The Electron-pair Bond Some Preliminaries

To introduce the concepts, we must of course start from the classic 1927 paper of Heitler and London [1], referred to by Pauling himself [2] as the greatest single contribution to the clarification of the chemist s conception of valence. .. since G.N.Lewis s suggestion that the chemical bond between two atoms consists of a pair of electrons held jointly by the two . The electron-pair bond in the hydrogen molecule was described using a wavefunction of the form 

Starting with just two atomic orbitals, xa,Xb, it is evidenty possible to construct various other types of wavefunction. Thus 

H being the Hamiltonian operator. Throughout this Chapter, we use the usual non-relativistic Born-Oppenheimer Hamiltonian in which no spin operators occur and the nuclear positions are considered fixed. 

It will be recalled that the approach of molecular orbital (MO) theory starts, on the other hand, from an independent-particle model (IPM) in which both electrons occupy the same bonding MO , f 1 = Xa + Xb, similar to the one used [4] for the hydrogen molecule ion, Hj. The bonding MO is in fact the approximate wavefunction for a single electron in the field of the two nuclei and allocating two electrons to this same MO, with opposite spins, yields the 2-electron wavefunction 

The spins must be paired in this case, to satisfy the Pauli principle, the spatial factor 0i(ri)0i(r2) being already symmetric. In the VB function, the electrons are allowed to change places , i.e. to be associated with either of the two nuclei A and B, by using the symmetrized product X i(ri)Xfl(r2) + Xs(ri)x i(r2) but in the MO approach each electron is automatically shared between the nuclei - because its orbital contains terms coming from both centres. In MO theory, then, bonding is not associated with exchange of electrons between differently localized AOs, but rather with the fact that the MOs themselves extend over more than one centre - the MOs are essentially delocalized over the centres and the bonding is associated with the 

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