Collective variables for the study of crystallisation

ABSTRACT

The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately, the time scale for crystallisation is much larger than what can be explored in standard simulations. Enhanced sampling methods can overcome this time scale hurdle. Many such methods rely on the definition of appropriate collective variables able to capture the slow degrees of freedom. To this effect, we introduce collective coordinates of general applicability to crystallisation simulations. They are based on the peaks of the three-dimensional structure factor that are combined non-linearly via the Deep Linear Discriminant Analysis machine learning method. We use these collective variables in the context of the on-the-fly probability enhanced sampling method that is a recent evolution of metadynamics. We demonstrate the validity of this approach by studying the crystallisation of a multicomponent system, Sodium Chloride, and a molecular system, Carbon Dioxide.

GRAPHICAL ABSTRACT

Keywords:

• Crystallisation
• phase transitions
• collective variables
• enhanced sampling simulations
• machine learning

Acknowledgments

The research was supported by the NCCR MARVEL (D&D1) funded by Swiss National Science Foundation and the European Union Grant No. ERC-2014-AdG-670227/VARMET. We thank CSCS, the Swiss National Supercomputing Centre for providing the computational resources.

Supporting information

The Supporting Information (SI) contains sections on the comparison between Debye SF and our approach, METAD vs. OPES comparison (Figure S3), and free energy difference plots (Figure S4 and S5) obtained from OPES simulations of NaCl and CO${}_2$ systems.

Code and data availability

All input files, codes, scripts, and instructions to reproduce the results presented in this manuscript can be found at the PLUMED-NEST repository with plumID:21.005 (https://www.plumed-nest.org/eggs/21/005/). Additionally, all simulations data are available from the authors upon request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by the NCCR MARVEL (D&D1) funded by Swiss National Science Foundation and the European Union Grant No. ERC-2014-AdG-670227/VARMET.