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Crystal Field Theory, , , , Crystal field theory (CFT) describes the breaking, of orbital degeneracy in transition metal, complexes due to the presence of ligands. CFT, qualitatively describes the strength of the metalligand bonds. Based on the strength of the metalligand bonds, the energy of the system is altered., This may lead to a change in magnetic properties, as well as color. This theory was developed by, Hans Bethe and John Hasbrouck van Vleck., , Basic Concept, , In Crystal Field Theory, it is assumed that the ions, are simple point charges (a simplification). When, applied to alkali metal ions containing a, symmetric sphere of charge, calculations of bond, energies are generally quite successful. The, approach taken uses classical potential energy, equations that take into account the attractive, and repulsive interactions between charged, particles (that is, Coulomb's Law interactions)., , a“ (1), , Ex —=—, r, , ‘Scanned with CamSeannet
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with, , e EF the bond energy between the charges and, , © qi and q» are the charges of the interacting, ions and, , e ris the distance separating them., , This approach leads to the correct prediction that, large cations of low charge, such as K~* and, Na‘, should form few coordination compounds., For transition metal cations that contain varying, numbers of d electrons in orbitals that are NOT, spherically symmetric, however, the situation is, quite different. The shapes and occupations of, these d-orbitals then become important in, building an accurate description of the bond, energy and properties of the transition metal, compound., , When examining a single transition metal ion, the, five d-orbitals have the same energy (Figure 1)., When ligands approach the metal ion, some, experience more opposition from the d-orbital, electrons than others based on the geometric, structure of the molecule. Since ligands approach, from different directions, not all d-orbitals interact, directly. These interactions, however, create a, splitting due to the electrostatic environment., , ‘Scanned with CamSeannet
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Negative charges, , distributed uniformly e, , over surface of a sphere e located at vertices, . of an octahedron, , PR, , on Negative charges, ve, , 6, , y?, , —, , a, , d,2, , , , Metal cation,, Me \ e, , , , , , Figure 1: Distributing a charge of -6 uniformly over, a spherical surface surrounding a metal ion causes, the energy of all five d orbitals to increase due to, electrostatic repulsions, but the five d orbitals, remain degenerate. Placing a charge of -1 at each, vertex of an octahedron causes the d orbitals to, split into two groups with different energies: the, d,2_y2 and d,2 orbitals increase in energy, while the,, d,y, dz, and dy, orbitals decrease in energy. The, average energy of the five d orbitals is the same as, for a spherical distribution of a -6 charge,, however. Attractive electrostatic interactions, between the negatively charged ligands and the, positively charged metal ion (far right) cause all, five d orbitals to decrease in energy but does not, affect the splittings of the orbitals. The two e,, orbitals point directly at the six negatively charged, ligands, which increases their energy compared, with a spherical distribution of negative charge. In, contrast, the three t,, orbitals point between the, negatively charged ligands, which decreases their, energy compared with a spherical distribution of, charge., , ‘Scanned with CamSeannet
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For example, consider a molecule with octahedral, geometry. Ligands approach the metal ion along, the x, y, and z axes. Therefore, the electrons in the, d.2 and d,2_,2 orbitals (which lie along these, axes) experience greater repulsion. It requires, more energy to have an electron in these orbitals, than it would to put an electron in one of the other, orbitals. This causes a splitting in the energy, levels of the d-orbitals. This is known as crystal, field splitting. For octahedral complexes, crystal, field splitting is denoted by A, (or A,.+). The, energies of the d.2 and d,2_,2 orbitals increase, due to greater interactions with the ligands. The, d,,,d,-, and d,. orbitals decrease with respect to, this normal energy level and become more stable., , ‘Scanned wth CamScanner
