Assessment of Different Quantum Mechanical Methods for the Prediction of Structure and Cohesive Energy of Molecular Crystals

Electron Localization and Mobility in Monolayer Fullerene Networks

The novel 2D quasi-hexagonal phase of covalently bonded fullerene molecules (qHP C60), the so-called graphullerene, has displayed far superior electron mobilities, if compared to the parent van der Waals three-dimensional crystal (vdW C60). Herein, we present a comparative study of the electronic properties of vdW and qHP C60 using state-of-the-art electronic-structure calculations and a full quantum-mechanical treatment of electron transfer. We show that both materials entail polaronic localization of electrons with similar binding energies (≈0.1 eV) and, therefore, they share the same charge transport via polaron hopping. In fact, we quantitatively reproduce the sizable increment of the electron mobility measured for qHP C60 and identify its origin in the increased electronic coupling between C60 units.

First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.

Organic crystal structure prediction via coupled generative adversarial networks and graph convolutional networks

Organic crystal structures exert a profound impact on the physicochemical properties and biological effects of organic compounds. Quantum mechanics (QM)-based crystal structure predictions (CSPs) have somewhat alleviated the dilemma that experimental crystal structure investigations struggle to conduct complete polymorphism studies, but the high computing cost poses a challenge to its widespread application. The present study aims to construct DeepCSP, a feasible pure machine learning framework for minute-scale rapid organic CSP. Initially, based on 177,746 data entries from the Cambridge Crystal Structure Database, a generative adversarial network was built to conditionally generate trial crystal structures under selected feature constraints for the given molecule. Simultaneously, a graph convolutional attention network was used to predict the density of stable crystal structures for the input molecule. Subsequently, the distances between the predicted density and the definition-based calculated density would be considered to be the crystal structure screening and ranking basis, and finally, the density-based crystal structure ranking would be output. Two such distinct algorithms, performing the generation and ranking functionalities, respectively, collectively constitute the DeepCSP, which has demonstrated compelling performance in marketed drug validations, achieving an accuracy rate exceeding 80% and a hit rate surpassing 85%. Inspiringly, the computing speed of the pure machine learning methodology demonstrates the potential of artificial intelligence in advancing CSP research.

Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties

Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.

Can Spin-Component Scaled MP2 Achieve kJ/mol Accuracy for Cohesive Energies of Molecular Crystals?

Attaining kJ/mol accuracy in cohesive energy for molecular crystals is a persistent challenge in computational materials science. In this study, we evaluate second-order Møller-Plesset perturbation theory (MP2) and its spin-component scaled models for calculating cohesive energies for 23 molecular crystals (X23 data set). Using periodic boundary conditions and Brillouin zone sampling, we converge results to the thermodynamic and complete basis set limits, achieving an accuracy of about 2 kJ/mol (0.5 kcal/mol), which is rarely achieved in previous MP2 calculations for molecular crystals. When compared to experimental data, our results have a mean absolute error of 12.9 kJ/mol, comparable to Density Functional Theory with the PBE functional and TS dispersion correction. By separately scaling the opposite-spin and same-spin correlation energy components, using predetermined parameters, we reduce the mean absolute error to 9.5 kJ/mol. Further fine-tuning of these scaling parameters specifically for the X23 data set brings the mean absolute error down to 7.5 kJ/mol.

Adsorption Affinities of Small Volatile Organic Molecules on Graphene Surfaces for Novel Nanofiller Design: A DFT Study

The adsorption of organic molecules on graphene surfaces is a crucial process in many different research areas. Nano-sized carbon allotropes, such as graphene and carbon nanotubes, have shown promise as fillers due to their exceptional properties, including their large surface area, thermal and electrical conductivity, and potential for weight reduction. Surface modification methods, such as the "pyrrole methodology", have been explored to tailor the properties of carbon allotropes. In this theoretical work, an ab initio study based on Density Functional Theory is performed to investigate the adsorption process of small volatile organic molecules (such as pyrrole derivatives) on graphene surface. The effects of substituents, and different molecular species are examined to determine the influence of the aromatic ring or the substituent of pyrrole's aromatic ring on the adsorption energy. The number of atoms and presence of π electrons significantly influence the corresponding adsorption energy. Interestingly, pyrroles and cyclopentadienes are 10 kJ mol-1 more stable than the corresponding unsaturated ones. Pyrrole oxidized derivatives display more favorable supramolecular interactions with graphene surface. Intermolecular interactions affect the first step of the adsorption process and are important to better understand possible surface modifications for carbon allotropes and to design novel nanofillers in polymer composites.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

