Skeletal Electron Research Articles

Are closed clusters expected from the ( n + 1) skeletal electron pairs rule in alanes and gallanes? A DFT structural study of A nH n + 2 (A = Al, Ga, and n = 4–6)

It has been suggested recently that the alanes Al n H n + 2 can be treated by the polyhedral skeletal electron pair theory (PSEPT) of Wade and Mingos (W–M) as it was successful for their borane congeners such as B n H n + 2 , well known as the deprotonated B n H n 2−. To do so, the neutral Al n H n + 2 have been considered as Al n H n 2− + 2H +. The additional hydrogens donate their electrons to the Al n H n polyhedral framework and according to the n + 1 electron pairs rule; these clusters should have closo-polyhedral structures. In this work the homologous gallanes, the structures and stabilities of Ga n H n + 2 are studied at high levels of calculational theory and we investigated the applicability of the W–M rule to the alanes and gallanes A n H n + 2 ( n = 4–6; A = Al, Ga). It will be shown that the presence of bridging hydrogen atoms reduces the compactness of the corresponding polyhedron and so these species do not have the closed structures. The computations were performed at B3LYP/6-311+G(d,p), BPW91/6-311G(d,p) and B3LYP/6-311+G(3df,2p) levels of theory. Our interest in these compounds includes their potential use as hydrogen storage species and future clean sources of energy.

ChemInform Abstract: Homoatomic Polyanions of Post-Transition Elements. Synthesis, Structure, and Characterization of the Paramagnetic Nonagermanide (3-) Ion Ge3- 9, a C2v Cluster with an Odd Skeletal Electron Count.

The salt K3(2,2,2-cryptand)3(PPh3)3Ge9 has been obtained by complexation of the KGe1.8 alloy by 2,2,2-cryptand in ethylenediamine with solute triphenylphosphine. The structure of the anion has been determined crystallographically and the results are supported by EPR and extended Huckel calculations.

ChemInform Abstract: Theoretical Aspects of Metal Cluster Chemistry

During the last twenty years the Polyhedral Skeletal Electron Pair Theory and the isolobal analogy have provided a theoretical basis for the rapid experimental developments, which have occurred in metal cluster chemistry. These theoretical principles have been underpinned by m.o. calculations on specific molecules and more generally by the Tensor Surface Harmonic Theory. This paper will review the important theoretical developments and relate them to the experimental and structural data which have been obtained for cluster compounds in our own and other laboratories. In particular the application of theoretical principles for rationalising and predicting the structures of cluster compounds of the platinum metals and gold are discussed. The bonding requirements of interstitial atoms and fragments are discussed, particularly in the context of interstitial C, B, N and transition metal atoms and diatomic fragments, e.g. C2 and C-H. POLYHEDRAL SKELETAL ELECTRON PAIR THEORY The historical development of the theoretical ideas which have contributed to the Polyhedral Skeletal Electron Pair Theory can be traced back to the pioneering work of Longuet-Higgins forty years ago. In the 1950's the contributions of Longuet-Higgins proved decisive since he not only provided a molecular orbital description of the bonding in diborane (ref. l), but also pioneered the application of molecular orbital theory ideas to deltahedral borides and boranes (ref. 2). The three-centre two-electron description of B-H-B and B-B-B bonds was elegantly generalised into the styx formalism and applied to all known boron hydrides by Lipscomb (ref. 3). The molecular orbital analysis of polyhedral boranes resulted in the successful prediction of the octahedral and icosahedral borane anions some years before they were structurally characterised (ref. 4). Hoffmann and Lipscomb (ref. 5) also developed the molecular orbital methodology of L nguet-Higgins in a general molecular orbital analysis of polyhedral borane anions, BnH;-, in 1962. In the 1960's Cotton and Haas (ref. 6) pioneered the development of molecular orbital ideas to metal cluster compounds of the early transition metals stabilised by halide ligands. Their analysis emphasised the important interactions which can result in such clusters from the overlap of the transition metal d orbitals. An alternative localised description of the bonding in such clusters, which resembled the styx methodology, was proposed by Kettle (ref. 7). These theoretical models tended to emphasise the inherent differences between metal and main group clusters and in common with ligand field theory tended to stress the role of the metal d orbitals. By the mid-nineteen sixties the major classes of transition metal IT -donor and acceptor clusters, and main group polyhedral borane and Zintl 'naked' clusters had been established but were viewed as distinct areas of inorganic chemistry. Experimental studies had, however, begun to indicate the artificiality of these subdivisions. The synthesis of polyhedral organometallic compounds from the reactions of acetylenes with metal carbonyls by HUbel and Braye and transition metallocarboranes by Hawthorne's group (ref. 8) clearly demonstrated that it was possible to synthesise polyhedral molecules with transition metal and main group atoms at the vertices. In addition the structural characterisation of Rh6(C0Il6 by Dahl (ref. 9) provided a real difficulty for the theoretical models which were most widely used. The bonding in Rh6(C0)16 could not be explained by the effective atomic number rule and was not amenable to a molecular orb'tal

