Some aspects of the calculation of lattice energies. II

Calculations of the lattice energies, which incorporate the variation of compressibility with pressure, have been extended to a wider range of alkali halides. The present calculations deal with compounds for which the data only justify a linear relation between compressibility and pressure, and consequently equations have been used with one fewer adjustable constant that those used in an earlier paper.

In general, the calculated lattice energies are larger (absolutely) than those from equations which ignore the variation of compressibility; and these larger values are usually in better agreement with the experiment.     

The phase change in potassium chloride

Equations for the interaction of ions in an ionic crystal, developed earlier¹, which allow for the variation of compressibility with pressure, have been applied to calculation of properties connected with the phase transition of potassium chloride under pressure. The data used were only for the high pressure form of the compound. It was found that the calculated transition pressure was much closer to the observed value, if these equations were used; but simpler equations which use a constant compressibility were somewhat better in their calculated values for the lattice energy, molar volume, and change of volume with pressure for the low pressure form of potassium chloride (NaCl structure). It is concluded that, while calculations on these equations form a sensitive test of these equations, the fitting of the equation to the structure needs to be more elaborate.     

Lattice energies: calculations from pressure—volume data,and uncertainties in the results

A method of calculating lattice energies is developed, which reproduces directly the observed pressure—volume curve of some simple ionic solids. The results in general are close to the experimental values, and show deviations usually between 5 and 10 kJ mole^?1. The calculated values are not systematically too high or too low. Some estimates are made of the effect of errors in the P–V curve on the calculated lattice energies.     

Density functional theory studies on the dissociation energies of metallic salts: relationship between lattice and dissociation energies

The formation and physicochemical properties of polymer electrolytes strongly depend on the lattice energy of metal salts. An indirect but efficient way to estimate the lattice energy through the relationship between the heterolytic bond dissociation and lattice energies is proposed in this work. The heterolytic bond dissociation energies for alkali metal compounds were calculated theoretically using the Density Functional Theory (DFT) of B3LYP level with 6‐311+G(d,p) and 6‐311+G(2df,p) basis sets. For transition metal compounds, the same method was employed except for using the effective core potential (ECP) of LANL2DZ and SDD on transition metals for 6‐311+G(d,p) and 6‐311+G(2df,p) calculations, respectively. The dissociation energies calculated by 6‐311+G(2df,p) basis set combined with SDD basis set were better correlated with the experimental values with average error of ca. ±1.0% than those by 6‐311+G* combined with the LANL2DZ basis set. The relationship between dissociation and lattice energies was found to be fairly linear (r>0.98). Thus, this method can be used to estimate the lattice energy of an unknown ionic compound with reasonably high accuracy. We also found that the dissociation energies of transition metal salts were relatively larger than those of alkaline metal salts for comparable ionic radii. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 827–834, 2001     

Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.     

Calculations of van der Waals interaction energies for Al, Cr, Fe, and Ir acetylacetonate crystals

Experimental data have been analyzed and interpreted for four volatile acetylacetonates of trivalent metals Al, Cr, Fe, and Ir. The crystal lattice energies were calculated by the atom-atom potential method. The lattice energies obtained by using the Buckingham potential are in better agreement with the sublimation heats of these metal complexes than those calculated from the Lennard-Jones potential. The experimental dependences of vapor pressure for the complexes are in satisfactory agreement with the values obtained from the calculated lattice energies and entropies of crystal-gas transitions.     

有效主量子数拓扑指数与分子总键能和晶格能的关系

作者定义ＡｊＢｋ分子的有效主量子数拓扑指数（Ｐ）为：Ｐ＝∑（ｎＡ·ｎＢ）－０．５。它与化合物的总键能（ΔＥ）、晶格能（Ｕ）呈现高度相关性,其直线回归方程为：ΔＥ＝－２８．４５１８＋１１１７．８９８Ｐ,Ｒ＝０．９３５４Ｕ＝１９６．６７０３＋１６６５．６２６６Ｐ,Ｒ＝０．９８８２用它预测ΔＥ、Ｕ,估算值与实验值基本吻合     

高硅沸石骨架结构及其稳定性的模拟计算(I)*

The lattice energy of a series of high-silica zeolites was determined using the lattice energy minimization method. The results were compared to the lattice energy of dense polymorphs of SiO2. All high-silica zeolites frameworks are only 30～67kJ•mol-1 less stable than α-quartz This may imply that there is little energy barrier to the formation of high-silica zeolites frame-works and explain the structural diversity observed for high-silica zeolites. The relationships of calculated lattice energies and framework Structures was disscussed. The results revealed a good linear relationship between framework density of these molecular sieves and all-silica framework lattice energies.     

