Lattice energy of crystal

The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. 

LATTICE ENERGY OF CRYSTAL. The decrease in energy accompanying the process of bringing the tons, when separated front each other by an infinite distance, to the positions they occupy in the stable lattice It is made up of contributions from the electrostatic forces between the ions, from the repulsive forces associated with the ovedap of electron shells, front the van der Waals forces, and from the zero-point energy. 

Far-l R studies of inorganic solids have also provided useful information about lattice energies of crystals and transition energies of semiconducting materials. 

Anisotropic atom-atom potentials based on X-ray molecular charge densities were applied in the evaluation of intermolecular interactions and lattice energies of crystals of glycylgjycine, dl-histidine and DL-prohne, /i-nitroaniline and p-amino- -nitrobiphenyl. The intermolecular HBs in the crystals were identified by topological analysis of the experimental charge densities. 

Other possible types of defects for ionic crystal is the generation of a vacancy of cation and anion with the equilibrium concentration at the same time, i.e., Schottky defect. Existence of vacancy results in a high lattice energy of crystal. The equation for calculation concentration of vacancy is similar to Eq. (5.53) for the NaCl type of crystal. 

The sizes of polyatomic (nonglobular) ions in crystals are also expressed by their thermochemical radii according to Jenkins and coworkers [47], Circular reasoning may be involved in their determination, because these radii depend on calculated lattice energies of crystals that in turn depend on the interionic distances. The assigned uncertainties of these radii are 19 pm for univalent and divalent anions increasing to twice this amount for trivalent ones and they are listed in Table 2.8 too. A further problem with these values is the use of the Goldschmidt radii for the alkali metal counterions, r°, rather than the Shannon-Prewitt ones [43,44] appropriate for ions in solution. 

The fact that the lattice energies of crystal polymorphs of rigid molecules are very similar was established by computation (Gavezzotti, A. Generation of Possible Crystal Structures from the Molecular Structure for Low-Polarity Organic Compounds, J. Am. Chem. Soc.1991,113,4622-4629). 

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