Density functional study of 8- and 11-vertex polyhedral borane structures: comparison with bare germanium clusters

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the polyhedral boranes B(n)H(n)(z) (n = 8 and 11, z = -2, -4, and -6) for comparison with isoelectronic germanium clusters Ge(n)(z). The energy differences between the global minima and other higher energy borane structures are much larger relative to the case of the corresponding bare germanium clusters. Furthermore, for both B(8)H(8)(2-) and B(11)H(11)(2-), the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade-Mingos rules, namely the D(2)(d) bisdisphenoid and the C(2)(v) edge-coalesced icosahedron, respectively. Only in the case of B(8)H(8)(2-) is there a second structure close (+2.6 kcal/mol) to the D(2)(d) bisdisphenoid global minimum, namely the C(2)(v) bicapped trigonal prism corresponding to the "square" intermediate in a single diamond-square-diamond process that can lead to the experimentally observed room temperature fluxionality of B(8)H(8)(2-). Stable borane structures with 3-fold symmetry (e.g., D(3)(h), C(3)(v), etc.) are not found for boranes with 8- and 11-vertices, in contrast to the corresponding germanium clusters where stable structures derived from the D(3)(d) bicapped octahedron and D(3)(h) pentacapped trigonal prism are found for the 8- and 11-vertex systems, respectively. The lowest energy structures found for the electron-rich boranes B(8)H(8)(4-) and B(11)H(11)(4-) are nido polyhedra derived from a closo deltahedron by removal of a relatively high degree vertex, as predicted by the Wade-Mingos rules. They relate to isoelectronic species found experimentally, e.g., B(8)H(12) and R(4)C(4)B(4)H(4) for B(8)H(8)(4-) and C(2)B(9)H(11)(2-) for B(11)H(11)(4-). Three structures were found for B(11)H(11)(6-) with arachno type geometry having two open faces in accord with the Wade-Mingos rules.     

Density functional theory study of nine-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(9)(z) clusters (z = -6, -4, -3, -2, 0, +2, and +4) starting from three different initial configurations. Double-zeta quality LANL2DZ basis functions extended by adding one set of polarization (d) and one set of diffuse (p) functions were used. The global minimum for Ge(9)(2)(-) is the tricapped trigonal prism expected by Wade's rules for a 2n + 2 skeletal electron structure. An elongated tricapped trigonal prism is the global minimum for Ge(9)(4)(-) similar to the experimentally found structure for the isoelectronic Bi(9)(5+). However, the capped square antiprism predicted by Wade's rules for a 2n + 4 skeletal electron structure is only 0.21 kcal/mol above this global minimum indicating that these two nine-vertex polyhedra have very similar energies in this system. Tricapped trigonal prismatic structures are found for both singlet and triplet Ge(9)(6)(-), with the latter being lower in energy by 3.66 kcal/mol and far less distorted. The global minimum for the hypoelectronic Ge(9) is a bicapped pentagonal bipyramid. However, a second structure for Ge(9) only 4.54 kcal/mol above this global minimum is the C(2)(v)() flattened tricapped trigonal prism structure found experimentally for the isoelectronic Tl(9)(9)(-). For the even more hypoelectronic Ge(9)(2+), the lowest energy structure consists of an octahedron fused to two trigonal bipyramids. For Ge(9)(4+), the global minimum is an oblate (squashed) pentagonal bipyramid with two pendant Ge vertices.     

