An empirical many-body potential energy function constructed from pair-interactions

A new empirical potential energy function (PEF) is proposed, which is formed from pair-interactions only, and containes the many-body contributions. The PEF satisfies bulk cohesive energy and bulk stability condition. The PEF is parameterized for copper, silver, and gold elements in fcc crystal structure. The elastic constantsC ₁₁ andC ₁₂ and the bulk modulus of the elements are calculated, and the structural stability and energetics of microclusters containing 3 to 7 atoms of the same elements are investigated.     

Flattened fullerenes

Quantum-chemical calculations of giant flattened fullerenes C _n (lentil-shaped) have been carried out. The topology, molecular and electronic structure of these fullerenes have been studied. Such molecules consist of two identical coronenoid fragments of a graphite layer, which are arranged one above the other, and a system of polycondensed five- and six-membered cycles, which form a side surface of the cluster. Polyhedral structures with isolated pentagons of three symmetry types (D _6h ,D _6d , andD _3h ) have been considered. The topology of these structures is described in terms of planar molecular graphs. Electronic structures of eleven flattened lentil-shaped C _n clusters (n = 72–216) have been studied in the π approximation. Most of the considered systems have closed or quasi-closed electron shells (according to Hückel) and rather large energy gaps separating the highest occupied and lowest unoccupied MO, which is indicative of their kinetic stability. Fragments of the potential energy surfaces of the C₇₂ and C₉₆ fullerenes have been studied by the MNDO, AM1, and MNDO/PM3 methods. For the C₉₆ cluster, two local energy minima, which correspond to the lentil-shaped isomers withD _6h andD _6d symmetry, have been determined. As a result of optimization of geometric parameters, it was found that all three methods give close values of heights (H = 6.7 Å) and diameters (D = 9.8 Å) for both isomers. The clusters change to quasi-two-dimensional systems (H«D) with increasing sizes of coronenoid fragments.     

Compositions of nanoparticles of hexagonal symmetry

The formulas for calculation of the number of atoms in nanoparticles with symmetry group D _6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D _6h are revealed: C _{? + 12z} , where z = 0, 1, 2, …, and C _? is C ₂, C ₆, C ₈, or C ₁₄. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.     

Ab initio study on the stability,geometry and electronic structure of the cyclopropenyl system

Results of an LCAO-MO-SCF investigation into the stability and geometry of the cyclopropenyl cation (C₃H₃⁺), anion (C₃H₃^?) and radical (C₃H₃^o) are presented. By independently varying the two relevant bond angles, the shape of the potential energy curves in the corresponding two-parameter space for these three species has been obtained. It is found that the cation is most stable in the D_3h nuclear configuration, while the anion has minimum energy in the C_s symmetry. In the specific case of the C₃H₃ radical, which exhibits an orbital, as well as spin-degeneracy, in the D_3h configuration, a strong Jahn-Teller effect is observed, leading to estimates for the non-symmetrical equilibrium configuration at C_2v and for the distortion energy of 12 kcal/mole from the D_3h symmetry. In terms of the population analysis and the contour diagrams, the electronic charge distribution has also been studied for these species in their most stable configurations.     

Group 14 structural variations: perhalo derivatives of the “dimetallenes”: dicarbenes, disilenes, digermenes, distannenes, and diplumbenes

Trends in the structural variations of all perhalo derivatives of dicarbenes and their Group 14 analogues have been studied. This included all M₂X₄ molecules, where M = C, Si, Ge, Sn, or Pb, and X = F, Cl, Br, or I. Mapping the potential energy surface of all molecules has uncovered several isomers. The stability of these isomers depends on both the Group 14 atoms and the halogen ligands. Several isomers were found stable; the ones that are global minima include (with their symmetries and an example in parenthesis): the typical ethene structure X₂M=MX₂ (D _2h, F₂C=CF₂), an X₃M–MX structure (C _S, F₃Si–SiF, a trifluorosilyl–silylene), another X₃M–MX structure (C ₁, Cl₃Si–SiCl), one more X₃M–MX structure with a single halogen bridge (C ₁, I₂Si–μI–SiI), a trans double halogen bridged structure (D _2h, FSn–μF₂–SnF), and another trans double-bridged structure with puckered ring (C _S, IPb–μI₂–PbI). Some of the other structures that are stable but are not the global minima include: a trans-bent structure X₂M–MX₂ (C _2h, all X₂Si–SiX₂), cis double-bridged structure (C _2v with planar ring, FPb–μF₂–PbF, or with puckered ring, C _2v, IGe–μI₂–GeI), and even a square bipyramidal structure (D _4h, Sn–μF₄–Sn). The energy differences between some of the structures are small and the application of another computational method and using a different basis set might alter their relative stabilities. Reasons for the difference in the stabilities of isomers have been discussed.     

