Density functional study on the structural, electronic, and magnetic properties of 3d transition-metal-doped Au5 clusters

Density functional theory study of the structure, stability, magnetic properties, and (hyper)polarizability of (sub-nm) rare-earth (RE) doped gold clusters: Au5RE with RE = Sc, Y, La-Lu

Rare-earth doped materials are of immense interest for their potential applications in linear and nonlinear photonics. There is also intense interest in sub-nanometer gold clusters due to their enhanced stability and unique optical, magnetic, and catalytic properties. To leverage their emergent properties, here we report a systematic study of the geometries, stability, electronic, magnetic, and linear and nonlinear optical properties of Au5RE (RE = Sc, Y, La-Lu) clusters using density-functional theory. Several low-energy isomers consisting of planar or non-planar configurations are identified. For most doped clusters, the non-planar configuration is energetically favored. In the case of La-, Pm-, Gd-, and Ho-doped clusters, a competition between planar and non-planar isomers is predicted. A distinct preference for the planar configuration is predicted for Au5Eu, Au5Sm, Au5Tb, Au5Tm, and Au5Yb. The distinction between the planar and non-planar configurations is highlighted by the calculated highest frequencies, with the stretching mode of the non-planar configuration predicted to be stiffer than the planar configuration. The bonding analysis reveals the dominance of the RE-d orbitals in the formation of frontier molecular orbitals, which, in turn, facilitates retaining the magnetic characteristics governed by RE-f orbitals, preventing spin-quenching of rare earths in the doped clusters. In addition, the doped clusters exhibit small energy gaps between frontier orbitals, large dipole moments, and enhanced hyperpolarizability compared to the host cluster.

Systematic Investigation of the Structure, Stability, and Spin Magnetic Moment of CrM n Clusters (M = Cu, Ag, Au, and n = 2-20) by DFT Calculations

Binary clusters of transition-metal and noble-metal elements have been gathering momentum for not only advanced fundamental understanding but also potential as elementary blocks of novel nanostructured materials. In this regard, the geometries, electronic structures, stability, and magnetic properties of Cr-doped Cu _n , Ag _n , and Au _n clusters (n = 2-20) have been systematically studied by means of density functional theory calculations. It is found that the structural evolutions of CrCu _n and CrAg _n clusters are identical. The icosahedral CrCu₁₂ and CrAg₁₂ are crucial sizes for doped copper and silver species. Small CrAu _n clusters prefer the planar geometries, while the larger ones appear as on the way to establish the tetrahedral CrAu₁₉. Our results show that while each noble atom contributes one s valence electron to the cluster shell, the number of chromium delocalized electrons is strongly size-dependent. The localization and delocalization behavior of 3d orbitals of the chromium decide how they participate in metallic bonding, stabilize the cluster, and give rise to and eventually quench the spin magnetic moment. Moreover, molecular orbital analysis in combination with a qualitative interpretation using the phenomenological shell model is applied to reveal the complex interplay between geometric structure, electronic structure, and magnetic moment of clusters. The finding results are expected to provide greater insight into how a host material electronic structure influences the geometry, stability, and formation of spin magnetic moments in doped systems.

Design of superatomic systems: exploiting favourable conditions for the delocalisation of d-electron density in transition metal doped clusters

The incorporation of transition metals into superatomic species has led to the proposal of highly tailorable systems, with the transition metal atoms typically acting as magnetic dopants. However, the extent to which d-electrons are able to delocalise from their ionic cores has not been fully recognised. In this work a variety of systems have been explored using a range of exchange-correlation functionals commonly used to explore cluster species, to test the extent of d-electron delocalisation under favourable conditions. Early transition metals have been shown to readily delocalise their valence d-electrons for superatomic shell closing, with higher period atoms showing a greater tendency for delocalisation. Our findings also provide the framework for the design of superatomic systems with large numbers of electrons being contributed from a single atom.