Density functional theory study of 10-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge10z germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 12 different initial configurations. The D4d 4,4-bicapped square antiprism found experimentally in B10H102- and other 10-vertex clusters with 22 skeletal electrons is calculated for the isoelectronic Ge102- to be the global minimum by more than 15 kcal/mol. The global minima found for electron-rich clusters Ge104- and Ge106- are not those known experimentally. However, experimentally known structures for nido-B10H14 and the pentagonal antiprism of arachno-Pd@Bi104+ are found at higher but potentially accessible energies for Ge104- and Ge106-. The global minimum for Ge10 is the C3v 3,4,4,4-tetracapped trigonal prism predicted by the Wade-Mingos rules and found experimentally in isoelectronic Ni@Ga1010-. However, only slightly above this global minimum for Ge10 (+3.3 kcal/mol) is the likewise C3v isocloso 10-vertex deltahedron found in metallaboranes such as (eta6-arene)RuB9H9 derivatives. Structures found for more electron-poor clusters Ge102+ and Ge104+ include various capped octahedra and pentagonal bipyramids. This study predicts a number of 10-vertex cluster structures that have not yet been realized experimentally but would be interesting targets for future synthetic 10-vertex cluster chemistry using vertex units isolobal with the germanium vertices used in this work.     

Density functional theory study of twelve-atom germanium clusters: conflict between the Wade-Mingos rules and optimum vertex degrees

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge(12)(z) bare germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 11 initial configurations. The Wade-Mingos rules are seen to have limited value in rationalizing the results since they frequently require vertex degrees higher than the optimum vertex degree of 4 for germanium. Thus the expected I(h) regular icosahedron is no longer the global minimum for Ge(12)(2-) although it remains a low energy structure for Ge(12)(2-) lying only 5.6 kcal mol(-1) above a bicapped arachno structure conforming to the Wade-Mingos rules. The three lowest energy structures for Ge(12)(4-) within 11 kcal mol(-1) are a prolate (elongated) polyhedron with six quadrilateral faces and eight triangular faces, the dual of the bisdisphenoid with four trapezoidal and four pentagonal faces, and a polyhedron with two quadrilateral and 16 triangular faces related but not identical to the polyhedron found in the known tetracarbon carboranes R(4)C(4)B(8)H(8). The lowest energy structures for the neutral Ge(12) are seen to be distorted versions of the icosahedron and the bicapped 10-vertex arachno lowest energy structures for Ge(12)(2-). The low energy structures for the even more hypoelectronic Ge(12)(2+) and Ge(12)(4+) are even more unusual including a hexacapped octahedron, a tetracapped square antiprism, and a double cube for Ge(12)(2+) and a C(2v) structure with a central unique degree 6 vertex for Ge(12)(4+).     

Endohedral beryllium atoms in ten-vertex germanium clusters: effect of a small interstitial atom on the cluster geometry

Ten-vertex clusters are unusually versatile because polyhedra with 3-, 4-, and 5-fold symmetry are possible and are found in experimentally known structures. Such clusters therefore provide useful probes for subtle effects on cluster structure such as changing the electron count or introducing an interstitial atom. In this connection, DFT shows that one of the smallest possible interstitial atoms, namely beryllium, has relatively little effect on the structures of Be@Ge(10)(z) (z = +2, 0, -2, -4) clusters. Thus the same C(3v) and D(4d) polyhedra are found as the lowest energy structures for the isoelectronic pairs Be@Ge(10)(2+)/Ge(10) and Be@Ge(10)/Ge(10)(2-). Even for the more complicated potential energy surfaces of the Be@Ge(10)(2-)/Ge(10)(4-) and Be@Ge(10)(4-)/Ge(10)(6-) systems, the lowest energy structures are remarkably similar. Thus the same C(2v) structures are the global minima for both Be@Ge(10)(2-) and Ge(10)(4-). Similarly, the same slipped pentagonal prism structures are the global minima for both Be@Ge(10)(4-) and Ge(10)(6-).     

Endohedral beryllium atoms in germanium clusters with eight and fewer vertices: how small can a cluster be and still encapsulate a central atom?

