Showing papers on "Lattice energy published in 2005"
TL;DR: In this article, a correlation between the particle size and the lattice parameter has been established in nanocerium oxide particles (3-30nm) and the variation in lattice parameters is attributed to lattice strain induced by the introduction of Ce3+ due to the formation of oxygen vacancies.
Abstract: A correlation between the particle size and the lattice parameter has been established in nanocerium oxide particles (3–30nm). The variation in the lattice parameter is attributed to the lattice strain induced by the introduction of Ce3+ due to the formation of oxygen vacancies. Lattice strain was observed to decrease with an increase in the particle size. Ce3+ ions concentration increased from 17% to 44% with the reduction in the particle size.
966 citations
TL;DR: A new gold embedded atom method (EAM) potential is fit using an improved force matching methodology which included fitting to high-temperature solid lattice constants and liquid densities and can conclude that it must result from a fundamental limitation in the EAM framework.
Abstract: We fit a new gold embedded atom method (EAM) potential using an improved force matching methodology which included fitting to high-temperature solid lattice constants and liquid densities. The new potential shows a good overall improvement in agreement to the experimental lattice constants, elastic constants, stacking fault energy, radial distribution function, and fcc/hcp/bcc lattice energy differences over previous potentials by Foiles, Baskes, and Daw (FBD) [Phys. Rev. B 33, 7983 (1986)] Johnson [Phys. Rev. B 37, 3924 (1988)], and the glue model potential by Ercolessi et al. [Philos. Mag. A 50, 213 (1988)]. Surface energy was improved slightly as compared to potentials by FBD and Johnson but as a result vacancy formation energy is slightly inferior as compared to the same potentials. The results obtained here for gold suggest for other metal species that further overall improvements in potentials may still be possible within the EAM framework with an improved fitting methodology. On the other hand, we also explore the limitations of the EAM framework by attempting a brute force fit to all properties exactly which was found to be unsuccessful. The main conflict in such a brute force fit was between the surface energy and the liquid lattice constant where both could not be fitted identically. By intentionally using a very large number of spline sections for the pair potential, electron-density function, and embedding energy function, we eliminated a lack of functional freedom as a possible cause of this conflict and hence can conclude that it must result from a fundamental limitation in the EAM framework.
246 citations
TL;DR: In this paper, the lattice energies of 47 crystal structures of organic compounds spanning a wide range of chemical functionalities are calculated using simple atom-atom potential energy functions, using coulombic terms with point-charge parameters, and using the PIXEL formulation, which is based on integral sums over the molecular electron density to obtain coulanombic, polarization, dispersion and repulsion lattice energy.
Abstract: The lattice energies of 47 crystal structures of organic compounds spanning a wide range of chemical functionalities are calculated using simple atom-atom potential energy functions, using coulombic terms with point-charge parameters, and using the PIXEL formulation, which is based on integral sums over the molecular electron density to obtain coulombic, polarization, dispersion and repulsion lattice energies. Comparisons among the different formulations, and the sensitivity and significance of the results against convenience, ease of application and number of parameters, are discussed. Improvements in the treatment of overlap repulsion in PIXEL are described, as well as a scheme for the minimization of the crystal lattice energy, based on the Symplex algorithm, which although computationally demanding, is shown to be feasible even with comparatively modest computing resources. The reproduction of experimental heats of sublimation is only marginally better with the PIXEL method, which however has great advantages in its being generally applicable in principle throughout the periodic table, at the expense of a minimal number of parameters, and in the fact that it sees the intermolecular interaction as the effect of the whole molecular electron density, in a physically more justifiable approach. This latter view in turn suggests a transition from a consideration of atom-atom bonds to a consideration of molecule-molecule bonding, opening a new view of packing factors in molecular crystals.
168 citations
TL;DR: Loiseau et al. as discussed by the authors used 2,6-naphthalenedicarboxylic acid as a rigid ligand to synthesize a new three-dimensional aluminum-organic framework, MIL-69 or Al(OH)2 octahedra corner-linked through the μ2-hydroxyl groups.
155 citations
TL;DR: A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented, based on the global minimization of the lattice enthalpy of the crystal.
Abstract: A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four-step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3-aza-bicyclo(3.3.1)nonane-2,4-dione (P2(1)/a, Z' = 1), allopurinol (P2(1)/c, Z' = 1), 1,3,4,6,7,9-hexa-azacycl(3.3.3)azine (Pbca, Z' = 2), and triethylenediamine (P6(3)/m, Z' = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.
