Molecular tight-binding method. II. One- and many-electron method for excess electron bands of molecular crystals

An ab initio method for calculating the energies of excess-electron bands in a molecular crystal is developed. These energies represent the electron affinities of a crystal. The present method employs a tight-binding approximation to describe the molecules in a crystal and a set of local functions to describe the excess electron. One- and many-electron formulations of the method are given, the latter takes into account the effect of polarization of all the molecules in the crystal by the excess electron. A scheme for approximate determination of the electronic-correlation corrections to the one-electron bands is developed and applied to calculation of the excess-electron bands in the HCP helium crystal.     

An ab initio method for approximation of the frozen molecular fragment

An ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.     

Intra‐ and intermolecular interactions in crystals of polar molecules. A study by the mixed quantum mechanical/molecular mechanical SCMP‐NDDO method

Stabilization energies of crystals of polar molecules were calculated with the recently developed NDDO‐SCMP method that determines the wave function of a subunit embedded in the symmetrical environment constituted by the copies of the subunit. The total stabilization energies were decomposed into four components. The deformation energy is the difference between the energy of the molecule in the geometries adopted in the crystal on the one hand, and in vacuo, on the other hand. Further energy components are derived from the molecular geometry found in the crystal phase. The electrostatic component is the interaction energy of the molecule with the crystal field, corresponding to the charge distribution obtained in vacuo. The polarization component is the energy lowering resulted in the self‐consistent optimization of the wave function in the crystal field. The rest of the stabilization energy is attributed to the dispersion–repulsion component, and is calculated from an empirical potential function. The major novelty of this decomposition scheme is the introduction of the deformation energy. It requires the optimization of the structural parameters, including the molecular geometry, the intermolecular coordinates, and the cell parameters of the crystal. The optimization is performed using the recently implemented forces in the SCMP‐NDDO method, and this new feature is discussed in detail. The calculation of the deformation energy is particularly important to obtain stabilization energies for crystals in which the molecular geometry differs considerably from that corresponding to the energy minimum of the isolated molecule. As an example, crystals of diastereoisomeric salts are investigated. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1679–1690, 2001     

A comparative three-dimensional Hartree–Fock crystal orbital study of double-stack organic charge-transfer (semi)conductors: TTF–TCNQ,TTF–DCNQI,and TTF–2,5-Me2-DCNQI

Three-dimensional crystal structures of the charge-transfer complexes of tetrathiafulvalene (TTF) with tetracyanoquinodimethane (TCNQ), (N,N′-dicyanbenzoquinondiimine (DCNQI), and N,N′-dicyan-2,5-dimethyl-1,4-benzoquinondiimine (2,5-Me₂-DCNQI) were studied within the ab initio Hartree–Fock crystal orbital approximation using the CRYSTAL92 routine package. A qualitative agreement with the experimental data was achieved, and a definite border between one-electron and many-electron effects in the specific physical properties of the crystals under study was drawn. The calculations led to the tentative conclusion that the true chemical reaction corresponding to the charge transfer in such systems is a two-step transfer of two electrons from the donor's HOMO to the acceptor's LUMO and not only single-electron transfer, as usually believed. Then, whether the system is conductive or semiconductive depends upon the degree of the charge transfer (one, two, or no electrons, respectively). But the final degree of the charge transfer and the density of states on the Fermi level should be determined by many-electron effects. The theoretical approach used in this work seems to be of crucial importance in designing organic crystals with specific physical properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 47–68, 1998     

Morphology of polypropylene crystals. I. Dilute solution-grown lamellar crystals

The dependence of crystalline morphology of isotactic polypropylene crystallized from dilute solutions on its molecular weight and growing conditions and the mechanism of crystal growth were studied by electron microscopy and electron diffraction. Lathshaped lamellar crystals 150–300 A. in thickness are obtained from fractionated polypropylene powders of M _w (average molecular weight) = 600,000 and 240,000, but not from the samples of M _w = 82,000 and 44,000, by means of isothermal crystallization at 130°C. for 20 hr. in dilute α-chloronaphthalene solution (0.005 wt.-%). Precipitation of the fractionated polypropylene sample of M _w = 82,000 from a dilute solution of carbitol gives typical dendritic crystals under the same isothermal crystallizing conditions as mentioned above. The mode of chain folding in these crystals based on the orientation and the crystal structure of the lamellar crystals agrees with that proposed by Sauer, Morrow, and Richardson. From the morphological observations, the mechanism of growth pertinent to polypropylene lamellar crystals is presumed to be as follows: fibrils at first aggregate, then the molecular chains are folded to form small lamellae, and then these small lamellae accumulate compactly to grow to large, lath-shaped, lamellar crystals.     

