Accelerated Organic Crystal Structure Prediction with Genetic Algorithms and Machine Learning.

We present a high-throughput, end-to-end pipeline for organic crystal structure prediction (CSP)─the problem of identifying the stable crystal structures that will form from a given molecule based only on its molecular composition. Our tool uses neural network potentials to allow for efficient screening and structural relaxation of generated crystal candidates. Our pipeline consists of two distinct stages: random search, whereby crystal candidates are randomly generated and screened, and optimization, where a genetic algorithm (GA) optimizes this screened population. We assess the performance of each stage of our pipeline on 21 molecules taken from the Cambridge Crystallographic Data Centre's CSP blind tests. We show that random search alone yields matches for ≈50% of targets. We then validate the potential of our full pipeline, making use of the GA to optimize the root-mean-square deviation between crystal candidates and the experimentally derived structure. With this approach, we are able to find matches for ≈80% of candidates with 10-100 times smaller initial population sizes than when using random search. Lastly, we run our full pipeline with an ANI model that is trained on a small data set of molecules extracted from crystal structures in the Cambridge Structural Database, generating ≈60% of targets. By leveraging machine learning models trained to predict energies at the density functional theory level, our pipeline has the potential to approach the accuracy of ab initio methods and the efficiency of empirical force fields.

The fourth-order expansion of the exchange hole and neural networks to construct exchange-correlation functionals.

The curvature Qσ of spherically averaged exchange (X) holes ρX,σ(r, u) is one of the crucial variables for the construction of approximations to the exchange-correlation energy of Kohn-Sham theory, the most prominent example being the Becke-Roussel model [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)]. Here, we consider the next higher nonzero derivative of the spherically averaged X hole, the fourth-order term Tσ. This variable contains information about the nonlocality of the X hole and we employ it to approximate hybrid functionals, eliminating the sometimes demanding calculation of the exact X energy. The new functional is constructed using machine learning; having identified a physical correlation between Tσ and the nonlocality of the X hole, we employ a neural network to express this relation. While we only modify the X functional of the Perdew-Burke-Ernzerhof functional [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], a significant improvement over this method is achieved.

Construction of self-interaction-corrected exchange-correlation functionals within the correlation factor approach.

To model the exchange-correlation hole ρXC(r, u) of Kohn-Sham theory, we employ the correlation factor ansatz, which has recently been developed in our group. In this ansatz, ρXC(r, u) is written as a product of the correlation factor fC(r, u) and an exchange-hole model ρX(r, u), i.e., ρXC(r, u) = fC(r, u)ρX(r, u). In particular, we address the one-electron, self-interaction error and introduce a modified correlation factor model where fC(r, u) is constructed such that it reduces identically to one in localized one-electron regions of a many-electron system. This self-interaction corrected exchange-correlation hole is then used to generate the corresponding exchange-correlation energy functional. The new functional is implemented into a Kohn-Sham program and assessed by calculating various molecular properties. We find that, overall, a significant improvement is obtained compared to previous versions of the correlation factor model.

The correlation factor model for the exchange-correlation energy and its application to transition metal compounds.

In the recently developed correlation factor (CF) model [Precechtelova et al., J. Chem. Phys. 143, 144102 (2015)], the exchange-correlation (XC) hole is approximated. Since various constraints satisfied by the XC-hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a CF. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle (ϵXr) as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. EC functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS).