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Issue 43, 2019
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Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices

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Abstract

Most chemical transformations (reactions or conformational changes) that are of interest to researchers have many degrees of freedom, usually too many to visualize without reducing the dimensionality of the system to include only the most important atomic motions. In this article, we describe a method of using Principal Component Analysis (PCA) for analyzing a series of molecular geometries (e.g., a reaction pathway or molecular dynamics trajectory) and determining the reduced dimensional space that captures the most structural variance in the fewest dimensions. The software written to carry out this method is called PathReducer, which permits (1) visualizing the geometries in a reduced dimensional space, (2) determining the axes that make up the reduced dimensional space, and (3) projecting the series of geometries into the low-dimensional space for visualization. We investigated two options to represent molecular structures within PathReducer: aligned Cartesian coordinates and matrices of interatomic distances. We found that interatomic distance matrices better captured non-linear motions in a smaller number of dimensions. To demonstrate the utility of PathReducer, we have carried out a number of applications where we have projected molecular dynamics trajectories into a reduced dimensional space defined by an intrinsic reaction coordinate. The visualizations provided by this analysis show that dynamic paths can differ greatly from the minimum energy pathway on a potential energy surface. Viewing intrinsic reaction coordinates and trajectories in this way provides a quick way to gather qualitative information about the pathways trajectories take relative to a minimum energy path. Given that the outputs from PCA are linear combinations of the input molecular structure coordinates (i.e., Cartesian coordinates or interatomic distances), they can be easily transferred to other types of calculations that require the definition of a reduced dimensional space (e.g., biased molecular dynamics simulations).

Graphical abstract: Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices

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Supplementary files

Article information


Submitted
05 Jun 2019
Accepted
23 Aug 2019
First published
18 Sep 2019

This article is Open Access
All publication charges for this article have been paid for by the Royal Society of Chemistry

Chem. Sci., 2019,10, 9954-9968
Article type
Edge Article

Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices

S. R. Hare, L. A. Bratholm, D. R. Glowacki and B. K. Carpenter, Chem. Sci., 2019, 10, 9954
DOI: 10.1039/C9SC02742D

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