Ab initio MRD-CI study of neutral and charged Ga2, Ga3 and Ga4 clusters and comparison with corresponding boron and aluminum clusters

MRD-CI calculations were performed on Ga, Ga₂, Ga₃, Ga₄ and on the corresponding positive and negative ions. In general, pseudopotentials were used, and 4s4p/2s2p basis sets withs andp diffuse functions and one or twod functions. For Ga₂, all-electron calculations were also performed. For Ga ₂ ^(±) , potential functions for ground and low-lying excited states are given. For Ga ₃ ^(±) , geometries were optimized both inC _2v andD _∞h symmetry. The lowest state of Ga ₃ ⁺ is found to be¹Σ _g ⁺ , of Ga₃ ⁴ A ₂, and of Ga ₃ ^{? 1} A ₁ (D _3h ). Ionization potentials and electron affinities of Ga₃ were evaluated. Many low-lying excited states of Ga ₃ ^(±) were found. Rhombic (D _2h , including squareD _4h ), tetrahedral (T _d ), T-shaped (C _2v ) and linear structures (D _∞h) were investigated in the search for the lowest state of Ga₄. A square-planar arrangement of the nuclei, withR _e = 5.30 a₀, was found to have the lowest energy. The other geometries lie about 0.5 eV higher. InD _2h symmetry, low-lying excited states of Ga₄, as well as ground and excited states of Ga ₄ ⁺ and Ga ₄ ^? were studied. Geometries, ionization potentials, electron affinities, atomization and fragmentation energies of Ga _n are compared with corresponding data for B _n and Al _n . Typical changes in going from first-row to third-row atoms are observed.     

Geometrical and electronic structure of hydrated CH 5 + and CH 5 −

Different conformations of isolated and solvated CH ₅ ⁺ and CH ₅ ^? ions have been studied by CNDO method with Wiberg's parametrization. The anion has been found to have a most stable conformation ofD _3h symmetry both in the gas phase and in solution. AC _s symmetry conformation is the most stable one for the isolated cation, whereas a conformation withC _4v symmetry is energetically preferred in solution.     

MB 8 2− (M = Be, Mg, Ca, Sr, and Ba): Planar octacoordinate alkaline earth metal atoms enclosed by boron rings

Complexes involving planar octacoordinate alkaline earth metal atoms in the centers of eight-membered boron rings have been investigated by two density functional theory (DFT) methods. BeB ₈ ^2? with D _8h symmetry is predicted to be stable, both geometrically and electronically, since a good match is achieved between the size of the central beryllium atom and the eight-membered boron ring. By contrast, the other alkaline earth metal atoms cannot be stabilized in the center of a planar eight-membered boron ring because of their large radii. By following the out-of-plane imaginary vibrational frequency, pyramidal C _8v MgB ₈ ^2? , CaB ₈ ^2? , SrB ₈ ^2? , and BaB ₈ ^2? structures are obtained. The presence of delocalized π and σ valence molecular orbitals in D _8h BeB ₈ ^2? gives rise to aromaticity, which is reflected by the value of the nucleus-independent chemical shift. The D _8h BeB ₈ ^2? structure is confirmed to be the global minimum on the potential energy surface.     

Evolution of bulk-like properties in mercury microclusters

The transition from non-metallic to metallic behavior of mercury microclusters, Hg _n , withn ranging from 2 to 79, is investigated using first principles tight-binding linear muffin-tin orbital method. Then dependence of the ionization potential, the cohesive energy, the energy gap, and the nature of the bonding indicates metallic behavior for Hg _n withn≧80. The average bond length of Hg clusters is found to be larger than that of the bulk. Our results are in good agreement with experiments.     

Tetra­ethyl­ammonium bis­(N,N‐diethyl­dithio­carbamato‐κ2S,S′)iodo­cadmate(II)

The title compound, (C₈H₂₀N)[Cd(C₅H₁₀NS₂)₂I], containing a heteroleptic five‐coordinate mononuclear anionic cadmium complex, crystallizes in ortho­rhom­bic form in the space group Pnma. Both anion and cation lie about mirror planes. Unlike other known [Cd(dtc)₂X]‐type complexes (where dtc is dithio­carbamate and X is a halogen or pseudohalogen), the central CdS₄I core shows a square‐pyramidal configuration, with a basal plane defined by four S atoms from two chelating dithio­carbamate ligands related by a symmetry plane. The central Cd atom is displaced from the basal S₄ plane towards the apical I atom of the square pyramid.     

The route to MBxNyCz molecular wheels: II. Results using accurate functionals and basis sets

Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiB_n (for n = 3–10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiB_xN_yC_z (for x, y, z = 0–10) and MB_nC_10−n (for n = 2 to 5 and M = Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiB_n clusters (for n = 3–8). Different isomers of TiB₁₀ clusters were also studied and a structural transition of 3D-isomer into 2D-wheel is presented. Substitution boron in TiB₁₀ by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB₃C₇. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first row.     

Explanation for the structural differences of S2+4, S04 and S2−4

An explanation for the geometry changes upon successive double reductions of S²⁺₄ (square planar, D_4h symmetry) to neutral S₄ (for which the structure is unknown) and finally to S^2?₄ (non-planar, C₂ symmetry) is given on the basis of orbital eigenvalues and wavefunctions calculated with the self-consistent-field Xα scattered-wave molecular orbital method.     

