What type of crystal is benzene

This corresponds with that observed by Campos-Gaxiola et al. The BTC and N3 pyridone form an 30 ring that is perpendicular to the previous ring. Labeling scheme for title compound. Dashed lines represent hydrogen bonds within the asymmetric unit. Symmetry codes: i ; ii ; iii ; iv ; v ; vi ; vii ; viii. However, the structure is reported to be in the monoclinic space group C c. Inspection of an overlay of the two structures reveals some differences between the two polymorphs Fig. This results in a change in the hydrogen-bonding motif, reversing the orientations of the pyridone moieties.

Perhaps the most prominent structural change is the orientation of the pyridone perpendicular to the plane of the BTC. In the title compound the pyridone rings are oriented with planes that are parallel to each other along the channels they occupy and are related by the screw axis parallel to the c axis.

The perpendicular pyridone rings in the Campos-Gaxiola structure alternate their orientation along the channel, related by the c -glide. The change in hydrogen-bonding directionality is propagated to the orientation of the N1 and N2 pyridone chains.

This is highlighted in Fig. Overlay of the title compound red with the Campos-Gaxiola light green structure. The BTC moiety is used as the target for overlay. The view is along the c axis of both structures. Non-H atoms depicted as arbitrary spheres, H atoms as short sticks. Presumably the differences in solvent composition and time for crystallization can yield one polymorph over the other.

Several crystallization attempts were made using the methodology described herein slow evaporation from methanol and all yielded mixtures of the and the co-crystals reported herein. No evidence of the Campos-Gaxiola structure was observed within the crystals examined reported as colorless rectangular prisms.

U iso H was set to 1. Analysis of the Flack x [0. Co-crystals of iodopentafluorobenzene with nitrogen donors: 2-D molecular assemblies through halogen bonding and aryl—perfluoroaryl interactions. A modular mol. In this work, we have accomplished this with cryst. Using variable-temp. Line shape anal. These values were arrived at by selecting from the most reliable x-ray diffraction data those which could be reconciled with crystal d.

A qual. Tentative values for the van der Waals radii of metallic elements in organometallic compds. A list of increments for the vol. B: Struct. Van der Waals Radii of Elements. The available data on the van der Waals radii of atoms in mols. The nature of the continuous variation in interat. A comparative study of crystallographic van der Waals radii. Important data sets of crystallog. The van der Waals radii for rare gases are detd.

Then, van der Waals radii for the other non-metallic and metallic elements, as presented in the literature and having been detd. Finally, certain outstanding problems related to the derivation and application of van der Waals radii are discussed, and further investigations of crystallog.

The halogen Evidence is given that they are attractive, based on a comparison of the no. C and halogen H contacts in halogen-substituted hydrocarbons. Pedireddi, V. Shekhar; Goud, B. Satish; Craig, Donald C. David; Desiraju, Gautam R. An anal.

A total of crystal structures yielded contacts corresponding to sym. This structure was reported to a very limited accuracy previously and the present work reveals an unusual twinned structure for this compd. The packing of the mols. The supramol. The similarities and differences between the behavior of carbon-bound and terminal metal-bound halogens and halide ions as potential hydrogen bond acceptors has been extensively investigated through examn. Halogens in each of these environments are found to engage in hydrogen bonding, and geometric preferences for these interactions have been established.

Furthermore, there are significant parallels between the behavior of moderately strong hydrogen bond acceptors X-M and the much weaker acceptors X-C. The underlying reasons for the obsd. The results are presented within the context of their potential applications in crystal engineering and supramol.

The broader implications of the results in areas such as halocarbon coordination chem. The distributions of the contacts within the sum of van der Waals radii rvdW vs.

This max. These results are in good agreement with our ab initio calcns. The theor. Attaching an electroneg. An electrostatic model is proposed based on two assumptions: The presence of a pos.

Halogen bonding: Recent advances. Solid State Mater. Elsevier Ltd. Halogen bonding XB , as a directional interaction between covalently bound halogen atoms XB donor and Lewis bases A, XB acceptor , has been recently intensively investigated as a powerful tool in crystal engineering. After a short review on the origin and general features of halogen bonding, current developments towards i the elaboration of three-dimensional networks, ii the interaction with anionic XB acceptors, iii its identification in biol.

However, when the halogen atom is strongly activated as in iodoperfluorinated mols. The relative roles of electrostatics and dispersion in the stabilization of halogen bonds. In this work we highlight recent work aimed at the characterization of halogen bonds.

