Method B

In the next approach, we tried to eliminate the contributions from the distant protons by only considering pairs of $({\bf r}_e-{\bf r}_{{\rm p}i},{\bf r}'_e-{\bf r}_{{\rm p}i})$ from the two open ends and the nearest proton. If the closest proton for the two ends is not the same then no pair is considered. The results from a simulation with the same parameter are given in Tab. 5.2. They show that the electrons are mainly in 1s ground state as expected. However, the drawback of this method is that it introduces a cut-off for the eigenstates displayed in Fig. 5.12, which is unphysical in the limit of high density, where one expects to find delocalized electronic states that cannot be represented by this approach.

Figure 5.12: Natural orbitals calculated with method B for the system studied in Fig. 5.11.