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note
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10 shows that at relatively low concentrations of addends the shift is negligible. Using our tight-binding calculations, we estimate that the shift is about 0.13 eV for 25% periodically functionalized (6, 6) tube with F addends. This shift will not affect the conclusions of our present study as we can see from the window of energy ranges we studied in Figure 2 and Figure 3. Also in our conductance calculations, we did not take into account the effect of spin polarization due to the unpaired election with F or COOH addends. From our ab initio calculations, we found that total energy difference between the result calculated from spin-polarized GGA calculation and that from the unpolarized GGA is only about 0.1 eV (with 1 F and 40 carbon atoms of the (5, 5) tube). Moreover, the energy difference between the spin doublet state and spin quartet state is found to be about 0.4 eV (with 1 COOH and 120 carbon atoms of the (5, 5) tube), indicating that high-spin states are not favorable. Therefore, we believe that the spin polarization effect is small and negligible in our formalism and would not affect our qualitative conclusions.
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