13C NMR Chemical Shifts of Single-Walled Carbon
The properties, separation and potential
applications of SWNTs are
currently under intense study. The wide
range of proposed applications stems from the fact that carbon
nanotubes have a diverse range of weights, electronic structures,
helicities and so forth. Considerable effort has been placed into
determining the experimental parameters that affect the molecular
architecture of the tubes. However, such efforts have been hampered by
the fact that even a combination of many experimental techniques does
not fully characterize a given sample.
One of the most versatile experimental tools to study the geometry and
electronic structure of molecules and
solids is nuclear magnetic resonance (NMR). Calculated 13C
NMR chemical shifts of different SWNTs
might be useful in helping experimentalists characterize the contents
of a given sample. Eventually, it might even
be possible to predict the widths and shapes of NMR signals from
nanotube samples with different
compositions using the data obtained from ab initio
calculations. To this end, we have performed
Density Functional Theory (DFT) calculations on finite and infinite
We have calculated the electronic structure and NMR chemical shifts of
larger (9,0) tubes capped either by half of a fullerene hemisphere or
by hydrogen . The results indicate
that the former is a small gap semi-conductor, in agreement with other
theoretical and experimental
work. The latter, on the other hand, was found to be metallic. The
chemical shift of the (9,0) tube
was predicted to be about 130 ppm. This value was estimated to be an
upper bound with an error of about
5 ppm. Taking into account previous theoretical studies , the
chemical shifts of metallic tubes were
estimated to be around 141 ppm.
Recently, we have computed the chemical shifts of a number of infinite (n,0)
SWNTs with 7 ≤ n ≤ 17 . Such tubes may be subdivided
into three families
characterized by Λ=mod(n,3). For the Λ=1, 2 families it was
previously found  that the chemical shifts δ can be fitted
well by the function
where D is the tube's diameter, B is the chemical shift
limit for infinite diameter and A(Λ) is a constant depending
upon the nanotube family. The calculated shifts are given below in Fig.
We have also studied the
small band gap (9,0), (12,0) and (15,0) species which were calculated
to have a significantly lower shift
than the other two families. However, it remains to be determined how
to identify these tubes from
large diameter members with Λ=1, 2. Moreover, we have found that it is
to compare the results of infinite and finite calculations if benzene
is used as the internal "computational" reference. For the (9,0) tube
capping was found to have a large effect on
the calculated shifts.
Fig. 1. Calculated chemical shifts of various SWNTs as a
function of the optimized tube diameter.
Currently we are studying the effects of functionalization, defects,
helicity and finite-size on the NMR chemical shifts of SWNTs.
Eventually, a study of metallic tubes is also planned.
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