The self-consistent symmetrized OPW method with an application to crystalline selenium

A review of the nonrelativistic self-consistent symmertrized orthogonalized-plane-wave (SCSOPW ) method used for determining electronic energy bands in periodic solids is given. Working equations based on the full use of group theory at all stages are presented for elemental crystals. As an example the method is applied to the trigonal selenium crystal.     

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

We are engaged in research directed toward the development of compact and accurate correlation functions for many-electron systems. Our computational tool is the variational method in which the many-electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many-fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance r_ij may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi “holes” are very easily obtained. Preliminary results are reported for He, H₂, and Li₂.     

Influence of lattice dynamics on charge transport in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene organic crystals from a theoretical study

The influence of lattice dynamics on carrier mobility has received much attention in organic crystalline semiconductors, because the molecular components are held together by weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. Recently, it has been shown that the dynamic disorder has little effect on hole mobility in the ab plane of pentacene, but a reasonable explanation is absent for such a puzzle. To better understand the effect of lattice vibrations on carrier transport, a further study is required for other organic materials. In this work, a mixed molecular dynamic and quantum-chemical methodology is used to assess the effect of nuclear dynamics on hole mobility in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene (DATT) crystals which exhibit high air stability with the hole mobility as large as that in rubrene-based devices. It is found that the lattice vibrations lead to an increasing encumbrance for hole transport in the ab plane of the DATT crystals as the temperature increases. By comparing the crystal structures of DATT and pentacene, the reduced hole mobility in DATT is attributed to the unsymmetric arrays of nearest-neighboring molecular dimers in the ab plane, because the electronic coupling exhibits unbalanced thermal fluctuations for the nearest-neighboring dimers which then induces a stronger oscillation for carriers along the directions with asymmetric packing. To further relate the dynamic disorder with hole transport, the variations of anisotropic mobilities are also analyzed. As a result, the negligible effect of lattice dynamics on the hole mobility in pentacene is explained by the centrosymmetric molecular packing of the nearest-neighboring molecular pairs in the ab plane.     

Identification of Molecular Crystals Capable of Undergoing an Acyl‐Transfer Reaction Based on Intermolecular Interactions in the Crystal Lattice

Investigation of the intermolecular acyl‐transfer reactivity in molecular crystals of myo‐inositol orthoester derivatives and its correlation with crystal structures enabled us to identify the essential parameters to support efficient acyl‐transfer reactions in crystals: 1) the favorable geometry of the nucleophile (? OH) and the electrophile (C?O) and 2) the molecular assembly, reinforced by C? H???π interactions, which supports a domino‐type reaction in crystals. These parameters were used to identify another reactive crystal through a data‐mining study of the Cambridge Structural Database. A 2:1 co‐crystal of 2,3‐naphthalene diol and its di‐p‐methylbenzoate was selected as a potentially reactive crystal and its reactivity was tested by heating the co‐crystals in the presence of solid sodium carbonate. A facile intermolecular p‐toluoyl group transfer was observed as predicted. The successful identification of reactive crystals opens up a new method for the detection of molecular crystals capable of exhibiting acyl‐transfer reactivity.     

First principles calculations of the L2,3-edge XANES spectra for V2O3

Vanadium L_2,3-edge XANES spectra have been calculated for V₂O₃ crystal. A fully relativistic first-principles many electron method based on the numerical solution of the Dirac equation was used. The key-points of the method are: (i) use of the molecular orbitals (MO); (ii) absence of any fitting parameters; (iii) possibility to apply to any ion in any symmetry; (iv) possibility of numerical analysis of the many-electron states in terms of the MO-based Slater determinants. The calculated spectra are in good agreement with experimental ones available in the literature, including the absolute values of the transition energy and the shape of the absorption bands. Experimental trends in the polarized XANES spectra of V₂O₃ are reproduced.     

Effect of polymorphism on the C?H stretching region of the infrared spectrum of polyethylene

A complex fine structure in the C? H stretching region of the infrared spectrum of deformed polyethylene single crystals is reported. The deformed crystals are shown to be transformed from the orthorhombic crystal form to a monoclinic structure. The previously deduced C_2/m monoclinic structure does not account for the appearance of the new bands. An alternative but similar monoclinic structure is proposed. The symmetry of this structure is consistent with the Fermi resonance interactions required for the observation of these bands.     