Specific Proton-Donor Properties of Glycine Betaine. Metric Parameters and Enthalpy of Noncovalent Interactions in its Dimer, Water Complexes and Crystalline Hydrate

Trimethylglycine (glycine betaine, GB) is an important organic osmolyte that accumulates in various plant species in response to environmental stresses and has significant potential as a bioactive agent with low environmental impact. It is assumed that the hydration of GB is playing an important role in the protective mechanism. The hydration and aggregation properties of GB have not yet been studied in detail at the atomistic level. In this work, noncovalent interactions in the GB dimer and its complexes with water and crystalline monohydrate are studied. Depending on the object, periodic and non-periodic DFT calculations are used. Particular attention is paid to the metric parameters and enthalpies of intermolecular hydrogen bonds. The identification of noncovalent interactions is carried out by means of the Bader analysis of periodic or non-periodic electron density. The enthalpy of hydrogen bonds is estimated using the Rosenberg formula (PCCP 2 (2000) 2699). The specific proton donor properties of glycine betaine are due to its ability to form intermolecular C-H∙∙∙O bonds with the oxygen atom of a water molecule or the carboxylate group of a neighboring GB. The enthalpy of these bonds can be significantly greater than 10 kJ/mol. The water molecule that forms a hydrogen bond with the carboxylate group of GB also interacts with its CH groups through lone pairs of electrons. The C-H∙∙∙O bonds contribute up to 40% of the total entropy of the GB-water interaction, which is about 45 kJ/mol. The possibility of identifying C-H∙∙∙O bonds by the proton nuclear magnetic resonance method is discussed.

Supramolecular Organization in Salts of Riluzole with Dihydroxybenzoic Acids—The Key Role of the Mutual Arrangement of OH Groups

Intermolecular interactions, in particular hydrogen bonds, play a key role in crystal engineering. The ability to form hydrogen bonds of various types and strengths causes competition between supramolecular synthons in pharmaceutical multicomponent crystals. In this work, we investigate the influence of positional isomerism on the packing arrangements and the network of hydrogen bonds in multicomponent crystals of the drug riluzole with hydroxyl derivatives of salicylic acid. The supramolecular organization of the riluzole salt containing 2,6-dihydroxybenzoic acid differs from that of the solid forms with 2,4- and 2,5-dihydroxybenzoic acids. Because the second OH group is not at position 6 in the latter crystals, intermolecular charge-assisted hydrogen bonds are formed. According to periodic DFT calculations, the enthalpy of these H-bonds exceeds 30 kJ·mol−1. The positional isomerism appears to have little effect on the enthalpy of the primary supramolecular synthon (65–70 kJ·mol−1), but it does result in the formation of a two-dimensional network of hydrogen bonds and an increase in the overall lattice energy. According to the results of the present study, 2,6-dihydroxybenzoic acid can be treated as a promising counterion for the design of pharmaceutical multicomponent crystals.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol^-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol^-1 per molecule for the X23 set and 0.19 kcal mol^-1 for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.