Symmetry adapted perturbation theory anal. Because these noncovalent interactions have a strong dispersion component, it is important that the computational method used to treat a halogen bonding system be chosen very carefully, with correlated methods such as CCSD T being optimal. It is also noted here that most forcefield-based mol. Recent attempts to improve the mol.

The halogen bond is an attractive interaction in which an electrophilic halogen atom approaches a neg. Short halogen atom contacts in crystals were known for around 50 years. Such contacts are found in two varieties: type I, which is sym. Both are influenced by geometric and chem. The authors' research group was using halogen atom interactions as design elements in crystal engineering, for nearly 30 years.

In this Account, the authors illustrate examples of crystal engineering where one can build up from previous knowledge with a focus that is provided by the modern definition of the halogen bond. The authors also comment on the similarities and differences between halogen bonds and H bonds. These interactions are similar because the protagonist atoms-halogen and H-are both electrophilic in nature.

The interactions are distinctive because the size of a halogen atom is of consequence when compared with the at. There is a clear geometric and chem. In parallel, exptl. Variable temp. In terms of crystal design, halogen bonds offer a unique opportunity in the strength, atom size and interaction gradation; this may be used in the design of ternary cocrystals.

Structural modularity in which an entire crystal structure is defined as a combination of modules is rationalized from the intermediate strength of a halogen bond.

The specific directionality of the halogen bond makes it a good tool to achieve orthogonality in mol. In a further development, halogen bonds play a systematic role in organization of LSAMs long range synthon aufbau module , which are bigger structural units contg.

With a formal definition in place, this may be the right time to look at differences between halogen bonds and H bonds and exploit them in more subtle ways in crystal engineering.

Noncovalent binding of the halogens to aromatic donors. Discrete structures of labile Br 2 complexes with benzene and toluene. Discrete structures of labile Br2 complexes with benzene and toluene. Precise mol. Molecular structures of the metastable charge-transfer complexes of benzene and toluene with bromine as the pre-reactive intermediates in electrophilic aromatic bromination.

New J. Successful crystn. Halogen bond tunability I: the effects of aromatic fluorine substitution on the strengths of halogen-bonding interactions involving chlorine, bromine, and iodine. Riley, Kevin E. In the past several years, halogen bonds are relevant in crystal engineering and biomedical applications. One of the reasons for the utility of these types of noncovalent interactions in the development of, for example, pharmaceutical ligands is that their strengths and geometric properties are very tunable.

That is, substitution of atoms or chem. The authors study halogen-bonding interactions involving aromatically-bound halogens Cl, Br, and I and a carbonyl oxygen. The properties of these halogen bonds are modulated by substitution of arom. Very good correlations are obtained between the interaction energies and the magnitudes of the pos. The substitution of fluorines in systems contg.

Also arom. Seven novel cocrystals of pyrene with halo-perfluorobenzenes F, Cl, Br, I were successfully prepd. The stoichiometries of pyrene to halo-perfluorobenzene were all Cited by. Download options Please wait Supplementary information PDF K. Article type Paper. Submitted 12 Dec Accepted 28 Mar First published 28 Mar Download Citation. Request permissions. Intermolecular interactions in crystals of benzene and its mono- and dinitro derivatives: study from the energetic viewpoint I.

More by Atreyee Banerjee. More by Dipti Jasrasaria. More by Samuel P. More by David J. Cite this: J. A , , 17 , — Published by American Chemical Society. Article Views Altmetric -. Abstract High Resolution Image. Molecular crystals have a variety of applications in pharmaceuticals, pigments, and organic electronics. Predicting the structures of these crystals computationally can be a valuable starting point, both for understanding the physical properties of existing materials and for designing new materials.

However, molecules can adopt different crystal structures, i. Physical properties of polymorphs may differ significantly, with potentially dramatic consequences for the bioavailability and stability of pharmaceuticals, 7 so a good CSP protocol should identify all the low-energy polymorphs rather than the single most-favorable structure. This requirement complicates the problem significantly because identifying multiple stable structures requires exploring high-dimensional configuration space.

Choosing the model potential is one of the key decisions in designing a CSP protocol. Many systems can be described adequately by atom—atom isotropic potentials, 8,9 typically with contributions from Pauli repulsion, dispersion, and electrostatic interactions. Alternatively, electronic structure calculations aim to compute the potential energy by solving for the full electronic wave function or electron density rather than by imposing an approximate model. Several approaches have attempted to combine the accuracy of electronic structure methods with the efficiency of classical force fields, typically by fitting a simple mathematical form to data from electronic calculations.

One such model 12 is employed in this work and is discussed in more detail below. Several approaches have been suggested to identify crystal structures for a given model potential.

