Can we rationalize the structure of small silicon-carbon clusters?

A theoretical study of clusters with using density functional theory is presented. Tests of various functionals demonstrate that local spin density approximation (LSDA) is the most adequate functional for the study of these systems. Structures, vibrational frequencies, and IR intensities of the lowest energy isomer of the studied clusters obtained using LSDA are described, and the unusual properties of the Si-C clusters are discussed. A quantitative analysis of the obtained structures was carried out, and relations between the coordinations, interatomic distances, and angles observed in the Si-C clusters were obtained through introduction of the notion of coordination. This analysis also shows that the carbon atoms mainly exhibit sp and sp² hybridizations, and that a majority of silicon atoms do not hybridize. This study is the fi rst step of the implementation of a semi-empirical potential, which would describe the moderately small Si-C clusters. Received: 20 October 1997 / Received in final form: 16 December 1997 / Accepted: 17 December 1997     

Improved endohedral fullerenelike structures of silicon clusters Si31–Si39 by density functional calculations

We extensively search for the endohedral silicon-fullerene structures of Si₃₁–Si₃₉ using the combination of a tight-binding potential with the density functional theory. The resulting structures of our best candidates characterize more compact features comparing to previous isomers [J. Am. Chem. Soc. 126, 13845 (2004); J. Chem. Phys. 124, 164311 (2006)]. Most of our best candidates belong to new families featuring different core/cage combinations or different original carbon fullerene cages with respect to those of previous isomers. Energy calculations reveal that our best candidates are more stable than the previous best ones at the PW91 level, except for n = 34 and 38. The predicted relative stabilities of these isomers remain even at finite temperatures. In addition, the densities of dangling-bond atoms in the surfaces of our Si₃₃ and Si₃₉ isomers are significantly lower than the previous best candidates, as well as lower than those of their neighbors. This finding together with the densities of the active sites in the surfaces of the previous best candidates of Si₃₄ and Si₃₈ is roughly consistent with the observed relative reactivities of the silicon clusters in the size range of n = 31-39.     

Temperature-dependent ionization potential of sodium clusters

The ionization potential of sodium clusters () at a finite temperature is studied using density functional theory and ab initio molecular dynamics. The threshold regions of the photoionization efficiency curves are deduced from the integrated IP distributions, which are obtained from the energy eigenvalues of the highest occupied Kohn-Sham states during molecular dynamics by applying a theoretically well-defined shift. The calculated ionization potentials are directly compared to the experimental values. The energetically best geometry of Na₅₅ is found to be a slightly distorted icosahedron. Received 16 April 1999 and Received in final form 6 July 1999     

Metallic evolution of small magnesium clusters

Structural and electronic properties of small magnesium clusters (N≤13) are studied using a first-principles simulation method in conjunction with the density functional theory and generalized gradient correction approximation for the exchange-correlation energy functional. It is observed that the onset of metallization of magnesium clusters is hard to assign since both the s-p hybridization and the energy gap between the valence and conduction bands do not evolve rapidly towards the known bulk properties. Instead these quantities show a slow and nonmonotonic evolution. Received 15 November 2000     

Structural and electronic properties of Bin (n = 2-14) clusters from density-functional calculations

The structural and electronic properties of Bi_n (n = 2-14) clusters have been systematically studied using gradient-corrected density-functional theory. For each cluster size, a number of structural isomers were constructed and optimized to search for the lowest-energy structure. The competition of several structural patterns such as cages, superclusters, and layered structures leads to the alternating appearance of these configurations as global minima. Although the tendency of Bi to form puckered-layer structures is already well-known, the electronic states of Bi_n clusters are still far from that of the bulk. As well, a remarkable even-odd atom number oscillation is observed in the structural and electronic properties of the clusters, implying that the stability of Bi_n clusters is mainly dominated by the electron shell effect rather than by geometrical packing. The theoretically calculated values for electron affinities agree well with available experimental data.     

Tight-binding study of structural and electronic properties of silver clusters

Tight-binding model is developed to study the structural and electronic properties of silver clusters. The ground state structures of Ag clusters up to 21 atoms are optimized by molecular dynamics-based genetic algorithm. The results on small Ag_n clusters (n = 3-9) are comparable to ab initio calculations. The size dependence of electronic properties such as density of states, s-d band separation, HOMO-LUMO gap, and ionization potentials are discussed. Magic number behavior at Ag₂, Ag₈, Ag₁₄, Ag₁₈, Ag₂₀ is obtained, in agreement with the prediction of electronic ellipsoid shell model. We suggest that both the electronic and geometrical effect play significant role in the coinage metal clusters. Received 7 August 2000     

Comparative study on the structure and properties of small C<Subscript>n</Subscript> and NaC<Subscript>n</Subscript> clusters

The structures, binding energies, and electronic properties of C_n and NaC_n (n=2–12) clusters have been systematically investigated using density functional theory (DFT). A number of previously undiscovered isomers of NaC_n clusters are reported, including fan-like, linear and three-dimensional structures. Moreover, NaC_n clusters with even n are found to be more stable than those with odd n, in contrast with the case of C_n clusters.     