Nanoscale MXene Interlayer and Substrate Adhesion for Lubrication: A Density Functional Theory Study

Understanding the interlayer interaction at the nanoscale in two-dimensional (2D) transition metal carbides and nitrides (MXenes) is important to improve their exfoliation/delamination process and application in (nano)-tribology. The layer-substrate interaction is also essential in (nano)-tribology as effective solid lubricants should be resistant against peeling-off during rubbing. Previous computational studies considered MXenes' interlayer coupling with oversimplified, homogeneous terminations while neglecting the interaction with underlying substrates. In our study, Ti-based MXenes with both homogeneous and mixed terminations are modeled using density functional theory (DFT). An ad hoc modified dispersion correction scheme is used, capable of reproducing the results obtained from a higher level of theory. The nature of the interlayer interactions, comprising van der Waals, dipole-dipole, and hydrogen bonding, is discussed along with the effects of MXene sheet's thickness and C/N ratio. Our results demonstrate that terminations play a major role in regulating MXenes' interlayer and substrate adhesion to iron and iron oxide and, therefore, lubrication, which is also affected by an external load. Using graphene and MoS₂ as established references, we verify that MXenes' tribological performance as solid lubricants can be significantly improved by avoiding -OH and -F terminations, which can be done by controlling terminations via post-synthesis processing.

Fast Quantum Approach for Evaluating the Energy of Non-Covalent Interactions in Molecular Crystals: The Case Study of Intermolecular H-Bonds in Crystalline Peroxosolvates

Energy/enthalpy of intermolecular hydrogen bonds (H-bonds) in crystals have been calculated in many papers. Most of the theoretical works used non-periodic models. Their applicability for describing intermolecular H-bonds in solids is not obvious since the crystal environment can strongly change H-bond geometry and energy in comparison with non-periodic models. Periodic DFT computations provide a reasonable description of a number of relevant properties of molecular crystals. However, these methods are quite cumbersome and time-consuming compared to non-periodic calculations. Here, we present a fast quantum approach for estimating the energy/enthalpy of intermolecular H-bonds in crystals. It has been tested on a family of crystalline peroxosolvates in which the H∙∙∙O bond set fills evenly (i.e., without significant gaps) the range of H∙∙∙O distances from ~1.5 to ~2.1 Å typical for strong, moderate, and weak H-bonds. Four of these two-component crystals (peroxosolvates of macrocyclic ethers and creatine) were obtained and structurally characterized for the first time. A critical comparison of the approaches for estimating the energy of intermolecular H-bonds in organic crystals is carried out, and various sources of errors are clarified.

π-Hole bonding in a new co-crystal hydrate of gallic acid and pyrazine: static and dynamic charge density analysis

A new cocrystal hydrate of gallic acid with pyrazine (4GA, Py, 4H₂O; GA₄PyW₄) was obtained and characterized by single crystal X-ray diffraction. In addition to structure determination, experimental charge density analysis was carried out in terms of Multipole Modelling (MP), X-ray wavefunction refinement (XWR) and maximum entropy method (MEM). As a part of XWR, the structural refinement via Hirshfeld atom refinement was carried out and resulted in O-H bond lengths close to values from neutron diffraction. A systematic comparison of molecular conformations and aromatic interactions in this new cocrystal hydrate was performed with other existing polymorphs of gallic acid. In GA₄PyW₄, the two symmetry-independent gallic acid molecules have a syn COOH orientation and form the common (COOH)₂ dimeric synthon. The carboxyl C atom displays the characteristics of π-holes with electropositive regions above and below the molecular plane and engages in acceptor-donor interactions with oxygen atoms of acidic O-H groups and phenol groups of neighbouring gallic acid molecules. The signature of the π-hole was identified from experimental charge density analysis, both in static density maps in MP and XWR as well as dynamic density in MEM, but it cannot be pinned down to a specific atom-atom interaction. This study presents the first comparison between an XWR and a MEM experimental electron-density determination.

