0 4 8 12 16 0 4 8 12 Intratube Transmission 0 4 8 12 (a) (7,7) SWNT Junction (b) (12,0) SWNT Junction (c) (13,0) SWNT Junction Metallic Semimetallic Semiconducting 2 N HOMO 10 -4 10 -2 10 0 10 -4 10 -2 10 0 Intertube Transmission -4 -3 -2 -1 0 1 2 Energy (eV) 10 -4 10 -2 10 0 (d) (7,7) SWNT Junction (e) (12,0) SWNT Junction (f) (13,0) SWNT Junction Semiconducting Semimetallic Metallic ( ) ( ) 2 O HOMOs  2 O LUMOs FIG. 5: (Color online) (a)–(c) Intratube transmission and (d)–(f) intertube transmission vs energy in eV relative to the Fermi energy for a pristine (black solid curves) SWNT junction, and with N$_{2}$ (blue dashed curves), and O$_{2}$ (red dash-dotted curves) physisorbed consisting of [(a) and (d)] metallic (7,7) SWNTs, [(b) and (e)] semimetallic (12,0) SWNTs, and [(c) and (f)] semiconducting (13,0) SWNTs. Schematics and isosurfaces of ± 0.02 e / ˚ A 3 for molecular orbitals on the physisorbed molecules are shown above the corresponding eigenenergies (dotted lines). range 2.3—2.8 ˚ A, as given in Table I. These results agree qual- itatively with previous theoretical studies for O$_{2}$ binding dis- tances and energies on isolated SWNTs. 12–19 curs. This is only slightly smaller than the expected band gap of ∼ 0.7 eV, based on a d − 1 fit to experimental data. 36 These results for the intratube transmission of pristine SWNTs also agree qualitatively with previous DFT studies of isolated (5,5), (10,10), (10,5), (11,0), and (12,0) SWNTs. 25,37,38 We also find in Figs. 5(a)–5(c) that neither O$_{2}$ nor N$_{2}$ physisorbed at a SWNT junction noticeably influence the intratube trans- mission. In Fig. 5 we also show isosurfaces and eigenenergies for the highest occupied and lowest occupied molecular orbitals (HOMO and LUMO) on physisorbed O$_{2}$ and N$_{2}$. For these weakly coupled molecules, the renormalized molecular levels may easily be identified with the molecular orbitals of the free O$_{2}$ and N$_{2}$ molecules. 39 Since the position of the molecular Figures 5(a)-5(c) show the intratube transmission for three prototypical SWNTs commonly found in experimental HiPco samples, 35 as shown in Fig. 3. In Fig. 5(a) we see that for a metallic armchair (7,7) SWNT, transmission occurs through two channels at the Fermi level. We see in Fig. 5(b) that the conductance for the semimetallic zigzag (12,0) SWNT resembles that found in Fig. 5(a) for a metallic SWNT, ex- cept for a tiny band gap of ≲ 0.05 eV at the Fermi level. In Fig. 5(c) we find for a semiconducting zigzag (13,0) SWNT a band gap of approximately 0.6 eV between the valence and conduction bands, through which no transmission oc- 4