Mullikens Orbital Correlation Diagram

Let us read the diagram from right to left. With the two X atoms separated, we imagine a very weak quadrupolar field perpendicular to their line of centers. 

Chapter 3. Diatomic Molecules and their Molecular Orbitals 

As the internuclear distance gets shorter, the distinction between bonding and antibonding orbitals makes itself felt. The familiar criteria for bonding are  

An MO is bonding if the electron density can be large between the nuclei 

The relative extent of the stabilization or destabilization of an MO at any particular internuclear distance depends on the overlap of the AOs centered on and X.  

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Another important contribution of Buenker and Peyerimhoff has been the duplication of the Mulliken-Walsh orbital correlation diagrams by ab initio calculations (see Chemical Reviews, 1974) and examination of their relation to Koopmans theorem. 

Fig. 3.5 displays Mulliken s [2] generalized orbital correlation diagram for homonuclear diatomic molecules, which has been of seminal importance for the elucidation of the electronic structure of molecules. Only the atomic levels n = 1,2 have been included on its right on the left, the orbitals of the united atom have been extended sufRciently that all of the necessary correlation lines can be drawn. The energetic spacing of the AOs is purely schematic, their order on the left being that common to silicon and sulfur, the united atoms corresponding to N2 and O2. The abcissa, is - of course - quite non-linear. 

Diatomic molecules are necessarily linear, but a triatomic molecule can be either linear like CO2 and HCN or bent like SO2 and H2O. Mulliken s correlation diagram procedure was extended to tri- and tetraatomic molecules by Walsh [1], who promulgated a set of simple but remarkably viable [2, 3, 4] rules for predicting whether or not a molecule will remain linear, from the effect of the departure from linearity on the energy of its occupied molecular orbitals. 

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