Showing papers on "Lattice energy published in 2006"
TL;DR: A simple and quantitative explanation for the relatively low melting temperatures of ionic liquids (ILs) is developed, and from very little experimental and computational data it is possible to predict fundamental properties such as melting points and dielectric constants of Ionic liquids with good accuracy.
Abstract: We have developed a simple and quantitative explanation for the relatively low melting temperatures of ionic liquids (ILs). The basic concept was to assess the Gibbs free energy of fusion (ΔfusG) for the process IL(s) → IL(l), which relates to the melting point of the IL. This was done using a suitable Born−Fajans−Haber cycle that was closed by the lattice (i.e., IL(s) → IL(g)) Gibbs energy and the solvation (i.e., IL(g) → IL(l)) Gibbs energies of the constituent ions in the molten salt. As part of this project we synthesized and determined accurate melting points (by DSC) and dielectric constants (by dielectric spectroscopy) for 14 ionic liquids based on four common anions and nine common cations. Lattice free energies (ΔlattG) were estimated using a combination of Volume Based Thermodynamics (VBT) and quantum chemical calculations. Free energies of solvation (ΔsolvG) of each ion in the bulk molten salt were calculated using the COSMO solvation model and the experimental dielectric constants. Under stand...
535 citations
TL;DR: A method by augmenting the density functional theory with an analytical, nonelectronic approach for accounting for the dispersion energy was tested for selected organic crystals and illustrated the feasibility of this method for the prediction of the lattice energy of organic crystals.
Abstract: Calculation of the lattice energy of organic crystals is needed for predicting important structural and physicochemical properties such as polymorphism and growth morphology. Quantum mechanical methods that can be used for calculating typical organic crystals are unable to fully estimate van der Waals energies in a crystal. A method by augmenting the density functional theory with an analytical, nonelectronic approach for accounting for the dispersion energy was tested for selected organic crystals. The results illustrate the feasibility of this method for the prediction of the lattice energy of organic crystals. It is also shown that the dispersion energy is a dominant component of the lattice energy, particularly for those organic crystals that have no hydrogen bonds.
98 citations
TL;DR: The high-resolution X-ray diffraction analysis of the electron density distribution and plane-wave density functional theory has been applied to estimate the lattice energy and barrier to rotation of a benzene ring in the crystal of (eta(6)-C(6)H(6))(2)Cr.
Abstract: The high-resolution X-ray diffraction analysis of the electron density distribution and plane-wave density functional theory has been applied to estimate the lattice energy and barrier to rotation of a benzene ring in the crystal of (η6-C6H6)2Cr. Experimental data made it possible to perform analysis of the metal−(π-ligand) bond and estimate the nature and energy of weak H···H and H···C intermolecular interactions in the crystal. Summation of the intermolecular H···H and H···C interaction energies makes it possible to reproduce the experimental sublimation enthalpy value with high accuracy.
83 citations
TL;DR: It is confirmed by variable-temperature powder X-ray diffraction that form A is the thermodynamic polymorph and B is the kinetic form of the enantiotropic system A-D, and re-ranking the calculated frames on consideration of both Econf (Spartan 04) and Ulatt energies gives a perfect match of frame #1 with stable structure A.
