Application of molecular mechanics to refine and understand the crystal structure of polythiophene and its oligomers

A molecular mechanics computational procedure, previously used for the refinement and the analysis of several crystalline polymers, was applied to investigate the crystal structures of the tetramer (T4) and hexamer (T6) of thiophene, as well as the crystal structure of polythiophene (PT). Simultaneous minimization of intra- and intermolecular energies of the T4 and T6 structures, obtained by Rietveld analysis of powder X-ray diffraction profiles, leads to molecular conformations showing smaller deviations from the ring co-planarity than the original models. For both oligomers the calculations confirm that the molecular centre of inversion is not a crystallographic centre of symmetry, as also revealed by X-ray diffraction of the T6 single crystal. This surprising effect appears to arise from intermolecular interactions between the terminal residues, hence is not relevant with respect to the PT polymer structure. The small energy cost for constraining the molecules at the crystallographic centre of symmetry is in agreement with experimental findings that reveal the existence of polymorphs for both T4 and T6. The calculations on the T6 single crystal were used to upgrade the MM2-like force field, which was then used to determine the minimum-energy model of the monoclinic crystal structure of polythiophene.     

Some features of the crystal and molecular structure of N-(1,2,4-triazol-5-yl)benzamidine and its hydrochloride

The crystal and molecular structures of N-(1,2,4-triazol-5-yl)benzamidine (1) and its hydrochloride (2) were determined by x-ray crystallography. In compound 1 both independent molecules are Z isomers of the anidine substituted in the imino group and 5-substituted 1H-1,2,4-triazoles. In the crystal the molecules of compound 1 are linked into a stable dimer by intermolecular hydrogen bonds. An undissociated HCl molecule was unexpectedly found in the structure of compound 2, while the structure of the base corresponded to the Z isomer of the amidine substituted in the amino group and to 2H-1,2,4-triazole substituted at position 5. The structures of compounds 1 and 2 are stabilized by an intramolecular hydrogen bond. The HCl molecule participates in the formation of intermolecular hydrogen bonds in compound 2.N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 6, pp. 1380–1386, June, 1992.     

Molecular recognition and crystal energy landscapes: an X-ray and computational study of caffeine and other methylxanthines

We introduce a new approach to crystal-packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom-atom contacts, and on the study of crystal energy landscapes over many computer-generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid-state phase behavior of caffeine and several methylxanthines (purine-2,6-diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X-ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine-water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono- and dimethylxanthines (theophylline, theobromine, and the 1,7-isomer, for which we present a single-crystal X-ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Molecular Recognition and Crystal Energy Landscapes: An X‐ray and Computational Study of Caffeine and Other Methylxanthines

We introduce a new approach to crystal‐packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom–atom contacts, and on the study of crystal energy landscapes over many computer‐generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid‐state phase behavior of caffeine and several methylxanthines (purine‐2,6‐diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X‐ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine–water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono‐ and dimethylxanthines (theophylline, theobromine, and the 1,7‐isomer, for which we present a single‐crystal X‐ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Effect of intermolecular hydrogen bonding on the molecular structures of imidazole and 1,2,4-triazole: A study by ab initio molecular orbital calculations

The effect of intermolecular hydrogen bonding in the solid state on the molecular structures of imidazole and 1,2,4-triazole has been studied by SCF ab initio molecular orbital calculations at the HF/6-31G^* level. The crystals of these species contain endless chains of molecules, connected by unusually strong N-H N hydrogen bonds. Our simulation of the crystal field, based on two simple models, unequivocally shows that hydrogen bond formation not only lengthens the N-H bond but also causes a concerted change in the length of two N-C bonds. The change indicates that the contribution of a polar canonical form to the structure of the molecule increases in going from the gaseous phase to the crystal. This provides a rationale for the strong intermolecular hydrogen bond occurring in the solid state. We have also optimized the geometry of the free molecules at the MP2/6-31G^* level, to investigate the effect that correcting for electron correlation has on the equilibrium structure of these systems.     

Modeling the interplay of inter- and intramolecular hydrogen bonding in conformational polymorphs

The predicted stability differences of the conformational polymorphs of oxalyl dihydrazide and ortho-acetamidobenzamide are unrealistically large when the modeling of intermolecular energies is solely based on the isolated-molecule charge density, neglecting charge density polarization. Ab initio calculated crystal electron densities showed qualitative differences depending on the spatial arrangement of molecules in the lattice with the greatest variations observed for polymorphs that differ in the extent of inter- and intramolecular hydrogen bonding. We show that accounting for induction dramatically alters the calculated stability order of the polymorphs and reduces their predicted stability differences to be in better agreement with experiment. Given the challenges in modeling conformational polymorphs with marked differences in hydrogen bonding geometries, we performed an extensive periodic density functional study with a range of exchange-correlation functionals using both atomic and plane wave basis sets. Although such electronic structure methods model the electrostatic and polarization contributions well, the underestimation of dispersion interactions by current exchange-correlation functionals limits their applicability. The use of an empirical dispersion-corrected density functional method consistently reduces the structural deviations between the experimental and energy minimized crystal structures and achieves plausible stability differences. Thus, we have established which types of models may give worthwhile relative energies for crystal structures and other condensed phases of flexible molecules with intra- and intermolecular hydrogen bonding capabilities, advancing the possibility of simulation studies on polymorphic pharmaceuticals.     

