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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., (open access.)

The crystal habit can have a profound influence on the physical properties of crystalline materials, and thus controlling the crystal morphology is of great practical relevance across many industries. Herein, this work investigates the effect of polymer additives on the crystal habit of metformin HCl with both experiments and computational methods with the aim of developing a combined screening approach for crystal morphology engineering. Crystallization experiments of metformin HCl are conducted in methanol and in an isopropanol-water mixture (8:2 V/V). Polyethylene glycol, polyvinylpyrrolidone, Tween80, and hydroxypropyl methylcellulose polymer additives are used in low concentrations (1-2% w/w) in the experiments to study the effect they have on modifying the crystal habit. Additionally, this work has developed computational methods to characterize the morphology "landscape" and quantifies the overall effect of solvent and additives on the predicted crystal habits. Further analysis of the molecular dynamics simulations is used to rationalize the effect of additives on specific crystal faces. This work demonstrates that the effects of additives on the crystal habit are a result of their absorption and interactions with the slow growing {100} and {020} faces., (© 2023 XtalPi Inc and Merck KGaA Darmstadt Germany. Small Methods published by Wiley-VCH GmbH.)

The chemical versatility and modular nature of Metal-Organic Frameworks (MOFs) make them unique hybrid inorganic-organic materials for several important applications. From a computational point of view, ab initio modeling of MOFs is a challenging and demanding task, in particular, when the system reaches the size of gigantic MOFs as MIL-100 and MIL-101 (where MIL stands for Materials Institute Lavoisier) with several thousand atoms in the unit cell. Here, we show how such complex systems can be successfully tackled by a recently proposed class of composite electronic structure methods revised for solid-state calculations. These methods rely on HF/density functional theory hybrid functionals (i.e., PBEsol0 and HSEsol) combined with a double-zeta quality basis set. They are augmented with semi-classical corrections to take into account dispersive interactions (D3 scheme) and the basis set superposition error (gCP). The resulting methodologies, dubbed "sol-3c," are cost-effective yet reach the hybrid functional accuracy. Here, sol-3c methods are effectively applied to predict the structural, vibrational, electronic, and adsorption properties of some of the most common MOFs. Calculations are feasible even on very large MOFs containing more than 2500 atoms in the unit cell as MIL-100 and MIL-101 with reasonable computing resources. We propose to use our composite methods for the routine in silico screening of MOFs targeting properties beyond plain structural features.

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol -1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r 2 SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

Following the development in recent years of progressively more accurate approximations to the exchange-correlation functional, the use of density functional theory (DFT) methods to examine increasingly large and complex systems has grown, in particular for solids and other condensed matter systems. However the cost of these calculations is high, often requiring the use of specialist HPC facilities. As such, for the purpose of large-scale high-throughput screening of material properties, a hierarchy of simplified DFT methods has been proposed that allows rapid electronic structure calculation of large systems, and we have recently extended this scheme to the solid state (sol-3c). Here, we analyze the applicability and scaling of the new sol-3c DFT methods to molecules and crystals composed of light-elements, such as small proteins and model DNA-helices. Furthermore, the calculation of the electronic structure of large to very large porous systems, such as metal-organic frameworks and inorganic nanoparticles, is discussed. The new composite methods have been implemented in the CRYSTAL17 code, which efficiently implements hybrid functionals and enables routine application of the new methods to large-scale calculations of such materials with excellent performance, even with small-scale computing resources.

Water molecules can arrange into a liquid with complex hydrogen-bond networks and at least 17 experimentally confirmed ice phases with enormous structural diversity. It remains a puzzle how or whether this multitude of arrangements in different phases of water are related. Here we investigate the structural similarities between liquid water and a comprehensive set of 54 ice phases in simulations, by directly comparing their local environments using general atomic descriptors, and also by demonstrating that a machine-learning potential trained on liquid water alone can predict the densities, lattice energies, and vibrational properties of the ices. The finding that the local environments characterising the different ice phases are found in water sheds light on the phase behavior of water, and rationalizes the transferability of water models between different phases.

Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the first time the free-energy landscape of a polymorphic crystalline polymer, syndiotactic polystyrene. Coarse-grained metadynamics simulations allow us to efficiently sample the landscape at large. The free-energy difference between the two main polymorphs, α and β, is further investigated by quantum-chemical calculations. The results of the two methods are in line with experimental observations: they predict β as the more stable polymorph under standard conditions. Critically, the free-energy landscape suggests how the α polymorph may lead to experimentally observed kinetic traps. The combination of multiscale modeling, enhanced sampling, and quantum-chemical calculations offers an appealing strategy to uncover complex free-energy landscapes with polymorphic behavior.

