Abstract

Crystal structure prediction involves a search of a complex configurational space for local minima corresponding to stable crystal structures, which can be performed efficiently using atom-atom force fields for the assessment of intermolecular interactions. However, for challenging systems, the limitations in the accuracy of force fields prevents a reliable assessment of the relative thermodynamic stability of potential structures. Here we present a method to rapidly improve force field lattice energies by correcting two-body interactions with a higher level of theory in a fragment-based approach, and predicting these corrections with machine learning. We find corrected lattice energies with commonly used density functionals and second order perturbation theory (MP2) all significantly improve the ranking of experimentally known polymorphs where the rigid molecule model is applicable. The relative lattice energies of known polymorphs are also found to systematically improve towards experimentally determined values and more comprehensive energy models when using MP2 corrections, despite remaining at the force field geometry. Predicting two-body interactions with atom-centered symmetry functions in a Gaussian process is found to give highly accurate results with as little as 10-20% of the training data, reducing the cost of the energy correction by up to an order of magnitude. The machine learning approach opens up the possibility of using fragment-based methods to a greater degree in crystal structure prediction, providing alternative energy models where standard approaches are insufficient.

Highlights

  • The prediction of crystal structures given only basic connectivity information of a molecule, such as a chemical diagram, is an important challenge for computational chemistry.[1,2] The motivations for crystal structure prediction (CSP) are three-fold

  • All of the fragment-corrected models correct the stability order (Fig. 7), predicting β to be more stable than α by between 0.82 kJ/mol (FIT+DMA+PBE) and 1.84 kJ/mol (FIT+DMA+MP2). These results are in good agreement with the relative energy calculated using the popular solid state PBE exchange-correlation functional70 with Grimme D3 dispersion82 (PBE-D3) method, which calculates the α form to be 0.93 kJ/mol less stable than β, but much smaller than the energy difference calculated with PBEh-MBD95

  • This is due to higher errors for maleic hydrazide than oxalic acid at small training fractions; these can be explained by the smaller dataset of 12,522 unique dimers compared to 16,379 in the oxalic acid set and the larger range of dimer energy corrections that must be learnt for maleic hydrazide; this reflects a greater range of dimer geometries for maleic hydrazide, whose hydrogen bond donors and acceptors can be combined in a range of motifs

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Summary

Introduction

The prediction of crystal structures given only basic connectivity information of a molecule, such as a chemical diagram, is an important challenge for computational chemistry.[1,2] The motivations for crystal structure prediction (CSP) are three-fold. The two most widely adopted approaches to ranking predicted structures[13] are anisotropic, multipole-based atom-atom force fields[14,15], and dispersion-corrected periodic Density Functional Theory (DFT-D) methods[16]. The latter are typically found to provide higher accuracy[17], but at a cost that is restrictive for larger systems. Incorporating fragment-based methods into CSP remains expensive, owing to the many two-body terms that must be calculated To overcome this high computational cost, we investigate using a machine learning method to map force field two-body interaction energies to a higher level of theory. The results of our machine learnt energy model are assessed by comparison to explicit QM calculations

Test Set Molecules
Crystal Structure Prediction
Fragment-Based Lattice Energy Model
Machine Learning of Dimer Energy Corrections
Crystal Structure Ranking using the Fragment-Based Approach
Polymorph Energy Differences
Gaussian Process Learning of Dimer Energy Corrections
Conclusions

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