A density-functional benchmark of vibrational free-energy corrections for molecular crystal polymorphism

Many crystal structure prediction protocols only concern themselves with the electronic energy of molecular crystals. However, vibrational contributions to the free energy ( Fvib) can be significant in determining accurate stability rankings for crystal candidates. While force-field studies have been conducted to gauge the magnitude of these free-energy corrections, highly accurate results from quantum mechanical methods, such as density-functional theory (DFT), are desirable. Here, we introduce the PV17 set of 17 polymorphic pairs of organic molecular crystals, for which plane wave DFT is used to calculate the vibrational free energies and free-energy differences (Δ Fvib) between each pair. Our DFT results confirm that the vibrational free-energy corrections are small, having a mean value of 1.0 kJ/mol and a maximum value of 2.3 kJ/mol for the PV17 set. Furthermore, we assess the accuracy of a series of lower-cost DFT, semi-empirical, and force-field models for computing Δ Fvib that have been proposed in the literature. It is found that calculating Fvib using the Γ-point frequencies does not provide Δ Fvib values of sufficiently high quality. In addition, Δ Fvib values calculated using various approximate methods have mean absolute errors relative to our converged DFT results of equivalent or larger magnitude than the vibrational free-energy corrections themselves. Thus, we conclude that, in a crystal structure prediction protocol, it is preferable to forego the inclusion of vibrational free-energy corrections than to estimate them with any of the approximate methods considered here.

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors

This review presents a critical and comprehensive overview of current experimental measurements of complete elastic constant tensors for molecular crystals. For a large fraction of these molecular crystals, detailed comparisons are made with elastic tensors obtained using the corrected small basis set Hartree-Fock method S-HF-3c, and these are shown to be competitive with many of those obtained from more sophisticated density functional theory plus dispersion (DFT-D) approaches. These detailed comparisons between S-HF-3c, experimental and DFT-D computed tensors make use of a novel rotation-invariant spherical harmonic description of the Young's modulus, and identify outliers among sets of independent experimental results. The result is a curated database of experimental elastic tensors for molecular crystals, which we hope will stimulate more extensive use of elastic tensor information-experimental and computational-in studies aimed at correlating mechanical properties of molecular crystals with their underlying crystal structure.

Non-Covalent Interactions in the Biphenyl Crystal: Is the Planar Conformer a Transition State?

A combined experimental and theoretical study of the biphenyl (BP) crystal is presented. The X-ray diffraction data collected at 100 K were subjected to Hirshfeld atom and multipole refinements of the electron density, ρ(r). A theoretical exploration of the potential energy surface (PES) of the crystal was also carried out. This investigation challenges the common assumption that the planar structure of BP in the phase I crystal is an average of two twisted configurations in a double-well potential. The theoretical computations provide compelling evidence that this structure corresponds to a minimum on the PES hence to a stable molecular arrangement. Consistently, the experiment showed no evidence of positional or dynamic disorder. The intramolecular hydrogen-hydrogen bonds detected are not repulsive. The topological analysis of the experimental and theoretical ρ(r) reveals that both the intra- and intermolecular H⋅⋅⋅H and the C-H⋅⋅⋅π contacts stabilize the BP crystal.

Balancing Cost and Accuracy in Quantum Mechanical Simulations on Collagen Protein Models

Collagen proteins are spread in almost every vertebrate's tissue with mechanical function. The defining feature of this fundamental family of proteins is its well-known collagen triple-helical domain. This helical domain can have different geometries, varying in helical elongation and interstrands contact, as a function of the amino acidic composition. The helical geometrical features play an important role in the interaction of the collagen protein with cell receptors, but for the vast majority of collagen compositions, these geometrical features are unknown. Quantum mechanical (QM) simulations based on the density functional theory (DFT) provide a robust approach to characterize the scenario on the collagen composition-structure relationships. In this work, we analyze the role of the adopted computational method in predicting the collagen structure for two purposes. First, we look for a cost-effective computational approach to apply to a large-scale composition-structure analysis. Second, we attempt to assess the robustness of the predictions by varying the QM methods. Therefore, we have run geometry optimization on periodic models of the collagen protein using a variety of approaches based on the most commonly used DFT functionals (PBE, HSE06, and B3LYP) with and without dispersion correction (D3^ABC). We have coupled these methods with several different basis sets, looking for the highest accuracy/cost ratio. Furthermore, we have studied the performance of the composite HF-3c method and the semiempirical GFN1-xTB method. Our results identify a computational recipe that is potentially capable of predicting collagen structural features in line with DFT simulations, with orders of magnitude reduced computational cost, encouraging further investigations on the topic.