IR Spectra of Paracetamol and Phenacetin. 1. Theoretical and Experimental Studies

IR spectra of paracetamol and phenacetin have been measured for powder crystals of these compounds and for their solutions in chloroform and dimethylsulfoxide. Ab initio calculations of their equilibrium geometry and vibrational spectra were carried out for spectrum interpretation. Differences between the experimental IR spectra of solutions and crystalline samples have been analyzed. Variations of molecular structure from the isolated state to molecular crystal were estimated based on the difference between the optimized molecular parameters of free molecules and the experimental bond lengths and angles evaluated for the crystal forms of the title compounds. The role of hydrogen bonds in the structure of molecular crystals of paracetamol and phenacetin is investigated, and spectral ranges with maximal intermolecular interactions are determined.     

Modified corrections for London forces in solid-state density functional theory calculations of structure and lattice dynamics of molecular crystals

Dispersion forces are critical for defining the crystal structures and vibrational potentials of molecular crystals. It is, therefore, important to include corrections for these forces in periodic density functional theory (DFT) calculations of lattice vibrational frequencies. In this study, DFT was augmented with a correction term for London-type dispersion forces in the simulations of the structures and terahertz (THz) vibrational spectra of the dispersion-bound solids naphthalene and durene. The parameters of the correction term were modified to best reproduce the experimental crystal structures and THz spectra. It was found that the accurate reproduction of the lattice dimensions by adjusting the magnitude of the applied dispersion forces resulted in the highest-quality fit of the calculated vibrational modes with the observed THz absorptions. The method presented for the modification of the dispersion corrections provides a practical approach to accurately simulating the THz spectra of molecular crystals, accounting for inherent systematic errors imposed by computational and experimental factors.     

Automated preparation method for colloidal crystal arrays of monodisperse and binary colloid mixtures by contact printing with a pintool plotter

Photonic crystals and photonic band gap materials with periodic variation of the dielectric constant in the submicrometer range exhibit unique optical properties such as opalescence, optical stop bands, and photonic band gaps. As such, they represent attractive materials for the active elements in sensor arrays. Colloidal crystals, which are 3D gratings leading to Bragg diffraction, are one potential precursor of such optical materials. They have gained particular interest in many technological areas as a result of their specific properties and ease of fabrication. Although basic techniques for the preparation of regular patterns of colloidal crystals on structured substrates by self-assembly of mesoscopic particles are known, the efficient fabrication of colloidal crystal arrays by simple contact printing has not yet been reported. In this article, we present a spotting technique used to produce a microarray comprising up to 9600 single addressable sensor fields of colloidal crystal structures with dimensions down to 100 mum on a microfabricated substrate in different formats. Both monodisperse colloidal crystals and binary colloidal crystal systems were prepared by contact printing of polystyrene particles in aqueous suspension. The array morphology was characterized by optical light microscopy and scanning electron microscopy, which revealed regularly ordered crystalline structures for both systems. In the case of binary crystals, the influence of the concentration ratio of the large and small particles in the printing suspension on the obtained crystal structure was investigated. The optical properties of the colloidal crystal arrays were characterized by reflection spectroscopy. To examine the stop bands of the colloidal crystal arrays in a high-throughput fashion, an optical setup based on a CCD camera was realized that allowed the simultaneous readout of all of the reflection spectra of several thousand sensor fields per array in parallel. In agreement with Bragg's relation, the investigated arrays exhibited strong opalescence and stop bands in the expected wavelength range, confirming the successful formation of highly ordered colloidal crystals. Furthermore, a narrow distribution of wavelength-dependent stop bands across the sensor array was achieved, demonstrating the capability of producing highly reproducible crystal spots by the contact printing method with a pintool plotter.     

Phonons in mixed crystals — the virtual crystal model for interacting bands with different trap depths

Phonons in disordered molecular solids are discussed within the virtual crystal limit, suitable for small trap depths. It is shown that the self-energy due to disorder is in general non-diagonal when bands with different trap depths are interacting. The introduction of an isotopic impurity, therefore, changes the principal axes of rotation in solids. Based upon this model, a method is now available to elucidate the band—band coupling. A useful products rule is derived that is independent of the intermolecular potential provided it is the same for both components. The product rule can be used to study the isotope effect on intermolecular potentials. These theoretical results are applied to the Raman spectra of pure and mixed crystals of naphthalene.     

