Ionic solid density calculation

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

Tsang and Falicov (49) have calculated the charge density distribution at corner sites in ionic and rare gas crystal surfaces. For ionic solids, low coordination number surface sites should have large charge density variations... 

Molecular volumes of the solid are calculated from observed densities at room temperature (as tabulated in Landolt s Tables), extrapolated to the melting point by using the thermal expansion. For the ionic ciystals, data on densities of liquids and solids are taken from Lorenz and Heiz, Z anory. allgem Chem., 145, 88 (1025). 

Another property of great interest is the ionicity of the bonding. To what extent do the atoms of the solid resemble neutral atoms, held together by covalent bonds, and to what extent are they like ions held together by electrostatic forces This is a difficult question. Even if we have an accurate X-ray picture of the electron density of a compound, it is very hard to say whether atoms or ions are being shown. The same is true for an electron density calculated by accurate quantum mechanical methods. 

Finally we should note a valuable approach developed by Pyper and coworkers for ionic solids in which HF methods are used first to obtain a set of crystal orbitals, the interactions between which are calculated as a function of distance including a full explicit evaluation of the exchange term (unlike the local density approximation used in the electron gas method). Estimates of the dispersive energy are then added to the resulting interaction energy. This approach is particularly successful for strongly ionic halides and oxides. 

Calculating the Empirical Foimula and Density of an Ionic Solid... 

A further simplication often used in density-functional calculations is the use of pseudopotentials. Most properties of molecules and solids are indeed determined by the valence electrons, i.e., those electrons in outer shells that take part in the bonding between atoms. The core electrons can be removed from the problem by representing the ionic core (i.e., nucleus plus inner shells of electrons) by a pseudopotential. State-of-the-art calculations employ nonlocal, norm-conserving pseudopotentials that are generated from atomic calculations and do not contain any fitting to experiment (Hamann et al., 1979). Such calculations can therefore be called ab initio, or first-principles. ... 

A vast number of directional Compton profiles have been measured for ionic and metallic solids, but none for free molecules. Nevertheless, several calculations of directional Compton profiles for molecules have been performed as another means of analyzing the momentum density. 

The (able below contains solubility and density data lor the salts Na SQ4 and MgS()4. Express their solubilities in terms of molar concentrations, molalities and mole fractions. Calculate the contractions in volume that occur when the solutions are made from the solid salts and the solvent. Comment on the results in terms of the ell ect of ionic charges. The concentrations have been cho-.cn to be comparable. 

A single-particle effect that adds features in the X-ray absorption spectrum of molecules not present in that of atoms is the shape resonance (74, 75). (In the case of solids this effect, caused by a modification of the density of states due to the presence of the other atoms in the molecule, is automatically accounted for in band calculations.) Localization of the excited electron inside the molecule in states resulting from an effective potential barrier located near the electronegative atoms in the molecule causes strong absorption bands in free molecules and near the inner-shell ionization limits of positive ions in ionic crystals (74). Consequently, molecular inner-shell spectra depart markedly from the corresponding atomic spectra. The type of structure of an inner-shell photoabsorption spectrum depends on the geometry of the molecule, the nature of its ligands, etc., and can sometimes be used to determine the structure of the molecule. 

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