Density calculation ionic

The recent band calculations by Brooks et al. show indeed from charge density calculations that in stoichiometric UO2 a purely ionic picture is incorrect the oxygen ion is singly charged, the second electron not being retained by the Madelung potential. Simple considerations based on mechanical properties and spectroscopic evidence had already pointed at these conclusions. 

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. 

Here too, charge density calculations (lS-16) reflect the structural properties of the material. Charge density plots for the Individual states near Ep demonstrate the 2D nature of Cu2-O2-03 dpa bands and the ID nature of the Cul-01-04 dpa bands. The Ionic Y (or R = rare earth) atoms act as electron donors and do not otherwise participate. Also, the partial DOS at Ep for Y give extremely low values for the conduction electrons (the same Is true for Gd). 

Calculate the empirical formula and density of ionic and metallic solids from a picture of the unit celL Be able to estimate the length of a cubic unit cell from the radii of the atoms/ions present. [Sections 12.3 and 12.5]... 

The constant electron density contour diagrams of one homonuclear and five heteronuclear diatomic molecules presented in Fig. 8.6 have been obtained by reasonably accurate quantum chemical calculations. The electric dipole moment of F2 is zero by symmetry. The electric dipole moments of heteronuclear molecules like LiFl, LiF, HF, CIF or CO may be calculated from their electron densities using equation (5.2). These dipole moments, in turn, allow us to calculate the ionic characters gic(calc) = /Xei(calc)(calc). In Table 8.1 we compare the calculated ionic characters of 21 heteronuclear diatomic molecules with their experimental counterparts. The agreement between experiment and calculations is good the average deviation between experimental and calculated values is less than 0.02 a.u, the maximum deviation (in KLi) is 0.05 a.u. 

Table 8.1. Atomic charges in the 21 heteronuclear diatomic molecules formed hy comhination of H, the alkali metal Li, Na or K, and the halogen F, Cl or Br atoms experimental and calculated ionic characters, q Q atomic charges calculated by natural atomic orbital (NAO) analysis, and by topological analysis of the electron densities (AIM) [2]. All charges in atomic units. Note that the chemical formulae have been written in such a way that the atom carrying net positive charge is listed first.

However, quantum-mechanically calculated ionic volumes can be used to predict crystal densities of ionic crystals, where the ionic volume is defined to be that contained within a selected isosurface of electron density. Following Jenkins et al. [58], the volume of the formula unit MpKq of an ionic crystal is simply the sum of the volumes of the ions contained in the formula unit ... 

Although the coordination number of the cation in NaCl comes out as predicted by the radius-ratio guideline and the density calculated for NaCl is very close to the actual value, it is instructive to know how good the correlation is between the known crystal structure and the structure predicted by radius-ratio calculations in each of the AB cases we will discuss. Table 7.9 shows that 58% of the compounds that assume a rock-salt structure are consistent with the radius-ratio calculation. Again we see that, although radius ratios are a useful guideline, we must use caution when drawing conclusions from a purely ionic, hard-sphere model for crystal structures. 

Unfortunately, it is not possible to calculate a (i.e., ACommon practice is a semi-empirical calibration The shift S is measured (with the same source) for two compounds to be considerd rather ionic with the resonant atom in two different charge states. Pertinent examples would be NpFj and NpF. Contact densities calculated with a self-consistent procedure for the free ions are used to obtain Ap(0). The constant a is then determined according to eq. (22). One certainly can raise a number of objections towards this method but it is still the most universal one. It is important, especially for the lanthanides and actinides, that relativistic charge densities p(0) are used. Details concerning isomer... 

The most widely used method for ionic liquid density measurement is the vibrating-tube densitometer a method which relies on a calibration as a function of temperature and pressure using appropriate reference fluid.For many reported ionic liquids this is not routinely performed and corrections for the case of viscous fluids (i.e., >100 mPas) are often ignored. Despite these factors the densities of ionic liquids measured with vibrating-tube densitometers have a standard uncertainty to within 0.1%. Alternative methods include the calculation of density through speed of sound measurements or piezometric methods. Both approaches are relatively complex technically but present the advantage of providing extra thermodynamic property data. 

Calculated Densities and Standard Deviation of Densities of Ionic Liquids Composed of the 1-/t-3-Methylimidazolium Cations (R = Ethyl, Butyl, and Hexyl) and the Chloride, Trifluoroacetate, Dicyanamide, and Bis(trifluoromethylsulfonyl)imide Anions along with Available Experimental and Other Calculated Values... 

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