Isolobal symbol

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. 

As Figure 15-2 shows, each of these fragments has a single electron in a hybrid orbital at the vacant site of the parent polyhedron. These orbitals are sufficiently similar to meet Hoffmann s isolobal definition. Using Hoffmann s symbol to designate... 

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.

Before concluding our discussion of the Fe(CO)4 unit it is worthy of comment that it is often thought of as a member of an isolobal series such as that given in Fig. 10.16. Members of an isolobal series are always shown as related to each other by the symbol —ir>. Membership of such a series is based on experimental evidence as much as theoretical, but members of an isolobal series usually have similar orbital patterns, both in terms of orientation and energy. Experimentally, they form similar compounds—so, each member of the middle series shown in Fig. 10.16 forms an H2 compound. However, of the members of this series only Fe(CO)4 has the A high, Bj low energy level pattern. Theoretically, this species is the only member of... 

A molecular entity such as "CHj, SnHj, Cl possessing an unpaired electron. (In these formulae the dot, symbolizing the unpaired electron, should be placed so as to indicate the atom of highest spin density, if this is possible). Paramagnetic metal ions are not normally regarded as radicals. However, in the isolobal analogy the similarity between certain paramagnetic metal ions and radicals becomes apparent. 

The isolobal relationship is symbolized by a double-headed arrow with a teardrop, as shown in 21.1. Note that the first three criteria are absolute while the last two are qualitative comparisons. This isolobal analogy is a model designed to... 

---