5-Fold symmetry in superatomic scandium clusters: exploiting favourable orbital overlap to sequester spin

The geometries and electronic structures of icosahedral A₁₃^C (A = Sc, Y; C = 0, ±1, ±2) clusters have been determined at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters demonstrate a complex electronic structure which provides insight into the anomalously high magnetic moment of icosahedral group 3 clusters and further contextualises the role of transition metals and d-electrons within the superatomic model. Embedded deeply within the density of states for these clusters are typical superatom orbitals which are populated up to the 2S level. Above the 2S-state there are three states of apparent F symmetry, which are preferentially singly occupied, followed by an abundance of approximately degenerate P-, G-, D- and F-states at the Fermi energy, which are at most singly occupied. In spite of apparent angular symmetry and a nodal structure reminiscent of superatomic orbitals these states are actually formed from preferential overlap of the valence d-orbitals of the cluster atoms. This analysis was further contextualised through analysis of the Sc₁₉ cluster, which shows a similar construction of Kohn-Sham states, but with the breaking of 5-fold symmetry along one of its Cartesian axes. Finally, this work clearly demonstrates the ability of d-electrons to give rise to superatomic orbitals is not just constrained by atomic species but also by the local environment of the atoms.

On the influence of exact exchange on transition metal superatoms

The electronic structure of A7C (A = Hg, Pd, V, Cr, Mn, Fe, Ni, Cu; C = 0, ±1, ±2) clusters has been determined using density functional theory methods. The A7C (A = Hg, Pd, Cr, Cu; C = 0, ±1, ±2) clusters all conform to the existing superatomic model, with a sufficiently stabilised local structure to prevent perturbation upon the introduction of exact exchange to the exchange correlation functional. For the A7C (A = Mn, Fe, Ni; C = 0, ±1, ±2) clusters the incorporation of exact exchange separates the atomic s- and d-electrons, leading to a net increase in the number of superatomic electrons. Conversely the incorporation of exact exchange into the exchange correlation functional decreases the number of superatomic electrons for the V7C (C = 0, ±1, ±2) clusters, owing to the radial extension of the d-orbitals influencing their ability to contribute into superatomic shells.

On the involvement of d-electrons in superatomic shells: the group 3 and 4 transition metals

The geometries and electronic structures of small M₇^C (M = Sc, Y, La, Ti, Zr, Hf; C = 0, ±1, ±2) clusters have been calculated at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters conform to the existing superatom model, with some contextual differences. There are a range of states which are populated by the outermost s and d-electrons of the constituent atoms, with an irregular Aufbau rule for the states formed from the atomic d-electrons. The states comprised of d-electrons present themselves as two states of P-symmetry and two states of F-symmetry, which are nearly degenerate, followed by states of D-symmetry, a shell ordering which arises due to the symmetry, and favourable overlap, of the contributing states. The effect of exact exchange in modulating the localisation of these states is also discussed. In addition, this study shows pseudo-superatomic states which arise due to the 5-fold symmetry of the clusters, materialising as either a ring or plane of electron density. In summary, these observations allow for an expansion of the role that early transition metals have within the existing superatom framework.

Insights into the structural, electronic and magnetic properties of V-doped copper clusters: comparison with pure copper clusters

The structural, electronic and magnetic properties of Cu_n+1 and Cu_nV (n = 1–12) clusters have been investigated by using density functional theory. The growth behaviors reveal that V atom in low-energy Cu_nV isomer favors the most highly coordinated position and changes the geometry of the three-dimensional host clusters. The vibrational spectra are predicted and can be used to identify the ground state. The relative stability and chemical activity of the ground states are analyzed through the binding energy per atom, energy second-order difference and energy gap. It is found that that the stability of Cu_nV (n ≥ 8) is higher than that of Cu_n+1. The substitution of a V atom for a Cu atom in copper clusters alters the odd-even oscillations of stability and activity of the host clusters. The vertical ionization potential, electron affinity and photoelectron spectrum are calculated and simulated for all of the most stable clusters. Compare with the experimental data, we determine the ground states of pure copper clusters. The magnetism analyses show that the magnetic moments of Cu_nV clusters are mainly localized on the V atom and decease with the increase of cluster size. The magnetic change is closely related to the charge transfer between V and Cu atoms.