The size-extensitivity of correlation energy estimators based on effective characteristic polynomials

Estimators $\Pi n$ for the correlation energy can be computed as roots of effective characteristic polynomials of degree $n$. The coefficients of these polynomials are derived from the terms of the perturbation series of the energy. From a fourth-order M{\o}ller-Plesset (MP4) calculation one can calculate with negligible effort a size-extensive estimator $\Pi 2$ that is in many cases much closer to the full CI correlation energy of the ground state than the MP4 value. [H.H.H. Homeier, J. Mol. Struct. (Theochem) 366, 161 (1996)] Here, we prove that the estimators $\Pi n$ for $n>2$ are size-extensive if they are calculated from the MP series.