chem8950 – In solving the canonical Hartree-Fock equations, it is common to use eigenfunctions of the core Hamiltonian as starting guesses for the canonical molecular orbitals. This eigenvalue equation looks as follows (Solution)

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where φp is a spatial function. Project this equation by χµ and then expand φp as a linear combination of atomic orbitals, φp = Pν χν Cνp, in order to arrive at the following matrix equation for the core guess.
HC = SC (H)µν = hχµ|hˆ|χνi (S)µν = hχµ|χνi (C)µp = Cµp
Derive the expansion of H in terms of Φ-normal-ordered excitations.
Derive the second Slater rule using Wick’s theorem, and explain why this matrix element evaluates to zero for canonical Hartree-Fock orbitals.
hΦ|H|Φai i = ?

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chem8950 – In solving the canonical Hartree-Fock equations, it is common to use eigenfunctions of the core Hamiltonian as starting guesses for the canonical molecular orbitals. This eigenvalue equation looks as follows (Solution)

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