Propagators in Quantum Chemistry, 2nd Edition

Chapter 10

Atomic and Molecular Orbitals

This chapter deals with the discussion and interpretation of approximate molecular electronic structure methods in terms of propagator concepts. Only situations with fixed nuclear frameworks are considered, and the discussion is limited to the description of states that are close in energy to the normal state of the system. We adopt the view that the main features of the electronic structure of such states can be developed in terms of atomic orbital representations of operators and that only valence shell orbitals need be considered.

10.1   Nonorthogonal Basis Sets

The treatment of orbital overlap in conjunction with the use of nonorthogonal basis sets deserves particular attention in treatments in terms of electron field operators. The definition of creation and annihilation operators and their anticommutation rules are basic for this development. Let {u_s(ξ)} be a set of atomic spin orbitals used to define the creation operators

and annihilation operators

The fundamental anticommutation rules

lead to the relations

For an orthonormal basis ...