Solid-State Conformational Flexibility at Work: Energetic Landscape of a Single Crystal-to-Single Crystal Transformation in a Cyclic Hexapeptoid

We describe the energetic landscape beyond the solid-state dynamic behavior of a cyclic hexapeptoid decorated with four propargyl and two methoxyethyl side chains, namely, cyclo-(Nme-Npa₂)₂, Nme = N-(methoxyethyl)glycine, Npa = N-(propargyl)glycine. By increasing the temperature above 40 °C, the acetonitrile solvate form 1A starts to release acetonitrile molecules and undergoes a reversible single crystal-to-single crystal transformation into crystal form 1B with a remarkable conformational change in the macrocycle: two propargyl side chains move by 113° to form an unprecedented "CH-π zipper". Then, upon acetonitrile adsorption, the "CH-π zipper" opens and the crystal form 1B transforms back to 1A. By conformational energy and lattice energy calculations, we demonstrate that the dramatic side-chain movement is a peculiar feature of the solid-state assembly and is determined by a backbone conformational change that leads to stabilizing CH···OC backbone-to-backbone interactions tightening the framework upon acetonitrile release. Weak interactions as CH···OC and CH-π bonds with the guest molecules are able to reverse the transformation, providing the energy contribution to unzip the framework. We believe that the underlined mechanism could be used as a model system to understand how external stimuli (as temperature, humidity, or volatile compounds) could determine conformational changes in the solid state.

Theoretical insights on acceptor-donor dyads for organic photovoltaics

The field of organic photovoltaics has witnessed a steady growth in the last few decades and a recent renewal with the blossoming of single-material organic solar cells (SMOSCs). However, due to the intrinsic complexity of these devices (both in terms of their size and of the condensed phases involved), computational approaches to accurately predict their geometrical and electronic structure and to link their microscopic properties to the observed macroscopic behaviour are still lacking. In this work, we have focused on the rationalization of transport dynamics and we have set up a computational approach that makes a combined use of classical simulations and Density Functional Theory with the aim of disclosing the most relevant electronic and structural features of dyads used for SMOSC applications. As a prototype dyad, we have considered a molecule that consists in a dithiafulvalene-functionalized diketopyrrolopyrrole (DPP), acting as an electron donor, covalently linked to a fulleropyrrolidine (Ful), the electron acceptor. Our results, beside a quantitative agreement with experiments, show that the overall observed mobilities result from the competing packing mechanisms of the constituting units within the dyad both in the case of crystalline and amorphous phases. As a consequence, not all stable polymorphs have the same efficiency in transporting holes or electrons which often results in a highly directional carrier transport that is not, in general, a desirable feature for polycrystalline thin-films. The present work, linking microscopic packing to observed transport, thus opens the route for the in silico design of new dyads with enhanced and controlled structural and electronic features.

Free-energy landscape of polymer-crystal polymorphism

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.

Structural Aspects of the Ortho Chloro- and Fluoro- Substituted Benzoic Acids: Implications on Chemical Properties

This article presents a detailed comprehensive investigation of the ortho fluoro- and chloro- substituted benzoic acids both, as isolated molecules and in the crystalline phase. Quantum chemical calculations performed within the density functional theory (DFT) formalism are used to investigate the potential energy landscapes of the molecules, taking into special consideration the effects of the interactions between the carboxylic group and the ortho halogen substituents, as well as the nature of these later on the structure and properties of the investigated systems. The structures of the relevant conformers of the molecules are discussed in comparative terms, and used to rationalize experimental data obtained for the compounds in the gas phase and isolated in low-temperature inert matrices. The UV-induced photofragmentation reactions of two of the compounds isolated in cryogenic inert matrices were studied as illustrative cases. The structures of the crystals reported previously in the literature are revisited and discussed also in a comparative basis. Particular emphasis is given to the analysis of the intermolecular interactions in the different crystals, using Hirshfeld surface analysis, the CE-B3LYP energy decomposition model and the HOMA index, and to their correlation with thermodynamic data.