Many employ molecular dynamics MD simulations to sample the feasible rearrangements of the crystal structure. However, the time scales associated with these solid—solid polymorphic transitions are long, and enhanced sampling techniques are needed.

Recent efforts to select order parameters using artificial neural networks may help to alleviate this problem. Benzene is a popular system for testing and benchmarking CSP protocols. Several model potentials are known to describe benzene accurately, and the simplicity and rigidity of the benzene structure makes CSP computationally feasible, even for ab initio methods.

Naming conventions for these polymorphs differ; we follow Raiteri et al. Under standard conditions, the orthorhombic benzene I polymorph is well understood to be the lowest-energy structure, 29 and it has been accurately characterized using both experimental and theoretical methods.

Most protocols find no evidence of the more controversial phases, but it remains unclear whether this absence is an artifact of incomplete or biased sampling. In the present work, we use a rigid-body anisotropic pair potential and basin-hopping global optimization to locate crystal structures of benzene. Basin-hopping global optimization has proved effective in structure prediction for a diverse range of systems, spanning atomic and molecular clusters, glass formers, and biomolecules.

This transformed landscape is easier to explore than the undeformed potential. We note that basin-hopping has also been used to refine quasi-random sampling in a recent contribution. We have expanded the basin-hopping global optimization method for periodic systems and used it to identify crystal structures of benzene.

We employ periodic boundary conditions with dynamic cell parameters, successfully locating the lowest-energy crystal structures of benzene without any experimental information. The paper is organized as follows: The model potential and the basin-hopping framework for periodic, rigid body systems are described in the Methods. In the Results and Discussion we present our results and compare them with experimental data available in the literature.

The Conclusions summarize our conclusions. Much of the previous work on benzene crystal structure prediction uses isotropic model potentials, 13,15 which assume that intermolecular forces are directionally independent.

Instead, we model benzene using the polycyclic aromatic hydrocarbon anisotropic potential PAHAP , 12 in which the interaction between two atoms depends on both the distance between them and the orientations of the corresponding molecules. Molecules are treated as rigid bodies with a fixed geometry that was obtained by in vacuo optimization by density functional theory DFT. PAHAP is a general model for polycyclic aromatic hydrocarbons, of which benzene is a special case.

The PAHAP model has previously been used to explore the energy landscapes of benzene clusters, 47 but not of crystalline benzene.

Basin-hopping is an efficient tool for locating low-lying minima of the PEL through exploration of a transformed landscape. At each step of the algorithm, every rigid benzene molecule was translated and rotated by a randomly selected amount, up to 0. The fictitious temperature of the Metropolis criterion was adjusted dynamically to maintain an acceptance ratio of around 0.

If accepted, the coordinates of the minimized structure were stored for later analysis and used as the starting point for the next step. The convergence condition for local minimization applied throughout corresponds to reduction of the root mean square gradient to 1. The geometry optimization procedure effectively transforms the PEL into the basins of attraction 42,51 of local minima. The minima themselves are unaffected, but downhill barriers on the landscape are eliminated, facilitating exploration of the landscape.

Basin-hopping does not require a priori knowledge of the important conformational coordinates, nor is any knowledge of the crystal space group required. However, the algorithm does not generate a thermodynamic ensemble of structures, so additional information is required to compute thermodynamic quantities from a landscape database.

Previous applications include atomic and molecular clusters, 41 biomolecules, 52 soft matter, 53,54 atomic crystals, 55 and loss function landscapes for neural networks.

GMIN provides a library of global optimization tools, mostly based on basin-hopping, and a wide selection of atomic interaction potentials for which these tools may be used. Our generalized rigid body framework can convert any potential known by GMIN into a rigid-body molecular model by defining groups of atoms whose relative positions are fixed and specified in the angle-axis coordinate system. Most previous applications have considered large supercells to reduce finite size effects, but without enforcing symmetry constraints, these supercells inevitably become disordered and noncrystalline.

To resolve this problem, we have introduced several refinements, which allow GMIN to use a simulation cell containing a small number of molecules, corresponding to only one or two primitive unit cells of the target polymorphs. This approach has two advantages: first, that the crystalline nature of the structures is automatically preserved by the periodic boundary conditions applied to a small unit cell. Second, the complexity of the PEL and computational cost of basin-hopping both increase significantly with the number of molecules, so using the smallest possible cell size reduces the cost of the CSP protocol and simplifies the subsequent analysis.

In general, one would perform basin-hopping CSP for a range of cell sizes to ensure that all polymorphs have been detected. Our refinements to the GMIN procedure were as follows. First, we implemented a standard Ewald summation scheme 60,61 to compute long-ranged electrostatic forces in reciprocal space.

