Molecular and electronic structure of some binary polyhedral clusters

The molecular and electronic structures of some polyhedral alternate molecules X_nY_n, where n=12, 16; X=B, Al, Si; Y=N,P,C, and of homoatomic clusters C₂₄, Si₂₄, C₃₂, and Si₃₂ are calculated in a valence approximation by the MNDO method. It is suggested that the σ-frameworks of these molecules are formed of four- and six-membered rings, with each X atom having only Y atoms as neighbors. The singlet states of all these systems have local minima on the corresponding potential energy surfaces with T_h symmetry for n=12 and T_d symmetry for n=16. The main structural parameters, heats of formation, ionization potentials, and effective charge distributions are given. It is concluded that the X_nY_n heteroatomic clusters can exist when X and Y are atoms of Group III and V elements, respectively, or both are atoms of Group IV elements. A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp.976–982, November–December, 1995. Translated by L. Smolina     

Molecular and electronic structures of some trimers of polyhedral carbon clusters

Geometries and electronic structures of four crimped linear carbon clusters were modeled by the MNDO/PM3 method. Three of these clusters (C₁₈₀ clusters) are trimers ofI _h -C₆₀ fullene, which differ from each other by the mode of linkage of the monomers. The fourth cluster (C₁₇₂ pseudo-trimer) consists of two C₅₈ fragments of C₆₀ fullerene linked to each other through the C₅₆ cluster. The optimum geometric parameters, hieats of formation, and ionization potentials were calculated for the above-mentioned systems as well as for the corresponding C₁₂₀ and C₁₁₆ dimers. The possibility of extrapolation of the data on dimers and trimers to linear oligomers of the C₆₀ and C₅₆ clusters with a larger number of repeating fragments is discussed. The character of linkages of monomers was analyzed for the two trimers under consideriation, which have the most complex mode of binding of the C₆₀ fullerene molecule and its fragments, using the C₆₀H₂₀ and C₇₂H₂₄ molecules (whose carbon skeletons model the structures of these linkages) as examples. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 7–12, January, 1998.     

Geometric and electronic structure of clusters

The interplay between electronic and geometric structure is investigated for covalently bonded phosphorus clusters. We use a modification of the molecular dynamics/ density functional (MD/DF) method of Car and Parrinello, describing the electronic structure by a simplified linear combination of atomic orbitals (LCAO) approach. The results show clearly the tendency of phosphorus to threefold coordination, and substantial variations in bond angles lead to a large variety of isomers.     

Influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.     

Interaction of triatomic germanium with lithium atoms: electronic structure and stability of Ge3Lin clusters

Quantum chemical calculations were applied to investigate the electronic structure of mono-, di-, and tri- lithiated triatomic germanium (Ge3Lin) and their cations (n = 0-3). Computations using a multiconfigurational quasi-degenerate perturbation approach (MCQDPT2) based on complete active space CASSCF wavefunctions, MRMP2 and density functional theory reveal that Ge3Li has a 2A' ground state with a doublet-quartet gap of 24 kcal/mol. Ge3Li2 has a singlet ground state with a singlet-triplet (3A' '-1A1) gap of 30 kcal/mol, and Ge3Li3 a doublet ground state with a doublet-quartet (4A' '-2A') separation of 16 kcal/mol. The cation Ge3Li+ has a 1A' ground state, being 18 kcal/mol below the 3A' state. The computed electron affinities for triatomic germanium are EA(1) = 2.2 eV (experimental value is 2.23 eV), EA(2) = -2.5 eV, and EA(3) = -5.9 eV, for Ge3-, Ge32-, and Ge33-, respectively, indicating that only the monoanion is stable with respect to electron detachment, in such a way that Ge3Li is composed of Ge3-Li+ ions. An atoms in molecules (AIM) analysis shows the absence of a Ge-Ge-Li ring critical point in Ge3Li. An electron localization function (ELF) map of Ge3Li supports the view that the Ge-Li bond is predominantly ionic; however, a small covalent character could be anticipated from the Laplacian at the Ge-Li bond critical point. The ionic picture of the Ge-Li bond is further supported by the natural bond orbital (NBO) results. The calculated Li affinity value for Ge3 is 2.17 eV, and the Li+ cation affinity value for Ge3- amounts to 5.43 eV. The larger Li+ cation affinity of Ge3- favors an electron transfer, resulting in a Ge3-Li+ interaction.     

