10 -3 10 -2 10 -1 10 0 10 -3 10 -2 10 -1 10 0 Fractional Coverage   of Ni Occupied Vacancies 0.1 1 10 100 CO Concentration [ppm] 10 -4 10 -3 10 -2 10 -1 10 0 O$_{2}$ CO CO Clean O$_{2}$ O$_{2}$ Clean (a) Monovacancy (b) Divacancy I (c) Divacancy II 10 2 10 3 0.1 1 10 100 CO Concentration [ppm] -10 1 0 10 1 Monovacancy Divacancy I Divacancy II Change in Resistance  $^{Δ}$R  [  / Ni Occupied Vacancy] (d) 3 conductances, i.e. G = ( G$_{↑}$ + G$_{↓}$ ) / 2. Next, we estimate the resistance of a CNT containing sev- eral impurities (a specific metal dopant with different molecu- lar adsorbates). Under the assumption that the electron phase- coherence length, l$_{φ}$ , is smaller than the average distance be- tween the dopants, d , we may neglect quantum interference and obtain the total resistance by adding the scattering resis- tances due to each impurity separately. The scattering resis- tance due to a single impurity is given by where G ( X ) is the Landauer conductance of the pristine CNT with a single metal dopant occupied by molecule X and 1 / ( 2 G$_{0}$ ) is the contact resistance of a (6,6) CNT. We may now obtain the total resistance per dopant site rel- ative to the reference background signal as a function of the target molecule concentration FIG. 3: Fractional coverage Θ in thermal equilibrium of Ni in a (a) monovacancy, (b) divacancy I, (c) divacancy II and (d) change in resistance Δ R per dopant site as a function of CO concentration in a background of air at room temperature and 1 bar of pressure. The reference concentration of CO is taken to be C$_{0}$ = 0.1 ppm. Note the change from linear to log scale on the y -axis at Δ R = 10 Ω . R$_{s}$ ( X ) = 1 /G ( X ) − 1 / ( 2 G$_{0}$ ) , (6) Δ R N ≈ ∑ X R$_{s}$ ( X )(Θ[ X,C ] − Θ[ X,C$_{0}$ ]) , (7) For a given background composition we may thus estimate the fractional coverages for each available adsorbate for a given type of doping. As an example, Fig. 3(a)-(c) shows the fractional coverage of a Ni atom occupying a monovacancy, divacancy I, and divacancy II, versus CO concentration in a background of air at room temperature and 1 bar of pressure. Due to the relatively small binding energy of N$_{2}$ and H$_{2}$O as compared to O$_{2}$ and CO, all Ni sites will be either empty or occupied by O$_{2}$ or CO. In particular, Ni in a monovacancy (top panel of Fig. 3) will be completely oxidized for all rel- evant CO concentrations. For the Ni occupied divacancy II structures we find the coverage of CO changes significantly around toxic concentrations ( ∼ 10 ppm). In Fig. 3(d) we show the change in resistance calculated from Eq. (7) as a function of CO concentration for Ni occu- pying the three types of vacancies. The background reference concentration of CO is taken to be C$_{0}$ = 0 . 1 ppm. For the monovacancy there is very little change in resistivity. This is because most active sites are blocked by O$_{2}$ at relevant CO concentrations, as shown in the upper panel of Fig. 3. For Ni in the divacancies there is, however, a change in resistance on the order of 1Ω per site. For concentrations above ∼ 1 ppm, the CO coverage of Ni in the divacancy II increases dramati- cally and this leads to a significant increase in resistance. where N is the number of dopants, Θ[ X,C ] is the fractional coverage of species X at concentration C of the target and C$_{0}$ is the reference concentration. Notice that the contact resis- tance drops out as we evaluate a change in resistance. We now return to the discussion of the validity of Eq. (7). As mentioned, the series coupling of individual scatterers should be valid when l$_{φ}$ < d . However, even for l$_{φ}$ > d and assuming that the Anderson localization length, l$_{loc}$ in the system exceeds l$_{φ}$ , Eq. (7) remains valid if one replaces the actual resistance R by the sample averaged resistance 〈 R 〉 [29]. At room temperature under ambient conditions, interac- tions with external degrees of freedom such as internal CNT phonons and vibrational modes of the adsorbed molecules would rapidly randomize the phase of the electrons. There- fore Eq. (7) should certainly be valid in the limit of low dop- ing concentrations. On the other hand, the total number of dopants, N , should be large enough for the statistical treat- ment of the coverage to hold. Finally, we stress that Eq. (7) represents a conservative estimate of the change in resistance. In fact, in the regime where l$_{φ}$ > l$_{loc}$ , i.e. in the Anderson localization regime, the resistance would be highly sensitive to changes in the fractional coverage of active sites. Calcula- tion of the actual resistance of the CNT in this regime would, however, involve a full transport calculation in the presence of To estimate the effect of adsorbates on the electrical con- ductance of doped CNTs, we first consider the change in con- ductance when a single molecule is adsorbed on a metal site of an otherwise pristine CNT. In Fig. 2(b) we show the calculated change in conductance relative to the metal site with no ad- sorbate. In contrast to the binding energies, there are no clear trends in the conductances. The sensitivity of the conductance is perhaps most clearly demonstrated by the absence of cor- relation between different types of vacancies, i.e. between the three panels in Fig. 2(b). Close to the Fermi level, the conduc- tance of a perfect armchair CNT equals 2 G$_{0}$ . The presence of the metal dopant leads to several dips in the transmission function known as Fano antiresonances [20]. The position and shape of these dips depend on the d -levels of the transi- tion metal atom, the character of its bonding to the CNT, and is further affected by the presence of the adsorbate molecule. The coupling of all these factors is very complex and makes it difficult to estimate or rationalize the value of the conduc- tance. For the spin polarized cases, we use the spin-averaged