Parameters of this summation scheme are given in the Supporting Information. Second, our simulation cells were small enough that the repulsive and dispersive interaction radii surrounding each atom extend beyond the boundaries of the cell, so that the usual minimum-image convention would exclude certain atom pairs that should interact for an extended crystalline system.

Instead, the pairwise potential U ij must be summed over the periodic images of atoms i , j in neighboring unit cells. Similarly, interactions up to M b and M c cells distant were included in the b and c directions, respectively.

Summing over periodic images using these limits captures the entire interaction sphere of each molecule without explicitly representing the coordinates of molecules in an extended supercell. We implemented this supercell summation as an independent module within GMIN, so that it can be applied to any existing potential for which periodic boundaries are defined.

Finally, a useful CSP procedure must be able to detect multiple crystal polymorphs with different densities and space groups. To this end, we extended GMIN to optimize the unit cell parameters simultaneously with the atomic coordinates.

This procedure is described in the following section. To explore crystal phase space rapidly, we performed an additional structural perturbation with every third basin-hopping step, in which the unit cell lengths and angles were randomly changed by up to 0.

To facilitate these optimizations, the atomic positions were expressed as fractions of the unit cell vectors instead of absolute coordinates. In this fractional representation, the absolute atomic positions change with variations in the unit cell size and shape. The matrix H and its derivatives with respect to the cell parameters are well-defined, so long as the cell volume is real and positive. When considering rigid bodies in the present work, the center of mass COM coordinates were represented fractionally, so that the absolute positions of the molecules depend on the unit cell parameters.

The angle-axis AA coordinates could also be represented fractionally. However, for simplicity, we assume that the molecular orientations are independent of the unit cell parameters, so the angle-axis coordinates are represented absolutely. The energy gradients with respect to absolute and fractional coordinates are not equivalent, but the gradient vanishes at a stationary point in either convention.

The reference benzene geometry used in the present work is centered at the origin and lies in the xy -plane of the fixed laboratory frame. The functional form given by Equation S2 provides the gradients of the energy with respect to the absolute rigid body coordinates directly. To optimize our rigid-body system, these gradients must be converted to the gradients with respect to fractional coordinates.

To prevent the unit cell from adopting physically unrealistic angle combinations during geometry optimization, the unit cell volume is constrained to be larger than zero with the use of a Weeks—Chandler—Andersen WCA style potential. Results and Discussion. These structures represent all of the well-understood benzene polymorphs.

Each polymorph is represented by multiple structures with slightly different atomic coordinates, due to variations in experimental conditions. Each experimental structure was optimized using the crystal potential energy function described above, and the resulting minima were compared to the original geometries. The energies of the minima and the CPU times required for optimization are given in Table 1. Geometric differences between the experimental and minimized structures were quantified using the root-mean-square deviation RMSD , defined as 7 Here x i and x j are two different atomic coordinate vectors.

D , M , and P are matrices encoding the global symmetries of the system: uniform translation, rotation, and permutation, respectively. The RMSD was calculated using the Fastoverlap alignment method, 67 an efficient algorithm for performing the minimization in eq 7. Fastoverlap aims to find the global minimum RMSD between two structures by selecting the transformation that maximizes the overlap between Gaussian functions centered on atomic coordinates of each structure.

Table 1. As our method optimizes molecular positions and orientations and not the configuration of the rigid benzene molecule itself, we adjusted the experimental structures so that they have the same benzene geometry as the one used in our simulations.

We then compared our calculated structures and the adjusted experimental structures by calculating the RMSD, which depends on the positions of all the atoms in the simulation cell, including hydrogen atoms. The RMSDs between the experimental and the minimized structures are small compared to the C—C and C—H bond lengths in most cases, confirming that minimization does not significantly alter the experimental geometry. The range in RMSDs and optimization costs, measured in LBFGS steps, indicates that there is considerable variation between experimental structures that correspond to the same polymorph.

These differences are likely due to the experimental temperature and pressure conditions as well as the experimental technique used to determine the crystal structure. We also optimized an experimental high-pressure structure reported previously 27,28 that was not deposited in the CCDC. This structure maps to a different minimum, matching the description of benzene II.

Each calculation was initialized from a randomly selected high-energy structure, and no knowledge of the polymorph unit cell parameters was assumed or used to bias the calculations.

The benzene potential used here supports a large number of local minima, many of which were sampled in our simulations of 10 4 BH steps, but most of them have energies that are too high to be experimentally relevant.

In Figure 1 we plot the energy per molecule as a function of molecular volume for the 15 lowest-energy minima, which have an energy per molecule that is within 5 kJ mol —1 of the global minimum structure.

