4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis

For mapping the original electronic structure Hamiltonian into the corresponding qubit Hamiltonian, we work in the second quantization formalism of quantum mechanics. Recall we introduced the first quantization in Section 4.1, Born-Oppenheimer approximation.

The Hartree-Fock (HF) method approximates an -body problem into one-body problems where each electron evolves in the mean field of the other electrons.

We can rewrite the electronic molecular Hamiltonian () as a linear combination of products of creation and annihilation operators (summarized in Figure 4.4):

where removes an electron from spin-orbital , and creates an electron in spin-orbital . The operation is the excitation operator, which excites an electron from the occupied spin-orbital into the unoccupied orbital . Constructing these were introduced in Section 2.1, Postulate 1 – Wave functions. The nuclear-nuclear ...