Ground state, growth, and electronic properties of small lanthanum clusters

Structure of small yttrium monoxide clusters, chemical bonding, and photoionization: threshold photoionization and density functional theory investigations

The photoionization (PI) spectra of small gas-phase yttrium monoxide clusters, YnO (n = 1-8), are investigated, and the adiabatic ionization energies are determined. The stable structures are obtained from density functional theory (DFT) calculations. The ground state structures are further confirmed by the CCSD(T) method. The PI spectra are calculated for these stable structures and are compared with the experimental PI spectra. The ground-state structures of the neutral and cation clusters are experimentally assigned with confidence on the basis of a favourable agreement between the experimental and calculated PI spectra. New structures are proposed for Y2O, Y6O, and Y8O compared to the previous literature. Y2O is a linear molecule in the ground state that was previously proposed as a C2v bent molecule. The YnO clusters become 3-dimensional from n ≥ 3. The O atom stays outside, bridging a triangular face of yttrium clusters. Chemical bonding between the yttrium and oxygen atoms is mostly ionic. The excess charge on the oxygen atom is around 1.4e-, transferred from the yttrium atoms bonded with it. Yttrium atoms are mostly covalently bonded. However, for the bigger clusters, free charges of both polarities appear on yttrium atoms that are not bonded with oxygen, indicating ionic interactions. Frontier orbitals consist of mainly delocalized 4d electrons with some 5s contributions, forming Y-Y bonding interactions, but with little contribution and zero contribution from the oxygen orbitals, regardless of the cluster size. The lost electron of YnO+ mostly comes from the 5s orbitals of all Y atoms in the cluster up to size n = 4, and then from 4d-5s hybrid orbitals from n ≥ 5, with the d contribution increasing with size. This is contrary to the previous view in the literature that photoionization occurs from a localized 4d orbital.

Threshold Photoionization and Density Functional Theory Investigations of Small Lanthanum Monoxide Clusters, LanO (n = 2-10)

Small lanthanum monoxide clusters, LanO (n = 2-10), have been studied by laser threshold photoionization (PI) spectroscopy and density functional theory (DFT). Ionization energies (IEs) gradually decrease with cluster size with oscillatory behavior at certain sizes at n = 4, 7, and 9, and the IEs are slightly lower than the corresponding bare Lan clusters. Mulliken charge analysis of the neutral and cation clusters indicates that the threshold PI occurs from a delocalized metal-based 5d orbital. The stable geometric structures and IEs for the LanO (n = 2-8) clusters have been determined from DFT. Zero electron kinetic energy and PI spectra have been calculated based on DFT calculations and compared with the experimental PI spectra. On the basis of favorable agreement between the simulated and experimental PI spectra, reliable ground-state geometric structures have been assigned. The O atom is negatively charged, equivalent to one electronic charge mainly transferred from La atoms bonded to it. Chemical bonding between the La and O atoms is ionic, whereas La atoms are mostly covalently bonded. No direct correlation is found between the electronic properties like the IE, electron affinity, and HOMO-LUMO gap and the stability of these clusters.

Ionization Energies and Ground-State Structures of Neutral Lan (n = 2-14) Clusters: A Combined Experimental and Theoretical Investigation

Neutral lanthanum clusters are studied by photoionization time-of-flight mass spectroscopy, laser threshold photoionization spectroscopy, and density functional theory (DFT). Mass abundance spectra (MS) registered at multiple photoionization wavelengths in the range of 195-230 nm by single photon ionization reveal the production of all sizes, La_n (n ≥ 50), in good abundance, nullifying previously predicted low abundances for certain sizes in the 3-14 size range. Also, the MS do not reveal the extraordinary stability of any specific size, as one would expect, from previous theoretical predictions of 7- and 13-atom clusters as magic. Ionization energies (IEs) are measured for La_n (n = 2-14) clusters. DFT has been used to determine the stable geometric isomers for 2- to 10-atom clusters and to calculate their IEs. The theoretical IEs of 2-7 atom clusters are in decent agreement with their experimental values; however, the theoretical IEs are somewhat lower by ∼0.4 eV for n ≥ 8 than their experimental IEs.

