Anharmonic thermal

With data averaged in point group m, the first refinements were carried out to estimate the atomic coordinates and anisotropic thermal motion parameters IP s. We have started with the atomic coordinates and equivalent isotropic thermal parameters of Joswig et al. [14] determined by neutron diffraction at room temperature. The high order X-ray data (0.9 < s < 1.28A-1) were used in this case in order not to alter these parameters by the valence electron density contributing to low order structure factors. Hydrogen atoms of the water molecules were refined isotropically with all data and the distance O-H were kept fixed at 0.95 A until the end of the multipolar refinement. The inspection of the residual Fourier maps has revealed anharmonic thermal motion features around the Ca2+ cation. Therefore, the coefficients up to order 6 of the Gram-Charlier expansion [15] were refined for the calcium cation in the scolecite. 

That the bond density is also of significance for heavier atoms is evident from the occurrence of the spherical-atom forbidden (222) reflection of diamond and silicon, even at low temperatures where anharmonic thermal effects (see chapter 2) are negligible. The historical importance of the nonzero intensity of the diamond (222) reflection is illustrated by the following comment made by W. H. Bragg, in 1921 ... 

The (/-orbital population analysis was performed with both the harmonic and a more complete anharmonic thermal motion treatment, as discussed in section 10.7.3. The harmonic map is shown here. 

Anharmonic Thermal Motion and the Bonding Anisotropy of Transition Metal Complexes... 

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... 

More quantitatively, the effect of the thermal motion follows from the anharmonic thermal motion formalisms discussed in chapter 2. In the bcc structure, the relevant nonzero anharmonic term in the one-particle potential is the anisotropic, cubic site-symmetry allowed, part of uJuku um in expression (2.39). The modified potential for the cubic sites is given by (Willis 1969, Willis and Pryor 1975)... 

Craven BM, Swaminathan S (1984, publ. 1985) Neutron diffraction carbon-hydrogen bond lengths corrected for harmonic and anharmonic thermal vibration. Thins Am Cryst Assoc 20 133-135... 

Zucker, U. H., and Schulz, H. Statistical approaches for the treatment of anhar-monic motion in crystals. 1. A comparison of the most frequently used formalisms of anharmonic thermal vibrations. Acta Cryst. A38, 563-568 (1982). 

The quantum yield of the photodissociation was estimated by using the excitation dependence of the diffraction efficiency from the anharmonic thermal grating (section III.F.l) created by a saturated absorption [116,117], The rate constant of the nongeminate recombination of photo-dissociated iodine in solution was extracted from the temporal profile of the TG signal. 

Photoisomerization of DODCI, 3,3 -diethyloxatricarbocyanine iodide (DOTCI), and l,3,3,r,3, 3 -hexamethylindotricarbocyanine iodide (HITCI) were investigated by the laser anharmonic thermal grating technique, which detects the higher order gratings induced by nonlinear absorption processes (Section III.F.l) [127]. Upon photoexcitation of these molecules, they are converted to relatively long-lived isomers from the excited singlet (S,) state (Fig. 19). 

Nonlinear Absorption. The nonlinear absorption contains the saturation of strongly allowed one-photon transitions and multiphoton absorption. These nonlinear optical processes were detected as an anharmonic thermal grating [116, 117]. 

YoshiasaA, Koto K, Kanamaru F et al (1987) Anharmonic thermal vibrations in wurtzite-t5rpe Agl. Acta Cryst B43 434-440... 

Rietveld method, has been applied to describe chemical bonding, dynamic disorder, and anharmonic thermal vibration. Computer programs such as Rietan for the Rietveld analysis and PRIMA for the MEM analysis, which incorporate MEM and optimized for powder diffraction are available. 

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