Deviations from experimental distance

Table V Deviations from Experimental Distance Constraints for Various Structural Solutions for Globoside...

The composite methods Wl, W2, W3, and W4 (where the W stands for the Weiz-mann Institute, where the methods were developed) use high-level coupled-cluster calculations to achieve extraordinary accuracy in thermochemical quantities [A. Karton et al., J. Chem. Phys., 125,144108 (2006) and references cited therein]. Wl has one empirically determined parameter, but W2, W3, and W4 have no empirical parameters. Wl and W2 use CCSD(T) and CCSD calculations with correlation-consistent basis sets, do exttapo-lations to the complete basis-set limit, and include relativistic corrections. W3 and W4 include CCSDT and CCSDTQ calculations, and W4 includes a CCSDTQ5 calculation with a small basis set. For various test sets of small molecules, the mean absolute deviation from experimental atomization energies or heats of formation is 0.6 kcal/mol for Wl, 0.5 kcal/mol for W2, 0.2 kcal/mol for W3, and 0.1 kcal/mol for W4. W4 also gives highly accurate bond distances, harmonic vibrational frequencies, vibrational anharmonic-ity constants, and dipole moments for small molecules [A. Karton and M. L. Marlin, J. Chem. Phys., 133, 144102 (2010) arxiv.org/abs/1008.4163]. These methods are limited to small molecules. 

Table 12-2. Experimental values and deviation from experiment of the R0 H bond distance, the symmetric (vs) and the antisymmetric (vas) stretching frequency [cm-1], the dipole moment [D], and the mean polarizability [A3] of the water molecule. The aug-cc-pVTZ basis set is used throughout. 

The shortest cation-anion distance in an ionic compound corresponds to the sum of the ionic radii. This distance can be determined experimentally. However, there is no straightforward way to obtain values for the radii themselves. Data taken from carefully performed X-ray diffraction experiments allow the calculation of the electron density in the crystal the point having the minimum electron density along the connection line between a cation and an adjacent anion can be taken as the contact point of the ions. As shown in the example of sodium fluoride in Fig. 6.1, the ions in the crystal show certain deviations from spherical shape, i.e. the electron shell is polarized. This indicates the presence of some degree of covalent bonding, which can be interpreted as a partial backflow of electron density from the anion to the cation. The electron density minimum therefore does not necessarily represent the ideal place for the limit between cation and anion. 

Equations of this type are most often used by experimentalists to fit their data to theory,52"54 as indications of an exponential 7(E) dependence are numerous. Vervey55 has used a similar approach to consider the volume-limited processes of ionic migration and obtained the same equation. In order to explain deviations of experimental behavior from that predicted by Eq. (40), Vermilyea56 has also taken into consideration the effect of electrostriction modifying the activation distance for migrating ions and obtained the following equation for the ionic current flow ... 

As anticipated in Sections 2.2.2 and 3.1, the unpaired electrons should not be considered as point-dipoles centered on the metal ion. They are at the least delocalized over the atomic orbitals of the metal ion itself. The effect of the deviation from the point-dipole approximation under these conditions is estimated to be negligible for nuclei already 3-4 A away [31]. Electron delocalization onto the ligands, however, may heavily affect the overall relaxation phenomena. In this case the experimental Rm may be higher than expected, and the ratios between the Rim values of different nuclei does not follow the sixth power of the ratios between metal to nucleus distances. In the case of hexaaqua metal complexes the point-dipole approximation provides shorter distances than observed in the solid state (Table 3.2) for both H and 170. This implies spin density delocalization on the oxygen atom. Ab initio calculations of R m have been performed for both H and 170 nuclei in a series of hexaaqua complexes (Table 3.2). The calculated metal nucleus distances in the assumption of a purely metal-centered dipolar relaxation mechanism are sizably smaller than the crystallographic values for 170, and the difference dramatically increases from 3d5 to 3d9 metal ions [32]. The differences for protons are quite smaller [32]. 

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