Nanotechnology has enabled the discovery of a multitude of novel materials exhibiting unique physicochemical (PChem) properties compared to their bulk analogues. These properties have led to a rapidly increasing range of commercial applications; this, however, may come at a cost, if an association to long-term health and environmental risks is discovered or even just perceived. Many nanomaterials (NMs) have not yet had their potential adverse biological effects fully assessed, due to costs and time constraints associated with the experimental assessment, frequently involving animals. Here, the available NM libraries are analyzed for their suitability for integration with novel nanoinformatics approaches and for the development of NM specific Integrated Approaches to Testing and Assessment (IATA) for human and environmental risk assessment, all within the NanoSolveIT cloud-platform. These established and well-characterized NM libraries (e.g. NanoMILE, NanoSolutions, NANoREG, NanoFASE, caLIBRAte, NanoTEST and the Nanomaterial Registry (>2000 NMs)) contain physicochemical characterization data as well as data for several relevant biological endpoints, assessed in part using harmonized Organisation for Economic Co-operation and Development (OECD) methods and test guidelines. Integration of such extensive NM information sources with the latest nanoinformatics methods will allow NanoSolveIT to model the relationships between NM structure (morphology), properties and their adverse effects and to predict the effects of other NMs for which less data is available. The project specifically addresses the needs of regulatory agencies and industry to effectively and rapidly evaluate the exposure, NM hazard and risk from nanomaterials and nano-enabled products, enabling implementation of computational 'safe-by-design' approaches to facilitate NM commercialization., (© 2020 The Authors.)

Due to their current and future technological applications, including realization of water filters and desalination membranes, water adsorption on graphitic sp 2 -bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and noncovalent interactions, in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed WaC18), which includes a single water molecule interacting with a broad range of carbon structures and various bulk (3D) and two-dimensional (2D) ice polymorphs. The performance of 28 approaches, including semilocal exchange-correlation functionals, nonlocal (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, is tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depend crucially on the DFT approach, ranging from 135 meV for local density approximation (LDA) to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems, FN-DMC deploys pseudopotentials (PPs) to substantially improve efficiency. In order to deal with nonlocal terms of PPs, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here, we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences-such as interaction and ionization energies-DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automation of FN-DMC and its much easier application in large systems.

A hierarchy of simplified Hartree-Fock (HF), density functional theory (DFT) methods, and their combinations has been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set global hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semiclassical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c, and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the CRYSTAL code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test bandgaps, vibrational frequencies, elastic constants, and dielectric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error for cohesive energies and unit cell volumes of molecular crystals of 1.5 kcal/mol and 2.8%, respectively. Lattice parameters of inorganic solids deviate by 3% from the references, and vibrational frequencies of α-quartz have standard deviations of 10 cm -1 . Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with a substantial increase in computational efficiency.

Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world's largest supercomputers. From this effort a consensus on the water-graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stages of CSP studies use relatively simple lattice energy approximations as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries, as well as inaccurate lattice energy rankings, and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here, we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all the inter- and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules, saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods, suggesting that it could be extended to even larger and more flexible molecules. On average, this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15) and experimental conformers (RMSD1) by 4% and 23%, respectively. The intermolecular interactions were then further optimised using distributed multipoles, derived from the molecular wave-functions, to accurately describe the electrostatic components of the intermolecular energies. In all cases, the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy, providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules, bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

Black phosphorus is a bulk solid allotrope of elemental phosphorus and can be seen as an infinite stack of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [M. Schütz, L. Maschio, A. J. Karttunen and D. Usvyat, J. Phys. Chem. Lett., 2017, 8, 1290-1294] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppresses London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional, we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations, however, do not support the existence of negative thermal expansion in black phosphorus, as reported in some theoretical studies.

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

In solution the PCy 3 /B(C 6 F 5 ) 3 pair is rapidly deactivated by nucleophilic aromatic substitution. In the solid state deactivation is effectively suppressed and the active frustrated phosphane/borane Lewis pair splits dihydrogen or adds to sulfur dioxide. A variety of phosphane/B(C 6 F 5 ) 3 pairs have been used to carry out active FLP reactions in the solid state. The reactions were analyzed by DFT calculations and by solid state NMR spectroscopy. The solid state dihydrogen splitting reaction was also carried out under near to ambient conditions with suspensions of the non-quenched phosphane/borane mixtures in the fluorous liquid perfluoromethylcyclohexane.

Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

A revised version of the well-established B97-D density functional approximation with general applicability for chemical properties of large systems is proposed. Like B97-D, it is based on Becke's power-series ansatz from 1997 and is explicitly parametrized by including the standard D3 semi-classical dispersion correction. The orbitals are expanded in a modified valence triple-zeta Gaussian basis set, which is available for all elements up to Rn. Remaining basis set errors are mostly absorbed in the modified B97 parametrization, while an established atom-pairwise short-range potential is applied to correct for the systematically too long bonds of main group elements which are typical for most semi-local density functionals. The new composite scheme (termed B97-3c) completes the hierarchy of "low-cost" electronic structure methods, which are all mainly free of basis set superposition error and account for most interactions in a physically sound and asymptotically correct manner. B97-3c yields excellent molecular and condensed phase geometries, similar to most hybrid functionals evaluated in a larger basis set expansion. Results on the comprehensive GMTKN55 energy database demonstrate its good performance for main group thermochemistry, kinetics, and non-covalent interactions, when compared to functionals of the same class. This also transfers to metal-organic reactions, which is a major area of applicability for semi-local functionals. B97-3c can be routinely applied to hundreds of atoms on a single processor and we suggest it as a robust computational tool, in particular, for more strongly correlated systems where our previously published "3c" schemes might be problematic.

Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko-Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction.

We report systematic temperature-dependent X-ray measurements on the most stable carbamazepine polymorph. This active pharmaceutical ingredient is used to demonstrate how the thermal expansion can probe certain intermolecular interactions resulting in anisotropic expansion behavior. We show that most structural features can be captured by electronic structure calculations at the quasi-harmonic approximation (QHA) provided a dispersion-corrected density functional based method is employed. The impact of thermal expansion on the phonon modes and hence free energy contributions is large enough to impact the relative stability of different polymorphs.

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-generalized gradient approximated TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce sufficiently accurate reaction electronic energies. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid-state FLPs.This article is part of the themed issue 'Frustrated Lewis pair chemistry'., (© 2017 The Author(s).)

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation, and second order Møller-Plesset theory. These wavefunction based correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is -107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions, but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

A comparative assessment of the accuracy of different quantum mechanical methods for evaluating the structure and the cohesive energy of molecular crystals is presented. In particular, we evaluate the performance of the semiempirical HF-3c method in comparison with the B3LYP-D* and the Local MP2 (LMP2) methods by means of a fully periodic approach. Three benchmark sets have been investigated: X23, G60, and the new K7; for a total of 82 molecular crystals. The original HF-3c method performs well but shows a tendency at overbinding molecular crystals, in particular for weakly bounded systems. For the X23 set, the mean absolute error for the cohesive energies computed with the HF-3c method is comparable to the LMP2 one. A refinement of the HF-3c has been attempted by tuning the dispersion term in the HF-3c energy. While the performance on cohesive energy prediction slightly worsens, optimized unit cell volumes are in excellent agreement with experiment. Overall, the B3LYP-D* method combined with a TZP basis set gives the best results. For cost-effective calculations on molecular crystals, we propose to compute cohesive energies at the B3LYP-D*/TZP level of theory on the dispersion-scaled HF-3c optimized geometries (i.e., B3LYP-D*/TZP//HF-3c(0.27) also dubbed as SP-B3LYP-D*). Besides, for further benchmarking on molecular crystals, we propose to combine the three test sets in a new one denoted as MC82.

We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.

Mean-field electronic structure methods like Hartree-Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chemical problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).

In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

Charge-assisted hydrogen bonds (CAHBs) play critical roles in many systems from biology through to materials. In none of these areas has the role and function of CAHBs been explored satisfactorily because of the lack of data on the energy of CAHBs in the condensed phases. We have, for the first time, quantified three types of CAHBs in both the condensed and gas phases for 1-(2'-hydroxylethyl)-3-methylimidazolium acetate ([C2OHmim][OAc]). The energy of conventional OH···[OAc](-) CAHBs is ∼10 kcal·mol(-1), whereas nonconventional C(sp2)H···[OAc](-) and C(sp3)H···[OAc](-) CAHBs are weaker by ∼5-7 kcal·mol(-1). In the gas phase, the strength of the nonconventional CAHBs is doubled, whereas the conventional CAHBs are strengthened by <20%. The influence of cooperativity effects on the ability of the [OAc](-) anion to deprotonate the imidazolium cation is evaluated. The ability to quantify CAHBs in the condensed phase on the basis of easier accessible gas-phase estimates is highlighted.

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm(3) and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3(atm) gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.

The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chemistry, ranging from supramolecular host-guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster "low-cost" methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular-orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree-Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10-30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.

