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.

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U = VAIS + UBIS (1)