132 citations
TL;DR: In this paper, the lattice energies of predicted and known crystal structures for 50 small organic molecules with constrained (rigid) geometries have been calculated with a model potential whose electrostatic component is described by atom-centered multipoles.
Abstract: The lattice energies of predicted and known crystal structures for 50 small organic molecules with constrained (rigid) geometries have been calculated with a model potential whose electrostatic component is described by atom-centered multipoles. In comparison to previous predictions using atomic point charge electrostatics, there are important improvements in the reliability of lattice energy minimization for the prediction of crystal structures. Half of the experimentally observed crystal structures are found either to be the global minimum energy structure or to have calculated lattice energies within 0.5 kJ/mol (0.1 kcal/mol) of the global minimum. Furthermore, in 69% of cases, there are five or fewer unobserved structures with lattice energies calculated to be lower than that of the observed structure. The results are promising for the advancement of global lattice energy minimization for the ab initio prediction of crystal structures and confirm the utility of representing electrostatic contributions to the energy with atom-centered multipoles.
107 citations
TL;DR: In this paper, the structural and electronic properties of tantalum compounds were studied by means of accurate first principle total energy calculations using the full-potential linearized augmented plane wave plus local orbitals (FP-LAPW+lo) method.
74 citations
TL;DR: A new approach to crystal-packing analysis is introduced, 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 theStudy of crystal energy landscapes over many computer-generated polymorphs,rather than a quest for the one most stable crystal structure.
Abstract: 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.
60 citations
TL;DR: In this article, the lattice enthalpy is given by ΔHL = UPOT + ∑si[(ci/2) - 2]RT where R is the gas constant and T is the absolute temperature.
Abstract: Incorporation of lattice potential energy, UPOT, within a Born–Fajans–Haber thermochemical cycle based on enthalpy changes necessitates correction of the energy of the lattice to an enthalpy term, ΔHL For a lattice containing si ions of type i in the formula unit, the lattice enthalpy is given by ΔHL = UPOT + ∑si[(ci/2) - 2]RT where R is the gas constant (= 8314 J K-1 mol-1), T is the absolute temperature, and ci is defined according as to whether the ion i is monatomic (ci = 3), linear polyatomic (ci= 5), or polyatomic (ci= 6), respectively
58 citations
TL;DR: In this article, the lattice energies for a variety of compounds that can be classified as double salts are calculated by summing the lattices energies of the constituent simple salts, and the implications of the simple salt approximation for the thermodynamics of geochemically important processes are discussed.
Abstract: The lattice energies for a variety of compounds that can be classified as double salts are calculated by summing the lattice energies of the constituent simple salts. A comparison with the lattice energies obtained from the Born-Haber or other thermodynamic cycles shows that the simple salt approximation reproduces these values generally to within 1.2%, even for compounds that have considerable covalent character. Application of this method to the calculation of the lattice energies of silicates, using the sum of the lattice energies of the constituent oxides are, on average, within 0.2% of the value calculated from the experimental enthalpies of formation. The implications of the simple salt approximation for the thermodynamics of geochemically important processes are discussed.
55 citations
TL;DR: Although this paper provides a significant advance over traditional search algorithms and empirical force fields in determining the structures and relative stabilities of diastereomeric salt pairs, the sensitivity of the computed lattice energies to the fine details of the ion conformations overtaxes current computational models and renders the design of diastsereomersic resolution processes by computational chemistry a challenging problem.
Abstract: A methodology for the computational prediction of the crystal structures and resolution efficiency for diastereomeric salt pairs is developed by considering the polymorphic system of the diastereomeric salt pair (R)-1-phenylethylammonium (R/S)-2-phenylpropanoate. To alleviate the mathematical complexity of the search for minima in the lattice energy due to the presence of two flexible entities in the asymmetric unit, the range of rigid-body lattice energy global optimizations was guided by a statistical analysis of the Cambridge Structural Database for common ion-pair geometries and ion conformations. A distributed multipole model for the dominant electrostatic interactions and high-level ab initio calculations for the intramolecular energy penalty for conformational distortions are used to quantify the relative stabilities of the p- and n-salt forms. While the ab initio prediction of the known structure of the p-salt as the most stable structure was insensitive to minor changes in the rigid-ion conformations considered, the relative stabilities of the known polymorphs and hypothetical structures of the n-salt were very sensitive. Although this paper provides a significant advance over traditional search algorithms and empirical force fields in determining the structures and relative stabilities of diastereomeric salt pairs, the sensitivity of the computed lattice energies to the fine details of the ion conformations overtaxes current computational models and renders the design of diastereomeric resolution processes by computational chemistry a challenging problem.
