Improving collective variables: The case of crystallization

Authors: Yue-Yu Zhang1*, Haiyang Niu1, GiovanniMaria Piccini1, Dan Mendels1, Michele Parrinello1

  1. Department of Chemistry and Applied Biosciences, ETH Zurich, c/o USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Ticino, Switzerland, and Institute of Computational Science, Università della Svizzera Italiana (USI), Via Giuseppe Buffi 13, CH-6900 Lugano, Ticino, Switzerland
  • Corresponding author email:

DOI10.24435/materialscloud:2019.0088/v1 (version v1, submitted on 12 December 2019)

How to cite this entry

Yue-Yu Zhang, Haiyang Niu, GiovanniMaria Piccini, Dan Mendels, Michele Parrinello, Improving collective variables: The case of crystallization, Materials Cloud Archive (2019), doi: 10.24435/materialscloud:2019.0088/v1.


Several enhanced sampling methods, such as umbrella sampling or metadynamics, rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis; the other is based on a variational approach to conformational dynamics and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. Wherever the different metastable states are well-separated, the method based on linear discriminant analysis, based on its harmonic version, is to be preferred because simpler to implement and less computationally demanding. The variational approach, however, has the potential to discover the existence of different metastable states.

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File name Size Description
MD5MD5: 513f0701fb321044bd5f584ea16982a6
310 Bytes README.txt for all the files
MD5MD5: 98527d3cd57690bbc0e7f4ce22126dc8
1.0 KiB Plumed input file for Na using HLDA combined XRD CVs
MD5MD5: 2ace6264235382d9c6a431712cb06c5d
97.6 MiB COLVAR file of Na using HLDA combined XRD CVs
MD5MD5: ef8baa15b97ffd9e8e5cba7894af40f9
1.3 KiB Plumed input file for Al using HLDA combined XRD CVs
MD5MD5: 4a61a79ea2938ac720033b6dfc5d643d
109.7 MiB COLVAR file of Al using HLDA combined XRD CVs


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.

External references

Journal reference
Y.-Y. Zhang, H. Niu, G. Piccini, D. Mendels, M. Parrinello, JCP, 150, 094509-094518 (2019) doi:10.1063/1.5081040


enhanced sampling MARVEL MARVEL/DD1 plumed HLDA crystalization

Version history

12 December 2019 [This version]