Orbit, splitting

Wliat is left to understand about this reaction One key remaining issue is the possible role of otiier electronic surfaces. The discussion so far has assumed that the entire reaction takes place on a single Bom-Oppenlieimer potential energy surface. Flowever, three potential energy surfaces result from the mteraction between an F atom and FI,. The spin-orbit splitting between the - 12 and Pi/2 states of a free F atom is 404 cm When... 

For high rotational levels, or for a moleeule like OFI, for whieh the spin-orbit splitting is small, even for low J, the pattern of rotational/fme-stnieture levels approaehes the Flund s ease (b) limit. In this situation, it is not meaningful to speak of the projeetion quantum number Rather, we first eonsider the rotational angular momentum N exelusive of the eleetron spin. This is then eoupled with the spin to yield levels with total angular momentum J = N + dand A - d. As before, there are two nearly degenerate pairs of levels assoeiated... 

Figure 4. Spin-orbit splitting in AT — 1 and 2 vibronic levels of the state of NCN. Solid lines connect the results of calculations thar employ ab initio computed potential curves [28], For comparison the results obtained by employing experimentally derived potential curves (dashed lines) [30,31] are also given. Full points represent energy differences between P — K — and P — K spin levels, and crosses are differences between P — K + I and P — K levels.

A different d orbital splitting results and the absorption now results in a deep blue colour ... 

The d orbital splitting depends on the oxidation state of a given ion hence twb complex ions with the same shape, ligands and coordination number can differ in colour, for example... 

Normally, you would expects all 2p orbitals in a given first row atom to be identical, regardless of their occupancy. This is only true when you perform calculations using Extended Hiickel. The orbitals derived from SCE calculations depend sensitively on their occupation. Eor example, the 2px, 2py, and 2pz orbitals are not degenerate for a CNDO calculation of atomic oxygen. This is especially important when you look at d orbital splittings in transition metals. To see a clear delineation between t2u and eg levels you must use EHT, rather than other semiempirical methods. 

Hudson has noted that any explanation of the a effect must account both for the enhanced nucleophilicity and the lack of effect on the Ka of the nucleophile he attributes the a effect to a balance (which is different for nucleophile-carbon and nucleophile-proton interactions) between an orbital splitting eontribution and an electrostatie bond polarity factor. 

Thc Crystal l-ield Siabili2ation Energy (CFSl ) is the additional stability which accrues to an ion in a complex, as compared to the free ion, because its d-orbitals are split In an octahedral complex a l2 electron increases the stability by 2/5Ao and an Cf, electron decreases it by 3/5Ao- In a tetrahedral complex the orbital splitting is reversed and an e electron therefore increases the stability by 3/5At whereas a t2 electron decreases it by 2/5Ai. 

The general idea of using different orbitals for different spins" seems thus to render an important extension of the entire framework of the independent-particle model. There seem to be essential physical reasons for a comparatively large orbital splitting depending on correlation, since electrons with opposite spins try to avoid each other because of their mutual Coulomb repulsion, and, in systems with unbalanced spins, there may further exist an extra exchange polarization of the type emphasized by Slater. 

The effect of inner orbital splitting on the thermodynamic properties of transition metal compounds and coordination complexes. P. George and D. S. McClure, Prog. Inorg. Chem., 1959,1, 381-463 (36). 

Perhaps only slightly less common than octahedral symmetry is tetrahedral symmetry. We now examine the d orbital splitting in this environment. The story is much the same as above, except that it is now convenient to place the four point charges of the tetrahedron as shown in Fig. 3-6. Here ligands are put at alternate... 

Some prefer to write 4,ei = - % A>ct in order to emphasize the inversion of t and e orbital subsets. However, if A and Z, e, are defined as the orbital splittings, it is probably best to omit the sign. 

Figure 7-8. Orbital splitting diagrams for dP complexes with elongated and compressed octahedra.

Fig. 18.4 (a) A portion of the orbital splitting for NHj/ZrCli as isolated ions and as a hydrogen-bonded ion pair. The HOMO is indicated by Projected overlap populations (positive values representing... 

Spin-orbit splittings as well as binding energies of a particular electron level increase with increasing atomic number. The intensity ratio of the peaks from a spin-orbit doublet is determined by the multiplicity of the corresponding levels, equal to 2j + 1. Hence, the intensity ratio of the j = and j = components of the Rh 3d doublet is 6 4 or 3 2. Thus, photoelectron peaks from core levels come in pairs -doublets - except for s levels, which normally give a single peak. 

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