Quantum chemical study of the structure of tetrasilacyclobutadiene,its dication,and dianion

MINDO/3 calculations have indicated the instability of the D _2h planar geometrical configuration of tetrasilacyclobutadiene relative both to pyramidalization of the silicon atoms with the formation of a nonplanar C _2h structure and acoplanarization of the silicon skeleton leading to a C _s nonplanar bicyclic structure. Such distortions are also characteristic for the D _4h structure of the tetrasilabicyclobutadiene dianion. The dication of tetrasilabicyclobutadiene has D _2d nonplanar symmetry, similar to that for the dication of cyclobutadiene.Physical and Organic Chemistry Research Institute, Rostov State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 6, pp. 23–32, November–December, 1989.     

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     

Geometrical and Electronic Properties of the Clusters of C<Subscript>20</Subscript> Cage Doped with Alkali Metal Atoms

Using first-principles density-functional theory based on the generalized gradient approximation, we have investigated the geometrical and electronic properties of the pure C₂₀ cage with D _3d symmetry and M@C₂₀(M = Li, Na, K, Rb, Cs) clusters with I _h symmetry. It is found that the interstitial M@C₂₀ clusters are energetically stable and have strong total magnetic moments. The stability is analyzed through charge distributions on the atoms and the magnetism is explained through the degeneracy and fractional occupation of the molecular orbitals.     

Structure and electronic properties of hollow‐caged C60 fullerene‐derived (MN4)nC6(10 − n) (M = Zn,Mg, Fe,n = 1−6) complexes

Unique hollow‐caged (MN₄)_nC_{6(10 ? n)} (M = Zn, Mg, Fe, n = 1?6) complexes designed by introduction of n porphyrinoid fragments in C₆₀ fullerene structure were proposed and the atomic and electronic structures were calculated using LC‐DFT MPWB95 and M06 potentials and 6‐311G(d)/6‐31G(d) basis sets. The complexes were optimized using various symmetric configurations from the highest O_h to the lowest C₁ point groups in different spin states from S = 0 (singlet) to S = 7 (quindectet) for M = Fe to define energetically preferable atomic and electronic structures. Several metastable complexes were determined and the key role of the metal ions in stabilization of the atomic structure of the complexes was revealed. For Fe₆N₂₄C₂₄, the minimum energy was reported for C_2h, D_2h, and D_4h symmetry of pentet state S = 2, so the complex can be regarded as unique molecular magnet. It was found that the metal partial density of states determine the nature of HOMO and LUMO levels making the clusters promising catalysts. © 2014 Wiley Periodicals, Inc.     

Organomagnesium clusters: Structure, stability, and bonding in archetypal models

We have studied the molecular structure and the nature of the chemical bond in the monomers and tetramers of the Grignard reagent CH₃MgCl as well as MgX₂ (X = H, Cl, and CH₃) at the BP86/TZ2P level of theory. For the tetramers, we discuss the stability of three possible molecular structures of C_2h, D_2h, and T_d symmetry. The most stable structure for (MgCl₂)₄ is D_2h, the one for (MgH₂)₄ is C_2h, and that of (CH₃MgCl)₄ is T_d. The latter is 38 kcal/mol more stable with chlorines in bridge positions and methyl groups coordinated to a Mg vertex than vice versa. We find through a quantitative energy decomposition analysis (EDA) that the tetramerization energy is predominantly composed of electrostatic attraction ΔV_elstat (60% of all bonding terms ΔV_elstat + ?E_oi) although the orbital interaction ?E_oi also provides an important contribution (40%).     

Structure and energetics of Li/Na, Li/K, and K/Na bimetallic hexamers

A systematic study of neutral mixed clusters, Li_6?x Na _x , Li_6?x K _x and K_6?x Na _x (x = 0–6), was performed within the framework of density functional theory. The aim of this work is to explore the geometry variation and the energy change of homonuclear hexamers (Li₆ and K₆) induced by impurities. It is found that the geometry of bimetallic hexamers varies with their compositions. The geometries of resulting clusters show evolution from D_4h symmetry for Li₆ to D_3h symmetry for Na₆ and K₆. The stability of bimetallic hexamers has been also explained in terms of binding energy, excess energy, the second difference in energy, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps. It is found that replacing each Li–Li bond with Li–Na or Li–K bonds decreases the cluster stability, while replacing each K–K bond by K–Na leads to stability enhancement. Examining the cluster stability, excess energy and second difference in energy reveal that among studied bimetallic hexamers, Li₂Na₄ is the most stable mixed hexamer.     

A new structural type in ternary chalcogenide chemistry: Structure and properties of Nb2Pd3Se8

A study of the NbPdSe system has afforded a new phase, Nb₂Pd₃Se₈. The structure of this phase has been established through single-crystal X-ray measurements. The compound crystallizes in space group D⁹_2h-Pbam with two formula units in a cell of dimensions a = 15.074(6), b = 10.573(4), c = 3.547(2)Å. In this unusual structure there are two chains of edge-sharing selenium trigonal prisms centered by niobium atoms. These chains conjoin through two types of palladium atoms—square planar and square pyramidal—each coordinated by selenium atoms. As a consequence of this conjunction tunnels extending along c result. Electrical conductivity measurements indicate that this material is a metallic-semiconductor.