L4 Linear Combination of Atomic Orbitals approximation

How can a many-electron (molecular orbital) wavefunction be approximated

As a product of single-electron wavefunctions. This approximation is needed as we CANNOT solve the Schrodinger equation exactly due to V_ee (electron-electron repulsions).

The Linear Combination of Atomic orbitals (LCAO)

The wavefunction of a molecular orbital is (approximately) the sum of the atomic orbitals.

minimal basis set

What is the significance of H₂⁺ being centrosymmetric in terms of c_A and c_B

The electron should be no more likely to be around one atom than the other

Taking the sum of the orbitals vs the difference

Dirac notation

Mainly for photochemistry - just a different way of writing wavefunction representations.

Operators get added before the line.

Two angled brackets introduced integration over all space.

Calculating the energy of a wavefunction using manipulation of the Schrodinger equation

This allows you to make a guess of the wavefunction to calculate its energy

determining the molecular orbital coefficient c_A

Overlap integral S_AB

Measures the extent to which the two AOs overlap. Tends towards 0 as the overlap lessens

Determining the energy of the H₂⁺ orbitals

Each of the 4 terms is negative

H_AA = H_BB and H_AB = H_BA

2 approximations to simplify this equation

What equation does this allow you to write