MO and VB Wave Functions for Homonuclear Diatomic Molecules

The MO approximation puts the electrons of a molecule in molecular orbitals, which extend over the whole molecule. As an approximation to the molecular orbitals, we usually use linear combinations of atomic orbitals. The VB method puts the electrons of a molecule in 

We begin with the ground state of He2. Each separated helium atom has the ground-state configuration 1. This closed-subshell configuration does not have any unpaired electrons to form valence bonds, and the VB wave function is simply the antisymmetrized product of the atomic-orbital functions. In the notation of Eq. (10.47), the He VB ground state wave function is the Slater determinant 

The subscripts a and b refer to the two atoms, and the bar indicates spin function j8. The 1 function in this wave function is a helium-atom Is function, which ideally is an SCF atomic function but can be approximated by a hydrogenlike function with an effective nuclear charge. The VB wave function for Hc2 has each electron paired with another electron in an orbital on the same atom and so predicts no bonding. 

In the MO approach, Hc2 has the ground-state configuration a-g s) (t% s). With no net bonding electrons, no bonding is predicted, in agreement with the VB method. The MO approximation to the wave function is 

The simplest way to approximate the (unnormalized) MOs is to take them as linear combinations of the helium-atom AOs agls = Sa + lij and o- li = li - Isb- With this approximation, (13.111) becomes 

The Is function in this wave function is a helium-atom Is function, which ideally is an SCF atomic function but can be approximated by a hydrogenlike function with an 

The VB wave function for H 2 has each electron paired with another electron in an orbital on the same atom and hence predicts no bonding. 

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