Rotation octahedral molecules

If your octahedral molecule has a center of symmetry, it also has nine planes of symmetry (three horizontal and six diagonal ), as well as a number of improper rotation axes or orders four and six. Can you find all of them If so, you can conclude that your molecule is of symmetry (9%. 

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... 

The entire group thus consists of the identity +9+8+6+9+6+ 9 = 48 operations. This group is denoted Oh. It is, of course, a very important type of symmetry since octahedral molecules (e.g. SF6), octahedral complexes [Co(NH3) + and IrCli"], and octahedral interstices in solid arrays are very common. There is a group O, which consists of only the 24 proper rotations from Ok, but this, like T, is rarely if ever encountered in Nature. 

The SFg molecule, 5.5, belongs to the point group, which is one of the cubic point groups. The relationship between the octahedron and cube is shown in Fig. 5.26a the X, y and z axes for the octahedron are defined as being parallel to the edges of the cube. In an octahedral molecule such as SF5, this means that the x, y and z axes coincide with the S F bonds. Table 5.4 gives part of the character table, and the positions of the rotation axes are shown in Fig. 5.26b. The SFg molecule is centrosymmetric, the S... 

Tetrahedral or octahedral molecules such as CH4 and SF4 are called spherical tops and have three equal moments of inertia for rotation about three mutually perpendicular axes. The gas-phase contour is similar to the perpendicular band of the linear molecule, with two broad wings and a central peak for all the IR-active vibrations. 

OK, your molecule does not have a C5 axis. However, if it has a C4 axis, it also has three binary rotation axes collinear with the C4 and six other binary axes. Look carefully to be sure that your molecule indeed belongs to one of the octahedral groups. 

Clodius, W. B., and Quade, C. R. (1985), Internal Coordinate Formulation for the Vibration-Rotation Energies of Polyatomic Molecules. III. Tetrahedral and Octahedral Spherical Top Molecules, /. Chem. Phys. 82, 2365. 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

A typical problem of interest at Los Alamos is the solution of the infrared multiple photon excitation dynamics of sulfur hexafluoride. This very problem has been quite popular in the literature in the past few years. (7) The solution of this problem is modeled by a molecular Hamiltonian which explicitly treats the asymmetric stretch ladder of the molecule coupled implicitly to the other molecular degrees of freedom. (See Fig. 12.) We consider the the first seven vibrational states of the mode of SF (6v ) the octahedral symmetry of the SF molecule makes these vibrational levels degenerate, and coupling between vibrational and rotational motion splits these degeneracies slightly. Furthermore, there is a rotational manifold of states associated with each vibrational level. Even to describe the zeroth-order level states of this molecule is itself a fairly complicated problem. Now if we were to include collisions in our model of multiple photon excitation of SF, e wou d have to solve a matrix Bloch equation with a minimum of 84 x 84 elements. Clearly such a problem is beyond our current abilities, so in fact we neglect collisional effects in order to stay with a Schrodinger picture of the excitation dynamics. 

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