Molecular orbital localised

With both (la) and (2a) above, lateral overlap of the p atomic orbitals on adjacent carbon atoms could lead to the formation of two localised n bonds as shown, and the compounds would thus be expected to resemble ethene, only twice as it were This is indeed found to be the case with (2), but (1) is found to behave differently in terms of its slightly greater stability (referred to above), in spectroscopic behaviour (see below), and in undergoing addition reactions more readily than does an isolated diene (p. 194). On looking more closely, however, it is seen that with (la), but not with (2a), lateral overlap could take place between all four p atomic orbitals on adjacent carbon atoms. Such overlap will result in the formation of four molecular orbitals (Fig. 1.2), two bonding ( and 2) and two anti-bonding (i//3 and 4)—the overlap of n atomic orbitals always gives rise to n molecular orbitals ... 

The molecular orbitals are changed so that corresponding to the deepest level ej, becomes increasingly localised at the atom r, and all others tend towards the MO s of the residual molecule. This condition is achieved by the migration of a node of each orbital until it cuts the bonds which connect atom r with the residual molecule. 

In the complex electrostatic field of a molecule, it is usually impracticable to obtain accurate molecular orbitals, so it is customary to express them approximately as linear combinations of atomic orbitals belonging to the constituent atoms. This is called the linear combination of atomic orbital or LCAO form. Although they are only approximate, the LOAO functions do show most of the properties of the precise orbitals. Both molecular and localised equivalent orbitals can be expressed in this manner. 

Thus it appears that the best equivalent orbitals in this molecule are not completely localised in the two double bonds but are to some extent distributed over the whole system. This failure to obtain localisation is the molecular-orbital analogue of resonance between valence structures. 

The main result that emerges from the discussions of particular eases is that it has proved possible to give a description of a molecule in terms of equivalent orbitals which are approximately localised, but which can be-transformed into delocalised molecular orbitals without any change in the value of the total wave function. The equivalent orbitals are closely associated with the interpretation of a chemical bond in the theory, for, in a saturated molecule, the equivalent orbitals are mainly localised about two atoms, or correspond to lone-pair electrons. Double and triple bonds in molecules such as ethylene and acetylene are represented as bent single bonds, although the rather less localised o-n description is equally valid. 

In molecular orbital language, back donation (or back bonding) means considerable participation of empty ligand orbitals (usually r ) in the occupied T-molecular orbitals mostly localised on the metal. We are fortunate to have the simple words "back donation" to describe such a state ot affairs. 

Representations of the molecular orbitals indicated by the alg and eg levels of Fig. 1-12 are shown in Fig. 1-13. They each contain contributions from metal orbitals (the s for the flj, and the dz2 and the dx2 y2 for the e) and from some or all of the ligands. It is difficult to equate these multi-centred orbitals to the more familiar individual metal-ligand interactions and bonds. The majority of chemists prefer to think in terms of localised bonding, rather than in terms of electrons delocalised over the metal and all six ligands. 

A modified version of the deMon DFT code [38] in which molecular orbitals are given as linear combinations of Gaussian-type atomic functions was used for the PWP computations. In order to localise the extreme points on the potential energy surfaces the Broyden-Fletcher-Goldfarb-Shanno minimisation algorithm [39]... 

The molecular orbital is symmetrical and the six ji electrons are said to be delocalised around the aromatic ring since they are not localised between any two particular carbon atoms. The aromatic ring is generally represented as shown in figure given below to represent this delocalisation of the n electrons. 

In such molecules alternative bonding description are possible. These may involve either localised (two centre) or delocalised (three or more centres) molecular orbitals. The overall distribution predicted may be the same in both cases. 

Heteronuclear diatomic molecules are naturally somewhat more complicated than the homonuclear comprehensive comparisons with homonuclear molecules were given by Mulliken [15]. The atomic orbital coefficients in the molecular orbitals ofheteronu-clear diatomic molecules are no longer determined by symmetry alone, and the electrons in the molecular orbitals may be shared equally between atoms, or may be almost localised on one atom. The molecular orbitals can still be classified as a or n, but in the absence of a centre-of-symmetry the g/u classification naturally disappears. Some heteronuclear molecules contain atoms which are sufficiently similar that the molecular orbitals resemble those shown in figure 6.7. In many other cases, however, the atoms are very different. This is particularly the case for hydride systems, like the HC1 molecule,... 

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