Improving collective variables: The case of crystallization.

Area of Science:

• Computational chemistry
• Materials science
• Statistical mechanics

Background:

• Enhanced sampling methods require collective variables (CVs) for efficiency.
• Determining optimal CVs is a significant challenge.
• Two recent methods aim to simplify CV identification.

Purpose of the Study:

• Compare linear discriminant analysis (LDA) and variational approaches for CV identification.
• Evaluate their performance in studying homogeneous crystallization of sodium (Na) and aluminum (Al).
• Identify efficient CVs as linear combinations of X-ray diffraction peak intensities.

Main Methods:

• Linear Discriminant Analysis (LDA) for CV selection.
• Variational approach using time-lagged independent component analysis (TICA).
• Application to homogeneous crystallization simulations of Na and Al.

Main Results:

• Both LDA and variational approaches showed similar performance.
• LDA (harmonic version) is preferred for well-separated metastable states due to simplicity and lower computational cost.
• The variational approach demonstrated potential in discovering distinct metastable states.

Conclusions:

• LDA and variational approaches are effective for identifying CVs in metal crystallization.
• Choice of method depends on the system's metastable state separation.
• Variational approach offers broader potential for exploring complex energy landscapes.