The antibonding orbital in Eq. 2 is not normalized (see Exercise 2G.21). Find the factor that normalizes it to 1, given that the individual atomic orbitals are each normalized. Express your answer in terms of the overlap integral S = ∫ψ_A1s ψ_B1s dτ. Confirm that the bonding and antibonding orbitals are mutually orthogonal—that is, that the integral over the product of the two wavefunctions is zero.

Exercise 2G.21

It is usually convenient to deal with wavefunctions that are “normalized,” which means that the integral ∫ψ² dτ = 1. The bonding orbital in Eq. 1 is not normalized. A wavefunction ψ can be normalized by writing it as Nψ and finding the factor N which ensures that the integral over (Nψ)² is equal to 1. Find the factor N that normalizes the bonding orbital in Eq. 1, given that the individual atomic orbitals are each normalized. Express your answer in terms of the “overlap integral” S = ∫ψ_A1s ψ_B1s dτ.

Transcribed Image Text:

U = UAIS + UBIS (1)