Oh point group

The Of, point group contains three C4 axes, four C3 axes, six C2 axes, three df, planes, six planes and a centre of inversion i. It also contains elements generated from these. 

This is the point group to which a sphere belongs and therefore the point group to which all atoms belong.  

Molecules belonging to the 4 point group are very highly symmetrical, having 15 C2 axes, 10 C3 axes, 6 C5 axes, 15 n planes, 10 axes, 6 5io axes and a centre of inversion i. In addition to these symmetry elements are other elements which can be generated from them. 

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What has been mentioned up to now allows us to infer that the relevant information needed for a representation is given by the characters of its matrices. In fact, the full information for a given group is given by its character table. This table contains the character files of a particular set of representations the irreducible representations. Table 7.2 shows the character table of the Oh point group. A character table, such as Table 7.2, contains the irreducible representations (10 for the Oh group) and their characters, the classes (also 10 for the Oh group), and the set of basis functions. 

An example will illustrate the above arguments. The ground state of a d1 octahedral complex ML6 is 2 Ag and the only excited state for this complex is 2Eg. In the Oh point group, Aj,z is Au- Also, this complex has the vibrational modes... 

All regular tetrahedral molecules, which belong to the Td point group (Section 4.2.8), may show such a rotational spectrum. However, those spherical rotors that are regular octahedral molecules and that belong to the Oh point group (Section 4.2.9) do not show any such... 

For a spherical rotor belonging to the octahedral Oh point group, Table A.43 in Appendix A, in conjunction with the vibrational selection rules of Equation (6.56), show that the only allowed transitions are... 

To test your understanding of the MO model for a typical octahedral coordination complex, construct an appropriate, qualitative MO diagram for Oh SHg (a model for known SF6). Hint first calculate the total number of MOs you should end up with from the number of available basis functions (AOs). Second, compare the valence AO functions of S with those of a transition metal (refer to Figure 1.9 and realize that, for a coordinate system with the H atoms on the x, y and z axes, the AO functions of the central atom and the symmetry-adapted linear combinations of ligand functions transform as s, aig p, tiu djey d dy, t2g dx2-y2 dz2, eg in the Oh point group). Now count the number of filled MOs and the number of S-H bonding interactions. 

To say that the x,y, and z axes are equivalent in the Oh point group (which denotes octahedral synunetry see Symmetry Point Groups) is to assert that there exist symmetry operations that interchange these axes. Thus, if we rotate the octahedron in Figme 1 and 2 by 120° about the axis that joins the centroids of the triangular faces defined by ligands 125 and 346, we are performing the symmetry operation C3 which transforms x - z, z - y and y - x. Thus, the function (x — y ) becomes (z — x ) and (2z — x — y )... 

Re(CO)e] belongs to the Oh point group and has a low-spin d electron configuration. This configuration is the same as the neutral hexacarbonyl complexes of the Group 6 elements (Cr, Mo, W), and they show similar photochemical reactivities. 

So, for instance, (100) generates ((100), (010), (001)) of type Tiu under the actions of the symmetry operators of the Oh point group. But, if it is required that the second Tiu is required to be orthogonal to the first one, with respect to integration over the unit sphere, then it is necessary to modify this second function with a Gram-Schmidt type transformation to obtain the distinct second set of Tiu symmetry, (5(300)-3(100), 5(030)-3(010), 5(003)-3(001)). 

Molecular geometries of the XH diatomic hydrides (X=Cu, Ag, Au) and XFg hexafluorides (X=S, Se, Mo, Ru, Rh, Te, W, Re, Os, Ir, Pt, U, Np, and Pu) molecules were assumed to be of CooV and Oh symmetry with their bond lengths taken from experiments [28-33]. As the spin function is explicidy included in eq.(l), the Cv and Oh point groups reduce to the CooV and Oh double groups, respectively, in the relativistic DV-Xa calculation. Symmetry orbitals... 

The L labels have been obtained from a correlation table such as Table 11. In the Oh point group Tx y z = tlu so, by applying Eq. (36) and consulting a table of direct products ... 

The Oh point group character table and the 0 (and 0 double group) multiplication table are given in Tables A1 and A2. 

To find the symmetry adapted combinations we first consider the application of the transformation operators Ot to the 33 atomic orbitals. We see at once that for all symmetry operations R of the Oh point group, the central atom M is left unchanged and consequently any Of will only transform metal orbitals into metal orbitals (or combinations of metal orbitals) and ligand orbitals into ligand orbitals (or combinations of ligand orbitals). Thus, we can immediately reduce rAO (the reducible representation using all 33 atomic orbitals) to the... 

Open the structure file for problem 3.29 this shows the structure of [Co(en)3] " where en stands for the didentate ligand H2NCH2CH2NH2 the H atoms are omitted from the structure. The complex [Co(en)3] " is generally described as being octahedral. Look at the character table for the Oh point group. Why does [Co(en)3] + not possess Oh symmetry What does this tell you about the use of the word octahedral when used a description of a complex such as [Co(en)3] + ... 

The characters of the resulting Fa representation are given in Table 6.23 (T ), together with those of the irreducible representations of the Oh point group. 

How can carbon, with only four valence orbitals, form bonds to more than four surrounding transition-metal atoms Ru6C(CO)n, with a central core of O synunetry, is a useful example. The 2s orbital of carbon has symmetry and the 2p orbitals have symmetry in the Oh point group. The octahedral Rue core has framework bonding orbitals of the same symmetry as in described earlier in this chapter (see Figure 15.13) ... 

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