TL;DR: In this article, the intermolecular interactions responsible for the ordering of the [2.2]paracyclophane molecule in a crystal at 100 K have been found out and their strengths and the lattice energy have been estimated on the basis of a high resolution X-ray diffraction study and plane-wave DFT calculations.
TL;DR: In this article, the crystal structures found in a manual search for polymorphs are discussed in conjunction with low energy crystal structures for barbituric acid, cyanuric acids, alloxan, parabanic acid, and urazole.
Abstract: The crystal structures found in a manual search for polymorphs are discussed in conjunction with low energy crystal structures found in a computational search for minima in the lattice energy, for barbituric acid, cyanuric acid, alloxan, parabanic acid, and urazole. Since all these molecules, with the exception of urazole, have crystal structures in which there are carbonyl groups not used in conventional hydrogen bonding, these results and the electrostatic properties of the molecules are used to interpret this unusual behavior. It appears that there is no great difference between the strengths of the various N-H donors and C=O acceptors within these molecules, and the observed crystal structures result from the compromise between the intermolecular interactions of the molecules.
TL;DR: It is found that the magnitude of the relaxation varies from material to material and does not simply correlate with the magnitudeof the principal elastic constants in an easily predictable fashion, or with the size of the cohesive lattice energy or length of the Burgers vector, which emphasises the need to model the non-linear forces and atomic structure of the core.
Abstract: In an accompanying article, we have described a methodology for the simulation of dislocations in structurally complex materials. We illustrate the applicability of this method through studies of screw dislocations in a structurally simple ionic ceramic (MgO), a molecular ionic mineral (forsterite, Mg2SiO4), a semi-ionic zeolite (siliceous zeolite A) and a covalent molecular crystalline material (the pharmaceutical, orthorhombic paracetamol-II). We focus on the extent of relaxation and the structure of the dislocation cores and comment on similarities and points of disparity between these materials. It is found that the magnitude of the relaxation varies from material to material and does not simply correlate with the magnitude of the principal elastic constants in an easily predictable fashion, or with the size of the cohesive lattice energy or length of the Burgers vector, which emphasises the need to model the non-linear forces and atomic structure of the core.
TL;DR: In this article, the basic information of sequences of characteristic atoms in the FCC Ti-Al lattice system, not only the states, potential energies, volumes of atoms at the lattice points, and average atomic states, average atomic potential energy wave planes, bond networks, ratio xTi/xAl, ordering degree and grain boundary for ordered FCC TiAl3-type alloys have been analyzed in the framework of the systematic science of alloys.
Abstract: It has been proved that according to the basic information of sequences of characteristic atoms in the FCC Ti–Al lattice system, not only the states, potential energies, volumes of atoms at the lattice points, and average atomic states, average atomic potential energies, average atomic volumes, and lattice constants of the cells, as well as cohesive energies, heats of formation and bulk moduli for D022–, L12– and C–TiAl3 compounds can be calculated, but also the compositional variations of the atomic states, atomic potential energies, atomic volumes, lattice constants, cohesive energies, and heats of formation of the ordered FCC TiAl3 type and disordered FCC TixAl(1−x) alloys and their Ti- and Al-components can be calculated in the framework of the systematic science of alloys. The average atomic state of the FCC TiAl3 compound consisting of ψ 12 Ti and ψ 8 Al characteristic atoms is 0.25[Ar](3dn)0.006 (3dc)2.974 (4sc)0.5085(4sf)0.5115+0.75[Ne](3sc)1.847(3pc)0.568(3sf)0.585. The weak-bonding ψ 8 Al atoms play a determining role in forming the FCC structure. The strong-bonding ψ 12 Ti atoms play a determining role in causing brittleness. The D022–TiAl3 compound is slightly more stable than the L12– and the C–TiAl3 compounds. The calculated lattice constants and heat of formation ( a = 0.3856 nm , c = 0.8622 nm , Δ H = - 37.07 kJ / mol ) of the D022–TiAl3 compound are in excellent agreement with experimental values. The relationships of brittleness with atomic states, potential energy wave planes, bond networks, ratio xTi/xAl, ordering degree and grain boundary for ordered FCC TiAl3-type alloys have been analysed.
