Showing papers on "Lattice energy published in 2004"

Enthalpies of Formation of Gas-Phase N3, N3-, N5+, and N5- from Ab Initio Molecular Orbital Theory, Stability Predictions for N5+N3- and N5+N5-, and Experimental Evidence for the Instability of N5+N3-

Abstract: Ab initio molecular orbital theory has been used to calculate accurate enthalpies of formation and adiabatic electron affinities or ionization potentials for N3, N3-, N5+, and N5- from total atomization energies. The calculated heats of formation of the gas-phase molecules/ions at 0 K are ΔHf(N3(2Π)) = 109.2, ΔHf(N3-(1∑+)) = 47.4, ΔHf(N5-(1A1‘)) = 62.3, and ΔHf(N5+(1A1)) = 353.3 kcal/mol with an estimated error bar of ±1 kcal/mol. For comparison purposes, the error in the calculated bond energy for N2 is 0.72 kcal/mol. Born−Haber cycle calculations, using estimated lattice energies and the adiabatic ionization potentials of the anions and electron affinities of the cations, enable reliable stability predictions for the hypothetical N5+N3- and N5+N5- salts. The calculations show that neither salt can be stabilized and that both should decompose spontaneously into N3 radicals and N2. This conclusion was experimentally confirmed for the N5+N3- salt by low-temperature metathetical reactions between N5SbF6 and...

Toward Crystal Structure Prediction for Conformationally Flexible Molecules: The Headaches Illustrated by Aspirin

Abstract: A crystal structure prediction study was carried out on aspirin, based on an analysis of its gas phase conformers and multiple searches for minima in the lattice energy with the molecule held rigid in low energy conformations. Various high levels of ab initio theory were used to estimate the gas phase conformations and energy differences, and accurate distributed multipole-based electrostatic models were used to estimate the electrostatic contribution to the lattice energies. The molecular conformation adopted in the crystal structure is close to a local minimum found in the gas phase ab initio energy using a B3LYP/6-31G(d,p) calculation. A MP2 optimization gives larger differences from the solid state molecular structure. The calculation using the B3LYP molecular conformer predicts the observed crystal structure as one of the most thermodynamically stable and generally the most plausible crystal structure. Alternative molecular conformers, including the gas phase global minimum energy structure and plana...

Hydrogen bonding in the crystal structures of the ionic liquid compounds butyldimethylimidazolium hydrogen sulfate, chloride, and chloroferrate(II,III).

Abstract: Four ionic liquid (IL) salts containing the 1-butyl-2,3-dimethylimidazolium (BDMIM) and 1-allyl-2,3-dimethylimidazolium (ADMIM) cations have been prepared; the characterization was based on IR spectroscopy and single-crystal structure determination. The compounds BDMIM[HSO4], BDMIMCl, ADMIMBr, and (BDMIM)4[FeIICl4][FeIIICl4]2 were chosen to incorporate anions significantly differing in hydrogen-bond-acceptor strength in order to elucidate the influence of directional bonding on crystal packing. The cations adopt different arrangements with respect to the counterions. The role of hydrogen bonding in these compounds is discussed with respect to its general significance for lattice energies of IL salts.

Quantum-chemical and force-field investigations of ice Ih: Computation of proton-ordered structures and prediction of their lattice energies

Abstract: The different possible proton-ordered structures of ice Ih for an orthorombic unit cell with 8 water molecules were derived. The number of unique structures was found to be 16. The crystallographic coordinates of these are reported. The energetics of the different polymorphs were investigated by quantum-mechanical density-functional theory calculations and for comparison by molecular-mechanics analytical potential models. The polymorphs were found to be close in energy, i.e., within approximately 0.25 kcal/mol H2O, on the basis of the quantum-chemical DFT methods. At 277 K, the different energy levels are about evenly populated, but at a lower temperature, a transition to an ordered form is expected. This form was found to agree with the ice phase XI. The difference in lattice energies among the polymorphs was rationalized in terms of structural characteristics. The most important parameters to determine the lattice energies were found to be the distributions of water dimer H-bonded pair conformations, in...

