On the size-dependence of the static self-energy in propagator calculations

Various approximations are used currently to evaluate the static part Σ(∞) of the self-energy or optical potential in molecular Green’s function calculations. Since its expansion is ruled out by the linked-cluster theorem, one generally assumes a size-intensive behavior of Σ(∞) in the thermodynamic limit of an infinite system. A detailed analysis of this size-dependence property is conducted using the formulation of crystalline orbitals (CO) for stereoregular polymers. In spite of the linked-cluster theorem, this study provides evidence for a logarithmic divergence with respect to the size of a chain for some forms of Σ(∞), computed with common approximation schemes. This is the direct outcome of the long-range character of the Coulombic interaction and can be related to a violation in the number of particles within the system. A proper size-intensive behavior implies an exact cancellation of the logarithmically divergent behavior of antigraphs. The conclusions drawn from CO analysis are confirmed by numerical tests on model oligomer systems.