Surface free energy and wettability of silyl layers on silicon determined from contact angle hysteresis

Using the literature data of the advancing and receding contact angles for water, diiodomethane and hexadecane measured on various hydrophobic silyl layers (mostly monolayers) produced on silicon wafers the apparent surface free energies gamma(s)(tot) were calculated by applying new model of the contact angle hysteresis interpretation. It was found that, for the same silyl layer, the calculated gamma(s)(tot) values to some degree depended on the probe liquid used. Therefore, thus calculated the surface free energies should be considered as apparent ones. Moreover, also the values of the dispersion component gamma(s)(d) of these layers depend on the probe liquid used, but to a less degree. This must be due to the strength of the force field originating from the probe liquid and the spacing between the interacting molecules. The relationships between gamma(s)(tot) and gamma(s)(d) are discussed on the basis of the equations derived. It may be postulated that applying proposed model of the contact angle hysteresis and calculating the apparent total surface free energies and the dispersion contributions better insight into wetting properties of the silyled silicon surface can be achieved.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part III. Effect of lattice vibrations

In crystal structure predictions possible structures are usually ranked according to static energy. Here, this criterion has been replaced by the free energy at any temperature. The effects of harmonic lattice vibrations were found by standard lattice‐dynamical calculations, including a rough estimate of the effects of thermal expansion. The procedure was tested on glycol and glycerol, for which accurate static energies had been obtained previously (Part II of this series). It was found that entropy and zero‐point energy give the largest contribution to free energy differences between hypothetical crystal structures, adding up to about 3 kJ/mol for the structures with lowest energy. The temperature‐dependent contribution to the energy and the effects of thermal expansion showed less variation among the structures. The overall accuracy in relative energies was estimated to be a few kJ/mol. The experimental crystal structure for glycol corresponded to the global free energy minimum, whereas for glycerol it ranked second at 1 kJ/mol. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 816–826, 2001     

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

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.     

Polarization energies,transport gap and charge transfer states of organic molecular crystals

A self-consistent calculation of electronic polarization in organic molecular crystals and thin films is presented in terms of charge redistribution in nonoverlapping molecules in a lattice. The polarization energies P₊ and P₋ of a molecular cation and anion are found for anthracene and perelynetetracarboxylic dianhydride (PTCDA), together with binding energies of ion pairs and transport gaps of PTCDA films on metallic substrates. The 500 meV variation of P₊+P₋ with film thickness agrees with experiment, as do calculated dielectric tensors. Comparisons are made to submolecular calculations in crystals.     

Density functional LCAO calculations for solids: Comparison among Hartree–Fock,DFT local density approximation,and DFT generalized gradient approximation structural properties

In this article, the results of a recently implemented DFT a posteriori and Kohn-Sham (KS ) linear combination of atomic orbital computational scheme for solids are presented. The equilibrium lattice parameters, bulk moduli, and lattice energies are calculated for eight crystallized systems. Local density approximation (LDA ) and generalized gradient approximation (GCA ) functionals and potentials are used. The maps of the Hartree-Fock (HF ) and Ks electronic densities and band structures are depicted. The KS results confirm the trend of the a posteriori scheme. Very good agreement between calculated and experimental lattice energies has been found for GGA potentials. © 1995 John Wiley & Sons, Inc.     