An Assessment of Lattice Energy Minimization for the Prediction of Molecular Organic Crystal Structures

Abstract: Lattice energy searches for theoretical low-energy crystal forms are presented for 50 small organic molecules, and we compare the experimentally observed crystal forms to these lists of hypothetical polymorphs. For each known crystal, the relative stability is calculated with respect to the global minimum energy structure, and we determine the number of unobserved structures lower in energy than the experimental form. The distributions of these relative energies and their rankings in the predicted lists are used to determine the efficacy of lattice energy minimization in crystal structure prediction. Although a simple form for the interaction energies has been used, the calculations produce almost a third of the known crystals as the global minimum in energy, and approximately a half of the known structures are within 1 kJ/mol of the global minimum. Molecules with no hydrogen-bonding capacity are most likely to be found close to the global minimum in lattice energy, while increasing the number of possible...

An Experimental and Theoretical Search for Polymorphs of Barbituric Acid: The Challenges of Even Limited Conformational Flexibility

Abstract: An experimental study of barbituric acid found a new P21/c polymorph with two conformations of barbituric acid in the asymmetric unit, one molecule adopting an envelope conformation and the other refining as planar. The new Form ii involves different hydrogen bond acceptors to Form i. An ab initio conformational analysis study found that barbituric acid can change its envelope conformation by over 20° from planar with a small energy change that can be compensated for by packing forces, so that the new Form ii is predicted to have a lower lattice energy than Form i. A computational search for minima in the lattice energy found many hypothetical structures of barbituric acid within the energy range of possible polymorphism, with a variety of hydrogen bonding acceptors and motifs. The search was found to be very sensitive to the assumed molecular structure of barbituric acid, so further plausible low energy variations in the molecular conformation would produce even more low energy crystal structures. Thus, ...

An Approach to Developing a Force Field for Molecular Simulation of Martensitic Phase Transitions between Phases with Subtle Differences in Energy and Structure

Abstract: D,L-Norleucine is one of only a few molecules whose crystals exhibit a martensitic or displacive-type phase transformation where the emerging phase shows a topotaxial relationship with the parent phase. The molecular mechanism for such phase transformations, particularly in molecular crystals, is not well understood. Crystalline phases that exhibit displacive phase transitions tend to be very similar in structure and energy. Consequently, the development of a force field for such phases is challenging as the phase behavior is determined by subtle differences in their lattice energies and entropies. We report an approach for developing a force field for such phases with an application to D,L-norleucine. The proposed procedure includes calculation of the phase diagram of the crystalline phases as a function of temperature to identify the best force field. D,L-Norleucine also presents an additional problem since in the solid state it exists as a zwitterion that is unstable in vacuo and therefore cannot be characterized using high-level ab initio calculations in the gas phase. However, a stable zwitterion could be obtained using Onsager's reaction-field continuum model for a solvent (SCRF) using both Hartree-Fock and density functional theory. A number of force fields and the various sets of partial charges obtained from the SCRF calculations were screened for their ability to reproduce the crystal structures of the two known phases, alpha and beta, Of D,L-norleucine. Selected parameter sets were then employed in free energy minimizations to identify the best set on the basis of a correct prediction of the alpha-beta phase transition. The Williams' nonbonded parameters combined with partial charges from SCRF-Polarized Continuum Model calculation were found to reproduce the structures of the phases accurately and also maintained their stability in extended molecular dynamics simulations in the Parrinello-Rahman constant stress ensemble. Moreover, we were also able to successfully simulate the phase transformation of the beta- to the alpha-phase. The identified force field should enable detailed studies of the phase transformations exhibited by crystals Of D,L-norleucine and hence enhance our understanding of martensitic-type transformations in molecular crystals.

Modeling steps and kinks on the surface of calcite.