Abstract: 4,4-Diphenyl-2,5-cyclohexadienone (1) crystallized as four conformational polymorphs and a record number of 19 crystallographically independent molecules have been characterized by low-temperature X-ray diffraction: form A (P2(1), Z'=1), form B (P1, Z'=4), form C (P1, Z'=12), and form D (Pbca, Z'=2). We have now confirmed by variable-temperature powder X-ray diffraction that form A is the thermodynamic polymorph and B is the kinetic form of the enantiotropic system A-D. Differences in the packing of the molecules in these polymorphs result from different acidic C-H donors approaching the C=O acceptor in C-H...O chains and in synthons I-III, depending on the molecular conformation. The strength of the C-HO interaction in a particular structure correlates with the number of symmetry-independent conformations (Z') in that polymorph, that is, a short C-HO interaction leads to a high Z' value. Molecular conformation (Econf) and lattice energy (Ulatt) contributions compensate each other in crystal structures A, B, and D resulting in very similar total energies: Etotal of the stable form A=1.22 kcal mol(-1), the metastable form B=1.49 kcal mol(-1), and form D=1.98 kcal mol(-1). Disappeared polymorph C is postulated as a high-Z', high-energy precursor of kinetic form B. Thermodynamic form A matches with the third lowest energy frame based on the value of Ulatt determined in the crystal structure prediction (Cerius2, COMPASS) by full-body minimization. Re-ranking the calculated frames on consideration of both Econf (Spartan 04) and Ulatt energies gives a perfect match of frame #1 with stable structure A. Diphenylquinone 1 is an experimental benchmark used to validate accurate crystal structure energies of the kinetic and thermodynamic polymorphs separated by <0.3 kcal mol(-1) (approximately 1.3 kJ mol(-1)).
83 citations
TL;DR: The arene-perfluoroarene recognition motif emerges as a dominant interaction in the non-hydrogen-bonding compounds studied here, to the point that asymmetric dimers formed over the stacking motif carry over to asymmetric units made of two molecules in the crystal both for pure compounds and for molecular complexes.
Abstract: The arene–perfluoroarene stacking interaction was studied by experimental and theoretical methods. A series of compounds with different possibilities for formation of this recognition motif in the solid state were synthesized, and their crystal structures determined by single-crystal X-ray diffraction. The crystal packing of these compounds, as well as the packing of related compounds retrieved from crystallographic databases, were analyzed with quantitative crystal potentials: total lattice energies and the cohesive energies of closest molecular pairs in the crystals were calculated. The arene–perfluoroarene recognition motif emerges as a dominant interaction in the non-hydrogen-bonding compounds studied here, to the point that asymmetric dimers formed over the stacking motif carry over to asymmetric units made of two molecules in the crystal both for pure compounds and for molecular complexes; however, inter-ring distances and angles range from 3.70 to 4.85 A and from 5 to 21°, respectively. Pixel energy partitioning reveals that whenever aromatic rings stack, the largest cohesive energy contribution comes from dispersion, which roughly amounts to 20 kJ mol−1 per phenyl ring, while the coulombic term is minor but significant enough to make a difference between the arene–arene or perfluoroarene–perfluoroarene interactions on the one hand, and arene–perfluoroarene interactions on the other, whereby the latter are favored by about 10 kJ mol−1 per phenyl ring. No evidence of special interaction which can be attributed to H⋅⋅⋅F confrontation was recognizable.
72 citations
TL;DR: Using a femtosecond laser pump-probe approach, the temporal evolution of the optical properties of the excitation of a solid by an ultrafast, intense laser are followed and show interesting correlation to nonthermal melting and lattice disordering processes.
Abstract: An open question about the dynamical behavior of materials is how phase transition occurs in highly nonequilibrium systems. One important class of study is the excitation of a solid by an ultrafast, intense laser. The preferential heating of electrons by the laser field gives rise to initial states dominated by hot electrons in a cold lattice. Using a femtosecond laser pump-probe approach, we have followed the temporal evolution of the optical properties of such a system. The results show interesting correlation to nonthermal melting and lattice disordering processes. They also reveal a liquid-plasma transition when the lattice energy density reaches a critical value.
70 citations
TL;DR: Lattice energies calculated by the empirically augmented quantum mechanical methods are in very good agreement with experimental values, suggesting the approach is acceptable and indicates that the long-range van der Waals or dispersion energy is a significant part of the lattice energy, which cannot be accurately estimated by the DFT methods alone.
