Orbital schemes

Figure 2.38 The effect of varying the relative energies of the metal and ligand orbitals upon the final molecular orbital scheme for a dimeric rhodium carboxylate. (Reprinted from Coord. Chem. Rev., 50, 109, 1983, with kind permission from Elsevier Science S.A., P.O. Box 564,...

Figure 4.17 A qualitative molecular orbital scheme for a cr-bonded complex ion [AuL2]+. (Reprinted with permission from Inorg. Chem., 1982, 21, 2946. Copyright (1982) American...

FIGURE 3.35 The molecular orbital schemes typical of those calculated for a diatomic oxide molecule, EO (where E = C for CO and E = N for NO). Note that the D-orbitals are formed from mixtures of s- and p/-orbitals on both atoms accordingly, we label them simply Id,... 

The orbital interactions are controlled by the overlap integrals (Scheme 9) and the energy gap between the orbitals (Scheme 10) ... 

Delocalization of electrons is important in chemistry. Electron delocalization is a major factor of the stabilities and the reactivities of molecules. The delocalization occurs through the interaction of an occupied orbital with a vacant orbital (Scheme 13). The two electrons occupy the stabilized orbital. There are no electrons in the destabilized orbital. The stabilization results from the interactions between the occupied and unoccupied orbitals. 

Radicals and excited states have an orbital occupied by one electron. The interaction of the singly occupied orbital with a vacant orbital (Scheme 15) and with a singly occupied orbital (Scheme 16) leads to the stabilization. The stabilized orbitals occupy one and two electrons, respectively. There are no electrons in the destabilized orbital. For the interaction with a doubly occupied orbital there are two electrons in the stabilized orbital and one electron in the destabilized orbital (Scheme 17). Although the destabilization of the out-of-phase combined orbital is greater than the stabilization of the in-phase combination, there is one more electron in the stabilized orbital. Net stabilization is then expected. 

The theory of two-orbital interactions has been described in the preceding sections. The elements of the chemical orbital theory also include the theories of of three-orbital interactions and cyclic interactions of more than two orbitals (Scheme 1). 

Non-cyclic interactions of two and three orbitals are described in the preceding chapters of this volume. We describe here cyclic interactions of three or more orbitals (Scheme 1). In 1982, cyclic orbital interaction was found in non-cyclic conjugation [15]. Interactions of bonds in molecules contain cyclic interactions of bond (bonding and antibonding) orbitals even if the molecular geometry is non-cyclic. The cyclic... 

We generate hybrid orbitals on inner atoms whose bond angles are not readily reproduced using direct orbital overlap with standard atomic orbitals. Consequently, each of the electron group geometries described in Chapter 9 is associated with its own specific set of hybrid orbitals. Each type of hybrid orbital scheme shares the characteristics described in our discussion of methane ... 

The physical meaning of our final equation is best seen on eqn 39. The term containing w is essentially the self-energy correction introduced by Mulliken in his analysis of electronegativities to account for the average repulsion of electrons occupying the same orbital. In order to get an idea of the orders of magnitude, let us apply eqn 39 to a model computation of FeCO, made to compare the ClPSl results of Berthier et al. [11] with those of a simple orbital scheme. Consider one of the two x systems of FeCO, treated under the assumption of full localization (and therefore strict cr — x separation)... 

Fig. 8.26 (Left) Isomer-shift correlation diagram for a systematic series of [(Me3cyclam-acetate) FcOO]"" complexes, whereX is an azide (Na ) or a nitrido (=N) group. (Right) Orbital scheme of [(Me3cyclam-acetate)Fe =N] ...

Two possible molecular orbital schemes, (3) and (4), are shown in the accompanying diagram. Orbital scheme (3) involves a cyclic array of six... 

The considerable number of molecular orbital calculations which have recently been made for sandwich compounds are however considered in some detail in Section 6. This has been done in order to make clear the relationship between the ligand field and molecular orbital approaches, and also to indicate the need for the use of a more sophisticated molecular orbital scheme than that adopted in this Introduction, i.e. one in which the a-framework of the rings is specifically included in the basis set as well as the rr-type orbitals. 

Fig. 22. Molecular Orbital Scheme for Mixed Sandwich Compounds.

One can visualize the effects of covalence on magnetic properties using a simple molecular orbital scheme. In the usual notation the orbitals considered for the transition metal M and the ligand X are ... 

Fig. 13. Molecular orbital scheme for octahedral fluoride complexes...

As metal atoms interact with nearest neighbors at relatively short distance, orbital overlap results in electron density being shared. As mentioned earlier, that electron density is delocalized in orbitals that are essentially molecular orbitals encompassing all of the atoms. The number of atoms that contribute an orbital to the molecular orbital scheme approaches the number of atoms present. As two atoms... 

On a more qualitative level, the bonding in the more stable isomer lb can be explained on the basis of the general molecular orbital scheme for bent (C2v) metallocenes containing 14 valence electrons, as shown in Fig. 5. The localization of three electron pairs in bonding orbitals (lal, 2 i, 2b2) is primarily responsible for the Si-Cp interaction the absence of a silicon orbital of a2 symmetry imposes the presence of a ligand-based non-bonding orbital. Structural adjustment from D5d (ferrocene type) to C2v... 

A simple molecular orbital scheme showing why p-oxo dimer formation is more likely to happen for Fe(III), d5, than for Co(III), d6, is shown in Figure 4.15. For d6 Co(III), the last electron goes into a 71 antibonding orbital, making reactions 4.16 and 4.17 less likely. 

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