Method D

Another alternative to deal with the contributions from multiple protons can be constructed by using the center of mass of the open polymer in order to select the appropriate proton. We suggest to calculate the center of mass coordinate of the open paths and select the protons, whose center of mass is closest. Then we consider only the separation of the open ends to this proton. This method has the advantage that every open path configuration leads to only one contribution, that it does lead to some localization of the generated pairs without introducing a sharp cut-off, which would be inappropriate for the analysis of delocalized state such as plane waves. We think that this procedure as well as method C should to be pursued further in order to construct the natural orbitals in a dense many-particle system. Appendix