The structure and stability of Si@Al<Subscript>12</Subscript>H<Subscript>n</Subscript> (n=1−14) clusters

Density functional theory has been employed in order to investigate the structure and stability of Si@Al₁₂H_n () clusters. Hydrogenated Si@Al₁₂ clusters exhibit pronounced stability for even numbers of H atoms. Large binding energy, HOMO-LUMO gaps and increased ionization potentials imply that these clusters should be physically and chemically stable. The analysis of the charge density of the HOMO plot illustrates that a pair of hydrogen atoms prefer to occupy opposing on-top sites for clusters with an even n number. Studies of deformation charge density plots demonstrate that significant charge transfer occurs from the Si@Al₁₂ to the H atoms.     

Structural,energetic and magnetic properties of small Ti<Subscript>n</Subscript> (n = 2–13) clusters: a density functional study

The structural, energetic, and magnetic properties of Ti _n clusters (n = 2 to 13 atoms) have been studied using Density Functional Theory (DFT), applying the pseudopotential LCAO method and the generalized gradient approximation for the exchange-correlation functional. The binding energy and the dissociation energy were calculated using the PBE and BLYP approximations for the exchange-correlation potential, in order to evaluate the performance of this functionals in predicting the energetic properties of small Ti clusters. The experimentally observed trend in the dissociation energy of Ti _n as a function of the cluster size is reproduced by both PBE and BLYP calculations. The effects of structural distortion on the magnetism of clusters were studied comparing the ground state structure against non-distorted clusters. It was found that the structural distortion has no effect on the total magnetic moment. For all studied clusters using the BLYP functional, with exception of Ti₆ and Ti₇, magnetism is predicted.     

Structure and magnetic properties of La-doped Si<Subscript>n</Subscript> (n = 1–12, 24) clusters: a density functional theory investigation

In the framework of density functional theory (DFT), the structure and magnetic properties of La-doped Si_n clusters have been systematically studied. It is found that La atom always prefers locating on the surface site of the clusters and no cage-like structures are found up to n = 12. The La atom doping remarkably enhances the stabilities of silicon clusters. In contrast to some other clusters with the magnetic moment completely quenched, La doping is shown to invariable magnetism with the total spin magnetic moment of LaSi_n clusters 1 _¼B up to n = 24, as that of a free La atom.     

Density functional theory study of the carbon chains C<Subscript>n</Subscript>X,C<Subscript>n</Subscript>X<Superscript>+</Superscript> and C<Subscript>n</Subscript>X<Superscript>-</Superscript> (X = O and Se; n = 1–10)

A theoretical study of C_nX, C_nX⁺ and C_nX^- (X = O and Se; n = 1-10) clusters is carried out employing the density functional theory and the B3LYP functional. All species are fully optimized using the basis set 6-31G(d) for all atoms and further, single-point computations are done using the B3LYP/aug-cc-pVTZ level. Molecular properties such as equilibrium parameters, dipole moment, infrared vibrational frequencies, Raman activities and rotational constant are predicted. The computations indicate that the equilibrium structures are either linear or quasi-linear. We report the different forms of electron affinities, ionization energy, atomization energy and binding energy of the C_nO and C_nSe chains. The results indicate parity effect is very apparent for electron affinity, ionization energy, and binding energy but the effect is less pronounced for atomization energy. The n-even linear chains have larger ionization energy and atomization energy than the n-odd ones but this effect is reversed for electron affinity. The findings from this work are critically discussed and they are very similar to those obtained previously for the hetero-atom doped carbon chains. This research indicates that n-odd carbon chains are more stable than n-even and this is the trend for the chalcogens carbon chains.     

DFT and GEGA genetic algorithm optimized structures of Cu<Subscript>n</Subscript><Superscript>ν</Superscript> (ν=±1,0,2; n=3-13) clusters

We report a study on small copper clusters \textCu_nⁿ\text{Cu}_n^{\nu} (ν= ±1,0,2; n=3-13) where the minimum energy structures were computed through a joint gradient embedded genetic algorithm (GEGA) technique, and further density functional theory (DFT) geometry reoptimization of the best GEGA cluster structures for each size and charge. Our results are compared to previous ab initio and DFT calculations, when available in the literature, and it is shown than a number of never reported structures for some clusters have been found. From an extensive calibration of some of the DFT commonly used approximate functionals and basis sets, a discussion on its performance and efficiency for Cu cluster calculations is provided. All GEGA found structures are subject to a second step DFT reoptimization process, at the final reported level of theory, BLYP/6-311+G(d), and it is observed that the symmetry found initially by GEGA for almost all of the 66 clusters studied is kept during the DFT reoptimization, which shows the reliability of the initial search algorithm employed. Several geometry-related-properties of these clusters are discussed and compared with some results available in the literature.     

