Advances in milestoning. II. Calculating time-correlation functions from milestoning using stochastic path integrals

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Molecular Dynamics

Background:

• Milestoning and transition interface sampling enhance equilibrium kinetics calculations from molecular dynamics.
• Existing methods are limited in applying these techniques to non-equilibrium statistical mechanics.

Purpose of the Study:

• To advance milestoning applications into non-equilibrium statistical mechanics for calculating time correlation functions.
• To introduce a novel methodology for calculating flux through milestones as a function of time and initial configuration.
• To develop a new formalism for autocorrelation of Langevin motion in discrete configuration space.

Main Methods:

• Developed a novel methodology to compute flux through milestones over time and initial configurations.
• Introduced a new formalism for autocorrelation of Langevin motion in discrete configuration space.
• Applied the method to analytically solved harmonic oscillator, numerically solved two-well potential, and atomistic simulations of alanine dipeptide.

Main Results:

• Successfully calculated time correlation functions in non-equilibrium systems.
• Validated the novel flux and autocorrelation methods across diverse test systems.
• Demonstrated the applicability to complex atomistic molecular dynamics simulations.

Conclusions:

• The developed methodology effectively extends milestoning to non-equilibrium statistical mechanics.
• This approach provides a powerful tool for calculating time correlation functions in complex systems.
• The findings open new avenues for analyzing molecular dynamics simulations beyond equilibrium kinetics.