Exfoliation Energy of Layered Materials by DFT-D: Beware of Dispersion!

In this work, we have computed the exfoliation energy (the energy required to separate a single layer from the bulk structure), the interlayer distance, and the thermodynamic state functions for representative layered inorganic minerals such as Brucite, Portlandite, and Kaolinite, while leaving the more classical 2D transition-metal dichalcogenides (like MoS₂) for future work. Such materials are interesting for several applications in the field of adsorption and in prebiotic chemistry. Their peculiar features are directly controlled by the exfoliation energy. In materials without cations/anions linking different layers, the interactions keeping the layers together are of weak nature, mainly dispersion London interactions and hydrogen bonds, somehow challenging to deal with computationally. We used Hartree-Fock (HF) and density functional theory (DFT) approaches focusing on the role of dispersion forces using the popular and widespread Grimme's pairwise dispersion schemes (-D2 and -D3) and, as a reference method, the periodic MP2 approach based on localized orbitals (LMP2). The results are highly dependent on the choice of the scheme adopted to account for dispersion interactions. D2 and D3 schemes combined with either HF or DFT lead to overestimated exfoliation energies (about 2.5 and 1.7 times higher than LMP2 data for Brucite/Portlandite and Kaolinite) and underestimated interlayer distances (by about 3.5% for Brucite/Portlandite). The reason is that D2 and D3 corrections are based on neutral atomic parameters for each chemical element which, instead, behave as cations in the considered layered material (Mg, Ca, and Al), causing overattractive interaction between layers. More sophisticated dispersion corrections methods, like those based on nonlocal vdW functionals, many body dispersion model, and exchange-hole dipole moment not relying on atom-typing, are, in principle, better suited to describe the London interaction of ionic species. Nonetheless, we demonstrate that good results can be achieved also within the simpler D2 and D3 schemes, in agreement with previous literature suggestions, by adopting the dispersion coefficients of the preceding noble gas for the ionic species, leading to energetics in good agreement with LMP2 and structures closer to the experiments.

XO-PBC: An Accurate and Efficient Method for Molecular Crystals

In this work, we propose the XO-PBC method, which combines the eXtended ONIOM method (XO) with the periodic boundary condition (PBC) for the description of molecular crystals. XO-PBC tries to embed a finite cluster cut out from the solid into the periodic environment, making it feasible to employ advanced molecular quantum chemistry methods, which are usually prohibitively expensive for direct PBC calculations. In particular, XO-PBC utilizes the results from force calculations to design the scheme to fragment the molecule when crystals are made of large molecules and to select cluster model systems automatically consisting of dimer up to tetramer interactions for embedding. By applying an appropriate theory to each model, a satisfactory accuracy for the system under study is ensured, while a high efficiency is achieved with massively parallel computing by distributing model systems onto different processors. A comparison of the XO-PBC calculations with the conventional direct PBC calculations at the B3LYP level demonstrates its accuracy at substantially low cost for the description of molecular crystals. The usefulness of the XO-PBC method is further exemplified, showing that XO-PBC is able to predict the lattice energies of various types of molecular crystals within chemical accuracy (<4 kJ/mol) when the doubly hybrid density functional XYG3 is used as the target high level and the periodic PBE as the basic low level. The XO-PBC method provides a general protocol that brings the great predictive power of advanced electronic structure methods from molecular systems to the extended solids.

Combined X-ray Crystallographic, IR/Raman Spectroscopic, and Periodic DFT Investigations of New Multicomponent Crystalline Forms of Anthelmintic Drugs: A Case Study of Carbendazim Maleate