ChemInform Abstract: Synthesis, Characterization and Bonding of Indium Clusters: Na7In11.8, a Novel Network Structure Containing closo-In16 and nido-In11 Clusters.

Reactions of the elements in proportions near 37.3 at. % Na at [approximately] 500, 410, and then 250C readily produce the well-crystallized title phase. The tetragonal structure at the indium-rich limit was solved by standard single-crystal X-ray means at room temperature. The network structure consists of interbonded clusters - the first example of closo-In[sub 16] icosioctahedra ([anti 4]m2 symmetry) that are 8-exo-bonded, 10-bonded nido icosahedra (fractional occupancy of the eleventh cluster site generates [approximately]36% 1,3-arachno units) and four-bonded indium atoms in pairs of triangle (In[sub 16]:In[sub 11(10)]:In[sub 1] = 1:4:12). Extended Hueckel calculations that include significant interactions between directional nonbonding pairs on atoms in neighboring In[sub 16] and In[sub 11] units indicate 2n + 4 skeletal electrons are necessary for each, with no nonbonding pairs on the latter, and a closed shell for 504 electrons per cell vs 507 for the refined stoichiometry. Observed properties are in good agreement; at the indium-rich limit, the phase is a poor metal ([rho][sub 295] [approximately] 540 [mu][Omega][center dot]cm) with a Pauli-like paramagnetism [chi][sub M] = (1.7 [minus] 1.8) [times] 10[sup [minus]4] emu/mol after correction for core and orbital diamagnetism. The intercluster interactions appear to be closely correlated with a small region of nonstoichiometrymore » and changes in the c lattice parameter. Some general factors in a diverse indium cluster chemistry are noted.« less

Synthetic Approach for Tunable, Size-Selective Formation of Monodisperse, Diphosphine-Protected Gold Nanoclusters

We report a new strategy that provides stringent control for the size and dispersity of ultrasmall nanoclusters through preparation of gold complex distributions formed from the precursor, AuClPPh3 (PPh3 = triphenylphosphine), and the L6 (L6 = 1,6-bis(diphenylphosphino) hexane) ligand prior to reduction with NaBH4 in 1:1 methanol/chloroform solutions. Monodisperse nanoclusters of distinct nuclearity are obtained for specific ligand ratios; [L6]/[PPh3] = 4 yields [Au8L64]2+, [L6]/[PPh3] = 0.4 yields [Au9L64Cl]2+, and [L6]/[PPh3] = 8 yields ligated Au10 cores in the form of [Au10L64]2+ and [Au10L65]2+. Polyhedral skeletal electron pair theory accounts for the stability of [Au9L64Cl]2+, which is the smallest closed-shell chlorinated cluster reported. Electrospray mass spectrometry and UV−vis spectra indicate that [Au9L64Cl]2+ and [Au10L6x]2+ (x = 4, 5) result from reactions involving [Au8L64]2+. Syntheses of small gold clusters containing chloride ligands open the possibility of constructing larger clusters via ligand exchange.

Cubane‐Like Bismuth‐Iron Cluster: Synthesis, X‐ray Crystal Structure and Theoretical Characterization of the [Bi4Fe8(CO)28]4– Anion

AbstractThe reaction of cyclo‐Bi4[Si(SiMe3)3]4 (1) with Na2[Fe(CO)4] in the presence of nBu4NCl leads to the formation of the cage compound [nBu4N]4[Bi4Fe8(CO)28] (2). According to X‐ray single‐crystal structure analysis, the faces of the tetrahedral Bi4 core are capped by Fe(CO)3 moieties in a μ3 fashion to give a cubanoid Bi4Fe4 framework. The four Fe(CO)4 fragments are μ1‐coordinated to bismuth, each. With 12 skeletal electron pairs the [Bi4Fe8(CO)28]4– anion (2a) is a Bi4Fe4 cubane. The negative charge is localized within cluster 2a according to the NBO analysis of its derivatives. The strength of metal–ligand interactions Bi–μ3‐Fe(CO)3 is responsible for the size of the cluster's cubic core. NICS computations at the cage centers of considered molecules show that 2a has paratropic character, whereas removal of four μ1‐Fe(CO)4 fragments from latter causes spherical aromaticity of the modified clusters [Bi4Fe4(CO)12]4– (2aa) and [Bi4Fe4(CO)12]2+ (2ab), mediated by a Bi4 cluster π orbital.

