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26.1: The Molecular Hamiltonian
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For a molecule, we can decompose the Hamiltonian operator.
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26.2: The Born-Oppenheimer Approximation
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As we already saw in the previous chapter, if a Hamiltonian is separable into two or more terms, then the total eigenfunctions are products of the individual eigenfunctions of the separated Hamiltonian terms.
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26.3: Solving the Electronic Eigenvalue Problem
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Once we have invoked the Born-Oppenheimer approximation, we can attempt to solve the electronic TISEq in Equation 27.2.7. However, for molecules with more than one electron, we need to—once again—keep in mind the antisymmetry of the wave function. This obviously means that we need to write the electronic wave function as a Slater determinant (i.e., all molecules but H+2 and a few related highly exotic ions).