Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Biased and accelerated molecular simulations (BAMS) enable studying long timescales but don't directly yield physical time scales.
• Recovering dynamics from BAMS is crucial for understanding natural and synthetic molecular systems.
• Previous work coupled BAMS with Extended Diffusion Theory (EDT) for orientational dynamics, assuming Brownian diffusion.

Purpose of the Study:

• To generalize Extended Diffusion Theory (EDT) to account for non-exponential relaxation and anomalous diffusion observed in molecular systems.
• To develop a computational method for recovering dynamics from BAMS in regimes beyond simple Brownian motion.
• To validate the Fractional Extended Diffusion Theory (FEDT) for analyzing molecular dynamics.

Main Methods:

• Developed a generalized theory based on a fractional Smoluchowski equation (FEDT).
• Adapted existing EDT calculation methods to implement the FEDT.
• Applied the FEDT to analyze the relaxation of intramolecular distances and molecular radius of gyration.

Main Results:

• The fractional Extended Diffusion Theory (FEDT) successfully captures non-exponential relaxation dynamics.
• FEDT accurately describes molecular behaviors exhibiting persistent long-time correlations and subdiffusive regimes.
• The developed algorithm demonstrates FEDT's practical value in recovering dynamics from BAMS.

Conclusions:

• FEDT provides a robust framework for recovering molecular dynamics from BAMS, extending beyond Brownian diffusion.
• The method is applicable to general situations, including both regular and anomalous diffusion regimes.
• This generalization enhances the utility of BAMS coupled with diffusion theories for molecular simulations.