Hypothetical Crystal Structures of Benzene at 0 and 30 kbar

Crystal Structure Prediction for Benzene Using Basin-Hopping Global Optimization

Organic molecules can be stable in distinct crystalline forms, known as polymorphs, which have significant consequences for industrial applications. Here, we predict the polymorphs of crystalline benzene computationally for an accurate anisotropic model parametrized to reproduce electronic structure calculations. We adapt the basin-hopping global optimization procedure to the case of crystalline unit cells, simultaneously optimizing the molecular coordinates and unit cell parameters to locate multiple low-energy structures from a variety of crystal space groups. We rapidly locate all the well-established experimental polymorphs of benzene, each of which corresponds to a single local energy minimum of the model. Our results show that basin-hopping can be both an efficient and effective tool for polymorphic crystal structure prediction, requiring no a priori experimental knowledge of cell parameters or symmetry.

High-pressure polymorphism in pyridine

Single crystals of the high-pressure phases II and III of pyridine have been obtained by in situ crystallization at 1.09 and 1.69 GPa, revealing the crystal structure of phase III for the first time using X-ray diffraction. Phase II crystallizes in P212121 with Z' = 1 and phase III in P41212 with Z' = ½. Neutron powder diffraction experiments using pyridine-d5 establish approximate equations of state of both phases. The space group and unit-cell dimensions of phase III are similar to the structures of other simple compounds with C 2v molecular symmetry, and the phase becomes stable at high pressure because it is topologically close-packed, resulting in a lower molar volume than the topologically body-centred cubic phase II. Phases II and III have been observed previously by Raman spectroscopy, but have been mis-identified or inconsistently named. Raman spectra collected on the same samples as used in the X-ray experiments establish the vibrational characteristics of both phases unambiguously. The pyridine molecules interact in both phases through CH⋯π and CH⋯N interactions. The nature of individual contacts is preserved through the phase transition between phases III and II, which occurs on decompression. A combination of rigid-body symmetry mode analysis and density functional theory calculations enables the soft vibrational lattice mode which governs the transformation to be identified.

Stepwise Homogeneous Melting of Benzene Phase I at High Pressure

We investigate, using molecular dynamics simulations, the spontaneous homogeneous melting of benzene phase I under a high pressure of 1.0 GPa. We find an apparent stepwise transition via a metastable crystal phase, unlike the direct melting observed at ambient pressure. The transition to the metastable phase is achieved by rotational motions, without the diffusion of the center of mass of benzene. The metastable crystal completely occupies the whole space and maintains its structure for at least several picoseconds, so that the phase seems to have a local free energy minimum. The unit cell is found to be unique—no such crystalline structure has been reported so far. Furthermore, we discuss the influence of pressure control on the melting behavior.

Exploring polymorphism of benzene and naphthalene with free energy based enhanced molecular dynamics

Prediction and exploration of possible polymorphism in organic crystal compounds are of great importance for industries ranging from organic electronics to pharmaceuticals to high-energy materials. Here we apply our crystal structure prediction procedure and the enhanced molecular dynamics based sampling approach called the Crystal-Adiabatic Free Energy Dynamics (Crystal-AFED) method to benzene and naphthalene. Crystal-AFED allows the free energy landscape of structures to be explored efficiently at any desired temperature and pressure. For each system, we successfully predict the most stable crystal structures at atmospheric pressure and explore the relative Gibbs free energies of predicted polymorphs at high pressures. Using Crystal-AFED sampling, we find that mixed structures, which typically cannot be discovered by standard crystal structure prediction methods, are prevalent in the solid forms of these compounds at high pressure.

Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

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.

Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy

Computation of lattice energies to an accuracy sufficient to distinguish polymorphs is a fundamental bottleneck in crystal structure prediction. For the lattice energy of the prototypical benzene crystal, we combined the quantum chemical advances of the last decade to attain sub-kilojoule per mole accuracy, an order-of-magnitude improvement in certainty over prior calculations that necessitates revision of the experimental extrapolation to 0 kelvin. Our computations reveal the nature of binding by improving on previously inaccessible or inaccurate multibody and many-electron contributions and provide revised estimates of the effects of temperature, vibrations, and relaxation. Our demonstration raises prospects for definitive first-principles resolution of competing polymorphs in molecular crystal structure prediction.

Temperature-accelerated method for exploring polymorphism in molecular crystals based on free energy

The ability of certain organic molecules to form multiple crystal structures, known as polymorphism, has important ramifications for pharmaceuticals and high energy materials. Here, we introduce an efficient molecular dynamics method for rapidly identifying and thermodynamically ranking polymorphs. The new method employs high temperature and adiabatic decoupling to the simulation cell parameters in order to sample the Gibbs free energy of the polymorphs. Polymorphism in solid benzene is revisited, and a resolution to a long-standing controversy concerning the benzene II structure is proposed.

Simulation of structural phase transitions by metadynamics

We describe here in detail the recently introduced methodology for simulation of structural transitions in crystals. The applications of the new scheme are illus trated on various kinds of crystals and the advantages with respect to previous schemes are emphasized. The relevance of the new method for the problem of crystal structure prediction is also discussed.

How molecules stick together in organic crystals: weak intermolecular interactions

This tutorial review introduces the fundamentals of intermolecular interactions in terms of the underlying physics and goes on to illustrate the most popular methods for the computer simulation of intermolecular interactions, from atom-atom potentials to ab initio methods, including intermediate, hybrid methods, with an appreciation of their relative merits and costs. Typical results are critically presented, culminating in the most difficult exercise of all, the computer prediction of crystal structures. Perspectives on our present and future ability to understand and exploit intermolecular interactions are given.

