3.1 5-AGNRs. Figure summarizes the present results for the 5-AGNRs (or 2x AGNRs) which, as mentioned earlier, have been also studied by several groups. as the energy separation of the end states. Obviously, for an open singlet ground state both definitions are equivalent, but this is not the case. As we can see in Fig. (a), the "one-body" ΔΕac=|(HOMO-1)-(LUMO+1)| gap after the discontinuity (or transition) at L≈100Å, which we have discussed in detail in a previous work, starts opening up at Lc, contrary to the "onebody" ΔΕzz (i.e., the open singlet HOMO-LUMO gap) which varies slowly and smoothly over the entire range of lengths. This is very strange indeed, if ΔΕzz is going to represent the real separation of the edge states, since ΔΕzz first appears at and after the transition at Lc. Such behaviour (smooth variation) should be better suited for ΔΕac. This is indeed verified in Fig. , which shows the HOMO-LUMO gap of the "edge modified AGNRs", which seems to saturate to the value of 1.22 eV, very close to the value of 1.25 eV, suggested from the behavior of the "normal" AGNRs in Fig.