Ionic and electronic structure of metal clusters

Structure and electron dynamics of sodium clusters are investigated within the local-density approximation for the electrons. We compare results from detailed ionic structure with those from a structure averaged jellium model and find that the dominance of the electron cloud overlays most of the differences in the background. Ionic structure is indispensable, however, to compute the surface energy of clusters and to provide an unprejudiced picture of cluster fission. For all cases, we compute the resonance spectra associated with electron dynamics. In particular, the very strong deformations during fission deliver unusual resonance modes with a broad spectral fragmentation.     

Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

The electronic structure of small lithium clusters

Ab initio molecular orbital calculations using the STO-6G and STO6-21G basis sets have been performed for the cluster series Li _n ⁺ , Li _n , and Li _n ^– (wheren=2–7). Thirty-two optimized structures are discussed and reported, many of which (especially for the anionic structures) have not yet been considered. The calculations suggest that for all three species the optimum geometries are planar. Of the two levels of theories that were investigated, STO-6G//STO-6G and STO6-21G//STO-6G, the latter hybrid theory was found to be less reliable. In particular, for the anionic structures these calculations should provide a platform from which more sophisticated, i.e., configuration interaction, geometry optimization can be performed.     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

F-structure of polyhedral water clusters

Energy and entropy characteristics of the F-structures of polyhedral water clusters containing tetragonal, pentagonal, and hexagonal faces with the intermolecular potential ST2 are studied.Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 4, pp. 77–82, July–August, 1993.Translated by L. Smolina     

Shell structure of electronic states of Cu clusters

Electronic states of icosahedral Cu₁₃ and Cu₁₂ clusters were calculated by the DV-Xα method which took into account of many-electron effects. The valence 3d orbitals are localized within atom and isolated from the valence 4s orbitals extended over the whole cluster. The characteristic feature of the states ofs valence electrons of Cu₁₃ cluster well corresponds to that of one-electron picture i.e. the shell model of the 3-dimensional isotropic harmonic oscillator potential. Electronic states of valence levels of Cu₁₂ cluster which have no central atom fairly well correspond to those of a combined potential of the harmonic oscillator and a 3-dimensional Gaussian potential barrier at the center of the cluster.     

Global optimization of clusters using electronic structure methods

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first‐principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high‐performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.     

Nodal structure of the electronic Wigner function of many-electron atoms and molecules

On the example of several atomic and small molecular systems, the regular behavior of nodal patterns in the electronic one-particle reduced Wigner function is demonstrated. An expression found earlier relates the nodal pattern solely to the dot-product of the position and the momentum vector, if both arguments are large. An argument analogous to the “bond-oscillatory principle” for momentum densities links the nuclear framework in a molecule to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic nodes. © 1996 John Wiley & Sons, Inc.     

Diatomics-in-molecules study of the geometric and electronic structure of Xen+ clusters

Dissociation energies as well as electronic and geometric structure of singly charged xenon cluster cations, Xe_n⁺ (n=3–35), are calculated using the extended diatomics-in-molecules method (including the spin–orbit coupling and the most important ionic and neutral three-body interactions) and the state-of-the-art ab initio diatomic curves for Xe₂⁺ due to Paidarová and Gadéa [Chem. Phys. 274 (2001) 1]. Cluster growth of Xe_n⁺ and size dependence of the positive charge delocalization are discussed. The calculated dissociation energies are used to estimate the evaporation energies for Xe_n⁺→Xe_n−1⁺+Xe and to study the stability of the Xe_n⁺ clusters. The results obtained are compared with available experimental and theoretical data.     

The enumeration of electron-rich and electron-poor polyhedral clusters

We present as dual processes the capping of closed triangulated polyhedra with apical atoms and the making of holes in such polyhedra either by puncture of the surface or by excision of atoms and their edges. These processes are shown to generate stable chemical species containing respectively less or more than 2n + 2 skeletal electrons. The former species are designated as electron-poor whereas the latter are called electron-rich. Pólya's enumeration method is used to enumerate the distinct ways of capping and excising the closed, triangulated polyhedra to yield systems containing from four to twelve vertices. For the enumeration of cappings the appropriate cycle index is that of the dual of the polyhedron being capped, whilst for the enumeration of the excisions the cycle index is that of the polyhedron being excised.     

Effects of surface roughness on the electronic structure of metallic clusters

We study the electronic level density in spherical clusters. Due to the granularity of the ionic background the surface is irregular at the microscopical level. We show that this affects the shell structure and that the level statistics display from the bottom to the top of the spectrum a transition from a poissonian behaviour to one consistent with the predictions of random matrices theory.