Crystal deformation during the growth of kink bands in oriented polyethylene

When oriented polyethylene is sheared at an angle to the orientation axis, kink bands often develop and grow, with a resulting change of the crystalline orientation. Beside the crystalline reorientation, the following changes within the kink bands have been observed with wide-angle x-rays: (a) partial transformation to a monoclinic from the normal orthorhombic unit cell; (b) partial alignment of the orthorhombic b axes; (c) rotation of the orthorhombic c axes of a fraction of the crystals around the kinks by an extra 40 to 60° beyond that of the fibrils; and (d) misalignment of the orthorhombic (hk0) planes by a few degrees. These results are suggested to arise, at least in part, from crystal flattening and from crystal twinning or pseudotwinning on planes intersecting the molecular axes.     

The influence of short‐chain branching on the morphology and structure of polyethylene single crystals

The influence of short‐chain branching on the formation of single crystals at constant supercooling is systematically studied in a series of metallocene catalyzed high‐molecular‐weight polyethylene samples. A strong effect of short‐chain branching on the morphology and structure of single crystals is reported. An increase of the axial ratio with short‐chain branching content, together with a characteristic curvature of the (110) crystal faces are observed. To the best of our knowledge, this is the first time that this observation is reported in high‐molecular‐weight polyethylene. The curvature can be explained by a continuous increase in the step initiation—step propagation rates ratio with short‐chain branching, that is, nucleation events are favored against stem propagation by the presence of chain defects. Micro‐diffraction and WAXS results clearly indicate that all samples crystallize in the orthorhombic form. An increase of the unit cell parameter a₀ is detected, an effect that is more pronounced than in the case of single crystals with ethyl and propyl branches. The changes observed are compatible with an expanded lattice due to the presence of branches at the surface folding. A decrease in crystal thickness with branching content is observed as determined from shadow measurements by TEM. The results are in agreement with additional SAXS results performed in single crystal mats and with indirect calorimetry measurements. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1751–1762     

Ab initio calculations of the ground-state potential energy surface for the C?F bond decomposition in n-fluoropropane within the method for approximation of the frozen molecular fragment

The recently proposed ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by a frozen molecular fragment was tested further in a case of the dissociation reaction of the C? F bond in n-fluoropropane. Results from the Hartree–Fock, multiple reference double-excitation configuration–interaction and second-order Møller–Plesset methods are presented. The reproduction of potential energy surfaces as well as the reproduction of electron density distribution are in excellent agreement with extended basis-set calculations. Different choices of fragments to be frozen have been examined.     

Continuous similarity measure between nonoverlapping X-ray powder diagrams of different crystal modifications

The problem of quantifying similarity between crystal structures is transformed into the problem of comparing the associated X-ray powder diagrams. A smooth similarity measure between two powder diagrams, termed a “fold,” is defined. In contrast to conventional comparison methods, the introduced method is still applicable when the peaks of the spectra to be compared have no overlap. The main areas of application of the method are the construction of a molecular crystal structure when only the experimental powder diagram is available and the analysis of possible crystal packings predicted on the basis of molecular information only. A suitable empirical parameterization of the fold has been derived from a large set of experimental and force-field-generated crystals. The analysis of the outcome of an ab initio packing of a flexible molecule is given as an example. The algorithmic details of the method are given as a FORTRAN 77 code. © John Wiley & Sons, Inc.     

X-ray diffraction method of the radial electron density distribution. Structure of nanophase supports and supported catalysts

The structure of the synthesized title compound is characterized by IR, UV-visible spectroscopy, and single crystal X-ray diffraction (XRD). The new compound (C₁₈H₂₃NS) crystalizes in the monoclinic P2₁/c space group. In addition to the crystal structure from the X-ray experiment, the molecular geometry, vibrational frequencies, atomic charge distribution, and frontier molecular orbital (FMO) analysis of the title compound in the ground state are calculated by density functional teory (B3LYP) with 6-311G(d,p) and 6-31G(d,p) basis sets. The results of the optimized molecular structure are presented and compared with the experimental values. The computed vibrational frequencies are used to determine the types of molecular motions associated with each of the observed experimental bands. To determine the conformational flexibility, the molecular energy profile of (1) is obtained by semi-empirical (AM1) and (PM3) calculations with respect to a selected degree of torsional freedom. Moreover, molecular electrostatic potential (MEP) and thermodynamic parameters of the title compound were calculated by the theoretical methods.