Abstract: Lattice energies of drug crystals are closely associated with many important physicochemical properties including polymorphism of the crystals Current quantum mechanical methods that can be applied to calculate the lattice energy of most drug crystals are not capable of fully considering the van der Waals interaction energy, a dominant component in the lattice energy Herein, we report the results of using empirically augmented quantum mechanical methods for predicting the lattice energies of selected drug crystals Long-range van der Waals energies were evaluated by atom–atom pairwise C
6
R
−6
functions that were damped at short interatomic distance where interatomic interactions could be better evaluated by density functional theory (DFT) The atomic C
6
coefficients were taken from literature, and three damping functions were tested For the quantum mechanical calculations, different basis sets were tested with aspirin as the model system Basis set superposition error (BSSE) was considered In addition to aspirin, acetaminophen Form I and Form II, and s(+)- and (±)-ibuprofen were calculated and the results were compared to experimental values Experimentally determined single crystal structures were optimized prior to both empirical and DFT energy calculations Lattice energies calculated by the empirically augmented quantum mechanical methods are in very good agreement with experimental values, suggesting the approach is acceptable The results also indicate that the long-range van der Waals or dispersion energy is a significant part of the lattice energy, which cannot be accurately estimated by the DFT methods alone Due to the empirical nature for estimating the dispersion energy, choosing the right empirical parameters is crucial The methods and parameters tested seem to be able to produce reliable values of lattice energies of the drug crystals
49 citations
TL;DR: In this paper, a detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin in terms of experimental and theoretical densities was conducted.
Abstract: Detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin in terms of experimental and theoretical densities shows significant differences in the intermolecular features when analyzed based on the topological properties via the quantum theory of atoms in molecules. The two forms, triclinic and monoclinic (Form A and Form B), pack in the crystal lattice via weak C−H···O and C−H···π interactions. Form A results in a head-to-head molecular stack, while Form B generates a head-to-tail stack. Form A crystallizes in P1 (Z‘ = 2) and Form B crystallizes in P21/n (Z‘ = 1). The electron density maps of the polymorphs demonstrate the differences in the nature of the charge density distribution in general. The charges derived from experimental and theoretical analysis show significant differences with respect to the polymorphic forms. The molecular dipole moments differ significantly for the two forms. The lattice energies evaluated at the HF and DFT (B3LYP) methods with...
46 citations
TL;DR: In this article, a set of 125 different structures with compositions between pyrope and grossular, and with different states of order of the exchangeable Mg and Ca cations have been calculated with a density functional electronic structure method.
Abstract: Static lattice energy calculations (SLEC), based on empirical pair potentials have been performed for a set of 125 different structures with compositions between pyrope and grossular, and with different states of order of the exchangeable Mg and Ca cations. Total energies of a subset of these configurations have been calculated with a density functional electronic structure method (ab initio). The excess energies derived from ab initio and SLEC results agree well with each other. Excess free energies of the 125 structures have been calculated at 300 and 1000 K and at 0 and 3 GPa and cluster expanded in a basis set of 8 pair-interaction parameters. These ordering parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the ranges of 300-1500 K and 0-3 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. The calculations predict the development of a significant short-range and long-range ordering at the intermediate 50/50 composition. The long-range ordered phase with I4 1 22 symmetry becomes stable below 600 K. Two miscibility gaps driven by the stability of the intermediate phase develop at both sides of the 50/50 composition. Activity-composition relations in the range of 600-1500 K and 0-3 GPa are described with high-order Redlich-Kister polynomials.
37 citations
TL;DR: In this paper, the static lattice energy (cold curve), phonon spectrum, and electronic density of states of compressed Cu from electronic structure theory were calculated and the inferred room temperature isotherm supported the proposed modification of the ruby standard of Dewaele et al.
35 citations
TL;DR: Alpha and beta, k and c, are obtained specifically for 2:2 salts by studying the ionic oxides, sulfates, and carbonates, finding that U(POT) approximately 2I(alpha/Vm(1/3) + beta), where alpha and beta are fitted constants and I is the readily calculated ionic strength factor of the lattice.