Structures of the beryllium-centered germanium clusters Be@Ge(n)(z) (n = 8, 7, 6; z = -4, -2, 0, +2) have been investigated by density functional theory to provide some insight regarding the smallest metal cluster that can encapsulate an interstitial atom. The lowest energy structures of the eight-vertex Be@Ge(8)(z) clusters (z = -4, -2, 0, +2) all have the Be atom at the center of a closed polyhedron, namely, a D(4d) square antiprism for Be@Ge(8)(4-), a D(2d) bisdisphenoid for Be@Ge(8)(2-), an ideal O(h) cube for Be@Ge(8), and a C(2v) distorted cube for Be@Ge(8)(2+). The Be-centered cubic structures predicted for Be@Ge(8) and Be@Ge(8)(2+) differ from the previously predicted lowest energy structures for the isoelectronic Ge(8)(2-) and Ge(8). This appears to be related to the larger internal volume of the cube relative to other closed eight-vertex polyhedra. The lowest energy structures for the smaller seven- and six-vertex clusters Be@Ge(n)(z) (n = 7, 6; z = -4, -2, 0, +2) no longer have the Be atom at the center of a closed Ge(n) polyhedron. Instead, either the Ge(n) polyhedron has opened up to provide a larger volume for the Be atom or the Be atom has migrated to the surface of the polyhedron. However, higher energy structures are found in which the Be atom is located at the center of a Ge(n) (n = 7, 6) polyhedron. Examples of such structures are a centered C(2v) capped trigonal prismatic structure for Be@Ge(7)(2-), a centered D(5h) pentagonal bipyramidal structure for Be@Ge(7), a centered D(3h) trigonal prismatic structure for Be@Ge(6)(4-), and a centered octahedral structure for Be@Ge(6). Cluster buildup reactions of the type Be@Ge(n)(z) + Ge(2) → Be@Ge(n+2)(z) (n = 6, 8; z = -4, -2, 0, +2) are all predicted to be highly exothermic. This suggests that interstitial clusters having an endohedral atom inside a bare post transition element polyhedron with eight or fewer vertices are less than the optimum size. This is consistent with the experimental observation of several types of 10-vertex polyhedral bare post transition element clusters with interstitial atoms but the failure to observe such clusters with external polyhedra having eight or fewer vertices.     

Density functional theory study of eight-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge8z(z=-6, -4, -2, 0, +2, +4) using nine initial geometries. For Ge8(2-) the D2d bisdisphenoid structure predicted by the Wade-Mingos rules is not computed to be the global minimum but instead lies 3.9 kcal mol-1 above the Td tetracapped tetrahedron global minimum predicted to exhibit spherical aromaticity. The hyperelectronic clusters Ge(8)4- and Ge8(6-) have nido B8H12 and square antiprism structures, respectively, as global minima in accord with the Wade-Mingos rules and experimental data on E(8)2+(E=Sb, Bi) cations. Hypoelectronic eight-vertex clusters isoelectronic and isolobal with Ge8, Ge8(2+) and Ge(8)4+ are not known experimentally. Their computed structures include smaller polyhedra having one or more capped triangular faces as well as more open non-polyhedral structures.     

Polyhedral structures with three-, four-, and five fold symmetry in metal-centered ten-vertex germanium clusters

Studies using density functional theory (DFT) at the hybrid B3LYP level indicate that the relative energies of structures with three-fold, four-fold, and five-fold symmetry for centered 10-vertex bare germanium clusters of the general type M@Ge(10) (z) depend on the central metal atom M and the skeletal electron count. For M@Ge(10) clusters with 20 skeletal electrons the DFT results agree with experimental data on the isoelectronic centered 10-vertex bare metal clusters. Thus the lowest energy structure for Ni@Ge(10), isoelectronic with the known Ni@In(10) (10-), is a C(3v) polyhedron derived from the tetracapped trigonal prism. However, Zn@Ge(10) (2+) is isoelectronic with the known cluster Zn@In(10) (8-), which has the lowest energy structure, a D(4d) bicapped square antiprism. For the clusters Ni@Ge(10) (2-), Cu@Ge(10) (-), and Zn@Ge(10) that have 22 skeletal electrons the lowest energy structures are the D(4d) bicapped square antiprism predicted by the Wade-Mingos rules. For the clusters Ni@Ge(10) (4-), Cu@Ge(10) (3-), and Zn@Ge(10) (2-) that have 24 skeletal electrons the lowest energy structures are C(3v) polyhedra with 10 triangular faces and 3 quadrilateral faces derived from a tetracapped trigonal prism by extreme lengthening of the edges of the capped triangular face of the underlying trigonal prism. For the clusters Cu@Ge(10) (5-) and Zn@Ge(10) (4-) that have 26 skeletal electrons the lowest energy structures are the D(5d) pentagonal antiprisms predicted by the Wade-Mingos rules and the C(3v) tetracapped trigonal prism as a somewhat higher energy structure. However, for the isoelectronic Ni@Ge(10) (6-) the relative energies of these two structure types are reversed so that the C(3v) tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D(5d) pentagonal prism and D(4d) bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.     

