The wave equation and molecular orbitals

It is important to say, from the start, that covalent bonding and other molecular properties can be studied quantum mechanically without reference to molecular orbitals. We are referring to valence bond theory which, being based on the orbital concept for atoms, was, in fact, the first quantum-mechanical theory of the chemical bond. In Chapter 8, we will make a more detailed reference to this method. Our main concern in this and the coming chapters is molecular orbital theory. 

The Schrodinger equation for H2 involves three particles two nuclei A and B of charge e and one electron (charge —e). Therefore, the potential energy of the system has two terms  

The first is the contribution of the electrostatic repulsion between the two nuclei, considered as point charges at a distance RabI and the second is the contribution of the attractions between the electron and each nucleus, at 

Within the constraints of the Born-Oppenheimer approximation, the wave equation to solve is 

The wavefunction r x,y,z) then becomes a product of one-variable functions 

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