Stuffed fullerenelike boron carbide nanoclusters

Viable stuffed fullerenelike boron carbide nanoclusters, C50B34, C48B36−2, and their isomers based on an icosahedral B84 fragment of elemental β-rhombohedral boron have been investigated using density functional theory calculations. The structure and the stability of these clusters are rationalized using the polyhedral skeletal electron counting and ring-cap orbital overlap compatibility rules. The curvature of the fullerene was found to play a vital role in achieving the most stable isomer C50B34(3B). The large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps, three dimensional aromaticity, and electron detachment energies support their high stability. Further, the IR and Raman active modes were recognized.

Macropolyhedral boron-containing cluster chemistry [S2B16H17]–. A new eighteen-vertex thiaborane anion

The novel eighteen-vertex macropolyhedral dithiaborane anion [S2B16H17]– 1 has been obtained as its [tmndH]+ salt from the reaction of [S2B17H17] 2 and tmnd in solution in the presence of [RhCl2(η5-C5Me5)]2. It has two cluster skeletal electrons more than the three previously reported eighteen-vertex dithiaborane {S2B16} species n-[S2B16H16], n-[S2B16H15]– and iso-[S2B16H16], and the anion consists structurally of an arachno {SB9} and a nido {B9} cluster unit fused with two boron atoms in common, and with an endo-to-exo sulfur bridge that also links the two subclusters together.

Unexpected transformation of a diamagnetic Mo3(μ3-S)(μ-S)3 to a paramagnetic Mo3(μ3-S)2(μ-S)3 cluster core by reaction of [Mo3S4(dppe)3Br3]PF6 with tBuSNa

The electron precise [Mo(3)(μ(3)-S)(μ-S)(3)(dppe)(3)Br(3)](+) incomplete cuboidal complex with six cluster skeletal electrons (CSE) can be converted to the paramagnetic bicapped [Mo(3)(μ(3)-S)(2)(μ-S)(3)(dppe)(3)](+) cluster with an unusual seven metal electron population by treatment with (t)BuSNa, which simultaneously serves as a reducing agent and a source of the additional capping sulfur atom.

Ti‐Substituted Boranes as Hydrogen Storage Materials: A Computational Quest for the Ideal Combination of Stable Electronic Structure and Optimal Hydrogen Uptake

Based on the Wade-Mingos n+1 rule for the closo-boranes (B(n)H(n) (2-)), a family of Ti-substituted closo-boranes has been designed computationally. Due to the isolobal relation of Ti to a BH(2-) group, these Ti-substituted boranes have n+1 pairs of skeletal electrons to fulfill the bonding requirement for such stable cages. The reported representatives, B(4)H(4)Ti(2)H(2) in particular, not only have stable electronic structures but also superior capability to adsorb hydrogen. The optimal binding energies and high gravimetric densities of hydrogen storage indicate their potential to store hydrogen for practical applications. Simultaneously achieving electronic stability and optimal hydrogen uptake may provide a way of overcoming the issue of aggregation in designing transition-metal-decorated hydrogen storage materials. This study invites experimental realization of novel boranes and provides new ideas for searching for hydrogen storage materials.

An overview of the electronic structure in trigonal bipyramidal clusters of main elements or mixed with transition metals

Equatorial/apical bond repartitioning in TBP clusters, formed by main group elements only (e.g., B5H5 2−, B3H3N2, etc.) or mixed with metal atoms (e.g., [(L2M)3S2] n , [(L3M)3S2] n , [(CpM)3S2] n ), is critically analyzed from the horizontal comparison of the experimental structures and in terms of basic MO concepts. The ideas are double-checked through specific DFT calculations or existing ab initio results. Based on the Wade’s rules for closo-clusters, the five vertices systems are normally characterized by six skeletal electron pairs. In the main group clusters, the electron delocalization at the equatorial edges depends on the electronegativity of the apical groups and for the Beq–Beq bonds an inverse relationship between bond strength and bond length is remarked. In [(L2M)3S2] n compounds with a total electron count (TEC) of 48, the six bonding electron pairs localize at the apical M–S bonds. In [(L3M)3S2] n or [(CpM)3S2] n , also with TEC = 48, the effective atomic number rule predicts three single M–M single bonds besides the six M–S apical ones. In actuality, only partial M–M bonding can be considered due to the intermediation of the capping sulphur atoms, that help shifting the antibonding character of populated radial levels with that of the vacant tangential ones (bonding). The qualitative MO arguments are supported by the topological nature of the calculated DFT wave functions. Moreover, the MO nature of three lowest LUMOs for 48e− species help to rationalize experimental structural trends observed for the addition of up to five electrons.