A(15)Tl(27) (A = Rb, Cs): A Structural Type Containing Both Isolated Clusters and Condensed Layers Based on the Tl(11) Fragment. Syntheses, Structure, Properties, and Band Structure

The isomorphous title compounds (and the ordered substitutional Rb(14)CsTl(27)) are obtained directly from reactions of the elements in sealed Ta below approximately 330 degrees C. Refinements of single-crystal data for the three established a structure with alternate layers of isolated pentacapped trigonal prismatic Tl(11)(7)(-) (D(3)(h)()) ions and condensed [Tl(16)(8-)] networks that are separated by cations. The condensed layer consists of Tl(11) units that share prismatic edges and are interbridged through waist-capping atoms (Tl(6/2)Tl(3)Tl(2)). (Rb(15)Tl(27): P&sixmacr;2m, Z = 1, a = 10.3248(6) ?, c = 17.558(2) ?.) The rubidium phase is a poor metal (rho(293) approximately 34 &mgr;Omega.cm) and is Pauli-paramagnetic. Extended Hückel band calculations indicate partially filled bands and a non-zero DOS at E(F), consistent with the observed metallic behavior, although appropriate cation tuning or modest anion doping should provide a Zintl phase. The band structure and COOP curves are also used to rationalize the distortion of the Tl(11) unit on condensation and the critical role of the interfragment bonds between waist-capping atoms in stabilizing the layer.     

Structural and Quantum Chemical Study of Bi(5)(3+) and Isoelectronic Main-Group Metal Clusters. The Crystal Structure of Pentabismuth(3+) Tetrachlorogallate(III) Refined from X-ray Powder Diffraction Data and Synthetic Attempts on Its Antimony Analogue

Pentabismuth(3+) tetrachlorogallate(III), (Bi(5)(3+))(GaCl(4)(-))(3), has been synthesized by reducing a BiCl(3)-GaCl(3) melt with bismuth metal and the crystal structure refined from X-ray (Cu Kalpha(1)) powder diffraction data. The structure was found to belong to space group R-3c, with the lattice parameters a = 11.871(2) ? and c = 30.101(3) ? (Z = 6). It is isostructural with the previously characterized Bi(5)(AlCl(4))(3). An attempt to synthesise the antimony analogue Sb(5)(GaCl(4))(3) by reducing a SbCl(3)-GaCl(3) mixture with gallium metal produced a black solid phase. The gallium content of this phase is consistent with the stoichiometry Sb(5)(GaCl(4))(3), and the Raman spectrum of the phase dissolved in SbCl(3)-GaCl(3) comprises strong, low-frequency bands attributable to Sb-Sb stretch vibrations in Sb(5)(3+) or another reduced antimony species. Quantum chemical analyses have been performed for the isoelectronic, trigonal pyramidal closo-clusters Sn(5)(2-), Sb(5)(3+), Tl(5)(7-), Pb(5)(2-), and Bi(5)(3+), both with extended Hückel (eH) and Hartree-Fock (HF) methods. The HF calculations were performed with and without corrections for the local electron-electron correlation using second-order M?ller-Plesset perturbation theory (MP2). All theoretical results are compared and evaluted with respect to experimental cluster structures and vibrational frequencies. The results from the calculations agree well with available experimental data for the solid-state structures and vibrational spectra of these cluster ions, except for the Tl(5)(7-) ion. Isolated Tl(5)(7-) is suggested to be electronically unstable because of the high charge density. The Sb(5)(3+) cluster ion is indicated to be stable. According to the calculations, Sn(5)(2-) and Pb(5)(2-) may be described in terms of edge-localized bonds without substantial electron density between the equatorial atoms, whereas Sb(5)(3+) and Bi(5)(3+) have electron density evenly distributed over all M-M vectors. Furthermore, the theoretical results give no support for a D(3h) --> C(4v) fluxionality of these clusters.     

