Molecular Orbitals for Other Diatomic Molecules

The MO method used with the hydrogen molecule can be applied to other diatomic molecules after some modifications have been made. Each electron is considered to move in the potential field produced by the nuclei, plus some additional electrical field which represents the average effect of all the other electrons. This gives rise to the following one-electron Hamiltonian operator  

In this equation, and are the distances of the electron from the two nuclei, and and Zg are the effective charge numbers of the two nuclei after allowance has been made for the screening effect of the other electrons. The final term represents the supposedly static potential field which arises from the charge distribution of the other electrons. 

We start by considering the following trial wavefunction for a heteronuclear diatomic molecule, AB  

and are atomic orbitals centred on atoms A and B, respectively and Cg are weighting factors for the two atomic wavefunctions, the best values of which have to be determined. The method to be discussed is quite general and can easily be extended to larger molecules. 

The expectation value for the energy of this trial wavefunction can be obtained from equation (8.3)  

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