The complexes [Fe(tbta)2](BF4)2·2EtOH (1), [Fe(tbta)2](BF4)2·2CH3CN (2), [Fe(tbta)2](BF4)2·2CHCl3 (3), and [Fe(tbta)2](BF4)2 (4) were synthesized from the respective metal salts and the click-derived tripodal ligand tris[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]amine (tbta). Structural characterization of these complexes (at 100 or 133 K) revealed Fe-N bond lengths for the solvent containing compounds 1-3 that are typical of a high spin (HS) Fe(II) complex. In contrast, the solvent-free compound 4 show Fe-N bond lengths that are characteristic of a low spin (LS) Fe(II) state. The Fe center in all complexes is bound to two triazole and one amine N atom from each tbta ligand, with the third triazole arm remaining uncoordinated. The benzyl substituents of the uncoordinated triazole arms and the triazole rings engage in strong intermolecular and intramolecular noncovalent interactions. These interactions are missing in the solvent containing molecules 1, 2, and 3, where the solvent molecules occupy positions that hinder these noncovalent interactions. The solvent-free complex (4) displays spin crossover (SCO) with a spin transition temperature T1/2 near room temperature, as revealed by superconducting quantum interference device (SQUID) magnetometric and Mössbauer spectroscopic measurements. The complexes 1, 2, and 3 remain HS throughout the investigated temperature range. Different torsion angles at the metal centers, which are influenced by the noncovalent interactions, are likely responsible for the differences in the magnetic behavior of these complexes. The corresponding solvent-free Co(II) complex (6) is also LS at lower temperatures and displays SCO with a temperature T1/2 near room temperature. Theoretical calculations at molecular and periodic DFT-D3 levels for 1-4 qualitatively reproduce the experimental findings, and corroborate the importance of intermolecular and intramolecular noncovalent interactions for the magnetic properties of these complexes. The present work thus represents rare examples of SCO complexes where the use of identical ligand sets produces SCO in Fe(II) as well as Co(II) complexes.

This study investigates the effect of substitution with different functional groups and of molecular flexibility by changing within the axle from a single C-C bond to a double C=C bond. Therefore, we present static quantum chemical calculations at the dispersion-corrected density functional level (DFT-D3) for several Leigh-type rotaxanes. The calculated crystal structure is in close agreement with the experimental X-ray data. Compared to a stiffer axle, a more flexible one results in a stronger binding by 1-3 kcal/mol. Alterations of the binding energy in the range of 5 kcal/mol could be achieved by substitution with different functional groups. The hydrogen bond geometry between the isophtalic unit and the carbonyl oxygen atoms of the axle exhibited distances in the range of 2.1 to 2.4 Å for six contact points, which shows that not solely but to a large amount the circumstances in the investigated rotaxanes are governed by hydrogen bonding. Moreover, the complex with the more flexible axle is usually more unsymmetrical than the one with the stiff axle. The opposite is observed for the experimentally investigated axle with the four phenyl stoppers. Furthermore, we considered an implicit continuum solvation model and found that the complex binding is weakened by approximately 10 kcal/mol, and hydrogen bonds are slightly shortened (by up to 0.2 Å).

The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of <0.5 kcal/mol compared to DFT-D are obtained.

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys-Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 Å and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.

A combined X-ray diffraction and theoretical study of the solid-state molecular and crystal structures of tribenzotriquinacene (TBTQ, 2) and its centro-methyl derivative (3) is presented. The molecular structure of the parent hydrocarbon displays C3v symmetry and the three indane wings adopt mutually orthogonal orientations, similar to the case in its previously reported methyl derivative (3). Also similarly to the latter structure, the bowl-shaped molecules of compound 2 form infinite molecular stacks with perfectly axial, face-to-back (convex-concave) packing and with parallel and unidirectional orientation of the stacks. The experimentally determined intra-stack molecular distance is 4.75 Å for compound 2 and 5.95 Å for compound 3. Whereas the molecules of compound 2 show a slight alternating rotation (±6°) about the common axis of each stack, those of compound 3 show perfect translational symmetry within the stacks. We used dispersion-corrected density functional theory to compute the crystal structures of tribenzotriquinacenes 2 and 3. The London dispersion correction was crucial for obtaining an accurate description of the crystallization of both analyzed systems and the calculated results agreed excellently with the experimental measurements. We also obtained reasonable sublimation energies for both compounds. In addition, the geometries and dimerization energies of oligomeric stacks of compound 2 were computed and showed smooth convergence to the properties of the infinite polymeric stack., (Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)