TL;DR: X-ray structure determinations of two different single crystals of octamethylferrocenium tetrafluoroborate revealed conformational polymorphism with ligand twist angles of 180 degrees and 108 degrees, respectively, which could be explained by the small lattice energy difference.
Abstract: X-ray structure determinations of two different single crystals of octamethylferrocenium tetrafluoroborate (OMFc(+)BF(4)(-)) revealed conformational polymorphism with ligand twist angles of 180 degrees and 108 degrees , respectively. Their concomitant occurrence could be explained by the small lattice energy difference of 3.2 kJ mol(-1). Temperature-dependent Moessbauer spectroscopy of (57)Fe-labeled OMFc(+)BF(4)(-) over the range 90 < T < 370 K did not show the anomalous sudden increase in the motion of the metal atom as observed in neutral OMFc. Broadened absorption curves characteristic of relaxation spectra were obtained with an isomer shift of 0.466(6) mm s(-1) at 90 K. The temperature dependence of the isomer shift corresponded to an effective vibrating mass of 79 +/- 10 Da and, in conjunction with the temperature dependence of the recoil-free fraction, to a Moessbauer lattice temperature of 89 K. The spin relaxation rate could be better described by an Orbach rather than a Raman process. At 400 K, a reversible solid-solid transition to a plastic crystalline mesophase was noted.
TL;DR: In this article, the electrochemical charge and discharge potential profiles of Zn-doped materials indicate a close relationship between the lattice energy and lattice parameters in the Zndoped spinel system and partial reversible behavior is observed at the 5 V region.
Abstract: Divalent cation doped lithiated Mn spinel with Zn and Mg as cathode materials for a lithium battery are investigated and partial reversible behavior is observed at the 5 V region. The electrochemical charge and discharge potential profiles of the Zn-doped materials indicate a close relationship between the lattice energy and lattice parameters in the Zn-doped spinel system. Lithium ions extracted from octahedral sites at the 5 V plateau during the charge cycle are partially reinserted back into the tetrahedral sites during the discharge step, which contributes to the partial reversible 5 V behavior. The significant findings reported here are that the strong tetrahedral site preference of divalent nonreactive cations such as Zn and Mg force Li cations onto octahedral sites in these materials, thus resulting in electroactivity at 5 V. In situ X-ray absorption spectroscopy measurements show that the Mn K edge is shifted to higher energy at the 4 V plateau during charge cycle and remains unchanged at the 5 V plateau. In situ Zn K-edge X-ray absorption near-edge structure measurements reveal that the valence state of zinc ions is unchanged at the 5 V plateau region. In situ Mn K-edge extended X-ray absorption fine structure studies suggest thatmore » O{sup 2-} ions in the Zn-spinel lattice are partially oxidized to O{sup -} at the 5 V plateau during the anodic process and O- ions are reduced back to O2- during the cathodic process at the 5 V plateau. The oscillations of the lattice parameters observed at the 5 V plateau region during the anodic charge step are attributed to chemical instability of O{sup -} ions.« less
TL;DR: The work shows that crystal structures of molecular compounds may be solved by lattice energy minimization from diffraction data of limited quality, even when indexing is not possible.
Abstract: The violet pigment methylbenzimidazolonodioxazine, C 22 H 12 Cl 2 N 6 O 4 (systematic name: 6,14-dichloro-3,11-dimethyl-1,3,9,11-tetrahydro-5,13-dioxa-7,15-diazadiimidazo[4,5-b:4',5'-m]pentacene-2,10-dione), shows an X-ray powder diagram consisting of only ca 12 broad peaks. Indexing was not possible. The structure was solved by global lattice energy minimizations. The program CRYSCA [Schmidt & Kalkhof (1999), CRYSCA. Clariant GmbH, Pigments Research, Frankfurt am Main, Germany] was used to predict the possible crystal structures in different space groups. By comparing simulated and experimental powder diagrams, the correct structure was identified among the predicted structures. Owing to the low quality of the experimental powder diagram the Rietveld refinements gave no distinctive results and it was difficult to prove the correctness of the crystal structure. Finally, the structure was confirmed to be correct by refining the crystal structure of an isostructural mixed crystal having a better X-ray powder diagram. The compound crystallizes in P1, Z = 1. The crystal structure consists of a very dense packing of molecules, which are connected by hydrogen bridges of the type N-H...O=C. This packing explains the observed insolubility. The work shows that crystal structures of molecular compounds may be solved by lattice energy minimization from diffraction data of limited quality, even when indexing is not possible.