Structural,electronic and magnetic properties of Au<Subscript>n</Subscript>Pt (n = 1−12) clusters in comparison with corresponding pure Au<Subscript>n+1</Subscript> (n = 1−12) clusters

An all-electron scalar relativistic calculation on Au _n Pt (n = 1−12) clusters has been performed by using density functional theory with the generalized gradient approximation at PW91 level. Our results reveal that all the lowest energy geometries of Au _n Pt  (n = 1−12) clusters may be generated by substituting Pt atom for one gold atom of the Au _n+1 cluster at the highest coordinated site. Compared with corresponding pure Au _n+1 cluster, the lowest energy geometries of Au _n Pt clusters are distorted slightly and still keep the planar structures due to the strong scalar relativistic effect in small gold cluster. The Au-Pt bonds are stronger and most Au-Au bonds far from Pt atom are weaker than the corresponding Au-Au bonds in pure Au _n+1 cluster. By substituting Pt atom for one gold atom of Au _n+1 cluster at the highest coordinated site, the relatively stable and inactive odd-numbered Au _n+1 cluster becomes the relatively unstable and reactive odd-numbered Au _n Pt cluster, and the relatively unstable and reactive even-numbered Au _n+1 cluster becomes the relatively stable and inactive even-numbered Au _n Pt  cluster chemically and electronically. All the Au _n Pt clusters prefer low spin multiplicity. The even-numbered Au _n Pt clusters are found to exhibit zero magnetic moment and the odd-numbered Au _n Pt clusters are found to possess magnetic moment with the value of 1 μ _B. The odd-even alterations of magnetic moments and electronic configurations for Au _n Pt clusters are very obvious and may be simply understood in terms of the electron pairing effect.     

Optical absorption spectra of boron clusters B<Subscript>n</Subscript> (n = 2–5) for application in nano scintillator – a time dependent density functional theory study

Boron nano-clusters of various shapes and sizes have potential applications asscintillating detector and hydrogen storage material. Using time dependent densityfunctional theory (TDDFT) as implemented in CASIDA we have studied the linear opticalabsorption spectra for boron clusters B_n (n = 2–5) and compared withpreviously reported results using Hatree-Fock (H-F) based method where the spectrum islimited to 8 eV due to exclusion of excitation into very high energy unoccupied orbital.The optical spectra fall in the visible and near UV region and are very much dependent onthe shape of the isomer. We have obtained additional peaks for B₂ linear, B₃ triangular, B₄ rhombus and square shapedisomers beyond 8 eV which were missing in the previous H-F based study and hassignificance as they fall below the ionization potential. We correlate the opticalspectrum with the shape of the Kohn-Sham orbitals and HUMO-LUMO gap and assess comparativestability of various B_n (n = 2–5) clusters in termsof HUMO-LUMO gap, bond-length and relative energy. TDDFT computed optical spectroscopycorrelated with Kohn-Sham orbitals and HUMO-LUMO gap and its comparison with H-F basedmethod may give significant knowledge regarding geometry and optical properties ofB_n (n = 2–5) clusters enablingto distingush between various isomers of B_n clusters.     

Peculiar thermodynamic properties of LJ<Subscript> N</Subscript> (N = 39–55) clusters

The solid-liquid phase transitions of Lennard-Jones clusters LJ_N (N=39–55) were simulated by a microcanonical molecular dynamics method using Lennard-Jones potential, and their thermodynamic quantities were calculated. The caloric curves of clusters (except N=42) have S-bend. To understand this behaviour, configurational and total entropies were evaluated, and dents on the entropy curves were taken as a sign of negative heat capacity. The heat capacities were evaluated for N=39–55 clusters using configurational entropy data. The potential energy distributions have bimodal behaviour for all clusters in the given range at the melting temperature. The distinct melting behaviour of LJ₄₂ was explained by the topology of the potential energy surface by examining the isomer distributions at phase transitions for LJ₃₉-LJ₅₅. The isomer distributions were found to be a useful way to interpret this behaviour and melting dynamics in general. Melting temperature, latent heat and entropy change upon melting values were reported and are consistent with literature values and values calculated from bulk thermodynamic properties. The dependence of these quantities on the size of the clusters was examined and it is found that latent heat is the key quantity to determine the magic numbers.     

