Energy-localized orbitals

N occupy an sp lone-pair in the plane of the ring (or the plane of the local PNP triangle) as in Fig. 12.26a. The situation at P is less clear mainly because of uncertainties concerning the d-orbital energies and the radial extent (size) of these orbitals in the bonding situation (as distinct from the free atom). In so far as symmetry is concerned, the sp lone-pair on each N can be involved in coordinate bonding in the jcy plane... 

Orbital amplitudes, 54 Orbital energies, 51, 53, 287 Orbital interactions general rules, 10, 38 Orbital labels group theoretical, 46, 51 localized types, 51 Orbital occupancies, 57 Oxygen, 88 Ozone, 151... 

Vertical ionization energies of the two highest molecular orbitals and of orbitals mainly localized on the substituent of a-substituted derivatives of furans, thiophenes, selenophenes, and tellurophenes have been determined.25 Assignments of some of the bands other than the first two in the photoelectron spectra of tellurophene and selenophene are proposed, and the effect of the ring on the orbitals mainly localized on the substituent is briefly discussed. 

FIGURE 20. Top Definition of the phase relationship of the three localized basis 7r-orbitals of a norbornadiene molecule with an exocyclic double bond in position 7. Bottom Correlation diagram of the experimental orbital energies j = —/ of norbornadiene 75, 7-methylidenenorbornadiene 196 and 7-isopropylidenenorbomadiene 206, with those of the corresponding monoenes... 

The term inert pair is often used for the tendency of the 6s2 electron pair to remain formally unoxidized in the compounds of Pb(n) [and also in the case of T1(I) and Bi(m) etc.]. As discussed above, this tendency can be related to relativity. Figure 59 shows the relativistic and non-relativistic valence orbital energies for Sn and Pb. The relativistic increase of the s-p gap leads to a 6s2 inert pair in the case of Pb. However, the situation is more complex if the local geometry at the heavy atom (Pb) is discussed. There are examples for both, stereochemically inactive and stereochemically active s2 lone pairs. 

As seen from Table 3.5, the Koopmans-type estimates are quite unrealistic in all cases. Such crude estimates give no real basis forjudging whether the delocalized or localized picture is preferable. If anything, the NBO orbital energies give better estimates of this type than do the MO orbital energies ... 

In atomic theory or molecular orbital theory, the chemical potential is related to the orbital energy [5,6]. In the case of one or two electrons in the same orbital, the local orbital energy s is equal to the local chemical potential ... 

The orbital energy contributions of the canonical orbitals, et, are the eigenvalues of the Hiickel-Wheland hamiltonian (39). If the localized orbitals XK are given in terms of the canonical orbitals by... 

Since all localized orbitals have approximately the same spatial extension, it stands to reason that their orbital energies rjn should be of the same order of magnitude. In fact, one finds for the four main types of localized 7r electron orbitals the following orbital energy values ... 

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

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