Abstract: This work presents modeling results on the cleavage face of calcite as well as on steps and isolated kinks on this face. We used static lattice energy minimization and interatomic potentials fitted to bulk properties. The energy needed to cleave a bulk calcite crystal along the {1 0 1 4} plane was calculated to be 0.59 J m−2 in agreement with previous studies using the same potentials. The perfect surface reconstructs in the top few atomic layers, but its symmetry corresponds to the bulk termination. By contrast, the (1 0 1 4) surface with cleavage steps present reconstructs to form a (2×1) super cell. This may help explain experimental observations of (2×1) symmetry on calcite surfaces. The energy required to form a monatomic obtuse step is calculated to be 1.3×10−10 J m−1 and for the acute step, 2.4×10−10 J m−1, suggesting that obtuse steps dominate on cleaved surfaces. Along the two types of steps, a total of 16 kink geometries exist. We calculated kink defect energy with two different approaches: on...

Characterization of complicated new polymorphs of chlorothalonil by X-ray diffraction and computer crystal structure prediction

Abstract: A simultaneous experimental and computational search for polymorphs of chlorothalonil (2,4,5,6-tetrachloro-1,3-benzenedicarbonitrile) has been conducted, leading to the first characterization of forms 2 and 3. The crystal structure prediction study, using a specifically developed anisotropic atom−atom potential for chlorothalonil, gave as the global minimum in the lattice energy a structure that was readily refined against powder diffraction data to the known form 1 (P21/a). The structure of form 2 was solved and refined from powder diffraction data, giving a disordered structure in the R3m (166) space group (Z = 3). It could also be refined against a P1 ordered model, starting from a low-energy hypothetical sheet structure found in the computational search. This shows that the disorder could be associated with the stacking of ordered sheets. The disordered structure for form 2 was later confirmed by single-crystal X-ray diffraction. The structure of form 3, determined from single-crystal diffraction, contains three independent molecules in the asymmetric unit in P21 (4) (Z = 6). Powder diffraction showed that this single-herringbone structure was similar to two low-energy structures found in the search. Further analysis confirmed that form 3 has a similar lattice energy and contains elements from both these predicted structures, which can be considered as good approximations to the form 3 structure.

Ordered binary crystal phases of Lennard-Jones mixtures

Abstract: The lattice energies at zero temperature are calculated, using Lennard-Jones interactions, for a large number of crystal structures associated with ordered binary compounds. In units of the AA interaction length and strength (i.e., σAA=eAA=1.0) we examine the lowest energy structures, including coexisting phases, across the space of cross-species interactions 0.6⩽σAB⩽1.1 and 1.0⩽eAB⩽2.0. The remaining parameters σBB=0.88 and eBB=0.5 are chosen so that the parameter space studied includes the space of binary glass-forming alloys. In addition to some large unit cell structures such as Ni3P and PuBr3 appearing among the lowest lattice energies, a number of low-energy structures based on close-packed lattices are found that do not correspond to any experimentally observed crystals. The prevalence and stability of metastable crystal phases at the compositions AB, A2B, and A3B is examined.

Dynamics in crystals of rigid organic molecules: contrasting the phonon frequencies calculated by molecular dynamics with harmonic lattice dynamics for imidazole and 5-azauracil

Abstract: Molecular dynamics simulations have been performed on crystalline imidazole at 100 K and 5-azauracil at 310 K with a model intermolecular potential that includes a distributed multipole representation of the molecular charge distribution using the program DL_MULTI. The anisotropic atom–atom electrostatic model enabled the experimental crystal structures to be reproduced well in a constant pressure simulation and the simulations showed a physically reasonable thermal expansion relative to the minimum in the static lattice energy. The rigid-body molecular motions in a subsequent constant volume simulation were analysed to obtain the k = 0 frequencies corresponding to different symmetry representations, via the translational and rotational velocity autocorrelation functions. These frequencies were contrasted with the corresponding harmonic lattice modes calculated with the same molecular model and intermolecular potential. The agreement was good, with most, but not all, modes decreasing in frequency in the f...

