A Non-Empirical Intermolecular Potential for Oxalic Acid Crystal Structures

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

Machine-Learned Fragment-Based Energies for Crystal Structure Prediction

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 prevent a reliable assessment of the relative thermodynamic stability of potential structures, while the cost of fully quantum mechanical approaches can limit applications of the methods. 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. 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 with the fragment corrections. Predicting two-body interactions with atom-centered symmetry functions in a Gaussian process is found to give highly accurate results using as little as 10-20% of the data for training, reducing the cost of the energy correction by up to an order of magnitude. The machine learning approach opens up the possibility of more widespread use of fragment-based methods in crystal structure prediction, whose increased accuracy at a low computational cost will benefit applications in areas such as polymorph screening and computer-guided materials discovery.

A First Principles Development of a General Anisotropic Potential for Polycyclic Aromatic Hydrocarbons

Standard empirical atom-atom potentials are shown to be unable to describe the binding of polycyclic aromatic hydrocarbon (PAH) molecules in the variety of configurations seen in clusters. The main reason for this inadequacy is the lack of anisotropy in these potentials. We have constructed an anisotropic atom-atom intermolecular potential for the benzene molecule from first principles using a symmetry-adapted perturbation theory based on density functional theory (SAPT(DFT)), interaction energy calculations and the Williams-Stone-Misquitta method for obtaining molecular properties in distributed form. Using this potential as a starting point, we have constructed a transferable anisotropic potential to model intermolecular interactions between PAHs. This new potential has been shown to accurately model interaction energies for a variety of dimer configurations for four different PAH molecules, including certain configurations which are poorly modeled with current isotropic potentials. It is intended that this potential will form the basis for further work on the aggregation of PAHs.

Synthon evolution and unit cell evolution during crystallisation. A study of symmetry-independent molecules (Z' > 1) in crystals of some hydroxy compounds

A kinetically favoured crystal, with many molecules in the asymmetric unit, may be a fossil relic of the crystal nucleus of a more stable polymorph.

Calculation of electrostatic and polarization energies from electron densities

We investigate procedures for calculating the electrostatic and polarization energies, Ees and Epol, associated with noncovalent interactions. The starting points are the electron densities of the isolated components and the complex; these could be obtained either computationally or experimentally. A slightly modified version of a scheme proposed by Gavezzotti is used to carry out numerical integrations over these electron densities. Our approach to estimating Epol is based upon partitioning the charge distributions of the components into overlapping and nonoverlapping regions. The effects of varying the integration parameters, computational techniques and basis sets are examined in detail for several noncovalently bound molecular dimers. Our results are in good agreement with the values of Ees and Epol produced by other methods, which require analytical integrations over interaction Hamiltonian matrix elements.

A Nonempirical Anisotropic Atom−Atom Model Potential for Chlorobenzene Crystals

A nearly nonempirical, transferable model potential is developed for the chlorobenzene molecules (C6ClnH6-n, n = 1 to 6) with anisotropy in the atom-atom form of both electrostatic and repulsion interactions. The potential is largely derived from the charge densities of the molecules, using a distributed multipole electrostatic model and a transferable dispersion model derived from the molecular polarizabilities. A nonempirical transferable repulsion model is obtained by analyzing the overlap of the charge densities in dimers as a function of orientation and separation and then calibrating this anisotropic atom-atom model against a limited number of intermolecular perturbation theory calculations of the short-range energies. The resulting model potential is a significant improvement over empirical model potentials in reproducing the twelve chlorobenzene crystal structures. Further validation calculations of the lattice energies and rigid-body k = 0 phonon frequencies provide satisfactory agreement with experiment, with the discrepancies being primarily due to approximations in the theoretical methods rather than the model intermolecular potential. The potential is able to give a good account of the three polymorphs of p-dichlorobenzene in a detailed crystal structure prediction study. Thus, by introducing repulsion anisotropy into a transferable potential scheme, it is possible to produce a set of potentials for the chlorobenzenes that can account for their crystal properties in an unprecedentedly realistic fashion.

Crystal structure predictions using five space groups with two independent molecules. The case of small organic acids

Crystal structure generations with two independent molecules have been performed for a series of carboxylic acids, using a slightly modified version of the OPLS force field. It was found that in this way the experimental structures with one independent molecule were produced as special cases, except for the molecules with four or more internal degrees of freedom. This work shows that a search with two independent molecules in only five space groups, although costly in computer power, can automatically also find structures with one independent molecule in many supergroups. Considering the observed abundances of structural classes, such a search should cover more than 95% of the possible homomolecular crystal structures.