Nearly-free-electron gas in a silicon cage

A systematic study of the ground state geometries, electronic structure, and stability of the metal (M) encapsulated MSi12 (M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni) clusters has been carried out within a gradient-corrected density functional formalism. It is shown that the ground state of most MSi12 clusters has the lowest spin multiplicity as opposed to the high spin multiplicity in free transition metal atoms. Consequently, a proper inclusion of the spin conservation rules is needed to understand the variation of the binding energy of M to Si12 clusters. Using such rules, CrSi12 and FeSi12 are found to exhibit the highest binding energy across the neutral while VSi−12 has the highest binding energy across the anionicMSi−12 series. It is shown that the variations in binding energy, electron affinity, and ionization potential can be rationalized within an 18-electron sum rule commonly used to understand the stability of chemical complexes and shell filling in a confined free-electron gas

Electronic counting rules for the stability of metal-silicon clusters

First principles electronic structure calculations have been carried out to examine the stability of cationic, neutral, and anionic MSi15, MSi16, and MSi17 (M=Sc, Ti, and V) clusters. ScSi16−, TiSi16, and VSi16+ are found to be particularly stable in agreement with recent experiments. It is shown that the enhanced stability can be reconciled within a model where each Si atom coordinated to the metal contributes one electron to the valence pool. Clusters where the total number of valence electrons obtained by summing one electron from each Si site coordinated to metal atom and the valence electrons of the metal attain 20 are found to be particularly stable. Combined with the earlier reported stability at 18 electrons, it is proposed that such valence pools might be looked upon as a nearly free electron gas inside a silicon cage

Magnetism of electrons in atoms and superatoms

The quantum states of electrons in small symmetric metallic clusters are grouped into shells similar to the electronic shells in free atoms, leading to the conceptual basis for defining superatoms. The filling of the electronic shells in clusters, however, do not follow Hund\u27s rule and usually result in non-magnetic species. It is shown that by embedding a transition metal in group II atoms, one can stabilize superatoms with unpaired electronic supershells. We demonstrate this intriguing effect through electronic structure studies of MnSrn (n = 6-12) clusters within first principles generalized gradient calculations. The studies identify an unusually stable magnetic MnSr9 species with a large exchange splitting of 1.82 eV of the superatomic D-states. It is shown that the exchange split d-states in the Mn atom induce exchange splitting in S and D superatomic shells because of the hybridization between orbitals of selected parity. The magnetic MnSr9cluster with 25 valence electrons has filled 1S2, 1P6, 1D10, 2S2 shells, making it highly stable, and an open shell of 5 unpaired D electrons breeding the magnetic moment. The stable cluster is resistant to collapse as two motifs are united to form a supermolecule

Enhanced magnetic moments of alkali metal coated Sc clusters: New magnetic superatoms

It is shown that the magnetic moments of Sc atoms can be significantly enhanced by combining them with alkali atoms. We present results of first principles electronic structure calculations of ScNan (1≤n≤12) clusters that indicate that a ScNa12 cluster consisting of a Sc atom surrounded by 12 Na atoms forming a compact icosahedral structure has a spin magnetic moment of 3μB that is three times that of an isolated Sc atom. This unusual behavior is analyzed in terms of the filling of the supershells 1S, 1P,… controlled by the nature and size of the alkali atoms and the more localized Sc 3d orbitals that hybridize weakly with Na sp orbitals. It is shown that even larger magnetic moments could be attained by controlling the relative position of 1S, 1P, and 3d states. Indeed, our studies indicate large magnetic moment five times that of an isolated Sc atom in the ScK12 and ScCs12 clusters, in which the 3d orbitals of Sc adopt a half-filled configuration, while the clusters are stabilized by filled 1S2, 1P6, and 2S2 shells, the features making them as new magnetic superatoms

Structural changes of Pd-13 upon charging and oxidation/reduction

First-principle generalized gradient corrected density functional calculations have been performed to study the stability of cationic and anionic Pd13 +/−, and neutral Pd13O2 clusters. It is found that while cationic Pd13 + favors a C s geometry similar to the neutral Pd13, both anionic Pd13 − and neutral Pd13O2 favor a compact ∼I h structure. A detailed analysis of the electronic structure shows that the stabilization of the delocalized 1P and 2P cluster orbitals, and the hybridization of the 1D orbitals with the oxygen atomic p orbitals play an important role in the energetic ordering of C s and ∼I h isomers. A structural oscillation is predicted during an oxidation/reduction cycle of Pd13 in which small energy barriers between 0.3 and 0.4 eV are involved