TL;DR: In this paper, the depolymerization enthalpy of 2D rhombohedral (R) phase compared to 1D orthorhombic (O) and 2D tetragonal (T) T-phases was investigated.
TL;DR: In this paper, the atomatom potential calculation of van der Waals energy E Skydragoncryst in crystal lattice was performed and compared to the experimentally obtained values of sublimation enthalpy for the complexes under study.
Abstract: Temperature dependence of saturated vapor pressure has been measured by gas saturation technique for volatile bis-chelates of palladium(II) with such ligands as acetylacetone, hexafluoroacetylacetone, diethyldithiocarbamate, diisopropyldithiophosphate, and also mixed ligand complex with acetylacetone and cyclooctadiene-2,4. Standard thermodynamic parameters of vaporization ΔH
T
0
and ΔS
T
0
were calculated. Crystal molecular packings and intermolecular interactions were analyzed basing on structural data. Atomatom potential calculation of van der Waals energy E
cryst in crystal lattice was performed and compared to the experimentally obtained values of sublimation enthalpy for the complexes under study.
TL;DR: In this paper, the crystal structures, thermal behaviour and phase transformations of a series of 2,6-disubstituted-N-phenylformamides have been investigated, and a mechanism for the phase change in 1 is proposed and rationalized through the examination of the structures themselves together with lattice energy calculations.
Abstract: The crystal structures, thermal behaviour and phase transformations of a series of 2,6-disubstituted-N-phenylformamides have been investigated. A phase transformation was only observed when chlorine was one of the substituents. Crystals of the room-temperature form of 2,6-dichloro-N-phenylformamide (1) and 2-chloro-6-methyl-N-phenylformamide (2) are isomorphous. Both compounds are orthorhombic at room temperature and transform to a monoclinic high-temperature form at 155 and 106 °C, respectively. The room-temperature structures of 1 and 2 consist of chains of N–H⋯O hydrogen-bonded molecules stacked in an alternating arrangement along the crystallographic a direction. The high-temperature forms of compounds 1 and 2 (grown by sublimation) are both monoclinic but not isomorphous, with one short axis of about 4.3 A, and consist of chains of N–H⋯O hydrogen-bonded molecules stacked along the short axis, related by translation. When both of the chlorine substituents are replaced by methyl groups, as in 2,6-dimethyl-N-phenylformamide (3), the crystals do not undergo any phase transition on heating and only an orthorhombic form, space group P212121, has been isolated. Examination of the molecular geometry and structural properties of 3 indicates that it is a hybrid structure of the low- and high-temperature forms of compounds 1 and 2. This contribution analyzes the effect of chloro-methyl exchange, the steering ability of chlorine, and the role of weak interactions on the structural and thermal properties of the compounds studied. In addition, a mechanism for the phase change in 1 is proposed and rationalized through the examination of the structures themselves together with lattice energy calculations.
TL;DR: In this paper, complete graph-based molecular connectivity indices are used to model different theoretical and experimental properties of a class of 20 alkali halides, as well as a theoretical quantum property of a certain class of fluorides and chlorides.
Abstract: Complete graph-based molecular connectivity indices are used to model different theoretical and experimental properties of a class of 20 alkali halides, as well as a theoretical quantum property of a class of fluorides and chlorides. The experimental properties are the lattice enthalpy, the binding enthalpy, and the polarizability in three different media of the alkali halides. The experimental lattice and binding enthalpy are used as training set to evaluate the other sets of theoretical energies, with which the two enthalpies have, finally, been “reconstructed.” The theoretical energies are Coulomb energy, polarization energy, van der Waals energy, repulsion energy, and zero-point energy. The lattice enthalpy descriptors are rather good descriptors of its constituent energies: Coulomb, van der Waals, repulsion, and zero-point. The descriptors of the binding enthalpies, instead, fail to model some of its constituent energies: Coulomb, polarization, van der Waals, and repulsion energies. All types of energies are described by basis molecular connectivity indices based on odd complete graph algorithms, which allow an optimal description of the “reconstructed” calculated enthalpies. A common description of the experimental lattice and binding enthalpies with a descriptor trained on the binding enthalpies alone has also been possible. The model of three sets of polarization values of the metal halides with a descriptor trained with one set of polarization values compares positively with a previous study on the polarization of organic compounds. The model of this property requires molecular connectivity basis indices based on a sequential complete graph algorithm. The model of the quantum theoretical property, the electron density at the bond critical point of a class of fluorides and chlorides, allows an interesting comparison with density functional theory calculations. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
TL;DR: In this paper, the lattice dynamics of crystals were investigated in the course of high-power electronic excitation, and it was revealed that atoms and ions are displaced from their regular sites for 100-300 fs.
