2
Ti V Cr Mn Fe Co Ni Cu Zn0
2
4
6
8Formation Energy E form  [eV] Empty Monovacancy
Empty Divacancy II
Empty Divacancy I
    Monovacancy     Divacancy I     Divacancy II
Carbon Nanotube Axis
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.
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
Eform[VC] = E[VC] + nE[C] −E[NT], (2)
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].
The adsorption energies for N 2, O 2, H 2O, CO, NH 3, and
H2S 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
Eads[X@M@VC] = E[X@M@VC] −E[X] −E[M@VC],
(3)
N 2
O 2
N 2
O 2
N 2
O 2
CO
2H O
3NH
2H S
CO
CO
2H O
3NH
2H S
2H O
3NH
2H S
N 2
O 2
N 2
O 2
N 2
O 2
CO
2H O
3NH
2H S
CO
CO
2H O
3NH
2H S
2H O
3NH
2H S MonovacancyDivacancy II Divacancy I
Divacancy II Divacancy I Monovacancy
Cr Fe Co Ni Cu ZnMnTi V
 0.0
(a) Adsorption Energy [eV]
−2.0 −1.5 −1.0 −0.5
Cr Fe Co Ni Cu ZnMnTi V
0.0 +0.5 +1.0
 0(b) Conductance Change [G  ]
−1.0 −0.5
FIG. 2: Calculated (a) adsorption energyEads in eV and (b) change in
conductance ∆G in units of G0 =2e2/h for N2, O2, H2O, CO, NH3,
and H 2S on 3d transition metals occupying a monovacancy (top),
divacancy I (middle), and divacancy II (bottom) in a (6,6) carbon
nanotube.
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.
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 O2 binds signiﬁcantly
stronger than any of the three target molecules on Ti, V , Cr,
and Mn (except for Cr in divacancy I where H 2S 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 H2O 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
Θ[X] = K[X]C[X]
1 + ∑
Y K[Y ]C[Y ], (4)
where K = k+/k−is the ratio of forward and backward rate
constants for the adsorption reaction,
K[X] = exp
[
−Eads[X] + TS [X]
kBT
]
. (5)
In these expressions C[X] is the concentration of species X,
S[X] is its gas phase entropy and T is the temperature. Ex-