High Resolution Image. Figure 1 also shows the minima obtained by optimizing CCSD structures labeled with the assignments given in Table 1 and two structures calculated by other CSP methods.

All five structures correspond to low-lying minima that were independently identified in a single basin-hopping run, demonstrating that our algorithm is exploring configuration space effectively. The minimum previously identified as the benzene I polymorph was located in every basin-hopping calculation, typically within a few steps, and always identified as the global minimum.

We illustrate the primitive cell of this structure in Figure 2 a. A molecule supercell used to calculate the RMSD 15 is shown in Figure 3 a, overlaid with the corresponding experimental crystal structure, and the calculated cell parameters are compared with experiment in Table 2. Table 2. Our calculated structure matches well with previous reports, 13,15,21,30 and its RMSD compared with the experimental structure is 0. Benzene III was identified by basin-hopping as the third lowest minimum, and its computed structure is shown in Figure 2 b.

This structure has been experimentally observed at high pressure 25,28,32 and has been successfully located in several theoretical studies. The cell parameters of the calculated and experimental structures are presented in Table 2. Optimal alignment of the experimental and calculated crystals gives an RMSD of 0. An illustration of the overlaid structures is given in Figure 3 b. Its computed structure is shown in Figure 2 c. In addition to the three experimental structures identified, basin-hopping runs located an orthorhombic minimum of benzene, which has box parameters close to those of the benzene V structure computed by Raiteri et al.

However, we were unable to find any experimental structure corresponding to this minimum. The polymorphs described above were all detected in every individual basin-hopping calculation, and one run would usually be sufficient to explore a crystal energy landscape.

To quantify the efficiency of our algorithm, we calculate the mean first encounter time MFET for each polymorph. The MFET is the average time taken to locate a particular minimum in a set of independent basin-hopping runs.

We used runs, each starting from a distinct high-energy configuration generated in preliminary basin-hopping runs; these initial configurations had a wide distribution of unit cell lengths and angles to ensure independence of the different calculations. As expected, these quantities are directly proportional.

The MFET is less than basin-hopping steps for all five polymorphs and as low as eight basin-hopping steps for benzene III, highlighting the efficiency of our approach in identifying experimentally relevant structures. The distribution of first encounter times is monotonically decreasing for all polymorphs, indicating that even short basin-hopping runs will locate most relevant polymorphs.

This result may imply that the benzene III structure, although slightly higher in energy than benzene I, occupies a larger volume of configurational space, which is located more easily by basin-hopping. This volume is related to the entropy of the polymorph, suggesting that thermodynamic effects may provide further insight. We found that the benzene II structure 71 P 4 3 2 1 2 symmetry corresponds to a local minimum for the anisotropic pair potential. However, the energy of this minimum and its RMSD from the experimental structure are both significantly higher than for other polymorphs see Table 1.

This asymmetry may arise from the higher energy of the benzene II polymorph, since the global optimization runs are intended to explore low-lying minima. Our observations are consistent with some experimental studies 33,34 that report benzene II as a metastable state. This metastability could also have an entropic contribution, which we will investigate in future work.

The organization of the underlying energy landscape determines how basin-hopping explores the local minima, explaining why some minima are more easily located than others. Further insight into this landscape structure for benzene could help to optimize the basin-hopping CSP procedure for other molecular crystals. An anisotropic pair potential for polycyclic aromatic hydrocarbons 12 was employed using rigid bodies 58 and periodic boundary conditions.

To implement this approach, we employed Ewald summation for the computation of long-range electrostatic interactions, and we used a recently developed supercell method 62 to calculate the supercell dimension on-the-fly.

We have simultaneously optimized the rigid-body positions and orientations and unit cell parameters, allowing for crystal structure prediction with small simulation cells. The use of a relatively simple molecule like benzene, which does not have the associated challenges of systems that contain both dispersion and hydrogen-bonding, allowed us to generate reliable statistics to benchmark the basin-hopping global optimization approach.

By calculating the mean first encounter time for each structure, we have demonstrated the efficiency of basin-hopping in locating experimentally relevant structures for crystalline polymorphs of benzene without any biasing parameter, symmetry restrictions, or a priori experimental data. In future work, we will consider how the thermodynamic state influences the relative stability of polymorphs. Temperature may be incorporated in our methodology by including vibrational entropy in the free energy basin-hopping approach.

We will also use our crystalline benzene framework to identify the minimum energy pathways, made up of transition states and intermediate minima, that connect different polymorph structures. Supporting Information. Author Information. Samuel P. David J. The authors declare no competing financial interest.