An algorithm and program of exhaustive search for possible tiling of a plane with polyominoes

Within the method of discrete modeling of packings in molecular crystals, an algorithm of the exhaustive search for all possible tiling variants of a plane with polyominoes with the given number of translationally independent cells has been developed on the basis of the packing code. The suggested algorithm was used to write the corresponding program for a personal computer.     

Generation of the structures of molecular crystals with two molecules related by the center of inversion in a primitive unit cell

An algorithm for the generation of possible crystal structures with two inversion-related molecules of known shape in a primitive unit cell is proposed within the method of discrete packing modeling in molecular crystals. The algorithm is based on the replacement of molecules by polycubes (geometric figures composed of identical cubes) and looking through a finite number of all the possible periodic packings of these polycubes with a given coefficient of packing. A program package for personal computers is developed on the basis of the proposed algorithm and is approved by the example of several crystal structures that were determined earlier by X-ray diffraction.     

Generation of structures of molecular crystals with two molecules related by a twofold axis or a plane of symmetry in a primitive unit cell

Within the method of discrete modeling of packings, an algorithm of generation of possible structures of molecular crystals with two molecules of known shape in the primitive unit cell, related by a twofold (screw or rotary) axis or a plane of mirror or glide reflection symmetry, is proposed. The algorithm is based on the approximation of molecules by polycubes (geometric figures composed of identical cubes) and calculation of all possible periodic packings of these polycubes with a specified packing factor. On the basis of this algorithm, a software package for personal computers is developed. Examples of approval of this package for several crystal structures, identified previously by X-ray diffraction analysis, are reported.     

Specific features of the crystal packing that enable styryl dyes of the pyridine series to undergo the solid-phase [2 + 2] photocycloaddition including the process with single crystal retention

The crystal packing of a number of styryl dyes of the pyridine series is analyzed. The structures of three dyes and three [2 + 2] photocycloaddition (PCA) products, 1,2,3,4-tetrasubstituted cyclobutanes, obtained in single crystals are determined by X-ray diffraction. Stacks of planar organic cations are characteristic of styryl dye packings. The proceeding of the PCA reaction as a single crystal-to-single crystal transformation in the syn head-to-head stacks is in principle impossible. The syn head-to-tail stacking packings are favorable for the PCA reactions resulting in the centrosymmetric rctt isomers of cyclobutane. The stacking packings, in which molecules are related by the twofold axes (the anti arrangement of molecules), are also favorable for PCA in single crystals. In this case, the products are the rtct isomers of cyclobutane. The presence of the I^? counterions in a packing is a factor impeding the PCA reaction, because the secondary I…H-C bonds increase the rigidity of the crystal lattice. The conditions necessary for proceeding the PCA reactions in styryl dyes as single crystal-to-single crystal processes are as follows: (1) the stacks split into pairs of organic cations (dimers) with the d distances within 4.2 Å in a dimer and d exceeding 4.2 Å between the dimers; and (2) the dimers are surrounded by flexible shells consisting of anions, solvate molecules, or flexible moieties of the organic cations themselves.     

Longitudinal optical-transverse optical (L.O.-T.O.) splitting on internal modes in the Raman spectra of noncentric crystals

A qualitative, but detailed, account of the phenomenon of L.O.-T.O. splitting in the Raman spectroscopy of noncentrosymmetric crystals is given. Tables are provided which give predictions for 45°, 90°, and 180° scattering geometries for all such crystals.     

Mesophase design: II. Molecular structure and crystal packing of 4-alkyloxycyanobiphenyls

A joint analysis of the molecular geometry and crystal packings of the members of a homologous series of 4-alkyloxycyanobiphenyl C _n H_{2n + 1}-O-C₆H₄-C₆H₄-CN with n = 5–12 does not reveal a direct relationship between the molecular geometry and mesogenic properties of these compounds. The crystal packings of all of them are built from alternating loose aliphatic and dense aromatic regions. The closely packed aromatic regions of crystals exhibit weak intermolecular directed interactions of different natures which are responsible for the occurrence of the mesophase. The type of mesophase depends on the number s of structure-forming elements, the ratio of their energies (if s > 1), and the melting temperature of the compound. A graph system is used to describe the crystal packings and the mesophase. It is shown that, although the mesophase graph is similar to the crystal graph, they may differ somewhat, because some symmetric limitations (for example, lattice) on the molecular associate structure are removed in the melt.     

Molecular structures and crystal packings of 2-styrylquinoxaline derivatives

The crystal and molecular structures of 2-styrylquinoxaline derivatives with different substituents in the styryl fragment are determined. The degree of planarity of the molecules studied varies in a very wide range, from 1.7° to 33.5°. In the ethylene fragment, the double bond is essentially localized. The bicycle-pedal disordering of the ethylene fragment is found in the crystals of the methoxy and oxyacetyl derivatives of 2-styrylquinoxaline. None of the packings contains packing motifs favorable for the photocycloaddition (PCA) reaction with single crystal retention. The crystal packings of these compounds and that of 2-(4-methylstyryl)quinoxaline are characterized by a stacking motif of the head-to-head type, which eliminates the possibility of PCA taking place with single crystal retention but is suitable for this reaction in polycrystalline films. The crystal packing of 2-(3,4-dimethoxystyryl)quinoxaline does not contain elements with stacking interactions.     

