Substitution isotropic

Two six-membered ring molecules, (—)-/rans-(2S,6S)-cyclohexanone-d2 23, and (+)-(2/ )-cyclohexanone-stretching regions by Polavarapu et al. (80). These molecules are chiral only due to isotropic substitution. 

Some transition metal complexes exhibit HFS due to the ligand this is called superhyperfine splittings (SHFS). Often SHFS are not completely resolved, but contribute to the line width. In such cases isotropic substitution of the ligand nuclei, such as deuterium for hydrogen, can allow the presence of SHFS to be confirmed. 

The conflicting serial/parallel models for IVR/VP are not readily distinguished until time resolved experiments can be performed on the systems of interest. Both models can relate the relative intensities of the emission features to the various model parameters, but the serial process seems more in line with a simple, conventional [Fermi s Golden Rule for IVR (Avouris et al. 1977 Beswick and Jortner 1981 Jortner et al. 1988 Lin 1980 Mukamel 1985 Mukamel and Jortner 1977) and RRKM theory for VP (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989)], few parameter approach. Time resolved measurements do distinguish the models because in a serial model the rises and decays of various vibronic states should be linked, whereas in a parallel one they are, in general, unrelated. Moreover, the time dependent studies allow one to determine how the rates of the IVR and VP processes vary with excitation energy, density of states, mode properties, and isotropic substitution. 

Neutron Diffraction with Isotropic Substitution (NDIS) for In Situ Studies of... 

Figure 6. Typical calculated X-band EPR spectra of Cr(III) coitqjlexes (a) an octahedral, isotropically substituted Cr(III) complex (g = gyy= gzz= 1-987 D = E = 0.000 cm ) and (b) a strongly distorted octahedral Cr(III) complex (ga = 1.987 gy, = g =1.865 D = 0.490 cm" E = 0.163 cm" ) [76]. Published spectra were digitized with permission using the WinDIG software [119].

Substituting the moments into the equilibrium equation, we obtain the equation for an isotropic viscoelastic plate,... 

Several generalizations of the inelastic theory to large deformations are developed in Section 5.4. In one the stretching (velocity strain) tensor is substituted for the strain rate. In order to make the resulting constitutive equations objective, i.e., invariant to relative rotation between the material and the coordinate frame, the stress rate must be replaced by one of a class of indifferent (objective) stress rates, and the moduli and elastic limit functions must be isotropic. In the elastic case, the constitutive equations reduce to the equation of hypoelastidty. The corresponding inelastic equations are therefore termed hypoinelastic. 

However, the matrix and dispersed material are isotropic, so Vm < 1/2 and Vd<1/2 (the usual limit on Poisson s ratio for an isotropic material as seen in Section 2.4). Thus, upon substitution of these values for v and Vrf, the value of 3 U /3v is seen to be always positive (even when 3U /3v is not zero) becanjselhFtypIcanefnr(l is always positive when b < 1/2. Finally, because 3 U /3v is always positive, the value of U when Equation (3.61) is used, corresponding to a minimum, maximum, or inflection point on the curve for U as a function of v, is proved to be a minimum, and in fact, the absolute minimum. 

The values for Cl2 are bx = 6.60, b2 = 3.62, both x 10 24 cm3. When these values are substituted in Eq. 43 together with R = 1.99 X 10 8 cm, one obtains ax == 1.79 and a2 = 2.36, both X 10 24 cm3. Thus, although the polarizability of the chlorine molecule is almost twice as great parallel than perpendicular to the axis, the atom is nearly isotropic with slightly greater polarizability perpendicular to the axis. 

Here e is the depth of the well and d is the distance to zero crossing point of the isotropic potential whereas at and bt are anisotropy parameters. Substituting this potential into Eq. (5.50) we get for each anisotropic term [202]... 

The physical meaning of and f L.., is obvious they govern the relaxation of rotational energy and angular momentum, respectively. The former is also an operator of the spectral exchange between the components of the isotropic Raman Q-branch. So, equality (7.94a) holds, as the probability conservation law. In contrast, the second one, Eq. (7.94b), is wrong, because, after substitution into the definition of the angular momentum correlation time... 

The estimated distribution of A1 atoms is shown in Figure 2. Both the siting as well as therelative concentration of A1 in the individual T sites significantly vary. Our QM-Pot calculations of ZSM-5 structures (PI symmetry) containing one A1 atom per unit cell resulted in the 24 structures corresponding to A1 substitution into the 24 distinguishable T sites of the monoclinic ZSM-5 and yielded 24 values of shieldings which were converted into 24 values of isotropic chemical shift. 

Solid-state 9Be and 13C NMR studies have been used to characterize the structure and dynamics of the methyl-substituted beryllocenes. The isotropic 9Be chemical shift has been found to vary with the coordination of the Cp rings, from —19.8ppm in 11 (rf/rf) to — 24.4ppm in 10 (rf/rf). The Cp rings of 11 display comparatively little motion from —100 to 80°C, whereas the rate of reorientation of the CsMes rings decreases substantially at low temperatures in 10.50... 

The isotropic germanium hyperfine coupling appears to be smaller for the triaryl radicals as compared with the trialkyl radicals. Since the hyperfine coupling to the germanium atom should increase markedly with increased s-character of the orbital containing the unpaired electron, this observation would imply that the aryl-substituted radicals are somewhat more planar than their alkyl-substituted analogues. 

C NMR chemical shifts of a series of higher substituted a-vinyl substituted vinyl cations 24-27 were calculated to explore the sensitivity of the predicted isotropic shifts to electron correlation, basis set and geometry effects in differently substituted l,3-dienyl-2-cations.51... 

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