Metallic and molecular orbital concepts in XMg8 clusters, X = Be-F

The electronic structure and stability of the XMg8 clusters (X = Be, B, C, N, O, and F) are studied using first principles theoretical calculations to understand the variation in bonding in heteroatomic clusters which mix simple divalent metals with main group dopants. We examine these progressions with two competing models, the first is a distorted nearly free electron gas model and the second is a molecular orbital picture examining the orbital overlap between the dopant and the cluster. OMg8 is found to be the most energetically stable cluster due to strong bonding of O with the Mg8 cluster. BeMg8 has the largest HOMO-LUMO gap due to strong hybridization between the Mg8 and the Be dopant states that form a delocalized pool of 18 valence electrons with a closed electronic shell due to crystal field effects. Be, B, and C are best described by the nearly free electron gas model, while N, O, and F are best described through molecular orbital concepts

Highly efficient (Cs8V) superatom-based spin-polarizer

Quantum transport through molecules and the possibility to manipulate spin has generated tremendous excitement. Here, we demonstrate unusual spin transport through a molecule of twoCs8V magnetic superatoms. Calculations based on density functional theory and nonequilibrium Green’s function methods find a much higher current for the spin-down charge carriers relative to the spin-up carriers in the model Au–(Cs8V)–(Cs8V)–Au device system with almost 100% spin polarization, indicating a highly efficient spin polarizer. The new behavior is rooted in strong coupling of the localized magnetic core on V and the itinerant electrons of the Cs shell atoms leading to nearly full spin polarization

Photoelectron imaging and theoretical investigation of bimetallic Bi1–2Ga−0–2 and Pb−1–4 cluster anions

We present the results of photoelectron velocity-map imaging experiments for the photodetachment of small negatively charged BimGan (m=1–2, n=0–2), and Pbn (n=1–4) clusters at 527 nm. The photoelectron images reveal new features along with their angular distributions in the photoelectron spectra of these clusters. We report the vertical detachment energies of the observed multiple electronic bands and their respective anisotropy parameters for the BimGan and Pbn clusters derived from the photoelectron images. Experiments on the BiGan clusters reveal that the electron affinity increases with the number of Ga atoms from n=0 to 2. The BiGa−2 cluster is found to be stable, both because of its even electron number and the high electron affinity of BiGa2. The measured photoelectron angular distributions of the BimGan and Pbn clusters are dependent on both the orbital symmetry and electron kinetic energies. Density-functional theory calculations employing the generalized gradient approximation for the exchange-correlation potential were performed on these clusters to determine their atomic and electronic structures. From the theoretical calculations, we find that the BiGa−2, Bi2Ga−3 and Bi2Ga−5 (anionic), and BiGa3, BiGa5, Bi2Ga4 and Bi2Ga6(neutral) clusters are unusually stable. The stability of the anionic and neutral Bi2Gan clusters is attributed to an even-odd effect, with clusters having an even number of electrons presenting a larger gain in energy through the addition of a Ga atom to the preceding size compared to odd electron systems. The stability of the neutral BiGa3 cluster is rationalized as being similar to BiAl3, an all-metal aromatic cluster

Closed-shell to split-shell stability of isovalent clusters

Metallic clusters containing 2, 8, 18, and 20 electrons are now known to exhibit enhanced stability that can be reconciled because of filled 1S, 1P, 1D, and 2S electronic shells within a simplified confined nearly free electron (NFE) gas. Here, we present first-principles studies on three isovalent clusters, i.e., ZnMg8, CuMg8−, and AuMg8−, each with 18 valence electrons. All the clusters exhibit local energetic stability but with differing origins. Although the stability of ZnMg8 can be reconciled within the conventional confined NFE picture with filled 1S2, 1P6, and 1D10shells, CuMg8− and AuMg8− are shown to be stable despite the unfilled D-shell. Their stability can be understood as a crystal field–like splitting of the otherwise degenerate D-shell because of internal electric fields of the positive ion cores that lead to a filled 1S2, 1P6, 1D8, 2S2 sequence separated by unfilled D2 states that form a large gap. We also examine the progression toward the metallic character in ZnMgn clusters, because isolated Mg and Zn atoms have filled valence 4s2 and 3s2 atomic states. As Mg atoms are added to a Zn atom, the excited atomic p-states in the Mg atoms hybridize rapidly with Zn and Mg s-states to promote a metallic character that evolves more rapidly than in pure Mgn clusters

Structural, electronic, and chemical properties of multiply iodized aluminum clusters

The electronic structure, stability, and reactivity of iodized aluminum clusters, which have been investigated via reactivity studies, are examined by first-principles gradient corrected density functional calculations. The observed behavior of Al13I−x and Al14I−x clusters is shown to indicate that for x⩽8, they consist of compact Al−13 and Al++14 cores, respectively, demonstrating that they behave as halogen- or alkaline earthlike superatoms. For x\u3e8, the Al cores assume a cagelike structure associated with the charging of the cores. The observed mass spectra of the reacted clusters reveal that Al13I−x species are more stable for even x while Al14I−x exhibit enhanced stability for odd x(x⩾3). It is shown that these observations are linked to the formation and filling of “active sites,” demonstrating a novel chemistry of superatoms