The seventh blind test of crystal structure prediction: structure ranking methods

Abstract

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol^-1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

Keywords: Cambridge Structural Database; blind test; crystal structure prediction; lattice energy; polymorphism.

Figure 1

Structure overlay of structures 28, 38, and 59 from the provided structure set for target XXVII, demonstrating the variation in TIPS conformation.

Figure 3

Examples of trans-square planar (left), cis-square planar (centre), and see-saw geometries of target XXVIII (right).

Figure 2

(Top) Lattice and free energy difference between structure 28 of molecule XXVII and structures 38, 61 and 59 which share the same core packing of the experimental form. The global minimum (black filled circle) of each group has been included to show if other packings were found to be more stable within an energy model. (Bottom) Lattice and free energy difference with respect to Form A of molecule XXVIII. The energy range between the global minimum (black filled circle) and the 100th ranked structure (open circle) is shown to highlight the position of the experimental structure within the CSP set. If a subset of less than 100 structures was used in the energy calculation, filled circle is used instead of an open circle. As the initial set of structures includes 500 structures, the experimental one can lie outside of the 1st–100th range. In both plots, groups are organized as in Table 2 ▸, with the methodology class shown at the top. Groups that did not participate in the ranking of these two compounds are shown with a grey cross, while those that did not reproduce the geometry of the most stable polymorph are displayed with a red cross. If any of the structures’ energies lie outside of the energy range considered, this is shown with an arrow.

Figure 4

Lattice and free energy difference of the experimental structures with respect to the most stable polymorph of molecule XXXI (top), XXXII (middle) and XXXIII (bottom). The energy range between the global minimum (black filled circle) and the 100th-ranked structure (open circle) is shown to highlight the position of the experimental structures within the CSP set. If a subset of less than 100 structures was used in the energy calculation, the filled circle is used instead of an open circle. As the initial set of structures of compounds XXXII and XXXIII includes 500 structures, the experimental one can lie outside of the 1st–100th range. Groups are organized as in Table 2 ▸, with the methodology class shown at the top of each plot. Groups that did not participate in the ranking of these compounds are shown with a grey cross, while those that did not reproduce the geometry of the most stable polymorph are displayed with a red cross. If any of the structures’ energies lie outside of the energy range considered, this is shown with an arrow. For molecule XXXI, Group 7 used a ranking method not based on thermodynamics but on topological probabilities (highlighted in red). In this case the higher the score, the more probable it is to observe a structure.