Abstract: The lattice energy of an ionic crystal, UPOT, can be expressed as a linear function of the inverse cube root of its formula unit volume (i.e., Vm-1/3); thus, UPOT ≈ 2I(α/Vm1/3 + β), where α and β are fitted constants and I is the readily calculated ionic strength factor of the lattice. The standard entropy, S, is a linear function of Vm itself: S ≈ kVm + c, with fitted constants k and c. The constants α and β have previously been evaluated for salts with charge ratios of 1:1, 1:2, and 2:1 and for the general case q:p, while values of k and c applicable to ionic solids generally have earlier been reported. In this paper, we obtain α and β, k and c, specifically for 2:2 salts (by studying the ionic oxides, sulfates, and carbonates), finding that UPOT{MX 2:2}/(kJ mol-1) ≈ 8(119/Vm1/3 + 60) and S°{MX 2:2}/(J K-1 mol-1) ≈ 1382Vm + 16.
TL;DR: In this paper, a semi-empirical method for evaluation of linear expansion coefficient from the lattice energy is presented, and developed to the complex crystals, which is in good agreement with the experimental values.
Abstract: By using the study of the lattice energy and the structural parameters of binary inorganic crystals, a new parameter reflecting the thermal expansion property has been found, the relation between the linear expansion coefficient and new parameter has been established. A semiempirical method for evaluation of linear expansion coefficient from the lattice energy is presented, and developed to the complex crystals. The estimated values of the linear expansion coefficients of both simple and complex crystals are in good agreement with the experimental values.
TL;DR: In this paper, the free energies of mixing have been calculated using the method of thermodynamic integration for a large set of different structures with compositions between pyrope and majorite and with different states of order of octahedral cations.
Abstract: Static lattice energy calculations, based on empirical pair potentials have been performed for a large set of different structures with compositions between pyrope and majorite, and with different states of order of octahedral cations. The energies have been cluster expanded using pair and quaternary terms. The derived ordering constants have been used to constrain Monte–Carlo simulations of temperature-dependent properties in the ranges of 1073–3673 K and 0–20 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. At zero pressure the cubic/tetragonal transition is predicted for pure majorite at 3300 K. The transition temperature decreases with the increase of the pyrope mole fraction. A miscibility gap associated with the transition starts to develop at about 2000 K and x maj = 0.8, and widens with the decrease in temperature and the increase in pressure. Activity–composition relations in the range of 0–20 GPa and 1073–2673 K are described with the help of a...
TL;DR: Temperature dependencies of saturated vapor pressure and heat capacities for the 2, 3, and 4-hydroxybenzoic acids were measured and thermodynamic functions of sublimation calculated and crystal lattice packing energies based on geometry optimization of the molecules in the crystal using diffraction data and the program Dmol(3) was carried out.
TL;DR: In this paper, a transferable potential for binary, highly ionic oxides is derived from a previous work, which is then employed to study the relaxation of the Al-terminated (0, 0, 0) α - Al 2 O 3 surface as well as the dynamics of this surface at non-zero temperatures using the molecular dynamics method.
TL;DR: A method is needed for calculating physically reasonable partial charges, delta, and well-defined and consistent asymptotic reference energies corresponding to the separated structural components for generalizing ion-based lattice potential energies beyond strictly ionic solids.
Abstract: Classical procedures to calculate ion-based lattice potential energies (UPOT) assume formal integral charges on the structural units; consequently, poor results are anticipated when significant cov...
TL;DR: In this paper, a set of self-consistent empirical potentials has been specially developed for this task, which illustrate the importance of size mismatch in determining magnitudes of the enthalpies of mixing and ordering in the quaternary carbonate (Ca,Mg,Fe,Mn) solid solution.
TL;DR: In this paper, the crystal structures of two polymorphs of scyllo-inositol were reported, and a lattice energy search was performed in parallel with the crystallization experiments.
