N$_{2}$ O$_{2}$ N$_{2}$ O$_{2}$ N$_{2}$ O$_{2}$ CO $_{2}$O 3 NH 2 H S CO CO 2 H O 3 NH 2 H S 2 H O 3 NH 2 H S N$_{2}$ O$_{2}$ N$_{2}$ O$_{2}$ N$_{2}$ O$_{2}$ CO 2 H O 3 NH 2 H S CO CO 2 H O 3 NH 2 H S 2 H O 3 NH 2 H S Monovacancy Divacancy II Divacancy I Divacancy II Divacancy I Monovacancy Cr Fe Co Ni Cu Zn Mn Ti V 0.0 (a) Adsorption Energy [eV] −2.0 −1.5 −1.0 −0.5 Cr Fe Co Ni Cu Zn Mn Ti V 0.0 +0.5 +1.0  0 (b) Conductance Change [G ] −1.0 −0.5 Ti V Cr Mn Fe Co Ni Cu Zn 0 2 4 6 8 Formation Energy  E form  [eV] Empty Monovacancy Empty Divacancy II Empty Divacancy I Monovacancy Divacancy I Divacancy II Carbon Nanotube Axis 2 FIG. 2: Calculated (a) adsorption energy E$_{ads}$ in eV and (b) change in conductance Δ G in units of G$_{0}$ = 2 e $^{2}$/h for N$_{2}$, O$_{2}$, H$_{2}$O, CO, NH$_{3}$, and H$_{2}$S on 3d transition metals occupying a monovacancy (top), divacancy I (middle), and divacancy II (bottom) in a (6,6) carbon nanotube. FIG. 1: Structural schematics and formation energy for a 3d tran- sition metal occupied monovacancy (black), divacancy I (gray), or divacancy II (white) in a (6,6) carbon nanotube. Formation energies of the empty vacancies are indicated by dashed lines. where E [ X @M@VC] is the total energy of molecule X on a transition metal atom occupying a vacancy, and E [ X ] is the gas phase energy of the molecule. is the total energy of the pristine nanotube with a physisorbed transition metal atom. We have considered the monovacancy and two divacancies shown in Fig. 1. The energy required to form an empty vacancy is obtained from E$_{form}$ [ VC ] = E [ VC ] + nE [ C ] − E [ NT ] , (2) From the adsorption energies plotted in Fig. 2(a), we see that the earlier transition metals tend to bind the adsorbates stronger than the late transition metals. The latest metals in the series (Cu and Zn) bind adsorbates rather weakly in the divacancy structures. We also note that O$_{2}$ binds significantly stronger than any of the three target molecules on Ti, V, Cr, and Mn (except for Cr in divacancy I where H$_{2}$S is found to dissociate). Active sites containing these metals are therefore expected to be completely passivated if oxygen is present in the background. Further, we find H$_{2}$O is rather weakly bound to most of the active sites. This ensures that these types of sensors are robust against changes in humidity. In thermodynamic equilibrium [27], the coverage of the ac- tive sites follows from where E [VC] is the total energy of the nanotube with a va- cancy of n atoms. The calculated formation energies for the 3d transition met- als are shown in Fig. 1. From the horizontal lines we see that both divacancies are more stable than the monovacancy. This may be attributed to the presence of a two-fold coordinated C atom in the monovacancy, while all C atoms remain three-fold coordinated in the divacancies. When a transition metal atom occupies a vacancy, the strongest bonding to the C atoms is through its d orbitals [26]. For this reason, Cu and Zn, which both have filled d-bands, are rather unstable in the CNT. For the remaining metals, adsorption in the monovacancies leads to quite stable structures. This is because the three-fold coor- dination of the C atoms and the CNT’s hexagonal structure are recovered when the metal atom is inserted. On the other hand, metal adsorption in divacancies is slightly less stable because of the resulting pentagon defects, see upper panel in Fig. 1. A similar behaviour has been reported by Krasheninnikov et al. for transition metal atoms in graphene [21]. where K = k$_{+}$/k$_{−}$ is the ratio of forward and backward rate constants for the adsorption reaction, The adsorption energies for N$_{2}$, O$_{2}$, H$_{2}$O, CO, NH$_{3}$, and H$_{2}$S on the metallic site of the doped (6,6) CNTs are shown in Fig. 2(a). The adsorption energy of a molecule X is defined by In these expressions C [ X ] is the concentration of species X , S [ X ] is its gas phase entropy and T is the temperature. Ex- perimental values for the gas phase entropies have been taken from Ref. [28]. Θ[ X ] = K [ X ] C [ X ] 1 + ∑ Y K [ Y ] C [ Y ] , (4) K [ X ] = exp$^{[}$ − E$_{ads}$ [ X ] + TS [ X ] k$_{B}$T ] . (5) E$_{ads}$ [ X @M@VC ] = E [ X @M@VC ] − E [ X ] − E [ M@VC ] , (3)