Water molecule symmetry coordinates

Metal hexacyanoruthenates possess a lower symmetry. Several compounds have highly disordered structures, especially when no alkali cations are present for charge compensation. Such a complex defect structure has been found for a completely potassium free Prussian blue precipitated very slowly from a solution in concentrated hydrochloric acid [25, 26]. Here, the structure still remains cubic face-centered however, one-third of the [M1 -1(CN)6] is vacant, randomly distributed and that space is filled with water molecules. The coordination sphere of the remaining ions is maintained... 

Metal hexacyanoruthenates possess a lower symmetry. Several compounds have highly disordered structures, especially when no alkali cations are present for charge compensation. Such a complex defect structure has been found for a completely potassium free Prussian blue precipitated very slowly from a solution in concentrated hydrochloric acid [25, 26]. Here, the structure still remains cubic face-centered however, one-third of the [M - (CN)(, is vacant, randomly distributed and that space is filled with water molecules. The coordination sphere of the remaining m1 -1 ions is maintained unchanged however, the mean coordination sphere of the M ions is decreased (mW(nC)4.5(H2O)i.5). No iron ions occupy interstitial positions, that is, only two types of iron environments exist. Since that special kind of Prussian blue has been the first and hitherto only Prussian blue that could be obtained as sufficiently large crystals to perform a single crystal structure analysis, practically all textbooks, and later publications present that defect structure as the real structure of Prussian blue, completely forgetting that this defect structure is an extreme that forms... 

The effect of the symmetry operations on the Cartesian displacement coordinates of the two hydrogen atoms in die water molecule. The sharp ( ) indicates the inversion of a coordinate axis, resulting in a change in handedness of the Cartesian coordinate system. 

The characters Xj for the examples in the previous section were calculated following the method described in Section 8.9, that is, on the basis of Cartesian displacement coordinates. Alternatively, it is often desirable to employ a set of internal coordinates as the basis. However, they must be well chosen so that they are sufficient to describe the vibrational degrees of freedom of the molecule and that they are linearly independent The latter condition is necessary to avoid the problem of redundancy. Even when properly chosen, the internal coordinates still do not usually transform following the symmetry of the molecule. Once again, the water molecule provides a very simple example of this problem. 

The internal coordinates for the water molecule are chosen as changes in the structural parameters defined in Fig. 3. The effect of each symmetry operation of the symmetry group ( 2 on these internal coordinates is specified in Table 2. Clearly, the internal coordinate Ace is totally symmetric, as the characters xy(Aa) correspond to those given for the irreducible representation (IR) Ai. On die other hand, the characters x/(Ar), as shown, can not be identified with a specific IR. By inspection of Table 2, however, it is apparent that the direct sum Ai B2 corresponds to the correct symmetry of these coordinates. In more complicated cases the magic formula can always be employed to achieve the correct reduction of the representation in question. 

Table 2 Symmetry of the internal coordinates for the water molecule.

FIGURE 5.5 Symmetry enhancement from coordinate to momentum space C2v to D2h for water molecule. 

The orientation of the primary alcohol group is gauche-trans. The hydrogen bonding consists of finite chains which intersect at four-coordinated water molecules on two-fold, crystallographic-symmetry axes. 

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

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