Delocalisation

Ferrocene Figure 2-47) provides a prime ex.ample of multi-haptic bonds, i.e, a situation where the electrons that coordinate the cyclopentadienyl rings with the iron atom arc contained in molecular orbitals delocalised over the iron atom and the 10 carbon atoms of the cyclopentadienyl rings [82. ... 

The Hard-Soft-Add-Base (HSAB) theory was developed by Pearson in 1963. According to this theory, Lewis acids and Lewis bases are divided into two groups on one hand hard acids and bases, which are usually small, weakly polarizable species with highly localised charges, and on the other hand soft acids and bases which are large, polarizable species with delocalised charges. A selection of Lewis acids, ordered according to their hardness in aqueous solution is presented in Table 1.3. 

Finally, the solvent also interacts with sites of the Lewis acid and the Lewis base that are not directly involved in mutual coordination, thereby altering the electronic properties of the complex. For example, delocalisation of charges into the surrounding solvent molecules causes ions in solution to be softer than in the gas phase . Again, water is particularly effective since it can act as an efficient electron pair acceptor as well as a donor. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

As described above, metallic CNTs are of great interest because they possess molecular orbitals which are highly delocalised. However, metallic CNTs are very difficult to use in actual devices because they require very low temperatures to control their carrier transfer. On the contrary, even at room temperature, the nonlinear /-V jas curve and the effective gate voltage dependence have been presented by using individual semiconducting SWCNTs [29]. 

The diazonium ion is a very weak electrophile since the positive charge can be delocalised into the aromatic ring, and its reactivity is modified by substituents... 

Two other theories as to the mechanism of the benzidine rearrangement have been advocated at various times. The first is the rc-complex mechanism first put forward and subsequently argued by Dewar (see ref. 1 pp 333-343). The theory is based on the heterolysis of the mono-protonated hydrazo compound to form a n-complex, i.e. the formation of a delocalised covalent it bond between the two rings which are held parallel to each other. The rings are free to rotate and product formation is thought of as occurring by formation of a localised a-bond between appropriate centres. Originally the mechanism was proposed for the one-proton catalysis but was later modified as in (18) to include two-protons, viz. 

Theory and experiments on valence delocalisation in mixed-valence compounds. P. Day, Comments Inorg. Chem., 1981,1,155-167 (23). 

Coordination compounds with delocalised ground states. The transition metal derivatives of dithioketones and ethylene(l,2)dithiolates (metal dithienes). G. N. Schrauzer, Acc. Chem. Res., 1969,2,72-80 (36). 

Mixed valence molecules electronic delocalisation and stabilisation. D. E. Richardson and H, Taube, Coord. Chem. Rev., 1984, 60,107 (40). 

Since plane waves are delocalised and of infinite spatial extent, it is natural to perform these calculations in a periodic environment and periodic boundary conditions can be used to enforce this periodicity. Periodic boundary conditions for an isolated molecule are shown schematically in Fig. 8. The molecular problem then becomes formally equivalent to an electronic structure calculation for a periodic solid consisting of one molecule per unit cell. In the limit of large separation between molecules, the molecular electronic structure of the isolated gas phase molecule is obtained accurately. 

Benzene has often been used as a test system for vibrational calculations using a variety of different electronic structure algorithms. The molecule exhibits regular hexagonal planar symmetry with six carbon atoms joined by a bonds and six remaining p-orbitals which overlap to form a delocalised n electron over all six carbon atoms. Table 1 shows comparisons of several different methods for benzene. 

The symmetrical bis(ylidyl)phosphenium chlorides 103, obtained from the reaction of trimethylsilyl ylides 102 with PCI3 are the first phosphenium salts which do not need counterions of low basicity such as AICI4 to be isolated (Scheme 30) [119]. The explanation of their stability lies in the delocalisation of the phosphenium charge in the two phosphonium parts. The reactivity study of these species is reported and for example the phosphenium 103 (R=Ph) adds ortho quinones to the central phosphorus to give the corresponding dioxaphospholenium salts 104 via a [4-1-1] cycloaddition. 

According to these consideration the diamino-substituted phosphenium (an alternative suggestion for its nomenclature is phosphanylium) cation, 5, and the phosphanetriylammonium (iminophosphenium) cation, 6, possess the largest intrinsic (gas phase) stabihties. Since in the X-ray structures the molecules are to a first-order isolated, this theoretical stability scale determined for the gas phase should also mimic the various trends of the stabilities of the cations and their chelation behaviour. The methylenephosphenium, 7, and the PjH cations, 8, suffer from poor stabihties. On the other hand the phosphirenium cation, 11, is considered to be fairly well stabilized. It is due to n-electron delocalisation of the positive charge in the phosphirenium cation. Intermediate cases in stabihty are the PO+ (9) and PS+ cations (10). Of further interest are the frontier orbital considerations, as shown in Fig. 2. 

Photoelectron spectroscopy, ab initio calculations [86] and NMR spectroscopy [87] support the contention that in the tetraphosphacubane, 33, n P—> a P-C delocalisation occurs (Scheme 20). 

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