Molecular and crystal structures of 1-methyl-2-Oxo-3-acetoxy-4-hydroxy-4-(Phenyl)piperidine, 1-ethyl-2-oxo-3,4-dihydroxy-4-(Pyridyl)piperidine, and 1-benzyl-2-oxo-3,4-dihydroxy-4-(Pyridyl)piperidine and the role of hydrogen bonds in molecular packing in crystals

The molecular and crystal structures of 1-methyl-2-oxo-3-acetoxy-4-hydroxy-4-(phenyl)hydropyridine, 1-ethyl-2-oxo-3,4-dihydroxy-4-(pyridyl)piperidine, and 1-benzyl-2-oxo-3,4-dihydroxy-4-(pyridyl)piperidine are determined by X-ray diffraction analysis. These three hydroxy derivatives of hydropyridine are the convenient model compounds in studies of the influence of intramolecular and intermolecular hydrogen bonds on the conformation and packing of molecules in crystals. The molecules of hydroxy derivatives possess a considerable conformational flexibility and can form an extended network of intramolecular and intermolecular hydrogen bonds. It is shown that these compounds more often than others form noncentrosymmetric and polysystem crystals. The role of the molecular association and the type of hydrogen-bonded associates (syntons) in crystal packing are discussed.     

Simple criterion of division of two-dimensional space of a periodic lattice into arbitrarily shaped polyominoes

The method of discrete modeling of molecular packings in crystals is further developed. A criterion of the translational division of the two-dimensional space into arbitrarily shaped polyominoes based on the comparison of the vector systems of the polyomino points with the points of the packing multispace is suggested. The analysis of the properties of this multispace has been performed for the first time in the present study.     

New force field for molecular simulation and crystal design developed based on the “data mining” method

The Data Mining algorithm is used to analyze the information of the Cambridge Structural Database (CSD) with the aim to develop a force field which describes intermolecular interactions. The force-field parameters obtained are successfully tested in calculations of sublimation energy; in construction of polar crystals; in prediction of crystal packings, including predictions based on X-ray powder diffraction data; and in prognosis of protein-ligand interactions and stability of polymorphs. The parametrization developed may also be used in other programs. The parameters are given for all the atomic species encountered in the CSD together with the instructions for their use.     

Dissymetrization of molecular crystals: a driving force for property formation

Phenomena of dissymetrization of molecular crystals are reviewed which lead to sector wise polar properties. Orientational disorder of prolate‐type dipolar molecules taking place at attachment sites can produce partial polar alignment of dipoles in corresponding growth sectors of molecular crystals nucleating into topologically centric packings. As a result bi‐polar crystals are obtained. In case of native polar groups, Monte Carlo simulations predict a basic behaviour for pyroelectric molecular crystals: the dipoles belonging to sectors of either the plus or minus direction of the unique axis show a non‐vanishing probability to be gradually reversed. Domain reversal may start upon a single orientational defect developing into complete sector reversal. Basic features of growth induced stochastic polarity formation are confirmed by scanning pyroelectric microscopy, phase sensitive second harmonic generation microscopy and x‐ray scattering. Real systems comprise channel‐type inclusion compounds, single component molecular crystals, solid solutions and long chain proteins in natural tissues. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural,thermal and optical studies on 2‐naphthol crystals

Single crystals of 2‐naphthol was grown in slow evaporation solution growth technique. Grown crystals were characterized by various characterization techniques. Powder X‐ ray diffraction studies reveal that the grown crystal belongs to monoclinic system with noncentrosymmetric space group. Vibrational bands of the various functional groups and their significance were investigated by analyzing the vibrational spectra. Melting point and the decomposition temperature of the grown crystal was premeditated from the thermal analysis. From the UV‐VIS‐NIR spectrum the electronic excitation mechanism and the transmittance abilities of the crystal was studied. Theoretical value of first static hyperpolarizability was calculated and compared with urea. Second harmonic generation efficiency of the crystal is 0.6 times that of KDP. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Organic inclusion complex strategy for designing nonlinear optical crystals for ultraviolet applications

Based on Molecular Engineering and Crystal Engineering concepts, a new method for designing nonlinear optical (NLO) crystal materials, the Organic Inclusion Complex (OIC) method has been demonstrated. In defining an appropriate optical transparent range with respect to the Molecular Engineering method, small organic molecules containing n-π conjugation were selected as “second order harmonic generation (SHG)-active units”(guests). Together with the Crystal Engineering method, chiral molecules were used as “molecular scaffolding” (hosts) to combine with the “SHG-active units” by hydrogen bonds. The former can provide a nonlinear optical effect. The latter leads to the OIC with a noncentrosymmetric structure and are expected to enhance the macroscopic nonlinearity in a synergistic mode of guest and host by inducing the guest molecular dipole alignment as well as other properties, such as thermal stability, mechanical strength and ease of growth. Here, we report two new inclusion complex crystals, urea-(d)tartaric acid (UDT) and urea-(dl)tartaric acid (UDLT) (here, d means dextral and dl means racemic). UDT and UDLT crystals belong to P2,2,2, and P2, space group, respectively. Bulk size crystals with high optical quality were successfully obtained from aqueous solution by using a temperature-lowering method. The experimental results show that these two crystals demonstrate higher NLO effects and shorter wavelength cutoff.     