Quantum chemistry calculations of the growth patterns, simulated photoelectron spectra, and electronic properties of LaASil (A = Sc, Y, La; l ≤ 10) compounds and their anions

The growth patterns, simulated photoelectron spectra, and electronic properties of LaASi_l (A = Sc, Y, and La; l ≤ 10) compounds and their anions were studied via quantum chemistry calculations using the Perdew-Burke-Ernzerhof (PBE) method and unprejudiced structural searching software ABCluster. The results revealed that the growth patterns of the most stable structures of neutral and anionic LaASi_l showed an adsorptive mode. The lowest-energy structures (LESs) of the LaASi_l (l ≤ 7) clusters were similar, except for those of anionic LaYSi₄^- and LaYSi₅^- and neutral LaScSi₇. Additionally, we investigated and calculated the photoelectron spectra, vertical detachment energies, adiabatic electron affinities, relative stability, charge transfer, magnetic moment, and chemical bond analysis of the LaASi_l ground-state structures. The La₂Si_l clusters exhibited higher stability than the LaYSi_l and LaScSi_l systems owing to their higher dissociation energies (DEs). The DEs of the LESs in the LaASi₃ molecule are higher than those of other clusters. Thus, the LaASi₃ cluster shows potential as a building framework for Si-based cluster materials with good stability. The natural population analysis data and chemical bond analysis results showed that the spd hybridization of the orbitals of the metal atoms in the LaASi_l system occurred. Except for the LaScSi₉ and LaScSi₁₀ clusters, the neutral LaASi_l compounds transform into the corresponding anions when an extra electron is accepted by the Si clusters.

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.

Probing the properties of size dependence and correlation for tantalum clusters: geometry, stability, vibrational spectra, magnetism, and electronic structure

A comprehensive investigation on the equilibrium geometry, relative stability, vibrational spectra, and magnetic and electronic properties of neutral tantalum clusters (Ta_n, n = 2–17) was performed using density functional theory (DFT). We perform a study of the size dependence and correlations among those descriptors of parameters, and showed these could provide a novel way to confirm and predict experimental results. Some new isomer configurations that have never been reported before for tantalum clusters were found. The growth behaviors revealed that a compact geometrical growth route is preferred and develops a body-centered-cubic (BCC) structure with the cluster size increasing. The perfectly fitted functional curve, strong linear evolution, and obvious odd–even oscillation behavior proved their corresponding properties depended on the cluster size. Multiple demonstrations of the magic number were confirmed through the correlated relationships with the relative stability, including the second difference in energy, maximum hardness, and minimum polarizability. An inverse evolution trend between the energy gap and electric dipole moment and strong linear correlation between ionization potentials and polarizability indicated the strong correlation between the magnetic and electronic properties. Vibrational spectroscopy as a fingerprint was used to distinguish the ground state among the competitive geometrical isomers close in energy. The charge density difference isosurface, density of states, and molecular orbitals of selected representative clusters were analyzed to investigate the difference and evolutional trend of the relative stability and electronic structure. In addition, we first calculated the ionization potential and magnetic moment and compared these with the current available experimental data for tantalum clusters.

A comprehensive investigation on the equilibrium geometry, relative stability, vibrational spectra, and magnetic and electronic properties of neutral tantalum clusters (Ta_n, n = 2–17) was performed using density functional theory (DFT).

Emergence of antiferromagnetic ordering in Tbn (n = 2-33) clusters

Using the density functional theory (DFT) under both frameworks of the local density approximation (LDA) and the generalized gradient approximation (GGA), we show that the anomalous magnetic moment of Tbn (n = 2-20, 22, 33) clusters found in recent experiment [J. Appl. Phys. 2010, 107, 09B526] is due to the antiferromagnetic or ferromagnetic couplings between Tb atoms in clusters. The local spin magnetic moment of Tb atoms is in the range 5.1-5.7 μ(B), which is faintly influenced by the cluster sizes, geometrical structures, and spin arrangements. Emphasis is made on the Tb13 cluster to eliminate the large magnetic discrepancy between the experiment and calculation. Geometrical evolution shows that the square-antiprism motif with one centered atom is competitive with the icosahedral motif for small Tb clusters n = 9-12, whereas the close packed icosahedral growth is clearly favored for large clusters n = 13-20, 22, 33. The clusters containing 4, 7, 10, 13, and 19 atoms are found to be more stable than their neighboring sizes, in agreement with the early mass spectral measurements. The electronic properties including the HOMO-LUMO energy gaps, ionization potentials, electron affinities, and electric dipole moments are calculated, and more importantly, the variational trends of the magnetic moment and electric dipole moment qualitatively fit well with the experimental observations.

