LCAO-MO wave function

The other major influence in the work has come from the papers of Mulliken and his co-workers, in particular the series (14) on population analysis of LCAO-MO wave functions and their relation to energies of atomization. As Mulliken suggested (14), we have attempted to relate... 

Equations (1.105) and (1.106) are the Heitler-London counterpart of the corresponding quantities (Equations 3.4 and 3.5 on page 340 of Ruedenberg s paper (1962), which refers to a LCAO-MO wave function. Ruedenberg calls Equation (1.106) the modification of the quasi-classical density due to the interference effect , while we, more literally, speak of exchange[a(r)b(r)], [b(r)a(r)] and overlap[—Sa1(r)], [—Sfe2(r)] densities. Finally, it is worth noting that, while ... 

The population analysis of a LCAO—MO wave function requires three kinds of indices the atomic populations... 

If tj>a symbolizes an atomic orbital centered on nucleus a, the spatial factor of the imnormalized LCAO-MO wave function for the H2 ground state is... 

The simple LCAO-MO wave function for the H2 ground electronic state is... 

In a trial LCAO-MO wave function for ground-state, which correlates with proton and a Is H atom as R- oo, we may use the hydrogen Is states 0A> = Q P(-rJao)/y/ and 0b> = exp(-rB/ao)/ A for Os. The overlap integral using these AOs becomes... 

The extension to N-electron LCAO-MO wave functions is due to Mulliken (1955). 

Electron correlation in the triplet is a consequence of the Pauli exclusion principle, which is embodied mathematically in the antisymmetrization of the electronic wave function. Anti-symmetrization results in zero probability for two electrons of the same spin simultaneously being in the same AO in an LCAO-MO wave function. This obviously reduces the Coulomb repulsion between these electrons from the value, Jxy, that is calculated by computing the Coulomb repulsion energy between a pair of uncorrelated electrons, one in f/x and the other in ffy. 

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