Showing papers on "Lattice energy published in 2016"

Building Blocks of Crystal Engineering: A Large-Database Study of the Intermolecular Approach between C–H Donor Groups and O, N, Cl, or F Acceptors in Organic Crystals

Abstract: The nature of CH···X interactions in organic crystals, with X being an electronegative atom, has been the subject of extensive consideration with sometimes contradictory results and ensuing opinions. We perform statistical analysis on large databases of crystal structures retrieved from the Cambridge Structural Database. Crystals containing C–H donors only are considered in conjunction with each of O, N, Cl, or F acceptors in turn. The analysis of Coulombic polarization and dispersion components reveals that the lattice energies of these crystals are largely dominated by dispersive interactions. The frequency of short H···X contacts decreases through the series CHO > CHN > CHCl > CHF, being just sporadic in the latter. The presence of such contacts is positively correlated with the Coulombic contribution to molecule–molecule interaction energies but do not generally determine the pair energy. Short CH···O or CH···N contacts are often relegated to weakly bound pairs; their minor energy contributions might ...

Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography

Abstract: ConspectusMolecular crystals occur widely in pharmaceuticals, foods, explosives, organic semiconductors, and many other applications. Thanks to substantial progress in electronic structure modeling of molecular crystals, attention is now shifting from basic crystal structure prediction and lattice energy modeling toward the accurate prediction of experimentally observable properties at finite temperatures and pressures. This Account discusses how fragment-based electronic structure methods can be used to model a variety of experimentally relevant molecular crystal properties. First, it describes the coupling of fragment electronic structure models with quasi-harmonic techniques for modeling the thermal expansion of molecular crystals, and what effects this expansion has on thermochemical and mechanical properties.Excellent agreement with experiment is demonstrated for the molar volume, sublimation enthalpy, entropy, and free energy, and the bulk modulus of phase I carbon dioxide when large basis second-or...

Influence of Ta substitution for Nb in Zn3Nb2O8 and the impact on the crystal structure and microwave dielectric properties

Abstract: Zn3(Nb1−xTax)2O8 (x = 0.02–0.10) ceramics were prepared via a solid-state reaction route and the dependence of their microwave dielectric properties on their structural characteristics were investigated. XRD patterns show that a single Zn3Nb2O8 phase with layered crystal structures was formed in ceramic samples with 0.02 ≤ x ≤ 0.10. The Raman spectrum was used for the first time to analyze the vibrational phonon modes of the Zn3Nb2O8 samples. Based on P–V–L dielectric theory, the intrinsic factors that influence the microwave dielectric properties were systematically investigated. According to the calculated results, the experimental dielectric constant had a close relationship with the theoretical dielectric constant. The Nb-site lattice energy was found to be a vital factor in explaining the change of the Q × f values. While the Nb-site bond energy increases, the |τf| value decreases which indicates that higher bond energy would result in a more stable system. This work presents a novel method to investigate the intrinsic factors that influence microwave dielectric properties.

Maximum hardness and minimum polarizability principles through lattice energies of ionic compounds

Abstract: The maximum hardness (MHP) and minimum polarizability (MPP) principles have been analyzed using the relationship among the lattice energies of ionic compounds with their electronegativities, chemical hardnesses and electrophilicities. Lattice energy, electronegativity, chemical hardness and electrophilicity values of ionic compounds considered in the present study have been calculated using new equations derived by some of the authors in recent years. For 4 simple reactions, the changes of the hardness (Δη), polarizability (Δα) and electrophilicity index (Δω) were calculated. It is shown that the maximum hardness principle is obeyed by all chemical reactions but minimum polarizability principles and minimum electrophilicity principle are not valid for all reactions. We also proposed simple methods to compute the percentage of ionic characters and inter nuclear distances of ionic compounds. Comparative studies with experimental sets of data reveal that the proposed methods of computation of the percentage of ionic characters and inter nuclear distances of ionic compounds are valid.

CCSD(T)/CBS fragment-based calculations of lattice energy of molecular crystals.