Solution-phase structural characterization of supramolecular assemblies by molecular diffraction

Structures of four molecular squares based on rhenium coordination chemistry have been characterized in the solution phase using pair distribution function (PDF) analyses of wide-angle X-ray scattering measured to better than 1 A spatial resolution. In this report we have focused, in particular, on a comparison of structures for pyrazine- and bipyridine-edged squares measured in solution with structures determined for these molecules in the solid state using X-ray crystallography and models derived from geometry optimization and molecular dynamics simulations using a classical force field. The wide-angle scattering for these assemblies is dominated by pair correlations involving one or more rhenium atoms, with both edge and diagonal Re-Re interactions appearing prominently in PDF plots. The pyrazine square is characterized by a relatively rigid structure in solution, with PDF peak positions and linewidths corresponding closely to those calculated from crystal structure data. For the bipyridine-edged square, the experimental PDF peaks measured along the molecular sides match the positions and linewidths of the PDF peaks calculated from static models. In contrast, PDF peaks measured across the diagonal distances of the molecular square deviate significantly from those calculated from the static crystallographic and energy minimized models. The experimental data are instead indicative of configurational broadening of the diagonal distances. In this respect, molecular dynamics simulations point to the importance of butterfly type motions that modulate the Re-Re diagonal distance. Indeed, the experimental data are reasonably well fit by assuming a bimodal distribution of butterfly conformers differing by approximately 25 degrees in the Re-Re-Re-Re torsion angle. Additionally, the measurements provide evidence for solvent ordering by the supramolecular assemblies detected as regions of solvent association and exclusion.     

Intermolecular covalent pi-pi bonding interaction indicated by bond distances, energy bands, and magnetism in biphenalenyl biradicaloid molecular crystal

Density-functional theory (DFT) calculations were performed for energy band structure and geometry optimizations on the stepped pi-chain, the isolated molecule and (di)cations of the chain, and various related molecules of a neutral biphenalenyl biradicaloid (BPBR) organic semiconductor 2. The dependence of the geometries on crystal packing provides indirect evidence for the intermolecular covalent pi-pi bonding interaction through space between neighboring pi-stacked phenalenyl units along the chain. The two phenalenyl electrons on each molecule, occupying the singly occupied molecular orbitals (SOMOs), are participating in the intermolecular covalent pi-pi bonding making them partially localized on the phenalenyl units and less available for intramolecular delocalization. The band structure shows a relatively large bandwidth and small band gap indicative of good pi-pi overlap and delocalization between neighboring pi-stacked phenalenyl units. A new interpretation is presented for the magnetism of the stepped pi-chain of 2 using an alternating Heisenberg chain model, which is consistent with DFT total energy calculations for 2 and prevails against the previous interpretation using a Bleaney-Bowers dimer model. The obtained transfer integrals and the magnetic exchange parameters fit well into the framework of a Hubbard model. All presented analyses on molecular geometries, energy bands, and magnetism provide a coherent picture for 2 pointing toward an alternating chain with significant intermolecular through-space covalent pi-pi bonding interactions in the molecular crystal. Surprisingly, both the intermolecular transfer integrals and exchange parameters are larger than the intramolecular through-bond values indicating the effectiveness of the intermolecular overlap of the phenalenyl SOMO electrons.     

Noncovalent Interactions and Crystal Structure Prediction of Energetic Materials

The crystal and molecular structures, intermolecular interactions, and energy of CL-20, HATO, and FOX-7 were comparatively predicted based on molecular dynamic (MD) simulations. By comparison, the 2D fingerprint plot, Hirshfeld surface, reduced density gradient isosurface, and electrostatic potential surface were studied to detect the intermolecular interactions. Meanwhile, the effects of vacuum and different solvents on the crystal habit of CL-20, HATO, and FOX-7 were studied by AE and MAE model, respectively. The energy calculation was also analysed based on the equilibrium structures of these crystal models by MD simulations. Our results would provide fundamental insights for the crystal engineering of energetic materials.     

Study of the interaction of imidazolidine-2-thione with molecular iodine

The crystal and molecular structure of the reaction product of imidazolidine-2-thione and molecular iodine of the composition (C₃H₆N₂S)2?3I₂ was established by X-ray diffraction. The crystal structure is composed of strongly connected five-component associates consisting of three I₂ molecules and two heterocyclic molecules. Quantum chemical calculations followed by the topological analysis of the electron density function provided an estimate of the strongest intermolecular interactions in the crystal structure of the molecular adduct.

