Crystal structure prediction (CSP)

Geometries of all the molecules studied were fully optimized at the B3LYP/6-311G(d,p) level of theory, using the Gaussian16 software⁴⁵, followed by frequency calculations to ensure that they are all true local minima. These molecular geometries were held rigid throughout crystal structure generation and lattice energy minimization.

Trial crystal structures were generated with one molecule in the asymmetric unit for the 23 most common space groups: P2₁/c (34.4%), P1¯ (24.8%), C2/c (8.4%), P2₁2₁2₁ (7.1%), P2₁ (5.1%), Pbca (3.3%), Pna2₁ (1.4%), Pnma (1.1%), Cc (1.0%), P1 (1.0%), C2 (0.8%), Pbcn (0.8%), Pca2₁ (0.7%), R3¯ (0.7%), P2/c (0.6%), C2/m (0.5%), P2₁/m (0.5%), Pc (0.4%), P2₁2₁2 (0.4%), I4₁/a (0.4%), Pccn (0.4%), Fdd2 (0.3%), and P4₂ (<0.3%); the values in the brackets are relative frequencies of the space groups reported in the Cambridge Structural Database.

CSP was performed using a quasi-random sampling procedure, as implemented in the Global Lattice Energy Explorer software³¹. The generation of crystal structures involved a low-discrepancy sampling of all structural variables within each space group: unit cell lengths and angles, and molecular positions and orientations within the asymmetric unit. Space-group symmetry was then applied, and a geometric test was performed for overlap between molecules, which was removed by lattice expansion (the SAT-expand method in ref. ³¹). Lattice energy calculations were performed with an anisotropic atom–atom potential using DMACRYS⁴⁶. Electrostatic interactions were modelled using an atomic multipole description of the molecular charge distribution (up to hexadecapole on all atoms) from the B3LYP/6-311G(d,p)-calculated charge density using a distributed multipole analysis⁴⁷. Atom–atom repulsion and dispersion interactions were modelled using a revised Williams intermolecular potential⁴⁸, which has been benchmarked against accurate, experimentally determined lattice energies for a range of molecular crystals⁴⁹, and was applied successfully in our earlier CSP studies of T2 and the related imide T1, reproducing the known crystal structures³. Charge–charge, charge–dipole and dipole–dipole interactions were calculated using Ewald summation; all other intermolecular interactions were summed to a 25-Å cut-off between molecular centres of mass. All accepted trial structures were lattice energy-minimized, and the search was run until a total of 5000 lattice energy minimizations had been performed in each space group.

Removal of duplicate structures was performed in two steps. First, all structures within a lattice energy window of 1.0 kJ mol⁻¹ and within a density window of ±0.05 g cm⁻³ were compared using powder X-ray diffraction (PXRD) patterns generated by Platon⁵⁰ (wavelength: 0.7 Å; two-theta range: 20°) using a constrained dynamic time-warping method to compare pairs of structures. Structures were considered a match when the Euclidean distance between the PXRD patterns (normalized by area) was <10. This was followed by using the COMPACK⁵¹ algorithm for clustering: 1.0 kJ mol⁻¹ and ±0.05 g cm⁻³ selection windows; a distance tolerance of 40% and a maximum value of the RMSD of 0.4 Å for 30 molecules.