Scanning tunneling microscopy/spectroscopy study of adsorption of C<Subscript>60</Subscript>F<Subscript>36</Subscript> molecules on the 7 × 7-Si(111) surface

Spatially resolved images of an individual C₆₀F₃₆ fluorofullerene molecules on Si(111)-7 × 7 surface have been obtained by means of scanning tunneling microscopy/spectroscopy (STM/STS). The presence of isomers with different symmetry (T, C ₃, C ₁) has been revealed in STM investigation of initial adsorption stage of C₆₀F₃₆ on silicon surface Si(111)-(7 × 7). The adsorbed fluorofullerene molecule can occupy any adsorption site of silicon surface (corner site, faulted half, unfaulted half) that indicates for strong molecule-substrate interaction. The HOMO-LUMO gap of the adsorbed C₆₀F₃₆ molecules have been estimated from current image tunneling spectroscopy (CITS) and z(V) with engaged feedback measurements. The value of HOMO-LUMO gap observed experimentally was 3 eV. The C₆₀F₃₆ molecules adsorption on Si(111)-(7 × 7) surface was stable and kept equilibrium configuration during several hours.     

Structural and magnetic properties of Fe<Subscript>m</Subscript>Y<Subscript>n</Subscript> (m + n = 7, Y = Ru,Rh, Pd,and Pt) nanoalloys

The structural and magnetic properties of the small binary clusters Fe _m Y _n (with m + n = 7, Y = Ru, Rh, Pd, Pt) were studied through extensive ab initio calculations, by means of the fully unconstrained version of the density-functional method, as implemented in the SIESTA code, within the generalized gradient approximation. The lowest energy state geometries, the chemical ordering, and the electronic and the magnetic structures were calculated. We found that the lowest energy geometrical structures for the pure Ru, Rh, Pd, Pt, and Fe heptamers, are a cube without an apex, a triangular prism capped on a square face, a decahedron, a side capped double square, and a decahedron, respectively. Starting from these geometries of the pure element heptamers, we followed the changes in the geometric structure as a function of the chemical composition. We analyzed all the different chemical arrangements, which depend on the particular geometry, and magnetic moment orientations, in the whole range of compositions. In general, there are important modifications to the magnetic moment of the Y atoms as soon as one of them is substituted by an Fe atom in the cluster. In contrast, under the same circumstances, the Fe magnetic moment takes values larger than 3 μ _B and keeps almost this value, insensitive to the structure, composition and chemical order of the system.     

Interaction of Cu cluster anions (Cu<Superscript>-</Superscript><Subscript>n</Subscript>, n = 8–11) with oxygen

The reaction of oxygen with Cu cluster anions consisting of 6–11 atoms was studied by means of Time-of-Flight mass (TOF) spectroscopy and Ultraviolet Photoelectron Spectroscopy (UPS). Using molecular oxygen, we found that a Cu^-_n cluster (n=6-11) can react only with one single oxygen molecule, which adsorbs molecularly, implying that the clusters studied here are less reactive towards oxygen chemisorption compared to the smaller clusters (n<5). This result indicates that chemical properties can alter significantly with increasing cluster size. Depending on the cluster source conditions, different cluster structures and reactivity patterns were found. These results are used to qualitatively describe the chemisorption energetics of oxygen on Cu cluster anions.     

Density functional theory study of neutral AlS_n(n=2-9) clusters

This paper investigates the geometrical structures and relative stabilities of neutral AlS n(n = 2-9) using the density functional theory.Structural optimisation and frequency analysis are performed at the B3LYP/6-311G(d) level.The ground state structures of the AlS n show that the sulfur atoms prefer not only to evenly distribute on both sides of the aluminum atom but also to form stable structures in AlS n clusters.The structures of pure S n are fundamentally changed due to the doping of the Al atom.The fragmentation energies and the second-order energy differences are calculated and discussed.Among neutral AlS n(n = 2-9) clusters,AlS 4 and AlS 6 are the most stable.     