     

Density functional theory study of triphenyl phosphite: molecular flexibility and weak intermolecular hydrogen bonding

The high conformational flexibility of triphenyl phosphite (TPP) is investigated by density functional theory (DFT) calculations. First, through a scan of the molecular potential energy surface, we bring to light a new stable conformation of an isolated molecule, not yet encountered in the crystal states of TPP. Different relevant conformations of the TPP monomer in the gas state are further presented and discussed in terms of molecular structure, relative energy, and dipole moments. Second, we considered dimer and trimer of TPP starting from their structural topology within the hexagonal crystal, which is characterized by the existence of molecular rods. It is shown that weak C-H...O intermolecular hydrogen bonds in TPP cannot definitely be excluded, and finally this point is discussed in the scope of the glacial state problem.     

Similarity recognition of molecular structures by optimal atomic matching and rotational superposition

An algorithm for similarity recognition of molecules and molecular clusters is presented which also establishes the optimum matching among atoms of different structures. In the first step of the algorithm, a set of molecules are coarsely superimposed by transforming them into a common reference coordinate system. The optimum atomic matching among structures is then found with the help of the Hungarian algorithm. For this, pairs of structures are represented as complete bipartite graphs with a weight function that uses intermolecular atomic distances. In the final step, a rotational superposition method is applied using the optimum atomic matching found. This yields the minimum root mean square deviation of intermolecular atomic distances with respect to arbitrary rotation and translation of the molecules. Combined with an effective similarity prescreening method, our algorithm shows robustness and an effective quadratic scaling of computational time with the number of atoms.     

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.     

Crystal structure of poly(ethylene-oxide) supramolecular assemblies

The formation of poly(ethylene oxide) (PEO) supramolecular complexes is discussed in terms of intermolecular interactions and molecular packing. On the basis of the different known crystal structures, several mechanisms are proposed. First, the PEO complexes can be formed by an Intercalation or Inclusion process, guest molecules diffusing into the PEO unit cell. On the other hand, molecular complexes based on hydrogen bonding cannot be obtained by such a way, their formation requires the complete removal of the initial PEO structure either by melting or dissolution. Finally the relations between the crystal lamellar morphology, the host-guest interactions and the PEO chain mobility are discussed.     

Electrostatic Energies in the 1,4‐Dichlorobenzene Polymorph Crystals: the Role of Charge Density Overlap Effects in Crystal Packing Analysis

Electrostatic and polarization energies for the three known polymorphic crystal structures of 1,4‐dichlorobenzene, as well as for one particularly stable virtual crystal structure generated by computer search, were calculated by a new accurate numerical integration method over static molecular charge densities obtained from high level ab initio molecular‐orbital calculations. Results are compared with those from standard empirical atom‐atom force fields. The new electrostatic energies, which include charge density overlap (penetration) effects, are seen to be much larger than and sometimes of opposite sign to those derived from point‐charge models. None of the four polymorphs is substantially more stable than the others on electrostatic‐energy grounds. Molecule‐molecule electrostatic energies have been calculated for the more important molecular pairs in each of the four structures; trends are found to be very different from those indicated by point‐charge energies or by total energies estimated with a parametric atom‐atom force field. Conclusions based exclusively on analysis of intermolecular atom contacts and point‐charge electrostatics may need to be modified in the light of the new kind of calculation.     

Minimum sequence requirements for selective RNA-ligand binding: a molecular mechanics algorithm using molecular dynamics and free-energy techniques

In vitro evolution techniques allow RNA molecules with unique functions to be developed. However, these techniques do not necessarily identify the simplest RNA structures for performing their functions. Determining the simplest RNA that binds to a particular ligand is currently limited to experimental protocols. Here, we introduce a molecular-mechanics based algorithm employing molecular dynamics simulations and free-energy methods to predict the minimum sequence requirements for selective ligand binding to RNA. The algorithm involves iteratively deleting nucleotides from an experimentally determined structure of an RNA-ligand complex, performing energy minimizations and molecular dynamics on each truncated structure, and assessing which truncations do not prohibit RNA binding to the ligand. The algorithm allows prediction of the effects of sequence modifications on RNA structural stability and ligand-binding energy. We have implemented the algorithm in the AMBER suite of programs, but it could be implemented in any molecular mechanics force field parameterized for nucleic acids. Test cases are presented to show the utility and accuracy of the methodology.     

Two-dimensional self-assembly of linear molecular rods at the liquid/solid interface

We report on the synthesis and scanning tunneling microscopy (STM) studies of a series of linear molecular rods (1-5) comprising different numbers and/or spatial arrangements of perfluorinated benzene and benzene subunits interlinked with diacetylenes in the para position and decorated with or without terminal dodecyl chains. The molecules organize themselves into well-ordered 2D crystal structures at the liquid/solid interface through intermolecular and molecule-substrate interactions. Whereas the molecules substituted by dodecyl chains form the lamellar structures with alternating rigid core rows and alkyl chain rows, the unsubstituted ones change the orientation of the rigid backbones with respect to the lamellar axis. The molecular arrangement is not influenced by fluoro substituents on any phenyl ring of the backbone, which suggests that the interactions between the π-conjugated backbones are dominated by close packing rather than by the dipole moments of the rods or fluorine-based intermolecular interactions.