Abstract: A comparative study of the lattice energy calculations for a data set of 25 molecular crystals is performed using an additive scheme based on the individual energies of up to four-body interactions calculated using the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD(T)) with an estimated complete basis set (CBS) description. The CCSD(T)/CBS values on lattice energies are used to estimate sublimation enthalpies which are compared with critically assessed and thermodynamically consistent experimental values. The average absolute percentage deviation of calculated sublimation enthalpies from experimental values amounts to 13% (corresponding to 4.8 kJ mol(-1) on absolute scale) with unbiased distribution of positive to negative deviations. As pair interaction energies present a dominant contribution to the lattice energy and CCSD(T)/CBS calculations still remain computationally costly, benchmark calculations of pair interaction energies defined by crystal parameters involving 17 levels of theory, including recently developed methods with local and explicit treatment of electronic correlation, such as LCC and LCC-F12, are also presented. Locally and explicitly correlated methods are found to be computationally effective and reliable methods enabling the application of fragment-based methods for larger systems.

4-Aminoquinaldine monohydrate polymorphism: prediction and impurity aided discovery of a difficult to access stable form

Abstract: Crystal structure prediction studies indicated the existence of an unknown high density monohydrate structure (Hy1B°) as the global energy minimum for 4-aminoquinaldine (4-AQ). We thus performed an interdisciplinary experimental and computational study elucidating the crystal structures, solid form inter-relationships, and kinetic and thermodynamic stabilities of the stable anhydrate (AH I°), the kinetic monohydrate (Hy1A) and this novel monohydrate polymorph (Hy1B°) of 4-AQ. The crystal structure of Hy1B° was determined by combining laboratory powder X-ray diffraction data and ab initio calculations. Dehydration studies with differential scanning calorimetry and solubility measurements confirmed the result of the lattice energy calculations, which identified Hy1B° as the thermodynamically most stable hydrate form. At 25 °C the equilibrium of the 4-AQ hydrate/anhydrate system was observed at an aw (water activity) of 0.14. The finding of Hy1B° was complicated by the fact that the metastable but kinetically stable Hy1A shows a higher nucleation and growth rate. The presence of an impurity in an available 4-AQ sample facilitated the nucleation of Hy1B°, whose crystallisation is favored under hydrothermal conditions. The value of combining experimental with theoretical studies in hydrate screening and characterisation, as well as the reasons for hydrate formation in 4-AQ, are discussed.

Computational and Experimental Characterization of Five Crystal Forms of Thymine: Packing Polymorphism, Polytypism/Disorder, and Stoichiometric 0.8-Hydrate

Abstract: New polymorphs of thymine emerged in an experimental search for solid forms, which was guided by the computationally generated crystal energy landscape. Three of the four anhydrates (AH) are homeoenergetic (A° – C), and their packing modes differ only in the location of oxygen and hydrogen atoms. AHs A° and B are ordered phases, whereas AH C shows disorder (X-ray diffuse scattering). Analysis of the crystal energy landscape for alternative AH C hydrogen bonded ribbon motifs identified a number of different packing modes, whose three-dimensional structures were calculated to deviate by less than 0.24 kJ mol–1 in lattice energy. These structures provide models for stacking faults. The three anhydrates A° – C show strong similarity in their powder X-ray diffraction, thermoanalytical, and spectroscopic (IR and Raman) characteristics. The already known anhydrate AH A° was identified as the thermodynamically most stable form at ambient conditions; AH B and AH C are metastable but show high kinetic stability. Th...

Activation of coherent lattice phonon following ultrafast molecular spin-state photo-switching: A molecule-to-lattice energy transfer

Abstract: We combine ultrafast optical spectroscopy with femtosecond X-ray absorption to study the photo-switching dynamics of the [Fe(PM-AzA)2(NCS)2] spin-crossover molecular solid. The light-induced excited spin-state trapping process switches the molecules from low spin to high spin (HS) states on the sub-picosecond timescale. The change of the electronic state (<50 fs) induces a structural reorganization of the molecule within 160 fs. This transformation is accompanied by coherent molecular vibrations in the HS potential and especially a rapidly damped Fe-ligand breathing mode. The time-resolved studies evidence a delayed activation of coherent optical phonons of the lattice surrounding the photoexcited molecules.