Abstract: We report on the crystal structures of two polymorphs of scyllo-inositol. Crystallization of this inositol initially failed to yield a single crystal suitable for structure solution, so a computational prediction of the low-energy forms was performed in parallel with the crystallization experiments. When a single crystal was finally grown, its structure failed to explain the powder X-ray diffraction pattern of the bulk material, which seemed to show a mixture of polymorphs. With the aid of the lowest-energy predicted crystal structure from a lattice energy search and the DASH program for structure solution from powder data, we propose the structure of the second polymorph. The combined use of single-crystal structure solution, structure solution from powder diffraction data, and a lattice energy search for possible structures, which was necessary for the elucidation of the second polymorph of scyllo-inositol, demonstrates the synergy between experimental and computational studies of molecular organic mate...
TL;DR: Structural and thermodynamic properties of crystalline monoclinic calcium apatites, Ca10(PO4)6(X)2 (X=OH, Cl), were investigated for the first time using a molecular dynamics technique under a wide range of temperature and pressure conditions.
Abstract: Structural and thermodynamic properties of crystalline monoclinic calcium apatites, Ca10(PO4)6(X)2 (X = OH, Cl), were investigated for the first time using a molecular dynamics (MD) technique under a wide range of temperature and pressure conditions. The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, yielding maximum deviations of ca. 2%. The standard molar lattice enthalpy of the apatites was also calculated and compared with previously published experimental and MD results for the hexagonal polymorphs. High-temperature simulation runs were used to estimate the isobaric thermal expansivity coefficient and study the behavior of the crystal structure under heating. The heat capacity at constant pressure, Cp, in the range 298−1298 K, was estimated from the plot of the molar enthalpy of the crystal as a function of temperature, Hm = (Hm,298 − 298Cp,m) + Cp,mT, yielding Cp,m = 635 ± 7 J·mol-1·K-1 and Cp,m = 608 ± 14 J·mol-1·K-1 for hydroxy- and ...
TL;DR: In this article, an expression for the energy which an electron loses per unit of time to initiate acoustic oscillations in the lattice in accordance to the Cherenkov mechanism is derived.
TL;DR: The physical stabilities of 5-Nor-Me O and R were determined using X-ray powder diffraction (XRPD), thermal analysis, hot-stage microscopy, solubility determination, and calculation of lattice energy as mentioned in this paper.
Abstract: 5-Nor-Me was prepared by a two-step synthesis. A disappearing polymorph, the yellow form (Y), was observed during synthesis, but pure Y could not be obtained with further purification by crystallization. The other two forms, red (R) and orange (O), were prepared by crystallization from tetrohydrofuran (THF) and absolute ethanol, respectively. Single-crystal structure data show that the 5-Nor-Me molecules in R and O have significantly different conformations; the thiophene ring and phenyl ring in 5-Nor-Me R are more planar than those in 5-Nor-Me O. The physical stabilities of 5-Nor-Me O and R were determined using X-ray powder diffraction (XRPD), thermal analysis, hot-stage microscopy, solubility determination, and calculation of lattice energy. DSC shows no difference for the R and O forms. The equilibrium melting point of R is shown to be 0.6 °C higher than O, and the lattice energy of R is lower than O. Slurry conversion studies indicate that R is more stable than O in the investigated temperature range...
TL;DR: The crystal structures of seven fundamental N-aminoazolium and N,N-diaminoazilium chlorides were determined by single-crystal X-ray diffraction as mentioned in this paper.
Abstract: The crystal structures of seven fundamental N-aminoazolium and N,N‘-diaminoazolium chlorides were determined by single-crystal X-ray diffraction. Their hydrogen-bonding networks and lattice architectures are discussed. Lattice energies were also calculated. Powder diffraction patterns of the bulk materials were consistent with those calculated from single-crystal diffraction data.