A density-functional study of the structural, electronic, magnetic, and vibrational properties of Ti8C12 metallocarbohedrynes

Calculations are presented for the structural, electronic, and vibrational properties of the different Ti8C12 metallocarbohedrynes. (Please note that we adopt the name "metallocarbohedrynes" instead of "metallocarbohedrenes" to denote the acetylenic nature of C2 units in this class of clusters demonstrated by several contributions in literature.) The density-functional theory (DFT) calculations are performed with the all-electron projector augmented-wave method and generalized gradient approximation for the exchange-correlation functional. We study the seven low-energy isomers of the Ti8C12 metallocarbohedrynes using spin-polarized DFT, where we find a correlation between the number of rotated carbon dimers and the cohesive energy of the structure. The electronic density of states (eDOS) show that C3nu, D*3d, and D3d isomers are spin polarized. The partial eDOS shows that, depending on the dimer orientation, carbon atoms and a subgroup of the metal atoms form a covalent framework while other metal atoms are bonded to this framework more ionically. This picture is further supported by the charge density of the different structures, where we see that the Ti atoms with higher charge density show less contribution to the covalent bonding of the Ti-C framework. The vibrational spectra of the different structures are calculated using the frozen-vibration method. Also, we calculate the vibrational spectra of the C3nu and C2nu structures using molecular-dynamics simulations at two different temperatures. The results of the simulations demonstrate the local stability of the structures beyond the harmonic limit explored by the frozen-vibration method.

Continuation calculations of boron- (aluminum-, titanium-, and nickel-) doped La13 clusters

In this work, we have calculated boron-, aluminum-, titanium-, and nickel-doped La13 clusters by DMOL method based on the density-functional theory. Two doping modes are employed: surface and center doping. The boron, aluminum, and nickel atoms prefer to occupy the surface sites while the titanium atom prefers to occupy the center site. The doped La13 clusters with these four kinds of atoms have lower binding energy than pure La13 clusters. The icosahedral isomers are of lower binding energy than cubotahedral and decahedral isomers for La12B(-1), La12Al(-1), and La12Ni, while doping makes the cubotahedral La12Ti stable with a binding energy a little lower than icosahedral La12Ti. There are electronic shell effects in icosahedral La12B(-1) and La12Al(-1). The icosahedral La12B(-1) is promising to be formed during the doped process experimentally. Furthermore, we have also discussed the distorted structures of center doping by bond lengths, density of states, and charge transfers.

First principles study of the carbon-(silicon-) doped La13 clusters

The structural stability and physical properties have been studied for carbon-(silicon-) doped La(13) clusters using DMOL method based on density-functional theory. Doped La(13) clusters prefer to be icosahedron. Substitutional doping with a carbon or silicon impurity makes some clusters closed electronic shell, especially in icosahedral isomers. Substitutional doping of icosahedral La(13) clusters is found to be favorable at surface sites of clusters, especially for Si-doped La(13) cluster, which is very likely to be formed during the doping process. In addition, the structural distortions due to the doping are discussed.

Structural stability and electronic state of transition metal trimers

Ground state geometries were searched for transition metal trimers Sc3, Y3, La3, Lu3, Ti3, Zr3, and Hf3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr3 and Hf3) or near equilateral triangle (Ti3, Sc3, Y3, La3, and Lu3). For rare earth trimers Sc3, Y3, La3, and Lu3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr3 and Hf3, equilateral triangle at singlet state is the most stable. For Ti3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc3, Zr3, and Hf3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr3) or fluxional (Sc3 and Hf3). For Y3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y3 is a bent molecule for the ground state. For La3, our calculation is in excellent agreement with previous theoretical study based on density functional methods.