From Delocalisation Energies

The r-delocalisation in the parent phospholide anion I (Fig. 3, R =R =H) can be expressed in the valence bond picture by resonance between the canonical structures lA-IC (and their mirror images). Phosphonio-sub-stituents (R =R =PH3 ) increase the weight of the 1,2-dipolaric canonical structure IB and induce thus, in essence, a partial r-bond localisation and a shift of r-electron density from the phosphorus to the adjacent carbon atoms [16]. Consequences of this effect are the decrease in delocalisation energy for reaction (1) depicted in Fig. 4, and lower C2-C3/C4-C5 and higher C3-C4 bond orders which are reproduced in concomitant variations of computed bond distances [16]. 

Fig. 4 Delocalisation energies AEi,2 (in kcal mol ) in (benzo)phospholides as computed from the isodesmic reactions (1) and (2). (R=H, from [16])...

One of the most remarkable features of the all-silicon backbone is that it leads to the delocalisation of a-electrons, a phenomenon which is essentially unknown in carbon chemistry.This can be understood in terms of the nature of the molecular orbitals associated with the Si-Si a-bonds. These are more diffuse than those associated with C-C a-bonds as they are constructed from higher energy 3s and 3p atomic orbitals. This leads to significant... 

In a semiconductor, as discussed in the previous section, localisation can also occur as the width of the allowed energy band is reduced, and this was defined in terms of a limiting mobility. The Anderson model shows that disorder can lead to localisation in metals as well as semiconductors. In metals, since conduction is due only to electrons within a partially filled band, the energy in the band tail that separates localised from delocalised electron states is termed the mobility edge. The onset of localisation in a metal occurs at a minimum conductivity. This can be seen as follows. For an electron at the Fermi energy its mean free path, l, is just the scattering time, r, multiplied by the electron velocity at the Fermi energy, vF. Then, from Equations (4.1) and (4.2) it follows that ... 

One final word of caution may be sounded on the delocalisation energies discussed in 3.2a and tabulated in Table 3-1. They have been calculated without reference whatever to any changes in the ex-framework which may be required to go from a hypothetical Kekule-structure to an actual, delocalised , conjugated system—changes which, energetically, may sometimes be quite large. For example, to convert a benzene Kekule-... 

Afterwards, the relative activation energies of the diastereoisomeric transition structures are split into contributions able to represent the factors the organic chemist is used to invoke in the attempt to "understand" the variety of the reaction outcome, i.e. steric and electrostatic repulsions, deformation energy of reactants, incipient bond energies, trough-space delocalisations and their subsets often called secondary interactions. The an ysis of delocalisation energies rests on the use of hybrid basis sets derived from Del Re s Maximum Localisation Criterion. ... 

Figure 2.23 The development of an energy band from delocalised molecular orbitals. Each atom in the molecule contributes one molecular orbital. An isolated atom has sharp energy levels (left-hand side). As the number of atoms increases, the number of discrete orbitals merges into a band of closely spaced energy levels (right-hand side)...

Ab initio calculations on all-ofs [lOJannulene confirm that energy is lowered substantially when distortion from planarity takes place [2]. When a planar geometry is considered, the energy surface in its vicinity is very flat and there is very little difference between a structure with localised double bonds or a delocalised structure [2,3]. Different approaches slightly favour bond alternation [2] and delocalisation [3]. It has been pointed out that with [lOJannulene the limit for equalisation of bonds in the (4n+2)annulenes may be being reached [3] the transition from delocalisation to localisation in the series will be gradual, with small distortions in borderline cases which would be very difficult to detect experimentally [3]. 

The electron energy levels in a solid are grouped together in delocalised energy bands which can be considered to arise from the diffraction of electron waves by the crystal lattice. The population of these energy levels is determined by the Fermi-Dirac distribution function ... 

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