Predicting structure of molecular crystals from first principles

A recently developed method, symmetry-adapted perturbation theory based on the density-functional description of monomers [SAPT(DFT)], is shown to be sufficiently accurate and numerically efficient to facilitate predictions of the structure of molecular crystals from first principles. In one application, a SAPT(DFT) potential was used to generate and order polymorphs of the cyclotrimethylene trinitramine crystal, resulting in the lowest-energy structure in excellent agreement with the experimental crystal. In a different application, a SAPT(DFT)-based calculation reproduced the lattice energy of the benzene crystal to within a few percent.

Molecular pair analysis: C-H...F interactions in the crystal structure of fluorobenzene? And related matters

The crystal structure of fluorobenzene is compared with isomorphous crystal structures of molecules of roughly similar shape. The lowest-energy fluorobenzene dimers are identified by theoretical calculations. Molecular pair analysis of the crystal structure of fluorobenzene and of an isomorphous virtual low-energy polymorph of benzene suggests that the important intermolecular interactions in the two structures are closely similar. In particular, the intermolecular C-H...F interactions in the fluorobenzene crystal have approximately the same structure-directing ability and influence on the intermolecular energy as the corresponding C-H...H interactions in benzene. Molecular pair analysis of the isomorphous crystal structures of benzonitrile, alloxan, and cyclopentene-1,2,3-trione indicates that essentially the same crystal structure can be adopted with quite different patterns of pair energies and atom-atom interactions. The question as to whether the packing radius of organic fluorine is larger or smaller than that of hydrogen, is addressed, but not answered.

Molecular recognition in organic crystals: directed intermolecular bonds or nonlocalized bonding?

Molecules are held together mainly by forces acting between individual atoms. Does the same apply to molecular clusters? Does intermolecular cohesion depend on weak bonds between individual atoms in different molecules or on less localized, more diffuse interactions between molecules? We discuss these questions from several viewpoints and in particular compare interpretations based on the extension of Bader's atoms in molecules (AIM) theory to cover closed-shell intermolecular interactions with interpretations based on the new pixel method for the calculation of coulombic, polarization, dispersion, and repulsion energies from the electron density of molecular clusters.

Vapor−Liquid and Vapor−Solid Phase Equilibria for United-Atom Benzene Models near Their Triple Points: The Importance of Quadrupolar Interactions

Gibbs ensemble Monte Carlo simulations were used to calculate the vapor-liquid and vapor-solid coexistence curves for benzene using two simple united-atom models. An extension of the Gibbs ensemble method that makes use of an elongated box containing a slab of the condensed phase with a vapor phase along one axis was employed for the simulations of the vapor-solid equilibria and the vapor-liquid equilibria at very low reduced temperatures. Configurational-bias and aggregation-volume-bias Monte Carlo techniques were applied to improve the sampling of particle transfers between the two simulation boxes and between the vapor and condensed-phase regions of the elongated box. An isotropic united-atom representation with six Lennard-Jones sites at the positions of the carbon atoms was used for both force fields, but one model contained three additional out-of-plane partial charge sites to explicitly represent benzene's quadrupolar interactions. Both models were fitted to reproduce the critical temperature and density of benzene and yield a fair representation of the vapor-liquid coexistence curve. In contrast, differences between the models are very large for the vapor-solid coexistence curve. In particular, the lack of explicit quadrupolar interactions for the 6-site model greatly reduces the energetic differences between liquid and solid phases, and this model yields a triple point temperature that is about a factor of 2 too low. In contrast, the 9-site model predicts a triple point of benzene at T = 253 +/- 6 K and p = 2.3 +/- 0.8 kPa in satisfactory agreement with the experimental data (T = 278.7 K and p = 4.785 kPa).

Conformation-family Monte Carlo: a new method for crystal structure prediction

A new global optimization method, Conformation-family Monte Carlo, has been developed recently for searching the conformational space of macromolecules. In the present paper, we adapted this method for prediction of crystal structures of organic molecules without assuming any symmetry constraints except the number of molecules in the unit cell. This method maintains a database of low energy structures that are clustered into families. The structures in this database are improved iteratively by a Metropolis-type Monte Carlo procedure together with energy minimization, in which the search is biased toward the regions of the lowest energy families. The Conformation-family Monte Carlo method is applied to a set of nine rigid and flexible organic molecules by using two popular force fields, AMBER and W99. The method performed well for the rigid molecules and reasonably well for the molecules with torsional degrees of freedom.

The prediction, morphology, and mechanical properties of the polymorphs of paracetamol

The analgesic drug paracetamol (acetaminophen) has two reported metastable polymorphs, one with better tableting properties than the stable form, and another which remains uncharacterized. We have therefore performed a systematic crystal structure prediction search for minima in the lattice energy of crystalline paracetamol. The stable monoclinic form is found as the global lattice-energy minimum, but there are at least a dozen energetically feasible structures found, including the well-characterized metastable orthorhombic phase. Hence, we require additional criteria to reduce the number of hypothetical crystal structures that can be considered as potential polymorphs. For this purpose the elastic properties and vapor growth morphology of the known and predicted structures have been estimated using second-derivative analysis and the attachment-energy model. These inexpensive calculations give reasonable agreement with the available experimental data for the known polymorphs. Some of the hypothetical structures are predicted to have a low growth rate and plate-like morphology, and so are unlikely to be observed. Another is only marginally mechanically stable. Thus, this first consideration of such properties in a crystal-structure prediction study appears to reduce the number of predicted polymorphs while leaving a few candidates for the uncharacterized form.