Ascent dynamics: an efficient algorithm probing long timescale dynamics

Molecular dynamics simulations play an essential role in biology, chemistry, and physics, providing valuable insights from the atomistic scale. However, the reached timescale is severely limited given that the integration time step must be smaller than the fastest motion in the system to discrete the time evolution. Recent hardware development has allowed the achievement of microsecond to millisecond timescale, which is still several orders shorter than multiple dynamical processes of interest. For instance, protein folding, nucleation and crystal growth, and glass transition usually occur on timescales of seconds or longer because the existence of metastable states separated by high free energy barriers leads to kinetic bottlenecks, and transitions between those metastable states become rare events. Numerous enhanced sampling methods have been developed to overcome timescale problems. Collective variable-based methods, such as metadynamics and adiabatic free energy calculations utilize the reaction coordinates as input to increase the sampling of configuration space. Path-based approaches, including transition-path sampling and transition interface sampling, provide information on the dynamics through various enhanced sampling of transitions between metastable states. State-based methods, such as nudged elastic band, and string methods, partition configurational space into discrete states and then combine information from shorter simulations between these states to obtain global information. However, there are limitations for each of the above methods, and many methods cannot probe kinetics explicitly. This work presents a new accelerated simulation method, ascent dynamics, which allows the system to escape deep energy minima through crossing saddle points by specifying index explicitly at finite temperatures. The trajectory data is then analyzed through the master equation to compute viscosity and relaxation time. To study supercooled liquids and glass, we tested the method on three systems: binary Lennard-Jones (BLJ) mixture, polydisperse mixture in two dimensions, and polydisperse mixture in three dimensions. Using this new method, relaxation time and viscosity are in agreement with traditional molecular dynamics simulation at high temperatures, but they can be probed reliably at the low temperatures regime. Our results show that we reach the timescale on the order of 10⁶s and achieve over ten orders of magnitude gain in the equilibration timescale compared to MD, thus paving the road for computational studies long timescale phenomena. By extracting the stretched exponent from the calculated correlation functions, we find that the stretched exponent keeps decreasing upon cooling. Furthermore, dynamical cluster analysis on the 3D polydisperse system reveals that the cluster size increases when the temperature is lowered. These observations indicate that dynamics become more and more heterogeneous at low temperatures. Direct visualization of the excitation and relaxation process in the 2D system suggests that the shape of cooperative motions is not string-like but varied, a discovery that may have important implications for theories of glass transition.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear, Plasma, Radiolgc Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Li, Zhixia

Contributors dc:contributor

• Z, Y
• Curreli, Davide
• Schweizer, Kenneth S
• Uddin, Rizwan

• Long timescale
• Dynamics
• Advanced sampling methods

Statement dc:rights

• Copyright 2022 Zhixia Li

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115739

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115739