Two New Polymorphs of the Organic Semiconductor 9,10-Diphenylanthracene: Raman and X-ray Analysis

Abstract: Raman microscopy in the lattice phonon region coupled with X-ray diffraction have been used to study the polymorphism in crystals and microcrystals of the organic semiconductor 9,10-diphenylanthracene (DPA) obtained by various methods. While solution grown specimens all display the well-known monoclinic structure widely reported in the literature, by varying the growth conditions two more polymorphs have been obtained, either from the melt or by sublimation. By injecting water as a nonsolvent in a DPA solution, one of the two new polymorphs was predominantly obtained in the shape of microribbons. Lattice energy calculations allow us to assess the relative thermodynamic stability of the polymorphs and verify that the energies of the different phases are very sensitive to the details of the molecular geometry adopted in the solid state. The mobility channels of DPA polymorphs are shortly investigated.

Equations of state for the α and γ polymorphs of cyclotrimethylene trinitramine

Abstract: Equations of state for the α and γpolymorphs of the energetic molecular crystal cyclotrimethylene trinitramine (RDX) have been developed from their Helmholtz free energies. The ion motion contribution to the Helmholtz free energy is represented by Debye models with density-dependent Debye temperatures that are parameterized to vibrational densities of states computed from dispersion-corrected density functional theory. By separating the vibrational density of states into low frequency modes of mainly lattice phonon character and high frequency modes of intramolecular character we were able to significantly improve the description of the heat capacity at low temperatures and the thermal contribution to the pressure. The ion motion contribution to the Helmholtz free energy of the high pressureγpolymorph was constructed from that of the αpolymorph to reproduce the temperature-independent transformation pressure seen experimentally. The static lattice energies for both polymorphs were constructed to reproduce published isothermal compression data. The equations of state have been applied to the prediction of the path of the principal Hugoniot in the equilibrium phase diagram.

Effects of a More Accurate Polarizable Hamiltonian on Polymorph Free Energies Computed Efficiently by Reweighting Point-Charge Potentials.

Abstract: We examine the free energies of three benzene polymorphs as a function of temperature in the point-charge OPLS-AA and GROMOS54A7 potentials as well as the polarizable AMOEBA09 potential. For this system, using a polarizable Hamiltonian instead of the cheaper point-charge potentials is shown to have a significantly smaller effect on the stability at 250 K than on the lattice energy at 0 K. The benzene I polymorph is found to be the most stable crystal structure in all three potentials examined and at all temperatures examined. For each potential, we report the free energies over a range of temperatures and discuss the added value of using full free energy methods over the minimized lattice energy to determine the relative crystal stability at finite temperatures. The free energies in the polarizable Hamiltonian are efficiently calculated using samples collected in a cheaper point-charge potential. The polarizable free energies are estimated from the point-charge trajectories using Boltzmann reweighting wit...

An optimized intermolecular force field for hydrogen‐bonded organic molecular crystals using atomic multipole electrostatics

Abstract: We present a re-parameterization of a popular intermolecular force field for describing intermolecular interactions in the organic solid state. Specifically we optimize the performance of the exp-6 force field when used in conjunction with atomic multipole electrostatics. We also parameterize force fields that are optimized for use with multipoles derived from polarized molecular electron densities, to account for induction effects in molecular crystals. Parameterization is performed against a set of 186 experimentally determined, low-temperature crystal structures and 53 measured sublimation enthalpies of hydrogen-bonding organic molecules. The resulting force fields are tested on a validation set of 129 crystal structures and show improved reproduction of the structures and lattice energies of a range of organic molecular crystals compared with the original force field with atomic partial charge electrostatics. Unit-cell dimensions of the validation set are typically reproduced to within 3% with the re-parameterized force fields. Lattice energies, which were all included during parameterization, are systematically underestimated when compared with measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%.