Na(23)K(9)Tl(15.3): An Unusual Zintl Compound Containing Apparent Tl(5)(7)(-), Tl(4)(8)(-), Tl(3)(7)(-), and Tl(5)(-) Anions

Reaction of the neat elements in tantalum containers at 400 degrees C and then 150 degrees C gives the pure title phase. X-ray crystallography shows that the hexagonal structure (P6(3)/mmc, Z = 2, a = 11.235(1) ?, b = 30.133(5) ?) contains relatively high symmetry clusters Tl(5)(7)(-) (D(3)(h)()), Tl(4)(8)(-) (C(3)(v)(), approximately T(d)), and the new Tl(3)(7)(-) (D(infinity)(h)()) plus Tl(5)(-), the last two disordered over the same elongated site in 1:2 proportions. Cation solvation of these anions is tight and specific, providing good Coulombic trapping of weakly bound electrons on the isolated cluster anions. The observed disorder makes the compound structurally a Zintl phase with a closed shell electron count. EHMO calculations on the novel Tl(3)(7)(-) reveal some bonding similarities with the isoelectronic CO(2), with two good sigma(s,p) bonding and two weakly bonding pi MO's. The Tl-Tl bond lengths therein (3.14 ?) are evidently consistent with multiple bonding. The weak temperature-independent paramagnetism and metallic conductivity (rho(293) approximately 90 &mgr;Omega.cm) of the phase are discussed.     

The maximum number of carbonyl groups around an Ru6C polyhedral cluster: hexanuclear ruthenium carbonyl carbides

Octahedral, trigonal prismatic, and capped square pyramidal structures have been optimized for the Ru(6)C(CO)(n) clusters (15 ≤ n ≤ 20) using density functional theory. The experimentally known very stable Ru(6)C(CO)(17) is predicted to have an octahedral structure in accord with experiment as well as the Wade-Mingos rules. The stability of Ru(6)C(CO)(17) is indicated by its high carbonyl dissociation energy of ~37 kcal mol(-1) and the high energy of ~33 kcal mol(-1) required for disproportionation into Ru(6)C(CO)(18) + Ru(6)C(CO)(16). Theoretical calculations predict a doubly carbonyl bridged octahedral Ru(6)C(CO)(17) structure to be ~0.7 kcal mol(-1) more stable than the experimentally observed singly bridged structure. A trigonal prismatic Ru(6)C(CO)(19) cluster isoelectronic with the known Co(6)C(CO)(15)(2-) dianion does not appear to be viable as indicated by a low carbonyl dissociation energy of 8.8 kcal mol(-1) and a required energy of only 4.9 kcal mol(-1) for disproportionation into Ru(6)C(CO)(20) + Ru(6)C(CO)(18). The predicted instability of Ru(6)C(CO)(n) (n ≥ 18) derivatives suggests a maximum of 17 external carbonyl groups around a stable polyhedral Ru(6)C structure.     

