Structural and electronic properties of small titanium clusters: A density functional theory and anion photoelectron spectroscopy study

Geometrical and magnetic properties of small titanium and chromium clusters on monolayer hexagonal boron nitride

Magnetic clusters on an insulating substrate are potential candidates for spin-based quantum devices. Here we investigate the geometric, electronic, and magnetic structures of small Ti and Cr clusters, from dimers to pentamers, adsorbed on a single-layer hexagonal boron nitride (h-BN) sheet within the framework of density functional theory. The stable adsorption configurations of the Ti clusters and Cr clusters composed of the same number of atoms are found to be totally different from each other. The difference in their bonding mechanisms has been revealed by the density of states and the charge density difference of the corresponding adsorption systems. While chemical bonds are formed between the Ti atoms and the supporting sheet, the Cr clusters are found in the physisorption state on the substrate. In addition, it is shown that the h-BN sheet is energetically favorable for building three-dimensional Ti clusters. These findings support the use of h-BN as a suitable decoupling substrate for manipulation of quantum spin states in small transition metal (TM) clusters and fabrication of devices based on them.

Ab initio DFT simulation of electronic and magnetic properties of Tin+1 and FeTin clusters

We report a computational investigation of the electronic and magnetic properties of neutral Ti_n+1 and FeTi_n (n = 1-10) clusters using ab initio calculations based on density functional theory (DFT) within the generalized gradient approximation (GGA). The best structures for Ti_n+1 and FeTi_n clusters are planar for size n < 5, while from n = 5, they showed a compact three-dimensional cage structure. For the best structures of the FeTi_n clusters, the Fe atoms favor the peripheral position with the highest coordination with the neighboring Ti atoms. The evolution as a function of the size of the average binding energies (Eb/atom) and HOMO-LUMO gaps of Ti_n+1 and FeTi_n (n = 1-10) clusters are studied. The stability results show that the Ti_n+1 clusters have relatively higher stability than the FeTi_n cluster with the same size. In addition, the vertical ionization potentials and electron affinities, chemical hardness, and atomic magnetic moment of Ti_n+1 and FeTi_n (n = 1-10) clusters are also investigated.

Dissociative Adsorption of N2 onto Size-Selected Tin+ and TinO+ (n ≤ 16) toward Nitrogen Fixation

The reactivity of titanium cluster ions and their oxides with molecular dinitrogen was examined using a tandem-type mass spectrometer at a low collision energy of 0.5 eV. The clusters can adsorb dinitrogen and release a titanium atom to consume the obtained excess energy. This indicates that N₂ adsorption energy is large enough to break the titanium cluster. While the smaller clusters have relatively low reactivity, the measured reaction cross section increases with the cluster size and reaches nearly one-third of the Langevin cross section at the larger clusters. Density functional theory calculations indicate that the reaction proceeds exothermically and that molecular dinitrogen adsorbs on the clusters dissociatively. It is suggested that the energy levels of the highest occupied molecular orbitals of the titanium clusters are decisively important for N₂ activation.

Identification of Magic Numbers in Homonuclear Clusters: The ε3 Stability Ranking Function

With the rise of cluster-assembled materials, an index that is able to rank and identify stable clusters or molecules is of great interest in materials sciences and engineering. In the present work, we applied a stability ranking function (ε³) in nanoclusters formed by simple metals (Na, Mg), main group elements (Al), or transition metals (Ti, Cu). The ε³ function parameters are molecular properties derived from the wave function. These parameters can be divided into kinetic and thermodynamic descriptors, in which the kinetic descriptors are the ionization potential and electronic excitation energy, while the atomization free Gibbs energy is the thermodynamic one. This simple ε³ function was able to identify the possible magic numbers of the studied clusters across the periodic table in a good agreement with previous experimental and theoretical works.

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.

Thermodynamically accessible titanium clusters TiN, N = 2–32

We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small Ti_N (N = 2–32) clusters.

