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The electric polarizability and the spread of the total position tensors areused to characterize the metallic vs insulator nature of large (finite)systems. Finite clusters are usually treated within the open boundary conditionformalism. This introduces border effects, which prevents a fast convergence tothe thermodynamic limit and which can be eliminated within the formalism ofperiodic boundary conditions. Recently, we have introduced an original approachto periodic boundary conditions, named Clifford Boundary Conditions. Itconsiders a finite fragment extracted from a periodic system and themodification of its topology into that of a Clifford Torus. The quantityrepresenting the position is modified in order to fulfill the systemperiodicity. In this work, we apply the formalism of Clifford BoundaryConditions to the case of Carbon Nanotubes, whose treatment results to beparticularly simple for the Zigzag geometry. Indeed, we demonstrate that at theH\"uckel level these nanotubes, either finite or periodic, are formallyequivalent to a collection of {\em non-interacting dimerized linear chains},thus simplifying their treatment. This equivalence is used to describe somenanotube properties as the sum of the contributions of the independent chainsand to identify the origin of peculiar behaviors (such as the conductivity).Indeed, if the number of hexagons along the circumference is a multiple ofthree a metallic behavior is found, namely a divergence of both the (perelectron) polarizability and total position spread of at least one linearchain. These results are in agreement with those in the literature fromTight-Binding calculations.

Mapping of H\"uckel Zigzag Carbon Nanotubes onto independent Polyene chains: application to periodic Nanotubes