Lattice energies of apatites and the estimation of ΔHf°(PO43-, g)

Abstract: Experimentally based lattice energies are calculated for the apatite family of double salts M(5)(PO(4))(3)X, where M is a divalent metal cation (Ca, Sr, Ba) and X is hydroxide or a halide. These values are also shown to be estimable, generally to within 4%, using the recently derived Glasser-Jenkins equation, U(POT) = AI(2I/V(m))(1/3), where A = 121.39 kJ mol(-)(1). The apatites exhibiting greater covalent character (e.g., M = Pb, Cd, etc.) are less well reproduced but are within 8% of the experimentally based value. The lattice energy for ionic apatites (having identical lattice ionic strengths, I) takes the particularly simple form U(POT)/kJ mol(-)(1) = 26680/(V(m)/nm(3))(1/3), reproducing cycle values of U(POT) well when V(m) is estimated by ion volume summation and employing a volume for the PO(4)(3)(-) ion (not previously quantified with an associated error) of 0.063 +/- 0.003 nm(3). A value for the enthalpy of formation of the gaseous phosphate ion, DeltaH(f)( ) degrees (PO(4)(3)(-), g), is absent from current thermochemical tabulations. Examination of solution and solid state thermochemical cycles for apatites, however, leads us to a remarkably consistent value of 321.8 +/- 1.2 kJ mol(-)(1). Experimental and estimated lattice energies were used along with other thermodynamic data to determine enthalpies, entropies, and free energies of dissolution for apatites of uncertain stabilities. These dissolution values are compared with the corresponding values for stable apatites and are used to rationalize the relative instability of certain derivatives.

Prediction of Solid Solution Formation in a Family of Diastereomeric Salts. A Molecular Modeling Study

Abstract: The possibility of solid solution behavior of diastereomeric salts, containing multiple resolving agents of the same family (Dutch Resolution), is predicted by molecular modeling. Super-cells containing different ratios of resolving agents in the diastereomeric salt are constructed and optimized, and their lattice energy is computed. The energy difference between these “simulated solid solutions” and the native structures is related in an understandable fashion to the probability of solid solution formation. This procedure is applied to a family of diastereomeric salts of ephedrine and cyclic phosphoric acids, for which the ternary diagrams have been determined experimentally at 25 °C in ethanol. Good agreement between experimental and computational results indicates that this relatively simple and fast method could predict the stable character of solid solution behavior in binary systems.

Structures and Properties of the Refractory Silicides Ti5Si3 and TiSi2 and Ti-Si-(Al) Eutectic Alloys

Abstract: The refractory titanium silicides Ti5Si3 and TiSi2 with complex hexagonal D88 and orthorhombic C54 lattice structures exhibit superior physical and mechanical properties, such as high lattice energies and melting temperatures; high hardness, elastic stiffness and flow stresses; low densities and excellent creep and oxidation resistance. The complex lattice structures and a large contribution of covalent bonding to the total binding energies of these compounds cause a lack in ductility due to sessile superdislocations. In order to improve the ductility and fracture toughness of silicide containing titanium-based alloys, binary and ternary Ti-Si-(Al) systems have been considered. Alpha titanium forms with the Ti5Si3 compound an eutectic system possessing large volume fractions of about 30 vol.% Ti5Si3 in the hexagonal α-Ti(Si) solid solution matrix.

Linear free energy relationships between dissolution rates and molecular modeling energies of rhombohedral carbonates.

Abstract: Bulk and surface energies are calculated for endmembers of the isostructural rhombohedral carbonate mineral family, including Ca, Cd, Co, Fe, Mg, Mn, Ni, and Zn compositions. The calculations for the bulk agree with the densities, bond distances, bond angles, and lattice enthalpies reported in the literature. The calculated energies also correlate with measured dissolution rates: the lattice energies show a log-linear relationship to the macroscopic dissolution rates at circumneutral pH. Moreover, the energies of ion pairs translated along surface steps are calculated and found to predict experimentally observed microscopic step retreat velocities. Finally, pit formation excess energies decrease with increasing pit size, which is consistent with the nonlinear dissolution kinetics hypothesized for the initial stages of pit formation.

