A time-dependent density-functional-theory (TD-DFT) approach is employed to investigate theoretically the optical response of Au nanoclusters of size around N = 150 atoms as a function of: (a) the approximation used for the DFT exchange-correlation (xc-) functional, (b) the shape of the nanocluster. The results of the local-density-approximation (LDA) and the van Leeuwen-Baerends (LB94) xc-functionals are compared on a set of 4 structural motifs: octahedral (N = 146), cuboctahedral (N = 147), icosahedral (N = 147), and cubic (N = 172), representative of both crystalline and noncrystalline motifs commonly encountered in the study of metal nanoclusters. It is found that the position of the peak in the photoabsorption spectrum is weakly dependent on the shape of the cluster but is strictly related to its size and to the DFT xc-functional used in the calculations, with the finding that the predictions of the LB94 xc-functional compare better with the available experimental data on the absorption spectrum of Au particles in this size range with respect to those of the LDA xc-functional. The detailed shape of the cluster becomes apparent in the form of the absorption spectrum, which can be symmetric or asymmetric in two different forms.

The optical properties of alloyed AgÀAu 147-atom cuboctahedral nanoclusters are theoretically investigated as a function of composition and chemical ordering via a time-dependent density functional theory (TDDFT) approach. Compositions 37À63%, 46À54%, and 63À37%, in AgÀAu, and three types of chemical ordering, coreÀshell, multishell and maximum mixing, are considered. Additionally, the optical spectra of pure Ag clusters with several structural motifs are also studied. It is found that (a) pure Ag clusters exhibit a neater dependence of the absorption peak on the shape of the cluster than Au clusters, (b) the absorption spectrum of alloyed clusters is not strongly affected by changes in chemical ordering, possibly because of their limited size, and (c) the optical absorption peak smoothly shifts to higher energies, gets narrower, and substantially gains in intensity by increasing Ag concentration, in excellent agreement with available experimental data. An analysis of the character of the electronic transitions mostly contributing to the absorption peak allows us to rationalize the notable difference between Ag and Au in terms of optical properties and the effect of alloying.

The construction of the exact quantum propagator of a particle subjected to a constant force offers a challenge to existing propagator methodology. Here, besides considering the traditional approach, which involves an expansion in the complete set of energy eigenstates, we illustrate (i) the merits of a rather more elegant procedure founded on the ‘‘disentanglement’’ of the time-evolution operator and (ii) the power of a general treatment based on a time-dependent variational approach.

In this paper we construct infinite families of non-linear maximum rank distance codes by using the setting of bilinear forms of a finite vector space. We also give a geometric description of such codes by using the cyclic model for the field reduction of finite geometries and we show that these families contain the non-linear maximum rank distance codes recently provided by Cossidente, Marino and Pavese.

Let A and B be two points of PG(2, q n ), and let be a collineation between the pencils of lines with vertices A and B. In this paper, we prove that the set of points of intersection of corresponding lines under is either the union of a scattered GF(q)-linear set of rank n + 1 with the line AB or the union of q − 1 scattered GF(q)-linear sets of rank n with A and B. We also determine the intersection configurations of two scattered GF(q)-linear sets of rank n + 1 of PG(2, q n ) both meeting the line AB in a GF(q)-linear set of pseudoregulus type with transversal points A and B.

We study intriguing sets in partial quadrangle

In this paper we study sets $X$ of points of both affine and projective spaces over the Galois field $\mathop{\rm{GF}}(q)$ such that every line of the geometry that is neither contained in $X$ nor disjoint from $X$ meets the set $X$ in a constant number of points and we determine all such sets. This study has its main motivation in connection with a recent study of neighbour transitive codes in Johnson graphs by Liebler and Praeger [Designs, Codes and Crypt., 2014]. We prove that, up to complements, in $\mathop{\rm{PG}}(n,q)$ such a set $X$ is either a subspace or $n=2,q$ is even and $X$ is a maximal arc of degree $m$. In $\mathop{\rm{AG}}(n,q)$ we show that $X$ is either the union of parallel hyperplanes or a cylinder with base a maximal arc of degree $m$ (or the complement of a maximal arc) or a cylinder with base the projection of a quadric. Finally we show that in the affine case there are examples (different from subspaces or their complements) in $\mathop{\rm{AG}}(n,4)$ and in $\mathop{\rm{AG}}(n,16)$ giving new neighbour transitive codes in Johnson graphs.

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