Propagators in Quantum Chemistry, 2nd Edition

Chapter 9

The Electron Propagator in Higher Orders

Improved descriptions of single-electron processes require treatments beyond the geometric approximation given by the Hartree-Fock electron propagator in Eq. (4.25). More elaborate approximations of the equation of motion (9.1)

may be generated in various ways. The discussion here will be confined to the use of perturbation theory.

Such a treatment can, with advantage, be expressed in terms of the superoperators introduced in Eq. (4.19) and in terms of a basis of field operators. The basis of fermion-like operators {X_i} = is chosen, such that the electron field operators correspond to the SCF spin orbitals. The field operator space supports a scalar product (X_i|X_j) = = , where ρ is the density operator defined in Eq. (4.33). The superoperator identity and the superoperator hamiltonian operate on this space of fermion-like field operators and, in particular, .

Perturbation theory starts with a partitioning of the hamiltonian, and thus ...