Tight-binding model for carbon nanotubes from ab initio calculations

Influence of long-range interactions on quantum interference in molecular conduction. A tight-binding (Hückel) approach

When certain pairs of atoms in a π-conjugated molecule are connected with nanometer-scale source and drain electrodes, the remarkable quantum interference (QI) effect may arise. In this case, the electron transmission probability is significantly suppressed due to the QI effect. Tight-binding approaches, such as the Hückel molecular orbital (HMO) model, have revealed important features of this quantum phenomenon. However, important deviations from experiments and from more sophisticated calculations are known for a variety of cases. Here, we propose an extension of the HMO method to include non-nearest-neighbor interactions. Such long-range interactions (LRIs) are implemented in the HMO model in the form of a damping function that decays as the topological distance-the number of bonds separating two atoms-gets larger. The proposed model is further developed so that a geometric modification, i.e., the rotation around a single bond, can be taken into account. Our results show that LRI affects both the location of the antiresonance peak due to QI and the intensity of QI, even suppressing it in some cases. These results agree well with what was observed in a Density Functional based Tight-Binding (DFTB) study reported in the literature. These properties can be interpreted on the basis of a graph-theoretic path-counting model as well as the molecular orbital theory. In addition, the geometric LRI model is shown to reproduce the change of transmission as a function of rotation around the single bond separating two benzene rings in biphenyl, in agreement with what was observed in both experiment and DFTB calculation.

Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data

This work presents a technique for the chirality (n, m) assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n, m) with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m) of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.

Probing optical spectra of carbon nanotubes with external fields

Here we present a theoretical study of the interplay between electronic and optical properties of carbon nanotubes. External perturbations such as electric and magnetic fields are applied on the systems which are probed by parallel and perpendicularly polarized light sources. We demonstrate that the optical transitions can be fully controlled by the fields. Likewise, extra optical excitations can be induced in different energy ranges of the absorption spectra due to degeneracy splitting of the states. In most of the theoretical works developed in this realm, a remarkable discrepancy between the results obtained via the tight binding approximation and first principle calculations is found. The disagreement can be enhanced when external perturbation fields act on the tubes forcing the realization of demanding charge self-consistent calculations. In this sense, we profit from novel parametrization schemes for the tight binding approach to describe the optical response of nanotubes of any diameter size and with similar accuracy to density functional theory.