Polyatomic clusters of the triel elements. Palladium-centered clusters of thallium in A(8)Tl(11)Pd,A = Cs,Rb, K

Reactions of the elements within welded Ta containers at approximately 600 degrees C followed by slow cooling give new A(8)Tl(11)Pd(x) products from an apparently continuous encapsulation of Pd atoms into the pentacapped trigonal prismatic anions in the isotypic rhombohedral (R3 macro c) A(8)Tl(11) phases. All systems also produce other phases at x < 1 as well, the simplest being the cesium system in which only trigonal Pd(13)Tl(9) is also formed. Cs(8)Tl(11)Pd(0.84(1)) was characterized by single-crystal means as close to the upper x limit in that system (R3 macro c, Z = 6, a = 10.610(1) A, c = 54.683(8) A). The Pd insertion causes an expansion of the D(3) host anion, particularly about the waist, to generate a trigonal bipyramidal PdTl(5) unit (d(Pd-Tl) approximately 2.6-2.8 A) centered within a somewhat larger Tl(6) trigonal prism, the remainder of the Tl(11) cluster. Strong Tl cage bonding is retained. Extended Hückel calculations show significant involvement of all Tl 6s, 6p and Pd 4d, 5s, 5p orbital sets in the central and cage bonding. The last valence electron is considered to be delocalized in a conduction band, as in A(8)Tr(11) examples, rather than occupying an antibonding e' LUMO across a gap of approximately 2.4 eV.     

Planarization of B7- and B12- clusters by isoelectronic substitution: AlB6- and AlB11-

Small boron clusters have been shown to be planar from a series of combined photoelectron spectroscopy and theoretical studies. However, a number of boron clusters are quasiplanar, such as B(7)(-) and B(12)(-). To elucidate the nature of the nonplanarity in these clusters, we have investigated the electronic structure and chemical bonding of two isoelectronic Al-doped boron clusters, AlB(6)(-) and AlB(11)(-). Vibrationally resolved photoelectron spectra were obtained for AlB(6)(-), resulting in an accurate electron affinity (EA) for AlB(6) of 2.49 ± 0.03 eV. The photoelectron spectra of AlB(11)(-) revealed the presence of two isomers with EAs of 2.16 ± 0.03 and 2.33 ± 0.03 eV, respectively. Global minimum structures of both AlB(6)(-) and AlB(11)(-) were established from unbiased searches and comparison with the experimental data. The global minimum of AlB(6)(-) is nearly planar with a central B atom and an AlB(5) six membered ring, in contrast to that of B(7)(-), which possesses a C(2v) structure with a large distortion from planarity. Two nearly degenerate structures were found for AlB(11)(-) competing for the global minimum, in agreement with the experimental observation. One of these isomers with the lower EA can be viewed as substituting a peripheral B atom by Al in B(12)(-), which has a bowl shape with a B(9) outer ring and an out-of-plane inner B(3) triangle. The second isomer of AlB(11)(-) can be viewed as an Al atom interacting with a B(11)(-) cluster. Both isomers of AlB(11)(-) are perfectly planar. It is shown that Al substitution of a peripheral B atom in B(7)(-) and B(12)(-) induces planarization by slightly expanding the outer ring due to the larger size of Al.     

Syntheses, structure, and bonding of Rb14(Mg1-xInx)30. A nonstoichiometric phase with an unusual substitution in the anion framework

The title compound Rb(14)(Mg(1-x)In(x))(30) (x = 0.79-0.88) has been obtained from high-temperature reactions of the elements in welded Ta tubes. There is no analogous binary compound without Mg. The crystal structure established by single-crystal X-ray diffraction means (space group P2m (No. 189), Z = 1 and a = b = 10.1593(3) Angstroms, c = 17.783(1) Angstroms for x = 0.851) features two distinct types of anionic layers: isolated pentacapped trigonal prismatic In(11)(7-) clusters and condensed [(Mg(x)In(1-x))(5)In(14)](7-) layers. The latter consists of analogous M(11) (M = Mg/In) fragments that share prismatic edges and are interbridged by trigonal M(3) units. The structure shows substantial differences from related A(15)Tl(27) (A = Rb, Cs) in which the cation A that centers a six-membered ring of Tl(11) fragments is replaced by M(3.) Both linear muffin-tin orbital and extended Hückel calculations are used to analyze the observed phase width and site preferences. We further utilize the results to rationalize the distortion of the M(11) fragment in the condensed layer and also to correlate with electrical properties. An isomorphous phase region (Rb(y)K(1-)(y))(14)(Mg(1-x)In(x))(30) (y = 0.52, 0.66 for x = 0.79) is also formed.     