TL;DR: The average oscillators wavelength, the average oscillator strength, oscillator energy, dispersion energy, lattice energy, and material dispersion of the glass materials to be calculated are calculated.
Abstract: A series of new lithium aluminum silicate (LAS) glass systems doped with chromium
ion is prepared. The reflectance and transmittance of the glass slabs are recorded. By
means of an iteration procedure, the glass refractive index n and the extinction
coefficient k and their dispersions are obtained. Across a wide spectral range of
0.2-1.6 μm,
the dispersion curves are used to determine the atomic and quantum constants of
the prepared glasses. These findings provide the average oscillator wavelength, the
average oscillator strength, oscillator energy, dispersion energy, lattice energy, and
material dispersion of the glass materials to be calculated. For optical waveguide
applications, the wavelength for zero material dispersion is obtained. Dilatometric
measurements are performed and the thermal expansion coefficient is calculated to
throw some light on the thermo-optical properties of the present glasses correlating
them with their structure and the presence of nonbridging oxygen ions.
Book•
01 Jan 2006
TL;DR: In this paper, the authors present an approach to identify Ionic compounds based on the AB and ABC Closest-Packed Arrangements of the unit cell of the Ionic compound.
Abstract: Chapter 1. Bonding and Composition. Types of Bonding. Ionic Compounds. Types of Ions. Names of Ions. Percent Composition and Empirical Formula. The Mole. Molar Mass (Formula Weight). Calculation of Empirical Formula from Percent Composition. Use of Oxide Data. Formulas for Solid Solutions. Covalent Character in Ionic Compounds. Interactions Between Ions. Some Laws of Electrostatics. Potential Energy of Charged Particles. Lattice Energy and Its Effect on Properties. Chapter 2. Structure of Ionic Compounds: Close-packing. Closest Packing of Ions. The Holes Between the Layers. Stacking Sequences. Closest Packing for Ionic Compounds. Relationship of Formula to Occupation of Voids. Chapter 3. The Symmetry of Crystals. Symmetry Elements. Hermann-Mauguin Notation (Point Groups). Crystal Systems. Chapter 4. Structure of Some Simple Closest-packed Compounds. Symmetry of the AB and ABC Closest-Packed Arrangements. The Unit Cell. The NaCl Structure. The Sphalerite Structure. Axial Relationships. Wurtzite, a Polymorph of Sphalerite. The Fluorite Structure. The Rutile Structure, Polyhedral Coordination Models. Chapter 5. Factors that Affect the Symmetry of the Unit Cell. Effect of Cation. The Chalcopyrite Structure and Solid Solution. Effect of the Anion. Some Oxy Anions. The Pyrite Structure. The Calcite Structure. Aragonite, A Polymorph of Calcite. Several Sulfates, Anhydrite and Barite. Several Silicates, Zircon and Beryl. Effect of Temperature and Pressure. Chapter 6. Physical Properties: Morphology. Morphology. Miller indices. Forms. Habit. Deviations in Crystal Growths. Parallel Growth. Twinning. Epitaxis and Pseudomorphism. Chapter 7. Physical Properties: Color. Light and the Electromagnetic Spectrum. The Nature of Electrons. Electron Configurations. The Crystal Field Model. Colored Cations. Ion Impurities. Crystal Defects. Chapter 8. Chemical Properties. Solubility. Energetics of Dissolution. Solubility Rules. Double Salts. Reaction with Acids. Types of Chemical Reactions. Water as Both Acid and Base. Strong and Weak Acids. Conjugate Bases. Use of Chemical Reactions for Identification. Appendices. 1. The periodic chart. 2. The elements: Symbols, melting points, boiling points, densities, and electronegativities . 3. Metallic, covalent, and ionic radii. 4. Quartz. 5. Crystal system identification practice. 6. Crystal classes and point groups. 7. Additional reading and resources.