Solubility of Alkali Metal Halides in the Ionic Liquid [C4C1im][OTf]

Abstract: The solubilities of the metal halides LiF, LiCl, LiBr, LiI, NaF, NaCl, NaBr, NaI, KF, KCl, KBr, KI, RbCl, CsCl, CsI, were measured at temperatures ranging from 298.15 to 378.15 K in the ionic liquid 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([C4C1im][OTf]). Li+, Na+ and K+ salts with anions matching the ionic liquid have also been investigated to determine how well these cations dissolve in [C4C1im][OTf]. This study compares the influence of metal cation and halide anion on the solubility of salts within this ionic liquid. The highest solubility found was for iodide salts, and the lowest solubility for the three fluoride salts. There is no outstanding difference in the solubility of salts with matching anions in comparison to halide salts. The experimental data were correlated employing several phase equilibria models, including ideal mixtures, van't Hoff, the λh (Buchowski) equation, the modified Apelblat equation, and the non-random two-liquid model (NRTL). It was found that the van't Hoff model gave the best correlation results. On the basis of the experimental data the thermodynamic dissolution parameters (ΔH, ΔS, and ΔG) were determined for the studied systems together with computed gas phase metathesis parameters. Dissolution depends on the energy difference between enthalpies of fusion and dissolution of the solute salt. This demonstrates that overcoming the lattice energy of the solid matrix is the key to the solubility of inorganic salts in ionic liquids.

Latent tracks and associated strain in Al 2 O 3 irradiated with swift heavy ions

Abstract: The morphology of latent ion tracks induced by high energy heavy ions in Al 2 O 3 was investigated using a combination of high resolution transmission electron microscopy (HRTEM), exit wave reconstruction, geometric phase analysis and numerical simulations. Single crystal α-Al 2 O 3 crystals were irradiated with 167 MeV Xe ions along the c -axis to fluences between 1 × 10 10 and 1 × 10 13 cm −2 . Planar TEM lamella were prepared by focused ion beam (FIB) and geometrical phase analysis was performed on the phase image of the reconstructed complex electron wave at the specimen exit surface in order to estimate the latent strain around individual track cores. In addition to the experimental data, the material excitation in a SHI track was numerically simulated by combining Monte-Carlo code, describing the excitation of the electronic subsystem, with classical molecular dynamics of the lattice atoms. Experimental and simulation data both showed that the relaxation of the excess lattice energy results in the formation of a cylinder-like disordered region of about 4 nm in diameter consisting of an underdense core surrounded by an overdense shell. Modeling of the passage of a second ion in the vicinity of this disordered region revealed that this damaged area can be restored to a near damage free state. The estimation of a maximal effective distance of recrystallization between the ion trajectories yields values of about 6–6.5 nm which are of the same order of magnitude as those estimated from the saturation density of latent ion tracks detected by TEM.

Cohesive Energies and Enthalpies: Complexities, Confusions, and Corrections

Abstract: The cohesive or atomization energy of an ionic solid is the energy required to decompose the solid into its constituent independent gaseous atoms at 0 K, while its lattice energy, Upot, is the energy required to decompose the solid into its constituent independent gaseous ions at 0 K. These energies may be converted into enthalpies at a given temperature by the addition of the small energies corresponding to integration of the heat capacity of each of the constituents. While cohesive energies/enthalpies are readily calculated by thermodynamic summing of the formation energies/enthalpies of the constituents, they are also currently intensively studied by computational procedures for the resulting insight on the interactions within the solid. In supporting confirmation of their computational results, authors generally quote "experimental" cohesive energies which are, in fact, simply the thermodynamic sums. However, these "experimental" cohesive energies are quoted in many different units, atom-based or calorimetric, and on different bases such as per atom, per formula unit, per oxide ion, and so forth. This makes comparisons among materials very awkward. Additionally, some of the quoted values are, in fact, lattice energies which are distinctly different from cohesive energies. We list large numbers of reported cohesive energies for binary halides, chalcogenides, pnictogenides, and Laves phase compounds which we bring to the same basis, and identify a number as incorrectly reported lattice energies. We also propose that cohesive energies of higher-order ionic solids may also be estimated as thermodynamic enthalpy sums.