X-ray diffraction and packing analysis on vintage crystals: Wilhelm Koerner's nitrobenzene derivatives from the School of Agricultural Sciences in Milano.

Abstract: The crystal structures of six nitrotoluene derivatives, synthesized by Wilhelm Koerner about a century ago and retrieved from a depository at the University of Milano, were determined. The correct assignment of molecular structures is verified. The geometry of the nitro groups and factors affecting the orientation of nitro groups with respect to the benzene ring are discussed, also using an auxiliary set of crystal structures retrieved from the Cambridge Structural Database. The crystal packings have been analyzed, and lattice energies have been calculated by atom–atom potential methods and by the newly proposed Pixel method. This method allows a more complete description of intermolecular potentials in terms of the interaction between molecular electron densities and separate Coulombic, polarization, dispersion and overlap repulsion energies. Lattice vibrations and external entropies were calculated by lattice-dynamical procedures. The results of the Pixel energy calculations allow a reliable, quantitative assessment of the relative importance of stacking interactions and hydrogen bonding in the rationalization of the recognition modes of nitrobenzene derivatives, which is impossible to attain using only qualitative atom– atom geometry concepts.

Structure and orientation of the moving vortex lattice in clean type-II superconductors

Abstract: The dynamics of the moving vortex lattice is considered in the framework of the time-dependent Ginzburg-Landau equation neglecting the effects of pinning. At high flux velocities the pinning dominated dynamics is expected to crossover into the interactions dominated dynamics for very clean materials recently studied experimentally. The stationary lattice structure and orientation depend on the flux flow velocity. For relatively velocities $Vl{V}_{c}=\sqrt{8\ensuremath{\pi}B∕{\ensuremath{\Phi}}_{0}}∕\ensuremath{\gamma}$, where $\ensuremath{\gamma}$ is the inverse diffusion constant in the time-dependent Ginzburg-Landau equation, and the vortex lattice has a different orientation than for $Vg{V}_{c}$. The two orientations can be desribed as motion ``in channels'' and motion of ``lines of vortices perpendicular to the direction of motion.'' Although we start from the lowest Landau level approximation, corrections to conductivity and the vortex lattice energy dissipation from higher Landau levels are systematically calculated and compared to a recent experiment.

Influence of the mechanical treatment on the structure and the thermal stability of alkaline-earth carbonates

Abstract: The change of specific surface during the grinding of alkaline-earth carbonates is depending on the lattice energy of these compounds. The maximum value reached by the specific surface area, before the particle aggregation begins, is higher the higher is the lattice energy of the salt. A mechanism has been proposed for explaining this behaviour that implies to assume that when the lattice energy increases, slipping of the lattice planes becomes more difficult and the fracture of the particles would be favoured with regards to the plastic deformation of the crystal. This model account for the changes observed for the activation energy and the enthalpy of the thermal decomposition of alkaline-earth carbonates as a function of grinding.

THE CHANGES OF BARRIER ENERGY IN FCCâBCC PHASE TRANSFORMATION BY SHEAR STRESSES

Abstract: The Lattice energy of a cubic nickel crystal has been calculated by using the embedded atom method The embedding energy has been determined by means of quantum mechanical approximations The lattice energy changes of the static structure including 864 atoms with Bain and shear stresses have been obtained The energies of the fcc and bcc phases caused by Bain stress have been compared The variation of the barrier energy required for the transition between these structures has been investigated as a function of shear stress intensity As a conclusion, we have determined that the barrier energy of fcc→bcc transition rises in shear stress fields Key Words: Phase Transition, Barrier Energy, Embedded Atom Method, Stress Fields

Relationships between crystal structures and thermodynamic properties of phenylbutazone solvates

Abstract: The relationships between the crystal structures and the thermodynamic properties of six phenylbutazone solvates were studied. From the crystal structures the free volume available to the solvent molecules, Vasm, the packing density of the solvent in the solvate channels, Kchan, and the lattice energy of each solvate, Elattice, were calculated and the intermolecular interactions in the solvates were identified. From the measured equilibrium vapor pressure of the solvent above each solvate and above each liquid solvent, the standard free energy, ΔGdes, enthalpy, ΔHdes, and entropy, ΔSdes, of desolvation of each solvate were calculated. Linear correlations between Kchan and ΔSdes, between Elattice and ΔHdes, and between Vasm and both ΔSdes and ΔHdes suggest that similar crystal structures afford smooth monotonic variations in intermolecular interaction energies.