Improving the Wang-Landau algorithm for polymers and proteins

The 1/t Wang-Landau algorithm is tested on simple models of polymers and proteins. It is found that this method resolves the problem of the saturation of the error present in the original algorithm for lattice polymers. However, for lattice proteins, which have a rough energy landscape with an unknown energy minimum, it is found that the density of states does not converge in all runs. A new variant of the Wang-Landau algorithm that appears to solve this problem is described and tested. In the new variant, the optimum modification factor is calculated in the same straightforward way throughout the simulation. There is only one free parameter for which a value of unity appears to give near optimal convergence for all run lengths for lattice homopolymers when pull moves are used. For lattice proteins, a much smaller value of the parameter is needed to ensure rapid convergence of the density of states for energies discovered late in the simulation, which unfortunately results in poor convergence early on in the run.     

Parametrization of semiempirical models against ab initio crystal data: evaluation of lattice energies of nitrate salts

A method to estimate the lattice energies E(latt) of nitrate salts is put forward. First, E(latt) is approximated by its electrostatic component E(elec). Then, E(elec) is correlated with Mulliken atomic charges calculated on the species that make up the crystal, using a simple equation involving two empirical parameters. The latter are fitted against point charge estimates of E(elec) computed on available X-ray structures of nitrate crystals. The correlation thus obtained yields lattice energies within 0.5 kJ/g from point charge values. A further assessment of the method against experimental data suggests that the main source of error arises from the point charge approximation.     

The effect of trimethylsilyl substituents in the monomer unit on the energy characteristics of surfaces of polynorbornenes obtained via metathesis polymerization

The surface properties of polynorbornenes obtained via metathesis polymerization are investigated via the wetting method. The incorporation of trimethylsilyl groups into the monomer unit causes decreases in the specific free surface energies of the investigated polymers. It is found that the dispersion terms of the specific free surface energies correlate with the free-volume and gas-permeability values of the polymers. As shown through the methods of differential scanning calorimetry and FTIR spectroscopy, during heating in air, the considered polynorbornenes undergo oxidative crosslinking, which increases their specific free surface energies. The interphase energies of crosslinked polynorbornenes are determined at their interfaces with liquids modeling polar and nonpolar phases, and the values of the work of adhesion of the crosslinked polynorbornenes to the model liquids are calculated. It is shown that the work of adhesion of the polymer to the polar phase decreases after introduction of trimethylsilyl groups, while the combination of polar and nonpolar phases give rise to an increase in the work of adhesion.     

Lattice energies of the alkali metal bifluorides: a correction

Revised auxiliary thermodynamic data allow an improvement in the lattice energies of the alkali metal and ammonium bifluorides which were calculated in a previous paper (Polyhedron 1985, 4, 489). The lattice energies of the bifluorides now exceed those calculated by classical ionic models, but the difference between the lattice energies of the fluorides and bifluorides decreases steadily with increasing cation size.     

Conformational analysis—LXXIX : An improved force field for the calculation of the structures and energies of carbonyl compounds

Our previously described force field method has been extended to allow the calculation of structures and energies of molecules containing aldehyde or ketone groups. The method has been applied to a large number of simple cyclic and acyclic compounds, and has been shown to give good structures and energies insofar as these can be checked against available experimental data. Strain energies of ketones have been calculated, and comparison of these values to strain energies in the hydrocarbon series is discussed.     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Ab initio molecular orbital calculations on the transition state for the addition of a methyl radical to vinyl monomers

Ab initio molecular orbital calculations have been performed on the transition state for the addition of methyl radical to twelve vinyl monomers using the SV 3–21G basis set. A linear relationship has been found between the calculated energies of activation and previously calculated energies of reaction. This supports the assumption of an Evans-Polanyi type rule in previous work which attempted to correlate reactivity with calculated energies of reaction. The activation energies obtained for methyl addition to butadiene and styrene were calculated to be negative. This is caused by errors introduced by a number of sources, viz. basis set superposition error, spin contamination and zero point energy. These errors are discussed. Previous authors have reported reasonable agreement between calculated activation energies at SV3–21G and experimental values for methyl addition to ethylene, this work suggests that this agreement was coincidental and results from the fortuitous cancellation of errors. The nature of the transition state for these radical addition reactions is discussed and the limitations of the SV3–21G basis set are highlighted. The theoretical prediction of activation energies for radical addition reactions would require much larger calculations, beyond the computational means of most research laboratories.