Lattice Parameter Behavior with Different Nd and O Concentrations in (U1−yNdy)O2±X Solid Solution

Abstract: The solid solution of (U1−yFPy)O2±x has the same fluorite structure as UO2±x, and the lattice parameter is affected by dissolved fission product and oxygen concentrations. The relation between the ...

Crystal structure and microwave dielectric characteristics of Co-substituted Zn1−xCoxZrNb2O8 (0 ≤ x ≤ 0.1) ceramics

Abstract: Wolframite structure Zn1−xCoxZrNb2O8 (x = 0, 0.02, 0.04, 0.06, 0.08, 0.10) ceramics were prepared by the conventional solid state method. The crystal structures were studied via X-ray diffraction, and lattice vibrational modes were obtained by Raman spectroscopy. It could be found that all the A-site (Zn2+/Co2+, Zr4+) and B-site (Nb5+) cations were octahedrally coordinated with oxygen anions from the diagrammatic sketch of the crystal structure. Rietveld refinement was used to analyze the crystal structure and the lattice parameters were obtained. Based on the complex chemical bond theory and lattice parameters, intrinsic factors such as the bond ionicity, lattice energy, bond energy and coefficient of thermal expansion were calculated. Based on the results, Nb–O bonds played an important role in affecting the microwave dielectric proprieties of Zn1−xCoxZrNb2O8 ceramics. Co2+ substitution would affect the crystal structure and influence the microwave dielectric properties. The tendency of the dielectric constant (er) could be predicted by the polarizability and bond ionicity of Nb–O bonds, and the er showed the same tendency with Raman shifts of Nb–O vibration modes. The variation of the quality factor (Qf) could be explained by the change of the lattice energy of Nb–O bonds and the full width at half maximum (FWHM) values of Nb-site Raman modes. The temperature coefficient of resonant frequency (τf) showed the same tendency with the bond energy, octahedral distortion and bond valence of Nb–O bonds, and the opposite tendency with the thermal expansion coefficient.

Using crystal structure prediction to rationalize the hydration propensities of substituted adamantane hydrochloride salts

Abstract: The crystal energy landscapes of the salts of two rigid pharmaceutically active molecules reveal that the experimental structure of amantadine hydrochloride is the most stable structure with the majority of low-energy structures adopting a chain hydrogen-bond motif and packings that do not have solvent accessible voids. By contrast, memantine hydrochloride which differs in the substitution of two methyl groups on the adamantane ring has a crystal energy landscape where all structures within 10 kJ mol−1 of the global minimum have solvent-accessible voids ranging from 3 to 14% of the unit-cell volume including the lattice energy minimum that was calculated after removing water from the hydrated memantine hydrochloride salt structure. The success in using crystal structure prediction (CSP) to rationalize the different hydration propensities of these substituted adamantane hydrochloride salts allowed us to extend the model to predict under blind test conditions the experimental crystal structures of the previously uncharacterized 1-(methylamino)adamantane base and its corresponding hydrochloride salt. Although the crystal structure of 1-(methylamino)adamantane was correctly predicted as the second ranked structure on the static lattice energy landscape, the crystallization of a Z′ = 3 structure of 1-(methylamino)adamantane hydrochloride reveals the limits of applying CSP when the contents of the crystallographic asymmetric unit are unknown.