Application of Koopmans' theorem for density functional theory to full valence-band photoemission spectroscopy modeling

In this work, Koopmans' theorem for Kohn-Sham density functional theory (KS-DFT) is applied to the photoemission spectra (PES) modeling over the entire valence-band. To examine the validity of this application, a PES modeling scheme is developed to facilitate a full valence-band comparison of theoretical PES spectra with experiments. The PES model incorporates the variations of electron ionization cross-sections over atomic orbitals and a linear dispersion of spectral broadening widths. KS-DFT simulations of pristine rubrene (5,6,11,12-tetraphenyltetracene) and potassium-rubrene complex are performed, and the simulation results are used as the input to the PES models. Two conclusions are reached. First, decompositions of the theoretical total spectra show that the dissociated electron of the potassium mainly remains on the backbone and has little effect on the electronic structures of phenyl side groups. This and other electronic-structure results deduced from the spectral decompositions have been qualitatively obtained with the anionic approximation to potassium-rubrene complexes. The qualitative validity of the anionic approximation is thus verified. Second, comparison of the theoretical PES with the experiments shows that the full-scale simulations combined with the PES modeling methods greatly enhance the agreement on spectral shapes over the anionic approximation. This agreement of the theoretical PES spectra with the experiments over the full valence-band can be regarded, to some extent, as a collective validation of the application of Koopmans' theorem for KS-DFT to valence-band PES, at least, for this hydrocarbon and its alkali-adsorbed complex.

Structural, electronic and magnetic properties of transition metal binary alloy clusters with isoelectronic components: case study with MnmTcn, TimZrn and MnmRen

With the goal of achieving an understanding of the properties of bimetallic alloy clusters having atoms of two isoelectronic elements, we have studied the structural, electronic and magnetic properties of MnmTcn, MnmRen and TimZrn clusters with m + n = 13 (n = 0, 1, 4, 6, 9, 12, 13), using first-principles density functional calculations. MnmTcn and MnmRen represent clusters of isoelectronic series with a half-filled d shell, while TimZrn represents an isoelectronic cluster series of early transition metals. Mn-rich alloy clusters are found to prefer compact structures and isoelectronic Tc-rich or Re-rich alloy clusters are found to adopt open structures. In contrast, TimZrn clusters are all found to stabilize in compact structures, irrespective of being Ti-rich or Zr-rich. This change in behavior between two isoelectronic series is found to be driven by differences in hybridization effects, due to differences in the evolution of the relative energy positions of the d level with respect to the s and p levels upon moving from 3d to 4d or 5d elements. This effect further competes with the magnetization effect to decide the morphology of the alloy clusters. Focusing on the magnetic properties of the studied clusters, we find that the single Tc atom substituted alloy cluster exhibits markedly improved magnetic properties compared to that of pure Mn clusters.

The critical re-evaluation of the aromatic/antiaromatic nature of Ti3(CO)3: a missed opportunity?

The nature of bonding and aromaticity of Ti(3)(CO)(3), a mill-shaped metal-carbonyl complex, is studied carefully. A unique bonding mechanism between metal and carbonyl groups is found in this species. Ti(3)(CO)(3) is an example of a metal-carbonyl complex with prominent metal to carbonyl donation. Moreover, it is proven that not only is Ti(3)(CO)(3) not an antiaromatic complex but also it is the first synthesized example of d-block, σ+π aromatic species. A quick survey among the first row of transition metals in the periodic table shows that other local minima with similar structures and aromaticity are present and Ti(3)(CO)(3) is the first synthesized species of an unknown family.

Ideal strength on clusters from first principles: the Ti(13) case

The mechanical behavior of a Ti(13) cluster, based on total energy mechanical quantum calculations is studied. The cluster geometry has been optimized and good agreement with previous reports has been found. Axial strain is applied along one of the principal axes and the changes on the energetic and vibrational properties of the system are followed. To characterize the cluster stability as a function of strain, vibrational frequencies and total energy have been calculated, to obtain the cluster maximum load tolerance for compression (C) and tensile (T). If the maximum load is defined through a vibrational instability, it happens to be two and half, and three times larger than when the maximum total energy is considered (C and T respectively). As a result of the induced strain along of the C(5) symmetry element, the cluster changes its point group symmetry from I(h) to D(5d), with an energy difference of 1.17 eV (for compression) and 0.33 eV (for tension) with respect to the ground state geometry. The electronic changes are also characterized, as function of the strain, by following the modifications of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and changes on the total atomic population.