Cobalt-centered ten-vertex germanium clusters: the pentagonal prism as an alternative to polyhedra predicted by the Wade-Mingos rules

One of the most exciting recent (2009) discoveries in metal cluster chemistry is the pentagonal prismatic Co@Ge(10)(3-) ion, found in [K(2,2,2-crypt)](4)[Co@Ge(10)][Co(1,5-C(8)H(12))(2)]·toluene and characterized structurally by X-ray diffraction. The complete absence of triangular faces in the pentagonal prismatic structure of Co@Ge(10)(3-) contradicts expectations from the well-established Wade-Mingos rules, which predict polyhedral structures having mainly or entirely triangular faces. A theoretical study on Co@Ge(10)(z) systems (z = -5 to +1) predicts a singlet D(5h) pentagonal prismatic global minimum for the trianion Co@Ge(10)(3-) in accord with this experimental result. Redox reactions on this pentagonal prismatic Co@Ge(10)(3-) trianion generate low-energy pentagonal prismatic structures for Co@Ge(10)(z) where z = 0, -1, -2, -4, and -5 having quartet, triplet, doublet, doublet, and triplet spin states, respectively. Similar theoretical methods predict a singlet C(3v) polyhedral structure for the monoanion Co@Ge(10)(-), similar to previous theoretical predictions on the isoelectronic neutral Ni@Ge(10) and the structure realized experimentally in the isoelectronic Ni@In(10)(10-) found in the K(10)In(10)Ni intermetallic. Redox reactions on this C(3v) polyhedral Co@Ge(10)(-) monoanion generate low energy C(3v) polyhedral structures for Co@Ge(10)(z) where z = 0, -2, -3, and -4 having doublet, doublet, triplet, and quartet spin states, respectively.     

Novel class of heterometallic cubane and boride clusters containing heavier group 16 elements

Thermolysis of an in situ generated intermediate, produced from the reaction of [Cp*MoCl(4)] (Cp* = η(5)-C(5)Me(5)) and [LiBH(4).THF], with excess Te powder yielded isomeric [(Cp*Mo)(2)B(4)TeH(5)Cl] (2 and 3), [(Cp*Mo)(2)B(4)(μ(3)-OEt)TeH(3)Cl] (4), and [(Cp*Mo)(4)B(4)H(4)(μ(4)-BH)(3)] (5). Cluster 4 is a notable example of a dimolybdaoxatelluraborane cluster where both oxygen and tellurium are contiguously bound to molybdenum and boron. Cluster 5 represents an unprecedented metal-rich metallaborane cluster with a cubane core. The dimolybdaheteroborane 2 was found to be very reactive toward metal carbonyl compounds, and as a result, mild pyrolysis of 2 with [Fe(2)(CO)(9)] yielded distorted cubane cluster [(Cp*Mo)(2)(BH)(4)(μ(3)-Te){Fe(CO)(3)}] (6) and with [Co(2)(CO)(8)] produced the bicapped pentagonal bipyramid [(Cp*MoCo)(2)B(3)H(2)(μ(3)-Te)(μ-CO){Co(3)(CO)(6)}] (7) and pentacapped trigonal prism [(Cp*MoCo)(2)B(3)H(2)(μ(3)-Te)(μ-CO)(4){Co(6)(CO)(8)}] (8). The geometry of 8 is an example of a heterometallic boride cluster in which five Co and one Mo atom define a trigonal prismatic framework. The resultant trigonal prism core is in turn capped by two boron, one Te, and one Co atom. In the pentacapped trigonal prism unit of 8, one of the boron atoms is completely encapsulated and bonded to one molybdenum, one boron, and five cobalt atoms. All the new compounds have been characterized in solution by IR, (1)H, (11)B, and (13)C NMR spectroscopy, and the structural types were unambiguously established by crystallographic analysis of 2 and 4-8.     

