Isolobal molecular fragments

An important contribution to the understanding of parallels between organic and inorganic chemistry has been the concept of isolobal molecular fragments, described most elaborately by Roald Hoffmann in his 1982 Nobel lecture. Hoffmann defined molecular fragments to be isolobal... 

Isolobal Relationship Two molecular fragments are isolobal if the number, symmetry properties, shapes and approximate energies of their frontier orbitals are the same. They may or may not also be isoelectronic. If the two fragments are isoelectronic, in the sense that the ratio of the number of electrons in frontier orbitals to the number of frontier orbitals is same, then the net charges on the two species will be the same. The orbitals whose similarity is critical in determining isolobality are called frontier orbitals. 

Two molecular fragments are isolobal if the number, symmetry properties, shapes, and approximate energies of their frontier orbitals are the same. They may or may not also be isoelectronic. For example, the HB and HC fragments are isolobal (but not isoelectronic), whereas the H2C and H2N moieties are both isolobal and isoelectronic. These relationships are illustrated in Fig. 1-23. As shown there, the symbol is used to express isolobality. Also shown in Fig. 1-23 is the idea that we may choose to picture the isolobality in more than one way. Thus, for the HB and HC fragments, we can either envision one sp hybrid orbital whose axis is colinear with the H—B or H—C bond, plus two p orbitals perpendicular to this axis, or we may envision a state of full hybridization, where the frontier orbitals in each case are three of the four in a set of sp3 tetrahedral hybrids. The orbitals whose similarity is critical in determining isolobality are called the frontier orbitals. 

In earlier chapters, there have been a variety of examples of similarities between organometallic chemistry and organic chemistry. Such similarities can be envisioned on a broader scale by considering frontier orbitals of the molecular fragments of which organometallic compounds are composed. In his 1981 Nobel lecture, Hoffmann described molecular fragments as isolobal,... 

The isolobal analogy can apply to any molecular fragment where the FMOs have the same size, shape, energy, and occupancy. The species do not necessarily have to have the same number of electrons missing from their valence shells, as do all of the examples in Table 19.4. Thus, for example, [Au(PPh3)], which has only 13 valence electrons, and the 17-electron species [Mn(CO)5] are isolobal, as shown in Figure 19.44, because their FMOs have similar shapes and energies. 

Fig. 8.34. The isolobal analogy between molecular fragments (symbolized by a double arrow with a loop). All species shown are electrically neutral and are derived conceptually from the first row that contains the generic" compounds CH4, CrLg, Mn(CO)3(C5H4), where L are ligands that offer an electron pair each. The second row is a result of an alchemical transmutation we remove an electron pair with a ligand L, but compensate for it by increasing the atomic number of the central atom by 1 (its additional electron enters the empty lobe). In such a way, all species in the second row have an orbital lobe carrying a single electron and each pair of them is isolobal. Similarly, in the third row, all species share the same two-lobe structure (all are mutually isolobal), while in the fourth row, we have the same three-lobe isolobal structures.

Isolobal Two molecular fragments with similar orbital energies and symmetries. 

Isolobal Two atoms or molecular fragments which bind by using atomic orbitals of the same symmetry type. 

The isolobal principle wholly arises from considerations about the electronic structure of molecular fragments at a microscopic level. Kinetic and thermodyn-... 

The axially symmetric metal carbonyl fragments M(CO)n (n = 1, 3, 4) have three outpointing hybrid orbitals with a high proportion of s and p orbital character, which are suitable for forming cluster skeletal molecular orbitals (77, 78, 238). The number and radial characteristics of these frontier molecular orbitals, which are illustrated schematically in Fig. 26a, are reminiscent of the frontier orbitals of a main group diatomic hydride fragment E—H, where E = C or B (Fig. 26b). To describe this similarity the term isolobal has been introduced (77). Molecular orbital... 

I have reviewed, in Chapter No. 12, the activation of arenes by the strongly electron-withdrawing 12-electron fragment CpFe+, isolobal to Cr(CO)3 and Mn(CO)3+, and its application to the synthesis of dendritic cores, dendrons, dendrimers, and metallodendrimers, including molecular batteries. 

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