Assembling of hydrogenated aluminum clusters

The electronic and atomic structure of Al₁₃H has been studied using Density Functional Theory. Al₁₃H has closed electronic shells. This makes the cluster very stable and suggests that it could be a candidate to form cluster assembled solids. The interaction between two Al₁₃H clusters was analyzed and we found that the two units preserve their identities in the dimer. A cubic-like solid phase assembled from Al₁₃H units was then modeled. In that solid the clusters retain much of their identity. Molecular dynamics runs show that the structure of the assembled solid is stable at least up to 150 K. A favorable relative orientation of the clusters with respect to their neighbors is critical for the stability of that solid. Received 21 November 2000     

Photodissociation spectroscopy of the chromium trimer ion

The electronic and geometric structures and photodissociation dynamics of the chromium trimer ion, Cr₃ ⁺, were investigated by photodissociation spectroscopy in the photon-energy range from 1.32 to 5.52 eV. The branching fractions of the product ions, Cr⁺ and Cr₂ ⁺, exhibit stepwise changes at the threshold energies for dissociation into Cr⁺+Cr₂, Cr+Cr₂ ⁺, Cr⁺+2Cr, and Cr^*+Cr₂ ⁺. It is noted that Cr₂ ⁺ is produced even above the threshold for atomization; the excess energy is redistributed to produce a fragment atom, Cr^*, in an excited state. The photodissociation action spectrum is well explained by a mixture of simulated spectra for two nearly-degenerate structural isomers identified by density functional calculations: those having a metastable C_2v structure and the most stable structure slightly distorted from the C_2v one. The barrier height between the two isomers which is lower than the zero-point energy suggests that Cr₃ ⁺ has an intrinsically floppy structure.     

Rings, towers, cages of ZnO

Theoretical electronic structure studies on (ZnO)_n (n= 2–18, 21) have been carried out to show that the transition from an elementary ZnO molecule to the bulk wurtzite ZnO proceeds via hollow rings, towers, and cages. Our first principles electronic structure calculations carried out within a gradient corrected density functional framework show that small Zn_nO_n (n=2–7) clusters form single, highly stable rings. Zn₃O₃ and the symmetric cage Zn₁₂O₁₂ are shown to be particularly stable clusters. Among larger clusters, the most stable are oblong cages, Zn₁₅O₁₅, Zn₁₈O₁₈, and Zn₂₁O₂₁, which are reminiscent of nanotubes.     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Simulation of small positively charged MgO clusters and study of their electronic densities

With the help of ab initio methods the clusters [(MgO)₁₃Mg] ^Q+ are simulated for Q = 0, 1, 2. Then, vacancy clusters [(MgO)₁₂Mg₂] ^Q+ obtained by removing one oxygen atom are computed for Q running from 0 to 4. These clusters exhibit a slight sphericity and generally shorter interatomic distances than in the crystal. The electronic densities variations are studied in function of Q. In particular, it is observed that the electronic density in the oxygen vacancy goes to a maximum when Q = 2. The ionisation potentials vary from approximately 4 to 14 eV when Q varies from 0 to 3, with a more rapid increase from Q = 1 to Q = 2. The stability study of vacancy clusters show that they experience a phase transition when their charge becomes equal to 2, in accordance with the features mentioned above. Received 14 September 1999 and Received in final form 2 December 1999     

Negative-ion photoelectron spectroscopy of acrylonitrile clusters containing a sodium atom

Cluster anions of a sodium atom with acrylonitrile molecules, (n = 0–6), have been studied by negative-ion photoelectron spectroscopy. In addition, theoretical calculations by using density functional theory have been performed to obtain optimized structures and vertical detachment energies. For Na(AN)^–, the spectrum can be explained by excitation of two different isomers of the anion. For , a broad band is found in the photoelectron spectrum, whose profile is almost identical with those of previously reported photoelectron spectra of and a negative ion of chemically synthesized 1,3,5-cyclohexanetricarbonitrile (CHTCN) molecule. From this resemblance of band profiles, we conclude that oligomerization of (AN)₃ takes place in and the CHTCN is formed as the intracluster reaction product.     