An incommensurately modulated structure of η'-phase of Cu(3+x)Si determined by quantitative electron diffraction tomography

The diffraction data of η'-Cu(3+x)(Si,Ge) were collected by 3D quantitative electron diffraction tomography on a submicrometer-sized sample, and the structure was solved by the charge-flipping algorithm in superspace. It is shown that the structure is trigonal, and it is incommensurately modulated with two modulation vectors q(1) = (α, α, 1/3) and q(2) = (-2α, α, 1/3), superspace group P31m(α, α, 1/3)000(-2α, α, 1/3)000. The modulation functions of some atoms are very complicated and reach amplitudes comparable with the unit cell dimensions. The modulated structure can be described as sheets of Cu clusters separated by honeycomb layers of mixed Si/Ge positions. The shape of the Cu clusters in the sheets strongly varies with the modulation phase, and the predominant form is an icosahedron. The striving of the Cu layers to form icosahedral clusters is deemed to be the main driving force of the modulation. The combination of methods used in this work can be applied to other structures that are difficult to crystallize in large crystals and opens new perspectives, especially for investigations of aperiodic or otherwise complex metallic alloys.     

Reduction of the host cationic framework charge by isoelectronic substitution: synthesis and structure of Hg7Ag2P8X6 (X = Br, I) and Hg6Ag4P8Br6

The first compounds, Hg(7)Ag(2)P(8)X(6) (X = Br, I) and Hg(6)Ag(4)P(8)Br(6), featuring the partial isoelectronic substitution of Hg(2+) for Ag(1+) in mercury-pnicogen frameworks have been obtained and structurally characterized. The new compounds are the supramolecular assemblies built of the covalently bonded metal-pnicogen frameworks trapping guests of different complexity. The frameworks feature the perfect ordering of Hg(2+) and Ag(1+) cations and contain P(2)(4)(-) and P(6)(6)(-) phosphorus clusters. The substitution of Hg(2+) with Ag(1+) leads to the reduction in charge of the host cluster-containing cationic matrix and concomitant replacement of the monatomic X(-) guest by a lesser amount of the AgBr(3)(2)(-) anions.     

Flattening of rhodium vertices in mixed rhodium-nickel carbonyl clusters: relationships to borane and zintl ion structures

The flattened deltahedra and related polyhedra found in hypoelectronic bare group 13 metal cluster anions are also found in some anionic mixed rhodium-nickel carbonyl clusters. In all cases the rhodium vertices rather than the nickel vertices are involved in the flattening process so that the rhodium vertices contribute four internal orbitals and the nickel vertices three internal orbitals to the skeletal bonding of the cluster. Thus, the 11-vertex cluster Rh(5)Ni(6)(CO)(21)(3-) has a D(3h) triflattened pentacapped trigonal prismatic structure similar to that found in the In(11)(7-) anion of the intermetallic K(8)In(11). Similarly the polyhedra in the 11-vertex cluster RhNi(10)(CO)(19)(3-) and the 9-vertex cluster Rh(3)Ni(6)(CO)(17)(3-) are both derived from a 10-vertex isocloso polyhedron by capping (for RhNi(10)(CO)(19)(3-)) or vertex removal (for Rh(3)Ni(6)(CO)(17)(3-)) followed by flattening all of the rhodium vertices. A D(3h) icosahedron with flattened rhodium vertices is found in the 12-vertex cluster Rh(3)Ni(9)(CO)(22)(3-).