kinetics.
• This method provides an alternative to traditional transition path ensemble analysis.
• The formalism enables the creation of statistically identical reactive trajectories.