TL;DR: In this article, it was shown that solid solutions, by means of insertion (e.g., due to solvent) or by way of substitution, can substantially modify the energy landscape between polymorphs, leading to the prediction of the existence of solid solutions.
Abstract: Polymorphism is a widespread phenomenon among molecular components, and usually the lattice energies of the different varieties are rather close. It is shown that solid solutions, by means of insertion (e.g., due to solvent) or by means of substitution (e.g., due to derivatives of the components), can substantially modify the energy landscape between polymorphs. Fluctuations in the transition temperatures lead to the prediction of the existence of solid solutions.
TL;DR: Conclusively, it has been verified that the lattice gas model is a useful tool to analyze thermodynamic properties of hydrogen storage materials.
Abstract: Recently, a lattice gas model was presented and successfully applied to simulate the absorption/desorption isotherms of various hydride-forming materials. The simulation results are expressed by parameters corresponding to several energy contributions, e.g., interaction energies. However, the use of a model system is indispensable in order to show the strength of the simulations. The palladium-hydrogen system is one of the most thoroughly described metal hydrides found in the literature and is therefore ideal for this purpose. The effects of decreasing the thickness of Pd thin films on the isotherms have been monitored experimentally and subsequently simulated. An excellent fit of the lattice gas model to the experimental data is found, and the corresponding parameters are used to describe several thermodynamic properties. It is analyzed that the contribution of H-H interaction energies to the total energy and the influence of the host lattice energy are significantly and systematically changing as a function of Pd thickness. Conclusively, it has been verified that the lattice gas model is a useful tool to analyze thermodynamic properties of hydrogen storage materials.
TL;DR: In this article, two elucidations of molecular structure have been used: molecular graph (vertexes are atoms, i.e., Li, Na, K, etc.).
TL;DR: In this paper, the phase separation in wurtzite InxGa1−xN is investigated theoretically by ab initio calculations, and the calculated mixing free energies are positive with a maximum at composition x = 0.4375 and the spinodal decomposition will occur while the lattice is in equilibrium and uniformity.
TL;DR: In this article, a new polarisable interatomic potential model for Na2SO4 was derived and used to calculate the uptake and segregation of Ca2+, Mg2+ and K+ impurities in the two phases and their effect on the equilibrium morphologies of the crystals.
TL;DR: In this article, the cohesive energy of three phases of solid cubic rubidium chloride, the zinc blende structured 4:4 phase, the 6:6 sodium chloride polymorph and the 8:8 phase with the cesium chloride structure, are computed using a non-empirical fully ionic model.
Abstract: The cohesive energetics of three phases of solid cubic rubidium chloride, the zinc blende structured 4:4 phase, the 6:6 sodium chloride polymorph and the 8:8 phase with the cesium chloride structure, are computed using a non-empirical fully ionic model. The rearrangement energies needed to convert free anions to their optimal states in-crystal, two-body inter-ionic potentials, plus the further contributions arising from electron correlation, are reported. The 'optimal' anion?anion potentials, computed by using at each geometry the optimal wavefunction, are compared with the 'frozen' potential using the same wavefunction at all geometries. The lattice energy of the 4:4 structure is predicted to be some 40?kJ?mol?1 smaller than that of either the 6:6 or the 8:8 phases. Introduction of the Axilrod?Teller triple dipole dispersion interactions and the vibrational zero point energy predicts the 8:8 phase to lie 3.2?kJ?mol?1 lower in energy than the 6:6 structure. This is both consistent with radius ratio arguments and supported by two separate experiments that strongly suggest that the 8:8 phase is favoured over the 6:6 structure at low temperatures even though the latter is more stable at ambient temperatures. A shell model description is presented for the ion-induced dipole interactions that arise both in small clusters and in crystals encapsulated in nanotubes. The elastic constants and entropy at 300?K predicted for the 6:6 phase from this model by using the GULP program agree well with experiment. A smaller entropy is predicted for the 8:8 structure.