Single- and multi-walled carbon nanotubes viewed as elastic tubes with Young's moduli dependent on layer number

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333 (1992)\rbrack and shows to be content with the classic shell theory by which the Young's modulus, the Poisson ratio and the effective wall thickness of SWNTs are obtained as $Y=4.70$TPa, $\nu=0.34$, $h=0.75{\rm \AA}$, respectively. The elasticity of a multi-walled carbon nanotube (MWNT) is investigated as the combination of the above SWNTs of layer distance $d=3.4 {\rm \AA}$ and the Young's modulus of the MWNT is found to be an apparent function of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$.Comment: 4 pages, 1 figur

Quadratically convergent algorithm for fractional occupation numbers

International audienceThe numerical solution of the electronic structure problem in Kohn-Sham density functional theory may in certain cases yield fractional occupancy of the single-particle orbitals. In this paper, we propose a quadratically convergent approach for simultaneous optimization of orbitals and occupancies in systems with fractional occupation numbers (FONs). The starting guess for orbitals and FONs is obtained via the relaxed constraint algorithm. Numerical results are presented for benchmark cases. © 2003 American Institute of Physic

An ab initio study of PuO 2±0.25 , UO 2±0.25 , and U 0.5 Pu 0.5 O2±0.25

Hybrid density functional theory has been used to systematically study the electronic, geometric, and magnetic properties of strongly correlated materials PuO2±x, UO2±x, and U0.5Pu0.5O2±x with x = 0.25. The calculations have been performed using the all-electron full- potential linearized augmented plane wave plus local orbitals basis (FP-L/APW+lo) method. Each compound has been studied at the ferromagnetic (FM) and anti-ferromagnetic (AFM) configurations with and without spin-orbit coupling (SOC) and full geometry optimizations. The optimized lattice constants, bulk moduli, and band gaps are reported. Total energy calculations indicate that the ground states are AFM for all compounds studied here and the band gaps are typically higher than 1.0 eV, characteristic of semiconductors. The total energy is lowered significantly and the band gaps increase with the inclusion of SOC. The chemical bonds between the actinide metals and oxygen atoms are primarily ionic in character