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Octahedral symmetry, effect

In an octahedral crystal field, for example, these electron densities acquire different energies in exactly the same way as do those of the J-orbital densities. We find, therefore, that a free-ion D term splits into T2, and Eg terms in an octahedral environment. The symbols T2, and Eg have the same meanings as t2g and eg, discussed in Section 3.2, except that we use upper-case letters to indicate that, like their parent free-ion D term, they are generally many-electron wavefunctions. Of course we must remember that a term is properly described by both orbital- and spin-quantum numbers. So we more properly conclude that a free-ion term splits into -I- T 2gin octahedral symmetry. Notice that the crystal-field splitting has no effect upon the spin-degeneracy. This is because the crystal field is defined completely by its ordinary (x, y, z) spatial functionality the crystal field has no spin properties. [Pg.45]

Notice that if the molecule has axial symmetry, Dxx = Dyy so that E=0. If the molecule has octahedral symmetry, Dxx = Dyy = Dzz so that D = E=0. Thus the appearance of a zero-field splitting into two or three levels tells the spectroscopist something about the symmetry of the molecule. It is possible, of course, to do spectroscopy on these energy levels at zero magnetic field. Our concern here is the effect of zero-field splitting on the ESR spectrum where a magnetic field is applied. [Pg.119]

Although the effect on the d orbitals produced by a field of octahedral symmetry has been described, we must remember that not all complexes are octahedral or even have six ligands bonded to the metal ion. For example, many complexes have tetrahedral symmetry, so we need to determine the effect of a tetrahedral field on the d orbitals. Figure 17.5 shows a tetrahedral complex that is circumscribed in a cube. Also shown are lobes of the dz- orbital and two lobes (those lying along the x-axis) of the dx> y> orbital. [Pg.621]

A Jahn-Teller distortion should also occur for configuration d. However, in this case the occupied orbital is a t g orbital, for example d, this exerts a repulsion on the ligands on the axes x and y which is only slightly larger than the force exerted along the z axis. The distorting force is usually not sufficient to produce a perceptible effect. Ions like TiF or MoClg show no detectable deviation from octahedral symmetry. [Pg.75]

In some cases, the CFSE attained by a transition metal ion in a regular octahedral site may be enhanced if the coordination polyhedron is distorted. This effect is potentially very important in most silicate minerals since their crystal structures typically contain six-coordinated sites that are distorted from octahedral symmetry. Such distortions are partly responsible for the ranges of metal-oxygen distances alluded to earlier, eq. (6.6). Note, however, that the displacement of a cation from the centre of a regular octahedron, such as the comparatively undistorted orthopyroxene Ml coordination polyhedron (fig. 5.16), also causes inequalities of metal-oxygen distances. [Pg.263]

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. [Pg.66]

In octahedral symmetry, the copper(ll) ion has a electronic ground state due to the d electron configuration with the unpaired electron in an Cg a anti-bonding orbital. An exact octahedral geometry of six-coordinate copper(II) complexes is never realized due to a strong Jahn-Teller effect. The symmetry of the Jahn-Teller active vibration is eg, the non-totally symmetric part of the symmetric square [Eg Eg]. For a Cu(Il)Lg complex, the two components of the degenerate eg vibration are shown in Fig. 1 a [2]. [Pg.58]

Six-coordinate complexes are expected lo be distorted from pure octahedral symmetry by the Jahn-Teller effect and this distortion is generally observed (Chapter IU. A number of five-coordinate complexes are known, both square pyrduiidal and trigonal bipyramidal. Four-coordination is exemplified by square planar and tctrahcdtal species as well as intermediate configurations. [Pg.305]


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Octahedral symmetry

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