Local variational study of 2d lattice energies and application to Lennard-Jones type interactions

Abstract: In this paper, we focus on finite Bravais lattice energies per point in two dimensions. We compute the first and second derivatives of these energies. We prove that the Hessian at the square and the triangular lattice are diagonal and we give simple sufficient conditions for the local minimality of these lattices. Furthermore, we apply our result to Lennard--Jones type interacting potentials that appear to be accurate in many physical and biological models. The goal of this investigation is to understand how the minimum of the Lennard--Jones lattice energy varies with respect to the density of the points. Considering the lattices of fixed area A, we find the maximal open set to which A must belong so that the triangular lattice is a minimizer (resp. a maximizer) among lattices of area A. Similarly, we find the maximal open set to which A must belong so that the square lattice is a minimizer (resp. a saddle point). Finally, we present a complete conjecture, based on numerical investigations and rigorous results among rhombic and rectangular lattices, for the minimality of the classical Lennard--Jones energy per point with respect to its area. In particular, we prove that the minimizer is a rectangular lattice if the area is sufficiently large.

Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

Abstract: We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P21/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P21/c phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.

Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

Abstract: We study the low-pressure (0 to 10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo (QMC) and density functional theory (DFT) methods. We consider the $Pbca$, $P4_32_12$, and $P2_1/c$ structures as the best candidates for phase I and phase II. We perform diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. We use density functional perturbation theory to compute phonon contribution in the free-energy calculations. Our DFT enthalpy-pressure phase diagram indicates that the $Pbca$ and $P2_1/c$ structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature $Pbca$ to $P2_1/c$ phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations show an estimate of 50.6$\pm$0.5 kJ/mol for crystalline benzene lattice energy.

Complex chemical bond theory, Raman spectra and microwave dielectric properties of low loss ceramics NdNbO4–xAl2O3

Abstract: In this work, low loss microwave dielectric materials of NdNbO4–x wt% Al2O3 ceramics were prepared via a solid-state reaction method. The complex chemical bond theory, phase composition, standard deviation (σ) of the bond angles, microstructures, microwave dielectric properties and vibrational phonon modes were investigated. Microscopic analysis showed that sintered specimens presented single monoclinic fergusonite phase. The Rietveld refinements and Raman spectra were used to evaluate the correlation between the complex chemical bond theory and the microwave dielectric properties. With an increase of Al2O3 content, the Raman shift of Ag (331 and 808 cm−1) toward to the bigger value direction and the FWHM of Ag (331 and 808 cm−1) decrease, which lead to a decrease in bond ionicity and increase in lattice energy. The microwave dielectric properties of NdNbO4–x wt% Al2O3 exhibit closely relationship with the complex chemical bond theory. The variation trend of dielectric constant was accordance with the bond ionicity. The Q × f value and τ f value were mainly dependence on the lattice energy and bond energy, respectively. Fine microwave dielectric properties for NdNbO4–3 wt% Al2O3 ceramic was obtained with er = 18.1, Q × f = 54,700 GHz (9.1 GHz), τ f = −0.51 ppm/°C sintered at 1150 °C for 4 h.

Characterization of microwave dielectric materials NiZrNb2O8 based on the chemical bond theory

Abstract: Wolframite structure NiZrNb2O8 ceramics were prepared by the solid state reaction method. Sintering characteristics and microwave dielectric properties were investigated under various sintering temperatures ranging from 1100 to 1300 °C. The micro-structure, crystal structure and phase composition were studied by the scanning electron microscopy techniques, X-ray diffraction and energy disperse spectroscopy, respectively. Refinement was used to analyze the crystal structure. Based on the cell parameters, the chemical bond theory was used to calculate the lattice energy, bond ionicity and the coefficient of thermal expansion for the characterization of correlations between properties and structures of NiZrNb2O8 ceramics. The microwave dielectric properties of NiZrNb2O8 were strongly dependent on the chemical bond ionicity, lattice energy and coefficient of thermal expansion. The e r values could be strongly dependent on the bond ionicity of the Nb–O bonds. The Q·f values were affected by the lattice energy of Nb–O bonds. As for the τ f values, it could be mainly affected by the coefficient of thermal expansion of Ni–O bonds. At the sintering temperature of 1250 °C, NiZrNb2O8 ceramics exhibited the excellent microwave properties of e r = 18.84, Q·f = 18, 142 GHz and τ f = −35.43 ppm/°C.