Quantification of Crystal Packing Similarity from Spherical Harmonic Transform

TL;DR

This paper introduces a novel computational method using spherical harmonics to quantify and classify molecular packing similarities in crystal structures, enabling rapid analysis of large datasets.

Contribution

The work presents a new spherical harmonic-based approach for objectively measuring and classifying crystal packing, improving upon previous subjective methods.

Findings

Successfully reproduces previous packing classifications

Analyzes 2000 hydrocarbon crystal datasets

Identifies common packing motifs

Abstract

In this work, we present a new computational approach to characterize and classify molecular packing in the solid states. The key idea is to project each neighboring molecule (or short contact) from the centered molecule into a unit sphere according to the interaction energy. Consequently, the similarity between two spherical images can be evaluated from the spherical harmonics expansion based on the maximum cross-correlation. We apply this approach to successfully reproduce the previous packing assignment on a small amount of data with an improved categorization. Furthermore, we conduct a packing similarity analysis over 2000 hydrocarbon crystal data sets and uncover a set of abundant packing motifs. Unlike the previous approaches based on the subjective visual comparison at the real space, our approach provides a more robust way to measure the packing similarity, thus paving the way for a rapid classification of large scale crystal data.