Chemical ordering in magic-size Ag–Pd nanoparticles

Abstract

Chemical ordering in magic-size Ag-Pd nanoalloys is studied by means of global optimization searches within an atomistic potential developed on the basis of density functional theory calculations. Ag-rich, intermediate and Pd-rich compositions are considered for fcc truncated octahedral, icosahedral and decahedral geometric structures. Besides a surface enrichment in Ag, we find a significant subsurface enrichment in Pd, which persists to quite high temperatures as verified by Monte Carlo simulations. This subsurface Pd enrichment is stronger in nanoparticles than in bulk systems and is rationalized in terms of the energetics of the inclusion of a single Pd impurity in an Ag host nanoparticle. Our results can be relevant to the understanding of the catalytic activity of Ag-Pd nanoparticles in those reactions in which subsurface sites play a role.

Depicting electronic distributions from accurate computational first principles: On the relationship between the complex patterns of bonding interaction and the back‐donation phenomenon

“…[25,35] The nature of the information contained in these quantities or topologic population analysis is supported in the QTAIM of Bader's theory. [25,35] The multiatomic magnitudes within the present approach, which are relevant to our study, are the covalent bond order (two-center bond populations), I XAXB and the three-center bond population contributed by all possible populations shared by three centers, I XAXBXC defined by [24,25,36,37] I XAXB 5 X i;j;k;l…”

“…It is worthy to emphasize that the tools we use here perform an attempt to extract the information contained in the ab initio N-electron state function at any theoretical level of approximation from their associated electron density and not from the use of molecular orbital models. To this end, such information may be transferred toward the fundamental chemical concepts that will be carried out by determining the classical descriptors of chemistry, as atomic charges, covalent bond orders, valences among others and the nonclassical 2e-3c populations (integrated or nonlocal formulation), [24][25][26] and by local descriptors like critical points of the electron densities, that is, total, paired, and unpaired ones, and/or of their Laplacian fields (local formulation). [8][9][10] These two formulations are complementary each other to assess the information contained in the density and hence allowing an electronic description of the systems in a qualitative and also a quantitative man-ner.…”

Donor‐acceptor interactions: Transition metal carbonyl group ligand [TM(CO)6]qcomplexes. A case study at correlated level from the topological density point of view

“…[24,25,46] Let us now introduce the magnitudes relevant to the present research within the topological framework. Covalent bond order (two-center bond populations) I ΩAΩB and the three-center bond population I ΩAΩBΩC populations shared by three centers, become expressed as [36,37,45,47]…”

“…ΩAΩBΩC indicates that all possible three-center electron populations are considered as its formula shows; Ω A and Ω B stand for the Bader's atomic domains in the physical space; [24,25,[45][46][47] n i the occupation number of the i-th natural orbital as well as S ij (Ω A ) the matrix elements of the overlap matrix over the physical domain Ω A in the orthonormal natural basis set {i, j, k, l, …}. [36,45,47] The symbol P…”

“…For an adequate understanding of the physico-mathematical information obtained from the calculations, this is transferred to the language of the fundamental chemical concepts that determine the classical magnitudes (descriptors) of chemistry, such as atomic charges, covalent bond orders, valences among others and their extensions to the case of nonclassical populations 2e-3c and 4e-3c. [35][36][37][38] In addition, the values of the electron density fields, that is, total, pairing and unpairing ones, their cps and the values of their Laplacian fields are considered as being the local descriptors. [32,39] They are complementary to nonlocal or integrated ones in order to provide a qualitative and also quantitative density description, out of the traditional chemical information aforementioned.…”