Octahedral molecule

Normal modes of vibration of tetragonal-pyramidal ZXY4 molecules. 

The trend in directly reflects the trend in the stretching force constant (and bond strength) since the central atom is not moving in this mode. In however, both X and Y atoms are moving, and the mass effect of ihe X atom cannot be ignored completely. Across the periodic table, the stretching frequencies increase as the oxidation state of the central atom becomes higher. Thus we have  

As in many other cases, the higher the oxidation state, the higher the frequency. The bending frequencies do not exhibit clear-cut trends. The effect of changing the halogen is seen in a number of series, for example  

All these metals are in the high-spin states. For occupation of the 

Weinstock et al. noted that the combination bands (P + pj) and ( 2+ s) appear with similar frequencies, intensities, and shapes in the infrared spectra of MoFcfd ) and RhF (if ). As is shown in Fig. 11-16, however, ( 2+ 3) was very broad and weak in TcF (d ), ReFfefi/ ), RuFfe(rf ), and OsFt,(d ). This anomaly was attributed to a dynamic Jahn-Teller effect. The static Jahn-Teller effect does not seem to operate in these compounds since no splittings of the triply degenerate fundamentals were observed. Perhaps the most fascinating 

The XeFs anion has 12 normal vibrations, which are classified into A ](R)+A2(IR)+2 j(IR)+2 2(R)+ 2 (inactive) under D5/, symmetry. Thus, only three vibrations (A 2 and 2Il ) are IR-active and only three vibrations (A +2 2) are Raman-active. In agreement with this prediction, the observed Raman spectmm of (CH3)4N[XeF5] exhibits three bands at 502 (symmetric stretch, A j), 423 (asymmetric stretch, E 2), and 377 cm (in-plane bending, As discussed in Sec. 1.11, the trigonal-bipyramidal and tetragonal-pyramidal structures can be ruled out since many more IR- and Raman-active bands are expected for these structures. 

The second example of a pentagonal planar XYs-type molecule is the IFs ion, which is isoelectronic with the XeFs ion. It was obtained as the N(CH3)4 salt from the reaction of N(CH3)4lF4 and N(CH3)4F in CH3CN solution, and the IR and Raman spectra were assigned under symmetry [1176]. 

Parker etal. [1263] measured the IR, Raman, and INS (inelastic neutron scattering) spectra of the [FeHg] ion and its deuterated analog listed at the end of Table 2.8a. These hexahydrido complexes are unsual in that the vi(Ai ) and V2(E ) frequencies are very close, although they are well separated in other XYg molecules. This result indicates that the stretching-stretching interaction force constant (f r in Appendix VII.6 is very small in the case of Fe-H(D) bonds. The vg frequencies of these compounds listed in Table 2.8a were obtained by INS spectroscopy. 

Several trends are noted in the octahedral XYg molecules listed in Table 2.8a, as described in Secs. 2.8.1.1-2.8.1.12. 

Mass of Csntral Atom Within the same family of the periodic table, the stretching frequencies decrease as the mass of the central atom increases, for example 

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This is the point group to which all regular octahedral molecules, such as SFe (Figure 4.12b) and [Fe(CN)6], belong. 

All regular fefrahedral molecules, which belong to fhe poinf group (Section 4.2.8), may show such a rofational spectrum. However, those spherical rotors that are regular octahedral molecules and that belong to the Of, point group (Section 4.2.9) do not show any such... 

Planar-octahedral equilibria. Dissolution of planar Ni compounds in coordinating solvents such as water or pyridine frequently leads to the formation of octahedral complexes by the coordination of 2 solvent molecules. This can, on occasions, lead to solutions in which the Ni has an intermediate value of jie indicating the presence of comparable amounts of planar and octahedral molecules varying with temperature and concentration more commonly the conversion is complete and octahedral solvates can be crystallized out. Well-known examples of this behaviour are provided by the complexes [Ni(L-L)2X2] (L-L = substituted ethylenediamine, X = variety of anions) generally known by the name of their discoverer I. Lifschitz. Some of these Lifschitz salts are yellow, diamagnetic and planar, [Ni(L-L)2]X2, others are blue, paramagnetic, and octahedral, [Ni(L-L)2X2] or... 