Polymorphism and design of noncentrosymmetric crystals of 4-hydroxybenzaldehyde-4-nitrophenylhydrazone and N′-(2-phenyl-1H-indole-3-aldehyde)-4-nitrophenylhydrazone

The products of crystallization of 4-hydroxybenzaldehyde-4-nitrophenylhydrazone (I) and N′-(2-phenyl-1H-indole-3-aldehyde)-4-nitrophenylhydrazone (II) from different solvents are studied by X-ray diffraction with the aim of examining the polymorphism of hydrazone derivatives. The structural features of the crystals prepared are analyzed. It is shown that, in the case when molecules of organic compounds with a high molecular hyperpolarizability are capable of forming stable acentric supramolecular associates in the crystal, knowledge of their polymorphism offers strong possibilities for designing the noncentrosymmetric crystal structure necessary for a manifestation of the nonlinear optical activity.     

Tetragonal packings of spheres

Nine regular tetragonal packings of spheres are considered. These packings satisfy the following conditions: all the spheres have the same dimensions and environment, i.e., belong to one regular system of points with the coordination number of the packing being not less than six. The examples of the real crystal structures corresponding to seven of these packings are considered.     

A tiling approach to counting inherent structures in hard potential systems

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by combining sets of elementary locally jammed structures but eliminates those final packings that either, do not tile space, or are not collectively jammed, through the use of tile incompatibility rules. The resulting theory contains a number of geometric quantities, such as the number of growth sites on a tile and the number of tile compatibilities that provide insight into the number of inherent structures in certain limits. We also show that these geometric quantities become quite simple in a system of highly confined hard discs.     

Synthesis,growth conditions,and crystal structures of alkali metal hypophosphites <Emphasis Type="Italic">M</Emphasis>H<Subscript>2</Subscript>PO<Subscript>2</Subscript>

Metal hypophosphites are widely used in various fields. However, their structures have not been adequately studied. The synthesis conditions (the temperature and precursors) were found and crystals of anhydrous Li, K, Rb, Cs, and NH₄ hypophosphites were grown. The structures of these compounds were established by X-ray diffraction analysis. These crystal structures can be described as packings of layers consisting of hypo-phosphite anions coordinated to metal cations. In all these salts, the hypophosphite anions serve as bridges between four cations belonging to the same layer. Each oxygen atom is bound to two cations.     

A short overview on practical techniques for protein crystallization and a new approach using low intensity electromagnetic fields

This contribution deals with a practical overview of some popular and sophisticated crystallization methods that help increase the success rate of a crystallization project and introduces a newly developed method involving low intensity electromagnetic fields. Aiming to suggest a methodology to follow, the present contribution is divided into two main parts in a logical order to get the best crystals for high resolution X-ray crystallographic analysis. The first part starts with a short review of the chemical and physical fundamentals of each crystallization method through different strategies based on physicochemical approaches. Then, practical non-conventional techniques for protein crystallization are presented, not only for growing protein crystals, but also for controlling the size and number of crystals. These include crystal growth in gels, counter-diffusion, seeding, and macromolecular imprinted polymers (MIPs). The second part shows the effects of coupling low intensity electric fields (in the scale of units of  μAmperes) with weak magnetic fields (in the scale of milli Tesla) applied to protein crystallization. This approach consists of a novel experimental set up, which was used to study the influence of the coupled fields on the crystallization of lysozyme in solution and in gel media. This new approach is based on the classical theories of transport phenomena and offers a more accessible strategy to obtain suitable crystals for X-ray characterization or Neutron diffraction investigations.     

Formation of crystal structure of cyanovinylbenzene derivatives: X-ray structure investigation of ethyl esters of 3,4-dimethoxy-, 3,4,5-trimethoxy-, and 4-fluorobenzylidenecyanoacetic acids

Ethyl esters of 3,4-dimethoxy-, 3,4,5-trimethoxy-, and 4-fluorobenzylidenecyanoacetic acids are investigated by X-ray diffraction analysis with the aim of elucidating the factors responsible for the formation of crystal structures of cyanovinylbenzene derivatives. The crystal data for other known derivatives of this series are analyzed. It is revealed that, in the absence of strong hydrogen bonding, the main structure-forming function in crystals is fulfilled by intermolecular contacts of two types, namely, staking contacts of parallel and antiparallel molecules. The staking contacts of antiparallel molecules are most frequently realized. It is assumed that their presence in the structure determines the prevailing formation of centrosymmetric packings in the compounds under consideration.     

Algorithm and computer-program search for variants of polyomino packings in plane

An algorithm and a computer program that can be used in the search for all possible periodic packings of a specified set of polyominoes with a specified packing factor have been developed. The algorithm is based on the method of discrete modeling of molecular packings.