5 only slightly, also in qualitative agreement with experiment, 5 as shown in Fig. 2. Although it is well-known DFT calculations underestimate band gaps, 37,42,43 since we are primarily interested in how the presence of O$_{2}$ or N$_{2}$ qualitatively changes the DOS and con- ductance, such calculations are still useful. levels is rather insensitive to the type of junction, it should also be insensitive to the exact binding geometry. This sug- gests that additional physisorbed molecules will influence the intertube transmission similarly. We find the intertube transmission is proportional to the density of states (DOS) for the system with peaks in the transmission at the van Hove singularities. This is consistent with transport between the SWNTs occurring in the tunneling regime, as expected for a SWNT separation of approximately 3.4 ˚ A. The presence of physisorbed molecules in the SWNT- SWNT gap should then increase the tunneling probability at energies near the eigenenergies of the molecular orbitals. This is evidenced by the distinct peaks in the intertube transmis- sion for each SWNT junction at energies corresponding to the HOMO of N$_{2}$ and the spin polarized HOMOs and LUMOs of O$_{2}$, as seen in Figs. 5(d)–5(f). Under such conditions, a SWNT junction behaves as a simple tunneling electron mi- croscopy (TEM) tip. By applying appropriate bias voltages, one may potentially probe the molecular orbitals of a ph- ysisorbed molecule to determine its chemical composition. For this reason, the sensitivity of SWNT network conduc- tivity to O$_{2}$ is at least partly due to the close proximity of the O$_{2}$ HOMOs to the Fermi energies of typical SWNTs ( ≈ 0.6 eV), as shown in Fig. 5. Further, it has been shown experi- mentally that defects inherent in physically realizable SWNTs yield p -type semiconductors. 1,40,41 The conductivity measured experimentally at small bias is thus at the energy of the va- lence band ε$_{VB}$ . In conclusion, we have proposed a possible microscopic ex- planation for the experimentally observed sensitivity of the electrical conductance of carbon nanotube networks to oxy- gen and nitrogen gases. Our DFT calculations suggests that O$_{2}$ and N$_{2}$ physisorbed in crossed SWNT junctions can have a large influence on the intertube conductance. In particular, for O$_{2}$ the close proximity of the highest occupied molecular orbitals with the Fermi level of the SWNT significantly in- creases electron tunneling across the gap. The effect is found to be larger for O$_{2}$ than for N$_{2}$ and for semiconducting rather than metallic SWNTs, in agreement with the experimental ob- servations. Our results suggests that the electrical properties of SWNT networks are to a large extent determined by crossed SWNT junctions. We thank E. I. Kauppinen, and K. W. Jacobson for useful discussions. D.J.M. and K.S.T. acknowledge financial support from NABIIT and the Danish Center for Scientific Comput- ing under Grant No. HDW-1103-06. The Center for Atomic- scale Materials Design (CAMD) is sponsored by the Lund- beck Foundation. C. M. acknowledges financial support from the National Physical Laboratory (NPL) and the Engineering and Physical Sciences Research Council (EPSRC-GB). As seen in Fig. 5(f), the O$_{2}$ HOMO eigenenergy is only about 0.3 eV below ε$_{VB}$ for a semiconducting (13,0) SWNT junction. 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