ON THE SIZE-DEPENDENCE OF THE STATIC SELF-ENERGY IN PROPAGATOR CALCULATIONS

Various approximations are used currently to evaluate the static part Sigma(infinity) 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 Sigma(infinity) 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 Sigma(infinity), 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. (C) 1995 American Institute of Physics.