The Electronic States of Diatomic Molecules

In the Born-Oppenheimer approximation, the nuclei of a molecule are assumed to he stationary when the electronic states are studied. 

The Schrodinger equation for the hydrogen molecule ion, hJ, can he solved in the Born-Oppenheimer approximation without additional approximations. The solutions are molecular orhitals that represent motion of the electron around both nuclei. 

Molecular orhitals can he represented approximately as linear combinations of atomic orbitals (LCAOMOs). 

The electronic wave functions of homonuclear diatomic molecules can be approximated as products of LCAOMOs. 

The valence-bond method is an alternative to the molecular orbital method. 

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There are three different schemes for building up the electronic states of diatomic molecules (a) from separated atoms, (b) from the united atom, and (c) from the molecular orbitals of the diatomic molecule itself. It is the correlation between the electronic states of the diatomic molecule as built up from the separated atoms and as determined from the molecular orbitals of the diatomic which is most valuable for any general consideration of reactions and excited states. The correlation of molecular states obtained by these two methods is not limited solely to diatomic molecules but also forms a valid approach for polyatomic molecular systems. The correlation of separated atoms with the hypothetical united atom has value for diatomics and has been applied to simple polyatomic molecules, especially those with a heavy atom or two and a number of hydrogen atoms. However, it is conceptually less appealing even for simple polyatomic molecules and completely inapplicable for complex polyatomic molecules. 

Wigner and Witmer s [5] characterization of the electronic states of diatomic molecules marked the triumphant entry of group theory into the field of molecular structure. It was focused primarily on considerations of angular momentum, which we have managed to sidestep almost completely thus far in the book by artificially reducing spherical or cylindrical symmetry to Thus, the cr... 

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