Influence of covalence and anion symmetry on the structure of small metal hydroxide clusters: Sodium versus silver hydroxide

An ab initio study of the Na_n(OH)_n, Na_n(OH)_n-1 ⁺, Ag_n(OH)_n, and Ag_n(OH)_n-1 ⁺ clusters with n up to four is presented. The results of this study show that, in accordance with experimental observations, the sodium hydroxide clusters are almost purely ionic, while the Ag-O bond exhibits a significant covalent character. The perturbation caused by the non-spherical OH^- group relatively to an atomic anion, as well as the influence on structures and energies of the covalent character of the metal-oxygen bond are determined. The appearance of metal-metal bonds in the silver hydroxide clusters is also discussed. Finally, the theoretical results obtained on the Na-OH clusters are compared to experimental results available on the dissociation of the Na_n(OH)_n-1 ⁺ clusters. Received 9 August 1999 and Received in final form 1st December 1999     

Cohesive properties of mercury clusters in the ground and excited states

Optimized structures and cohesive energies of small mercury clusters (Hg_N; N = 3–7, 13, 19) are calculated with the spin-orbit diatomics-in-molecules method. The theory takes into account the effect of s-p mixing which tends to enhance the binding energies in the ground state. It is shown that excimer clusters have significantly short optimum bond lengths and their atomic geometries differ considerably from those in the ground state. Excitation energy gap depends sensitively on both cluster size and nearest-neighbor separation. Numerical results are compared with other theories and experiments.     

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12-212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest-energy isomers of bare Au₂₈ and Au₅₅ clusters, whereas in the size-range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters [Au₂₈(SCH₃)₁₆ and Au₃₈(SCH₃)₂₄], density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high-resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1-2 nm, can be detected using currently available experimental HRTEM techniques.     

Infrared ion dip and ultraviolet spectroscopy of 4-phenyl imidazole, its tautomer, 5-phenyl imidazole, and its multiply hydrated clusters

Mass-resolved resonant two photon ionisation (R2PI) and infrared ion dip spectra have been recorded for 4-phenylimidazole (4PI) and its singly and multiply hydrated clusters 4PI(H₂O)_{n = 0 - 4}, under supersonic expansion conditions. In the case of 4PI(H₂O)_0,1, it has also been possible to record infrared spectra in both the ground (S₀) and excited (S₁) states. Combining the experimental data with the results of ab initio calculations has led to the structural assignment of each cluster. In each case, the water molecules bind primarily to the NH site of the imidazole ring. Clusters with n≥ 2 incorporate linear water chains, in which the proton donating terminus bridges either to the π-electron system (n = 2) or to the >N: atom site (n = 3, 4) on the imidazole ring. Despite the creation of a “water wire”, connecting the donor and acceptor sites of imidazole, there is no evidence of proton transfer in either the ground or excited state. Received 20 December 2001 Published online 13 September 2002     

The aluminum arsenides Al<Subscript>m</Subscript>As<Subscript>n</Subscript> (m + n = 2–5) and their anions: Structures,electron affinities and vibrational frequencies

Geometries, electronic states and electron affinities of Al_mAs_n and Al_mAs _n (m+n=2–5) clusters have been examined using four hybrid and pure density functional theory (DFT) methods. Structural optimization and frequency analyses are performed using a 6-311+G(2df) one-particle basis set. The geometries are fully optimized with each DFT method independently. The three types of energy separations reported in this work are the adiabatic electron affinity (EA_ad), the vertical electron affinity (EA_vert), and the vertical detachment energy (VDE). The calculation results show that the singlet structures have higher symmetry than that of doublet structures. The best functional for predicting molecular structures was found to be BLYP, while other functionals generally underestimated bond lengths. The largest adiabatic electron affinity, vertical electron affinity and vertical detachment energy, obtained at the 6-311+G(2df)/BP86 level of theory, are 2.20, 2.04 and 2.27 eV (AlAs), 2.13, 1.94 and 2.38 eV (AlAs₂), 2.44, 2.39 and 2.47 eV (Al₂As), 2.09, 1.80 and 2.53 eV (Al₂As₂), 2.01, 1.57 and 2.36 eV (AlAs₃), 2.32, 2.11 and 2.55 eV (Al₂As₃), 2.40, 1.45 and 3.26 eV (AlAs₄), 1.94, 1.90 and 2.07 eV (Al₄As), respectively. However, the BHLYP method gives the largest values for EA_ad and EA_vert of Al₃As and EA_ad of Al₃As₂, respectively. For the vibrational frequencies of the Al_nAs_m series, the B3LYP method produces good predictions with the average error only about 10 cm^-1 from available experimental and theoretical values. The other three functionals overestimate or underestimate the vibrational frequencies, with the worst predictions given by the BHLYP method.     

Assessing the validity of theoretical results

We present recent theoretical results for the V₃ and Au₄ clusters. Calculations of the V₃ doublet system indicate that the 6-311+G(d) basis set is sufficiently flexible to provide reliable minimum energy structures and vibrational frequencies, that these structures and frequencies are insensitive to spin contamination of the wave function when the BPW91 functional is used, and that changing to the B3LYP functional may result in very different structures and frequencies. A computationally less expensive scalar relativistic treatment of Au₄ clusters gives structural properties that are in good agreement with those obtained using a four-component method. Received 30 November 2000