Site symmetry model

When free molecules are incorporated in a lattice, their axes are first oriented, i.e., v h the angle between the u and the a axis is 6 = 63.6 °. This is one aspect of the oriented gas model . However, as Fig. 2.7-9a shows, the molecules are not exactly planar the hydrogen atoms are directed toward the neighboring S atoms. The symmetry plane (j uv) of the free molecule is thus lost, the new point group of the molecule is determined by the symmetry of the lattice site, Q. According to the site symmetry model, the a and b species are therefore combined to afford a species a, while the U2 and hj species afford a , see Table 2.7-3 and Fig. 2.7-8. 

It is also apparent that there remains much to be done in developing our understanding of the model interactions that best characterize the spectra of higher-valent Pu compounds and indeed of the actinides in general. The synthesis of new compounds with a variety of different site symmetries could be of particular value in developing more detailed crystal-field... 

Fig. 2.4. The symmetry model of allostery. Shown here is the succesive binding of a hgand L to a protomer of a tetrameric protein with four ligand-binding sites according to the symmetry model. T tense form, R relaxed form.

Using the symmetry model, the fraction of the binding sites occupied at any given substrate concentration can be described with an expression that includes the substrate dissociation constants for the two conformations (KR and Kr) and the equilibrium constant between the T and R conformations in the absence of substrate, L = [T]/[R], Thus, the symmetry model attempts to explain the difference between Kx and K2 in equation (3) by introducing a third independent parameter. Considering that equation (3) can fit the experimental data for a dimeric enzyme with only two pa-... 

Phosphofructokinase was one of the first enzymes to which Monod and his colleagues applied the symmetry model of allosteric transitions. It contains four identical subunits, each of which has both an active site and an allosteric site. The cooperativity of the kinetics suggests that the enzyme can adopt two different conformations (T and R) that have similar affinities for ATP but differ in their affinity for fructose-6-phosphate. The binding for fructose-6-phosphate is calculated to be about 2,000 times tighter in the R conformation than in T. When fructose-6-phosphate binds to any one of the subunits, it appears to cause all four subunits to flip from the T conformation to the R conformation, just as the symmetry model specifies. The allosteric effectors ADP, GDP, and phosphoenolpyruvate do not alter the maximum rate of the reaction but change the dependence of the rate on the fructose-6-phosphate concentration in a manner suggesting that they change the equilibrium constant (L) between the T and R conformations. 

Very similar results have been observed for YV04 (with a VO]- group). In Ba3(V04)2 the site. symmetry is C3 . Therefore only one or three inequivalent excited species are expected. The latter possibility turned out to be the case. This confirms the model sketched [52],... 

The crystal-field parameters introduced in sect. 4.1 still contain all the structural information about the local environment. Therefore, a direct comparison of crystal-field parameters derived from different hosts, even with the same site symmetry, is not reasonable. In addition, the crystal-field parameters cannot be directly related to the distance and angle variations induced by the high-pressure application. Widely used models which extract the structural information from the crystal-field parameters are the angular-overlap (Jprgensen et al., 1963) and superposition model (Bradbury and Newman, 1967). In the case of f elements, the superposition model has been employed widely for the analysis of crystal-field parameters. 

Optimized structure of the F3Si-0-0 radical in ground state (Cs symmetry), modeling the site in silica, is shown in the Figure 7.16d. The unpaired electron occupies the 2px atomic orbital of the terminal oxygen atom (the X-axis is perpendicular to the plane of symmetry). The first electronically excited state (2A ) of the radical is related to the electronic transition of the lone pair of the terminal O atom to the 2px atomic orbital of the same atom. The energy of this vertical transition was found to be equal to AE — 0.5 eV. 

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