All six terminal atoms are equivalent in a regular octahedral molecule. 

A transargononic structure for sulfur, with six bonds formed by sp3d2 hybrid orbitals, was suggested for sulfur in the octahedral molecule SF6 long ago, and also for one of the sulfur atoms, with ligancy 6, in binnite (Pauling and Neuman, 1934). Some transargononic structures of metal sulfides have been proposed recently by Franzen (1966). 

Now consider a molecular stretching vibration that alternately elongates and compresses axial (parallel to z, let s say) and equatorial bonds as outlined in Fig. 7-3. Imagine an extreme vibration of this kind that eventually distorts an octahedral molecule so as to gradually remove two trans ligands (again, let this direction be... 

C09-0103. How many different structural isomers are there for octahedral molecules with the general formula A Xz Draw three-dimensional structures of each. 

C09-0104. Identity which of the four octahedral molecules shown here are equivalent ... 

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%. 

We discuss molecules with a valence shell containing five electron pair domains in Section 4.6. The preferred arrangements of five valence shell domains, the trigonal bipyramid and the square pyramid, are not regular polyhedra and therefore exhibit special features not found in tetrahedral and octahedral molecules. Molecules with seven and more electron pair domains in the valence shell of a central atom are not common, although they are of considerable interest. They are restricted to the elements of period 4 and higher periods, with very small ligands such as fluorine, and are discussed in Chapter 9. 

FIGURE 5.13 The molecular orbital diagram for an octahedral molecule. 

The operators S , S(II), S(in),... are the symmetry-adapted operators (Iachello and Oss, 1991). The construction of the symmetry-adapted operators of any molecule will become clear in the following sections where the cases of benzene (D6h) and of octahedral molecules (Oh) will be discussed. 

As a second example of construction of symmetry adapted operators, we consider the case of octahedral molecules, XY6 (Figure 6.6). The symmetry-adapted operators can be constructed by inspection. There are two types of interactions ... 

The Hamiltonian operator that preserves the symmetry of octahedral molecules can now be constructed. For XY6 molecule it is... 

X-Y stretching vibrations of octahedral molecules are thus characterized by four quantities, Ay, Ayy, 7i Y yy- The results of some sample calculations are shown in Table 6.3. Isotopic substitutions can also be considered, using the method of Section 6.9. 

Iachello, F., and Oss, S. (1991a), Model of n Coupled Anharmonic Oscillators and Applications to Octahedral Molecules, Phys. Rev. Lett. 66, 2776. 

Formula HeTeOe or Te(OH)e MW 229.64 hydrogen-bonded octahedral molecules... 

Let us consider the construction of molecular orbitals from linear combinations of atomic orbitals (LCAO MOs) for an octahedral molecule... 

A. D. Buckingham and G. C. Tabisz. Collision-induced Raman scattering by tetrahedral and octahedral molecules. Molec. Phys., 36 583, 1978. 

Threefold axes are quite common. Both pyramidal and planar AB3 molecules possess threefold proper axes passing through the atom A and perpendicular to the plane of the three B atoms. A tetrahedral molecule, AB4, possesses four threefold axes, each passing through the atom A and one of the B atoms. An octahedral molecule, AB6, also possesses four threefold axes, each passing through the centers of two opposite triangular faces and the A atom. 

This problem of spurious or, as they are conventionally called, redundant coordinates always arises when there are sets of angles that form a closed group, as in the case just considered, in planar cyclic molecules and also in three dimensions (e.g., tetrahedral and octahedral molecules). Several of the examples discussed in Section 10.7 will illustrate the point further. Redundant coordinates can usually be recognized without much difficulty, though troublesome cases sometimes arise. 

The conformation of lowest energy appears to be that of C3v symmetry. Part of the experimental difficulties stems from the fact that the molecule is highly dynamic and probably passes through several conformations. In either of the two models shown in Fig. 6.13, the Xe—F bonds near Ihe lone pair appear to be somewhat lengthened and distorted away from the lone pair however, the distortion is less titan would have been expected on the basis of the VSEPR model. That the latier model correctly predicted a distortion at all at a time when others were predicting a highly symmetrical octahedral molecule (all other hexafluoride such as SF6 and UF are perfectly octahedral) is a signal success, however. 

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