Coordinates, atomic symmetry

In the case of trisulfane the protonation may occur either at a terminal or at the central sulfur atom. Both ions were found to be of Ci symmetry. On the basis of their Gibbs energies the ion [H2S-S-SH]+ is by 9 kJ mol more stable than the tautomer [HS-S(H)-SH]+ at 298 K. While the SS bonds in the latter ion are of almost identical length (205.4 and 205.7 pm), they are rather different in the former ion (214.9 and 200.9 pm) with the longer one originating from the three-coordinate atom [70]. These two ions have not been observed yet. 

Fig. 18. Top transition coordinates (with symmetry species) of conformational transition states of cyclohexane (top and side views). Hydrogen displacements are omitted. The displacement amplitudes given are towards the C2v-symmetric boat form, and towards >2-symmetric twist forms (from left), respectively. Inversion of these displacements leads to the chair and an equivalent T>2-form, respectively. Displacements of obscured atoms are given as open arrows, obscured displacements as an additional top. See Fig. 17 for perspective conformational drawings. Bottom pseudorotational normal coordinates (with symmetry species) of the Cs- and C2-symmetric transition states. The phases of the displacement amplitudes are chosen such that a mutual interconversion of both forms results. The two conformations are viewed down the CC-bonds around which the ring torsion angles - 7.3 and - 13.1° are calculated (Fig. 17). The displacement components perpendicular to the drawing plane are comparatively small. - See text for further details.

Fig. 3. Conventional scheme of consequent temperature-dependent symmetry breakings triggered by JT or pseudo JT effects. G = R(3)/n(N)Ci is the symmetry of an atomic gas, where R(3) is the group of rotations of the free atom, 77(A) is the group of permutation and Q is inversion the primed values have the same meaning for the gas of molecules. Crystal I and crystal II denote two crystal phases with decreasing symmetry, respectively. QM, gL, Gc> Gc> and QC" are the separate and independent coordinates of symmetry breaking, while the temperature scale is in common.

A crystal structure is described by a collection of parameters that give the arrangement of the atoms, their motions and the probability that each atom occupies a given location. These parameters are the atomic fractional coordinates, atomic displacement or thermal parameters, and occupancy factors. A scale factor then relates the calculated structure factors to the observed values. This is the suite of parameters usually encountered in a single crystal structure refinement. In the case of a Rietveld refinement an additional set of parameters describes the powder diffraction profile via lattice parameters, profile parameters and background coefficients. Occasionally other parameters are used these describe preferred orientation or texture, absorption and other effects. These parameters may be directly related to other parameters via space group symmetry or by relations that are presumed to hold by the experimenter. These relations can be described in the refinement as constraints and as they relate the shifts, Ap,-, in the parameters, they can be represented by... 

More generally, it is the detailed angular properties of the d functions which, combined with the symmetry of the surroundings, are responsible for the coefficients to the or e t parameters of AOM. Understood in this way. Table 8 consists solely of S5unmetry coefficients (cf. footnote to p. 92). The reason is that, once the coordinates of one of the coordinating atoms (the hgators) are fixed, those of the rest are determined by... 

The cobalt atoms in Fig. 14.1 are stereogenic and the site symmetries are C2v and D4h, for (A) and (B), respectively. The term stereogenic center is at present used to designate a coordinated atom that was formerly called an asymmetric atom [2],... 

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