Atomic asphericity and anharmonic thermal motion

Though the anharmonic components of the thermal motion decrease rapidly with temperature, as described in chapter 2, they will be present to some extent even if the motion is reduced to zero-point vibrations. 

The vibrational displacements corresponding to the anharmonic terms in the potential are most pronounced in the directions away from the stronger bonding interactions, in which restoring forces are weaker. Thus, for the tetrahedral site symmetry of the diamond structure, the anharmonicity causes a larger mean-square displacement in directions opposite to the covalent bonds. At lower 

In low-spin transition metal complexes, the preferential occupancy of the d orbitals in the crystal field tends to create excess density in the voids between the bonds, which means that anharmonicity tends to reinforce the electron density asphericity. We will discuss, in the following sections, to what extent the two effects can be separated by combined use of aspherical atom and anharmonic thermal motion formalisms. 

Mallinson et al. (1988) have performed an analysis of a set of static theoretical structure factors based on a wave function of the octahedral, high-spin hexa-aquairon(II) ion by Newton and coworkers (Jafri et al. 1980, Logan et al. 1984). To simulate the crystal field, the occupancy of the orbitals was modified to represent a low-spin complex with preferential occupancy of the t2g orbitals, rather than the more even distribution found in the high-spin complex. The complex ion (Fig. 10.14) was centered at the corners of a cubic unit cell with a = 10.000 A and space group Pm3. Refinement of the 1375 static structure factors (sin 8/X 1.2 A 1) gave an agreement factor of R = 4.35% for the spherical-atom model with variable positional parameters (Table 10.12). Addition of three anharmonic thermal 

A final refinement of the static data with both sets of parameters gave a further small decrease in the R factor to 3.98%, and, reassuringly, temperature parameters smaller than three times their estimated standard deviations. At least for static data, the refinement properly attributes the asphericity to the multipole functions. 

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