A critical comparison of general-purpose collective variables for crystal nucleation

TL;DR

This study critically compares two collective variables for crystal nucleation, revealing similar effectiveness in driving nucleation but highlighting differences in correlation with the committor probability, informing better order parameter choices.

Contribution

It provides a comparative analysis of entropy-based and permutation vector-based collective variables for crystal nucleation, highlighting their strengths and limitations.

Findings

Both variables effectively drive nucleation with bias potential.

They exhibit similar free-energy barriers and structural features.

Changing the order parameter improved correlation with the committor probability.

Abstract

The nucleation of crystals is a prominent phenomenon in science and technology that still lacks a full atomic-scale understanding. Much work has been devoted to identifying order parameters able to track the process, from the inception of early nuclei to their maturing to critical size until growth of an extended crystal. We critically assess and compare two powerful distance-based collective variables, an effective entropy derived from liquid state theory and the path variable based on permutation invariant vectors using the Kob-Andersen binary mixture and a combination of enhanced-sampling techniques. Our findings reveal a comparable ability to drive nucleation when a bias potential is applied, and comparable free-energy barriers and structural features. Yet, we also found an imperfect correlation with the committor probability on the barrier top which was bypassed by changing the order parameter definition.