Abstract: The lattice dynamics of crystals is investigated in the course of high-power electronic excitation. It is revealed that, at W
e
< W
eo
, atoms and ions are displaced from their regular sites for 100–300 fs. Subsequent relaxation of the crystal lattice in response to a strong local electric field induced by the collisional displacement of ions occurs for 10–50 ns in an oscillatory manner with a period of 0.5–1.5 ps.
TL;DR: The crystal structure of the solid phase of the dipolar aprotic solvent gamma-butyrolactone (BL1), C(4)H(6)O(2), has been solved using the atom-atom potential method and Rietveld-refined against powder diffraction data collected at T = 180 K with a curved position-sensitive detector using Debye-Scherrer diffraction geometry with monochromatic X-rays.
Abstract: The crystal structure of the solid phase of the dipolar aprotic solvent gamma-butyrolactone (BL1), C(4)H(6)O(2), has been solved using the atom-atom potential method and Rietveld-refined against powder diffraction data collected at T = 180 K with a curved position-sensitive detector (INEL CPS120) using Debye-Scherrer diffraction geometry with monochromatic X-rays. It was first deduced from the X-ray experiment that the lattice parameters are a = 10.1282 (4), b = 10.2303 (5), c = 8.3133 (4) A, beta = 93.291 (2) degrees and that the space group is P2(1)/a, with Z = 8 and two independent molecules in the asymmetric unit. The structure was then solved by global energy minimization of the crystal-lattice atom-atom potentials. The subsequent GSAS-based Rietveld refinement converged to the final crystal-structure model indicator R(F(2)) = 0.0684, profile factors R(p) = 0.0517 and R(wp) = 0.0694, and a reduced chi(2) = 1.671. After further cycles of heating and cooling, a powder diffraction pattern markedly different from the first pattern was obtained, again at T = 180 K, which we tentatively assign to a second polymorph (BL2). All the observed diffraction peaks are well indexed by a triclinic unit cell essentially featuring a doubling of the a axis. An excellent Le Bail fit is obtained, for which R(p) = 0.0312 and R(wp) = 0.0511.
TL;DR: The set/liq melt model is proposed in this paper, where the melt is composed of numerous small domains, within each of which the ions form regular (crystal-type) structures (regliq).
Abstract: Although melting is a most familiar physical phenomenon, the nature of the structural changes that occur when crystals melt are not known in detail. The present article considers the structural implications of the changes in physical properties that occur at the melting points, T m , of the alkali halides. This group of solids was selected for comparative examination because the simple crystal lattices are similar and reliable data are available for this physical change. For most of these salts, the theoretical lattice energies for alternative, regular ionic packing in 4:4, 6:6 and 8:8 coordination arrangements are comparable. Density differences between each solid and liquid at T m are small. To explain the pattern of quantitative results, it is suggested that the melt is composed of numerous small domains, within each of which the ions form regular (crystal-type) structures (regliq). The liquid is portrayed as an assemblage of such domains representing more than a single coordination structure and between which dynamic equilibria maintain continual and rapid transfers of ions. T m is identified as the temperature at which more than a single (regular) structure can coexist. The interdomain (imperfect and constantly rearranging) material (irregliq) cannot withstand shear, giving the melt its fluid, flow properties. From the physical evidence, it is demonstrated that the structural changes on melting are small: these can accommodate only minor modifications of the dispositions of all, or most, ions or larger changes for only a small fraction. This proposed representation, the set/liq melt model, may have wider applicability.
TL;DR: Elimination of the n-hexane molecules from this computer-generated solid and subsequent simulated annealing resulted in a crystal structure that corresponds to the experimentally observed beta-phase within the limits of the force field calculations, implying solvent directed crystallisation of a metastable polymorphic molecular crystal.
