Propagators in Quantum Chemistry, 2nd Edition

Chapter 11

The Pariser-Parr-Pople Model

11.1   Introduction

Propagator or Green’s function methods are employed in this chapter to analyze the many-electron problem in planar unsaturated molecules as treated within the Pariser-Parr-Pople (PPP) model. A derivation of the model in many-electron theory serves to demonstrate the nature of the approximations involved. Applications are presented for the case of weakly interacting atoms. A decoupling procedure for Green’s functions proposed by the authors is shown capable of yielding a correct description of this case.

Propagators have the advantage of giving direct information about transition energies and amplitudes from a reference state, but like density matrices, they suffer from a lack of simple ways generally to ensure so-called N-representability or correspondence to proper many-electron state vectors. Nevertheless, the propagator approach to semi-empirical many-electron theory appears to have certain advantages over other methods. Such treatment has led to useful relations between matrix elements in the PPP-model¹.

The molecular orbital method is a very flexible and often successful tool for analyzing electronic structure-dependent properties. Its deficiencies are intimately connected with the treatment of superpositions of configurations. In particular, the molecular orbital model is not satisfactory when the overlap between relevant valence orbitals on adjacent atoms is smaller than 1/2. This result was particularly well illustrated ...