The interaction of Cr(CO)3 on the (n, 0) nanotube side-walls: a density functional study through a cluster model approach

Density functional calculations have been performed to investigate the functionalization of single-wall carbon nanotubes (SWNTs) with the Cr(CO)₃ metal fragment, employing extended molecular models. A circumcoronene molecule (C₅₄H₁₈), made by the fusion of 19 hexagonal carbon rings, can be regarded as a fragment of a graphene sheet. To reproduce the curvature of the SWNT surface, suitable geometric constraints have been imposed on the C₅₄H₁₈ model, freezing the positions of the outer hydrogens along the directions of the nanotube C-C bonds. Geometry optimizations have then been performed under this constraint on the Cr(CO)₃-C₅₄H₁₈ complexes, pointing out the most favourable coordination sites on the hexagonal rings of the carbon atom surface and the electronic properties of the resulting system. The effect of the curvature on the metal coordination to nanotubes has been analysed by investigating the interaction of the Cr(CO)₃ metal complex with the C₅₄H₁₈ molecules, modelling (n, 0) nanotubes with different degrees of curvature, i.e. with various values of the chiral vector (n, 0).     

Stability, Convergence, and Conditioning of Stationary Iterative Methods of the Form x(I+1)=Px(I)+q for the Solution of Linear Systems

A statistical approach to the study of the stability of a stationaryiterative method for solving a linear system x=Px+q is studied.An asymptotic stability factor is introduced. The relationsbetween this stability measure, the spectral radius of the iterationmatrix, and the condition number of the system are studied.The special case when the iteration matrix is normal is treatedseparately from the general one. For iteration matrices thatare normal, the following logical implications are found: large condition number large asymptotic stability factor poorconvergence. In the general case, a large asymptotic stability factor doesnot imply poor convergence, i.e.: large condition number large asymptotic stability factor poorconvergence.     

Structure of phosphorus-selenium glasses: results from ab initio molecular dynamics simulations

Car-Parrinello molecular dynamics calculations have been carried out for phosphorus-selenium mixtures of compositions corresponding to overall stoichiometrics PSe and P₂Se. Comparison of the calculated structure factors with those obtained in neutron scattering experiements suggests that the real materials are characterized by the presence of substantial numbers of well defined molecular units.     

Computation of the acetone ultraviolet spectrum in gas phase and in aqueous solution by a mixed discrete/continuum model

The ultraviolet spectrum of acetone in vacuum and in aqueous solution has been computed by different quantum mechanical methods coupled to the polarizable continuum model (PCM) for describing bulk solvent effects. The results in vacuo show that the time-dependent density functional theory (TDDFT) approach using the PBEO functional reproduces quite well the result obtained at the CASPT2 level. Supermolecule computations confirm that water molecules belonging to the first shell of polar groups (here the carbonyl oxygen) must be explicitly included in the quantum mechanical treatment, whereas the effect of other solvent molecules (which is far from being negligible) can be reliably described by the PCM. Moreover, statistical averaging effects have been taken into account by performing canonical molecular dynamics (MD) simulations followed by TDDFT quantum mechanical computations on representative clusters of increasing dimensions immersed in a polarizable continuum. The results show that the combined MD/DFT/PCM approach is reliable and effective, although the performances of the force field used in the MD simulations must be further investigated.