chem8950 – Derive the recursive equation for the wavefunction, starting from the λ-dependent Schr¨odinger equation. (Solution)

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Ψ(λ) = Φ + R0(λVc − E(λ))Ψ(λ) (1)
Assume intermediate normalization and note that R0H0 = −Q follows** from the definition of R0.
**Extra Credit: Define “resolvent” and explain why this follows from your definition.
Determine the first- and second-order components of Ψ by differentiating equation 1. You do not need to

fully evaluate and simplify your answer, but you should eliminate all terms that vanish and explain why each one evaluates to zero.
Evaluate the following contributions to the CI doubles and quadruples coefficients.
(2)
Use your answer to show that .

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