Abstract: Two crystalline modifications of 1,1,3,3,5,5-hexachloro-1,3,5-trigermacyclohexane have been experimentally obtained as phase pure products and studied by single-crystal X-ray diffraction. The six-membered heterocycles adopt a chair conformation in the alpha-phase; this polymorph is accessible by crystallisation from solution and from the melt. In contrast, the beta-form is built up from boat-shaped molecules; it can exclusively be crystallised from n-hexane. At the molecular level, formation energies of the 1,1,3,3,5,5-hexachloro-1,3,5-trigermacyclohexane conformers have been compared by using molecular mechanics, semiempirical and ab-initio quantum mechanical calculations. Possible reasons for the selective formation of the alpha- or beta-phase in specific solvents have been considered. Formation of the metastable phase is suggested to occur via a hypothetical intermediate of composition [(GeCl2CH2)3].0.5C6H14. For such an in-silico solvate, a crystal structure of favourable lattice energy, closely related to the experimentally observed beta-modification, has been found through global energy minimisation. Elimination of the n-hexane molecules from this computer-generated solid and subsequent simulated annealing resulted in a crystal structure that corresponds to the experimentally observed beta-phase within the limits of the force field calculations. This scenario implies solvent directed crystallisation of a metastable polymorphic molecular crystal.
TL;DR: In this paper, it has been shown that at nonadiabatic conditions in which the Born-Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on nuclear momenta, the fermionic ground-state energy of the studied system can be stabilized by nonadiabiatic electron-phonon interactions at broken translation symmetry.
Abstract: The theory of the nonadiabatic electron–vibration interactions has been applied to the study of MgB2 superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born–Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground-state energy of the studied system can be stabilized by nonadiabatic electron–phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground-state energy. The model study of MgB2 yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 A/atom of in-plane out-of-phase BB atoms displacements out of the equilibrium (E2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium–high symmetry clumped nuclear structure at the level of the Born–Oppenheimer approximation. The calculated Tc is 39.5 K. The resulting density of states exhibits two-peak character, in full agreement with the tunneling spectra. The peaks are at ±4 meV, corresponding to the change of the π band density of states, and at ±7.6 meV, corresponding to the σ band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
TL;DR: In this article, the density functional theory (DFT) calculations at the B3LYP/6-21G* level were performed on crystalline benzotrifuroxan (BTF) and the energy gap between the highest occupied crystal orbital and lowest unoccupied crystal orbital (LUCO) is 3.89 eV, indicating that the crystal is an electrical insulator.
Abstract: Density Functional Theory (DFT) calculations at the B3LYP/6-21G* level were performed on crystalline benzotrifuroxan (BTF). The frontier bands are generally quite flat. The energy gap between the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO) is 3.89 eV, indicating that the crystal is an electrical insulator. All the atoms of BTF make up both the lower and the higher energy bands. The projection of density of state (DOS) indicates that there exists no region with much higher reactivity as other explosives, since the coplanar rings of BTF are conjugated. An anisotropic impact on the bulk makes the electron transfer from carbon atoms to nitrogen and oxygen atoms, which lowers the strength of the C–C bond. The crystal lattice energy is predicted to be –47.39 kJ/mol. The elastic constants C11, C22, and C33 are predicted to be 191.48 GPa, 94.39 GPa, and 347.42 GPa, respectively. The large differences of C11, C22, and C33 indicate the anisotropic properties of BTF upon impacting. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
TL;DR: In this article, the authors used the attachment energy method to predict the morphology of sodium and rubidium dodecyl sulfates using a plate-like morphology for both materials, in good agreement with the experimental morphologies.
Abstract: Refined interatomic potential parameters are determined for sodium dodecyl sulfate (SDS) and rubidium dodecyl sulfate (RDS) and used to calculate the lattice energies of these systems Comparisons of these values with the experimental “sublimation enthalpies” show good agreement between the calculated and experimental (−17313, 14550 kcal/mol; −17640, 15576 kcal/mol) values, respectively These parameters are utilized to predict the morphology of sodium and rubidium dodecyl sulfates using the attachment energy method, with the simulations revealing a platelike morphology for both materials, in good agreement with the experimental morphologies Analysis of the intermolecular bonding within the crystal structures of both SDS and RDS reveal weak van der Waals interactions between the hydrocarbon tails, resulting in a predicted slow growth perpendicular to the principal faces of these crystals
TL;DR: In this article, the DV-Xα cluster method was used to calculate the covalency of noble metal halides with diamond structure, zinc blend structure and rock salt structure.