Rafał Podeszwa

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.

A molecular crystal structure prediction (CSP) protocol used in the seventh blind test is presented. The seventh blind test was divided into two stages and included seven targets, with crystals containing from one to three molecules in asymmetric units, monomers built of up to 100 atoms, and all targets containing monomers with flexible degrees of freedom. Some targets were cocrystals and one target was a salt. These diverse targets were treated using a CSP protocol starting from finding the global and local minima conformations of the target molecule. Subsequently, an ab initio two-body rigid-monomer six-dimensional force field (aiFF) was developed for the global-minimum conformer. These aiFFs were then used in CSPs consisting of packing and lattice-energy minimization stages. Flexible-monomer CSPs were used for some targets. To describe the intramonomer FF, either generic empirical FFs or reparametrized FFs of this type were used, with some parameters fitted to ab initio energies of monomers in the latter case. A novel packing procedure was applied for two targets in stage 1. The success rate in the structure generation stage was 15% in submission phase and 54% in post-submission phase, while the corresponding values in the structure rating stage were 33% and 89%. We conclude that the inexpensive conformer-based approach with rigid-monomer CSPs can be recommended for investigations of crystals with flexible monomers. An advantage of this protocol is that it is fully based on first-principles quantum mechanics and generates tailor-made FFs suitable for use in subsequent molecular dynamics simulations investigating temperature-dependent effects. However, empirical intramonomer FFs reparametrized using ab initio data are not yet adequate for CSPs.

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.

Determination of topological invariants of graphene flakes, nanotubes, and fullerenes constitutes a challenging task due to its time-intensive nature and exponential scaling. The invariants can be organized in a form of a combinatorial polynomial commonly known as the Zhang-Zhang (ZZ) polynomial or the Clar covering polynomial. We report here a computer program, ZZPolyCalc, specifically designed to compute ZZ polynomials of large carbon nanostructures. The curse of exponential scaling is avoided for a broad class of nanostructures by employing a sophisticated bookkeeping algorithm, in which each fragment appearing in the recursive decomposition is stored in the cache repository of molecular fragments indexed by a hash of the corresponding adjacency matrix. Although exponential scaling persists for the remaining nanostructures, the computational time is reduced by a few orders of magnitude owing to efficient use of hash-based fragment bookkeeping. The provided benchmark timings show that ZZPolyCalc allows for treating much larger carbon nanostructures than previously envisioned.

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

We demonstrate that the atom-based charge model implemented in the current versions of the density functional tight binding (DFTB) method fails to reproduce the correct charge distribution of a range of systems, including homonuclear molecules, graphene, and nanotubes, resulting in serious distortions in the electrostatic interactions for such systems caused by the missing quadrupole moments. In particular, this failure seriously impacts the long- and medium-range interaction energies of the DFTB plus dispersion (DFTB-D) model, leading to incorrect predictions of translational or rotational barriers in such systems. We show explicitly on examples of H₂ and N₂ that correct quadrupole moments—and consequently correct electrostatic interactions—can be restored in such systems by adding additional bond (ghost) sites to the homonuclear molecules. Attempts to determine the point charges associated with the additional sites using the usual Mulliken population analysis lead to unphysical results. Instead, these charges can be determined using the actual DFTB densities used in the parameterization process. For homonuclear molecules, we propose an extension to the DFTB-D model by adding charges that reproduce the physically correct quadrupolar charge distribution. The resulting DFTB-D-Q model greatly improves the rotational barriers for interactions of molecular hydrogen and nitrogen with benzene.

Ab initio wave-function-based methods can predict intermolecular force fields very accurately for monomers containing a few atoms. These methods are, however, too time consuming for larger molecules, in particular for any molecules of biological interest or molecules forming energetic solid state materials. The density-functional theory (DFT) methods would be fast enough, but are currently not able to predict the very important dispersion component of the force field. A new perturbational method that is capable of computing the force fields accurately will be presented. This method is based on a DFT description of isolated molecules but computes intermolecular forces using expressions beyond DFT. Calculations for model compounds have shown that the new method reproduces all components of the intermolecular force, including dispersion, extremely well, in fact challenging the accuracy of wave-function-based methods. At the same time, the computer resources required by this method are similar to those of the standard DFT. The method has already been applied to interactions of two monomers containing 12 atoms each, and it should be able to handle interactions of molecules containing 20 and more atoms.