Synthesis of multicomponent solid forms is an important method of modifying and fine-tuning the most critical physicochemical properties of drug compounds. The design of new multicomponent pharmaceutical materials requires reliable information about the supramolecular arrangement of molecules and detailed description of the intermolecular interactions in the crystal structure. It implies the use of a combination of different experimental and theoretical investigation methods. Organic salts present new challenges for those who develop theoretical approaches describing the structure, spectral properties, and lattice energy Elatt. These crystals consist of closed-shell organic ions interacting through relatively strong hydrogen bonds, which leads to Elatt > 200 kJ/mol. Some technical problems that a user of periodic (solid-state) density functional theory (DFT) programs encounters when calculating the properties of these crystals still remain unsolved, for example, the influence of cell parameter optimization on the Elatt value, wave numbers, relative intensity of Raman-active vibrations in the low-frequency region, etc. In this work, various properties of a new two-component carbendazim maleate crystal were experimentally investigated, and the applicability of different DFT functionals and empirical Grimme corrections to the description of the obtained structural and spectroscopic properties was tested. Based on this, practical recommendations were developed for further theoretical studies of multicomponent organic pharmaceutical crystals.

Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

Extension and evaluation of the D4 London-dispersion model for periodic systems

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredients are additional reference polarizabilities for highly-coordinated group 1-5 elements derived from pseudo-periodic electrostatically-embedded cluster calculations. To illustrate the performance of the updated method, several test cases are considered, for which we compare D4 to its predecessor D3(BJ), as well as to a comprehensive set of other dispersion-corrected methods. The largest improvements are observed for solid-state polarizabilities of 16 inorganic salts, where the D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides values in good agreement with experimental and/or high-level references. These results suggest the application of the proposed D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.

Ildiz G, Paixão JA, Castiglioni C, Fausto R. Polymorphism in 1-methylhydantoin: investigation by periodic DFT calculations and characterization of the third polymorph

In previous studies, two different polymorphs of 1-methylhydantoin were identified (forms I and II) and characterized using infrared and Raman spectroscopies, and X-ray diffraction. In this work, a new polymorph of the compound (III) is described.

Extending and assessing composite electronic structure methods to the solid state

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.

Cost-Effective Quantum Mechanical Approach for Predicting Thermodynamic and Mechanical Stability of Pure-Silica Zeolites

Several computational techniques for solid-state applications have recently been proposed to enlarge the scope of computer simulations of large molecular systems. In this contribution, we focused on two of these, namely, HF-3c and PBEh-3c. They were recently proposed by the Grimme's group, as "low-cost" ab initio-based techniques for electronic structure calculation of large systems and were proved to be effective essentially for organic molecules. HF-3c is based on a Hartree-Fock Hamiltonian with a minimal Gaussian quality basis set, whereas PBEh-3c is a density functional theory (DFT) based method with a hybrid functional and a medium-quality basis set. Both HF-3c and PBEh-3c account for dispersion (London) interactions and are free from the basis set superposition error due to limited basis set size, through several pairwise semiempirical corrections. To the best of our knowledge, despite the promising results on the cost-accuracy side of molecular simulations of organic molecules, these methods have been used only in few cases for solid-state applications. In this contribution, we studied the performance of HF-3c and PBEh-3c for predicting the properties of inorganic crystals to enlarge the applicability of these cheap and fast methodologies. As a testing ground, we have chosen a well-known class of material, e.g., microporous all-silica zeolites. We benchmarked geometries, formation energies, vibrational features, and mechanical properties by comparing the results with literature data from both experiment and computer simulation. For structures, HF-3c is extremely accurate in predicting the zeolites cell volume, albeit we do not include any vibrational contribution, neither zero point nor thermal, on the computed volumes, which may introduce small variations in the predicted values. For the energetic, the relative stability of the zeolites using the DFT//HF-3c approach allows predictions within the experimental error for most of the cases taken into consideration when the experimental enthalpies were corrected back to electronic energies by using the HF-3c thermodynamic contributions computed in the harmonic approximation. This strategy is particularly convenient, as the slow step (geometry optimization) is carried out with the cheapest HF-3c method, whereas the fast step (single point energy evaluation) is carried out with costly DFT methods. In this sense, the use of the DFT//HF-3c approach results to be a promising one to predict the stability and structure of microporous materials. Finally, the HF-3c method predicts the mechanical properties of the zeolite set in reasonable agreement with respect to those computed with the state-of-the-art DFT simulations, indicating the HF-3c method as a possible technique for the mechanical stability screenings of microporous materials.

