Atomistic simulations that calculate the atomic interactions on the fly from an electronic structure calculation using an independent particle approximation are nowadays the most important ab initio simulation scheme. A major limiting factor of this method is the cubic scaling of the algorithms used. Recently we presented an expression for the grand canonical potential describing a system of uncorrelated fermions [F. R. Krajewski and M. Parrinello, Phys. Rev. B 71, 233105 (2005)]. We found that this expression can be evaluated within a linear scaling computational effort using Monte Carlo methods, leading to linear scaling algorithms for metals and semiconductors [F. R. Krajewski and M. Parrinello, Phys. Rev. B 73, 041105 (2006)]. We also mentioned that for one-dimensional systems the electronic structure calculation can be performed within linear scaling with a deterministic algorithm. In this work we extend this idea and show that the electronic structure problem can be solved exactly within the linear scaling computational effort for quasi-one-dimensional systems, avoiding the application of Monte Carlo techniques and the resulting noise on the electronic properties. The linear scaling scheme is applied to various types of tight binding carbon nanotubes with up to ${10}^5$ atoms.

• Received 7 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.125107