Atomistic Study of Fracture of Crystalline Materials by Lattice Green's Function Method: Effects of Anharmonicity of Lattice Vibration

Abstract: Using the lattice Green's function approach which includes the temperature dependence of the materials parameters, we study the both cleavage and dislocation emission processes in the fracture of crystalline materials. Firstly, we calculate the Green's function for the defective lattice, with dislocation and crack, by solving the Dyson equation. After the lattice Green's functions have been determined, the relaxation problem for the reconstituted bonds in the cohesive zone is solved. The external force F with tensile and shear components is applied, as a pair of forces, to the atoms at the center of the crack. In this lattice Green's function calculation the temperature effects resulting from the anharmonicity of lattice vibrations are included by introducing the thermal lattice expansion, temperature dependent force constant matrix and temperature dependent non-linear cohesive forces at the crack tip region. We compare the cleavage and dislocation emission processes at the absolute zero temperature with ...

Determination of Basicities of Organic Solvents and Absolute Electrode Potentials (E 0-Values) of Monovalent Ions in Organic Solvents based on Absolute Values of Gibbs Energies of Solvation of Single Ions

Abstract: Single ion Gibbs energies of monovalent ions in fourteen solvents (water, methanol, NMF, PC, ethanol, n-propanol, iso-propanol, n-butanol, t-butanol, ethylene glycol, acetone, THF, 1,4-dioxan, acetonitrile) with or without (ion-dipole, ion-induced dipole, ion-quadrupole) interactions were determined. The basicity of the solvents was determined from the absolute values of ΔG 0 solvation(H + ) or ΔG 0 solution(H + ) based on single standard state utilising the modified Born equation suggested by Lahiri. The method involves no arbitrary assumptions. A single scale for the absolute electrode potentials (E 0 values) has been determined based on calculated Gibbs energies of solvation or solution of single ions. Appropriation of Gibbs energies of solvation of electrolytes into single ion values is not possible. Gibbs energies of formation of electrolytes in solvents must be taken into consideration. Stabilisation energies of electrolytes (MX) in solvents akin to lattice energies in solids were determined.

The Use of Quantum-Chemical Semiempirical Methods to Calculate the Lattice Energies of Organic Molecular Crystals. Part III: The Lattice Energy of Borazine (B3N3H6) and its Packing in the Solid State*

Abstract: A previously presented quantum-chemical scheme has been used to calculate the lattice energies of borazine (B 3 N 3 H 6 ), the low pressure polymorph of benzene (C 6 H 6 ), and of borazine in the low-pressure benzene lattice utilizing some frequently used semiempirical methods (CNDO/2, INDO, MINDO/3, MNDO, AM1, PM3, MSINDO). With all methods the lattice energy of the title compound was found to be less favourable than that of isoelectronic benzene, which offers an explanation of the significantly lower melting point of B 3 N 3 H 6 . Calculation of the lattice energy of borazine in the crystal lattice of the low-pressure modification of benzene revealed that the interactions between the molecules in this environment are not so stabilizing as those in its own lattice. This is predominantly due to a less favourable contribution of the dispersion energy. The semiempirical results have qualitatively been confirmed by quantum-chemical calculations on small molecular clusters at the MP2/6-31+G*//HF/6-31+G* level of ab initio theory. In these calculations we assumed pairwise additivity of the intermolecular interactions and calculated the energy of interaction between a reference molecule and all those neighbours to which the shortest intermolecular distance does not exceed 3 A.