Structural formulae and non-independent bonds

All the information that can be known about a system in a given stationary state is contained in the state function 5 (r), particularly molecular electron densities. The use of electron density to interpret atoms in molecules, bonds and structures constitutes a bridge between the concept of state function and the physical model of matter in real space. 

It is found that, in general, the molecular charge densities obtained from single determinant SCF calculations carried essentially to the Hartree-Fock limit (see page 163) are accurate to within 2-5% of the total charge density at any point in space, except perhaps for very large distances from the nuclei. Coulomb electron correlation effects are relatively small in particular, the value of p(r) in the neighbourhood of a bond critical point calculated in that way exceeds the value obtained from a correlated wavefunction by only a few per cent. 

Whatever the level of approximation used in the calculation, in general the molecular orbitals (m.o.s) for polyatomic molecules have contributions from the orbital functions of several atoms. They are non-localized, in the sense that they do not just involve each atom and a neighbour, as might be suggested by the traditional structural formulae. An exception is provided by the occurrence of localized m.o.s as non-bonding orbitals, namely for symmetry considerations, as is the case for the non-bonding electron pair of 7T symmetry in the H2O molecule studied in the previous chapter. 

Although in some cases there is a close relation between the concentration of charge predicted by the laplacian of p(r) given by Eq. (8.2) and the symmetry properties of the highest occupied and lowest unoccupied m.o. (HOMO and LUMO), one of the virtues of the orbital model is that the relative phases of the orbitals determine their symmetry properties and their effective overlap (as we have already seen in Chapter 7 and will return to in future chapters). 

The relation between delocalized m.o.s and structural formulae can begin by just counting the total number of bonding and anti-bonding electrons, Ab and Aab respectively, and then determine what could be called a global bond order as the sum of the multiplicities of the several bonds in the molecule  

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Structured formulae and non-independent bonds non-bonding electrons (at higher energy) ... 

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