Stable Tin (n = 2−15) Clusters and Their Geometries: DFT Calculations

We present a detailed structural analysis for small Tin (n = 2-15) clusters based on ab initio quantum mechanical calculations of their binding energies, frontier orbital gaps, and second energy derivatives. Local density approximation calculations revealed that while the smaller clusters (n < or = 8) prefer hexagonal atomic arrays with bulklike crystal symmetry, the bigger clusters prefer pentagonal atomic arrays. From the stability criteria of the magic number clusters we could identify three magic number clusters Ti7, Ti13, and Ti15. While the most stable configuration of Ti7 is a decahedral bipyramid induced by tetrahedral atomic arrays, the most stable configuration of Ti13 is an icosahedron. The other stable cluster Ti15 takes a closed-shell icosahedron-like configuration with both pentagonal and hexagonal symmetries. The stability of the Tin clusters strongly depends on their geometries and charge states. The HOMO-LUMO gap of the Tin clusters approaches its bulk value for n > 8. While there is not much difference between the HOMO and LUMO isosurface charge distributions for the Ti7 and Ti13 clusters in their most stable configurations, they are very different in the case of Ti15. Such a distinct charge distribution in Ti15 indicates its singular chemical selectivity over the other two magic number clusters.

Phenyl-Coinage Metal (Ag, Au) Complexes: an Anion Photoelectron Spectroscopy and Density Functional Study

The important intermediate phenyl-coinage metal complexes (Ag(m)C6H5(-), Au(m)C6H5(-)), which are produced from the reactions between coinage metal clusters formed by laser ablation and the benzene molecules seeded in argon carrier gas, are studied by PES (photoelectron spectroscopy) and DFT (density functional theory). The EAs (adiabatic electron affinities) of these complexes are obtained from PES at both 308 and 193 nm photon energies and show odd-even alternation. Calculations with DFT are carried out on the structural and electronic properties of Ag(m)C6H5(-) and Au(m)C6H5(-); the adiabatic detachment energy and the calculated DOS (density of states) for the ground state of a given anion are in good agreement with the experimental PES results. The observed spectra are also compared with those of the pure coinage metal clusters, which reveal that there are some similarities between them and the phenyl acts like an additional metal atom in the clusters. Furthermore, the bonding between phenyl and metal is analyzed, suggesting that phenyl group binds perpendicularly on metal clusters through C-M sigma bond.

Homonuclear transition-metal trimers

Density-functional theory has been used to determine the ground-state geometries and electronic states for homonuclear transition-metal trimers constrained to equilateral triangle geometries. This represents the first application of consistent theoretical methods to all of the ten 3d block transition-metal trimers, from scandium to zinc. A search of the potential surfaces yields the following electronic ground states and bond lengths: Sc3(2A1',2.83 A), Ti3(7E',2.32 A), V3(2E",2.06 A), Cr3(17E',2.92 A), Mn3(16A2',2.73 A), Fe3(11E",2.24 A), Co3(6E",2.18 A), Ni3(3A2",2.23 A), Cu3(2E',2.37 A), and Zn3(1A1',2.93 A). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies DeltaE(M3-->M2+M) are 49.4 kcal mol(-1)(Sc3), 64.3 kcal mol(-1)(Ti3), 60.7 kcal mol(-1)(V3), 11.5 kcal mol(-1)(Cr3), 32.4 kcal mol(-1)(Mn3), 61.5 kcal mol(-1)(Fe3), 78.0 kcal mol(-1)(Co3), 86.1 kcal mol(-1)(Ni3), 26.8 kcal mol(-1)(Cu3), and 4.5 kcal mol(-1)(Zn3).

First-principles study of the electronic structures of icosahedral TiN (N=13,19,43,55) clusters

We have studied the electronic structures of icosahedral Ti(N) clusters (N=13, 19, 43, and 55) by using a real-space first-principles cluster method with generalized gradient approximation for exchange-correlation potential. The hexagonal close-packed and fcc close-packed clusters have been studied additionally for comparisons. It is found that the icosahedral structures are the most stable ones except for Ti(43), where fcc close-packed structure is favorable in energy. We present and discuss the variation of bond length, the features of the highest occupied molecular orbitals and the lowest unoccupied molecular orbital, the evolution of density of states, and the magnetic moment in detail. The results are in good agreement with the predictions from the collision-induced dissociation and size-selected anion photoelectron spectroscopy experiments.

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

The DMol cluster method based on density-functional theory has been employed to study the structural stability and electronic structure of La(n) (n=2-14) clusters. The ground states have been found out for lanthanum clusters. The Jahn-Teller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd-even alternation and that 7- and 13-atom clusters are magic. Further, the HOMO-LUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.