Density-functional study of Si<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 10–15) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic properties of Si _n C _n (n = 10–15) clusters. We find that the Si _n C _n clusters prefer cagelike structures. An extensive isomer search shows that the lowest-energy arrangements are those in which the silicon atoms and the carbon atoms form two distinct subunits. It is found that the carbon atoms favor to form fullerene-like structure due to the sp ²-like bond. The silicon atoms are trying to cope with an unfavorable sp ² environment, but distorted tetrahedra still show up somewhere of the cagelike structures. On the basis of the lowest-energy geometries obtained, the binding energy, HOMO–LUMO gap, Mulliken charge, ionization potential and electron affinity of the clusters have been computed and analyzed. An electronic charge transfer from the Si-populated to the C-populated regions is observed.     

Structures and energetics of BenGen (n = 1–5) and Be2nGen (n = 1–4) clusters

Cluster geometries and energies of Be_nGe_n (n = 1–5) and Be_2nGe_n (n = 1–4) have been examined in theoretical electronic structure calculations. Structure optimisations were carried out using DFT B3LYP/6-31G(2df) and the energies of the optimum geometries were ordered in QCISD(T) calculations. Be and Ge bond to each other and to other atoms of their own kind, creating a great variety of low-energy clusters in a variety of structural types. Comparisons of the germanide clusters with previously explored silicide and carbide structures reveal some structural similarities, but the germanides have much more in common with the beryllium silicides than with the carbides. However, germanide clusters show a greater tendency to form cage-like structures with potential in technological applications.     

Computational investigation of CO adsorbed on Au<Subscript>x</Subscript>, Ag<Subscript>x</Subscript> and (AuAg)<Subscript>x</Subscript> nanoclusters (x = 1 − 5, 147) and monometallic Au and Ag low-energy surfaces

Density functional theory calculations have been performed to investigate the use of CO as a probe molecule for the determination of the structure and composition of Au, Ag and AuAg nanoparticles. For very small nanoclusters (x = 1 ? 5), the CO vibrational frequencies can be directly correlated to CO adsorption strength, whereas larger 147-atom nanoparticles show a strong energetic preference for CO adsorption at a vertex position but the highest wavenumbers are for the bridge positions. We also studied CO adsorption on Au and Ag (100) and (111) surfaces, for a 1 monolayer coverage, which proves to be energetically favourable on atop only and bridge positions for Au (100) and atop for Ag (100); vibrational frequencies of the CO molecules red-shift to lower wavenumbers as a result of increased metal coordination. We conclude that CO vibrational frequencies cannot be solely relied upon in order to obtain accurate compositional analysis, but we do propose that elemental rearrangement in the core@shell nanoclusters, from Ag@Au (or Au@Ag) to an alloy, would result in a shift in the CO vibrational frequencies that indicate changes in the surface composition.     

A first principles study of the adsorption and dissociation of CO<Subscript>2</Subscript> on the δ-Pu (111) surface

A complete understanding of the nature of the 5f electrons has been and continues to be a major scientific problem in condensed matter physics. Bulk and surface electronic structure studies of the actinides as also atomic and molecular adsorptions on the actinide surfaces provide a path towards this understanding. In this work, ab initio calculations within the framework of density functional theory have been used to study the adsorption of molecular CO₂ and the corresponding partially dissociated (CO + O) and completely dissociated (C + O + O) products on the δ-Pu (111) surface. The completely dissociated C + O + O configurations exhibit the strongest binding with the surface (7.92 eV), followed by partially dissociated products CO + O (5.08 eV), with molecular CO₂ adsorption having the lowest binding energies (2.35 eV). For all initial vertically upright orientations, the CO₂ molecule physisorbs or do not bind to the surface and the geometry and orientation do not change. For all initial flat lying orientations chemisorption occurs, with the final state corresponding to a bent CO₂ molecule with bond angles of 117°–130° and the elongation of the CO bond. For CO + O co-adsorption, the stable configurations corresponded to CO dipole moment orientations of 100°–172° with respect to the surface normal and the elongation of the CO bond. The most stable chemisorption cases correspond to anomalously large rumpling of the top Pu layer. The interactions of the CO₂ and CO with the Pu surface have been analyzed using the energy density of states and difference charge density distributions. The nature and the behavior of the 5f electrons have also been discussed in detail in the context of this study.