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

Crystal-energy landscapes of active pharmaceutical ingredients using composite approaches

Composite methods employing dispersion-corrected DFT consistently identify experimentally isolated polymorphs as the lowest-energy crystal structures of common APIs.

Solving the enigma of weak fluorine contacts in the solid state: a periodic DFT study of fluorinated organic crystals

The nature and strength of weak interactions with organic fluorine in the solid state are revealed by periodic density functional theory (periodic DFT) calculations coupled with experimental data on the structure and sublimation thermodynamics of crystalline organofluorine compounds. To minimize other intermolecular interactions, several sets of crystals of perfluorinated and partially fluorinated organic molecules are considered. This allows us to establish the theoretical levels providing an adequate description of the metric and electron-density parameters of the C–F⋯F–C interactions and the sublimation enthalpy of crystalline perfluorinated compounds. A detailed comparison of the C–F⋯F–C and C–H⋯F–C interactions is performed using the relaxed molecular geometry in the studied crystals. The change in the crystalline packing of aromatic compounds during their partial fluorination points to the structure-directing role of C–H⋯F–C interactions due to the dominant electrostatic contribution to these contacts. C–H⋯F–C and C–H⋯O interactions are found to be identical in nature and comparable in energy. The factors that determine the contribution of these interactions to the crystal packing are revealed. The reliability of the results is confirmed by considering the superposition of the electrostatic potential and electron density gradient fields in the area of the investigated intermolecular interactions.

The nature and strength of weak C–H⋯F–C and C–F⋯F–C interactions and their role in organofluorine molecular crystals were studied using periodic DFT coupled with CSD data mining and experimental sublimation enthalpies.

Pervasive Delocalisation Error Causes Spurious Proton Transfer in Organic Acid-Base Co-Crystals

Dispersion-corrected density-functional theory (DFT-D) methods have become the workhorse of many computational protocols for molecular crystal structure prediction due to their efficiency and convenience. However, certain limitations of DFT, such as delocalisation error, are often overlooked or are too expensive to remedy in solid-state applications. This error can lead to artificial stabilisation of charge transfer and, in this work, it is found to affect the correct identification of the protonation site in multicomponent acid-base crystals. As such, commonly used DFT-D methods cannot be applied with any reliability to the study of acid-base co-crystals or salts, while hybrid functionals remain too restrictive for routine use. This presents an impetus for the development of new functionals with reduced delocalisation error for solid-state applications; the structures studied herein constitute an excellent benchmark for this purpose.

Protonated nucleobases are not fully ionized in their chloride salt crystals and form metastable base pairs further stabilized by the surrounding anions

This paper presents experimental charge-density studies of cytosinium chloride, adeninium chloride hemihydrate and guaninium dichloride crystals based on ultra-high-resolution X-ray diffraction data and extensive theoretical calculations. The results confirm that the cohesive energies of the studied systems are dominated by contributions from intermolecular electrostatic interactions, as expected for ionic crystals. Electrostatic interaction energies (Ees) usually constitute 95% of the total interaction energy. The Ees energies in this study were several times larger in absolute value when compared, for example, with dimers of neutral nucleobases. However, they were not as large as some theoretical calculations have predicted. This was because the molecules appeared not to be fully ionized in the studied crystals. Apart from charge transfer from chlorine to the protonated nucleobases, small but visible charge redistribution within the nucleobase cations was observed. Some dimers of singly protonated bases in the studied crystals, namely a cytosinium-cytosinium trans sugar/sugar edge pair and an adeninium-adeninium trans Hoogsteen/Hoogsteen edge pair, exhibited attractive interactions (negative values of Ees) or unusually low repulsion despite identical molecular charges. The pairs are metastable as a result of strong hydrogen bonding between bases which overcompensates the overall cation-cation repulsion, the latter being weakened due to charge transfer and molecular charge-density polarization.

Simplified DFT methods for consistent structures and energies of large systems

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.