Geometry and chemical bonding in polyhedral boranes, metallaboranes, and dimetallaboranes: From closo to isocloso to oblatocloso polyhedra

Abstract The geometry and chemical bonding in the closo metal-free boranes B n H n 2 - and the isoelectronic carboranes CB n - 1 H n - and C2Bn−2Hn with 2n + 2 skeletal electrons are based on the most spherical deltahedra with a preference for degree 5 vertices, particularly for the boron atoms. Such deltahedral boranes can be considered to be three-dimensional aromatic systems, as indicated by strongly diatropic nucleus independent chemical shift values for B n H n 2 - (n = 6, 8, 9, 12). Metallaborane structures, particularly those with 9–11 vertices and only 2n rather than 2n + 2 apparent skeletal electrons, are often based on isocloso deltahedra with the metal atom at a degree 6 vertex. Dimetallaborane structures, particularly the rhenium derivatives Cp2Re2Bn−2Hn−2 (8 ⩽ n ⩽ 12), are based on highly non-spherical and very oblate deltahedra with the metal atoms typically at degree 6 or 7 vertices, which are the lowest curvature sites of the deltahedra. A viable model for the skeletal bonding in such dimetallaboranes can be developed if each of the two metal vertices is assumed to contribute five internal orbitals to the skeletal bonding. This leads to 2n + 4 skeletal electrons, which are partitioned into n surface bonds and a formal metal–metal double bond inside the oblate deltahedron.

The loss of CO from [Rh12(μ12-Sn)(CO)27]4−: Synthesis, spectroscopic and structural characterization of the electron-deficient, icosahedral [Rh12(μ12-Sn)(CO)25]4− and [Rh12(μ12-Sn)(CO)26]4− tetra-anions

Heating (80 degrees C) the electron-precise, Sn-centred, icosahedral cluster [Rh(12)Sn(CO)(27)](4-) under a nitrogen atmosphere affords in sequence the electron-deficient icosahedral [Rh(12)Sn(CO)(26)](4-) and [Rh(12)Sn(CO)(25)](4-) derivatives. The reaction is reversible in solution and the parent compound is quantitatively regenerated upon exposure to carbon monoxide. The reaction course has been unravelled via a combination of Band-target Entropy Minimization (BTEM) IR analysis and X-ray studies. While icosahedral clusters displaying electron counts formally exceeding 13 skeletal electron pairs (SEP) are known, [Rh(12)Sn(CO)(26)](4-) and [Rh(12)Sn(CO)(25)](4-) show for the first time that icosahedral clusters may also be stabilized with a deficiency of SEPs with respect to the requirement based on the cluster-borane analogy. In contrast to the behaviour of the electron-precise cluster [Rh(12)Sn(CO)(27)](4-), the electron-deficient cluster [Rh(12)Sn(CO)(25)](4-) undergoes reversible electrochemical reductions.

Rules for macropolyhedral boranes

Based on extensive computational studies, rules to derive the thermodynamically most stable macropolyhedral borane for any formula between B n H n −4 to B n H n +8 were identified. Formally, the macropolyhedral boranes may be obtained by condensing regular convex borane clusters where as many BH 3 moieties are eliminated as vertexes are shared in the macropolyhedral framework. Macropolyhedral boranes consisting of two cluster fragments may be classified according to their general formulae ranging from B n H n −4 to B n H n +8. For each of these formulae, various structure types are conceivable differing in the number of shared vertexes and in the types of combined cluster fragments. However, for each general formula, only one structure type is known experimentally and this one is also computationally found to be thermodynamically preferred! For each class of macropolyhedral B n H m boranes, a preferred number of shared vertexes is identified, and this determines the number of skeletal electron pairs. With this knowledge, the type of fused clusters, i.e. the most favourable framework, may be predicted. The concept of preferred fragments may be applied to even predict the distribution of vertexes among the fused fragments in the thermodynamically most stable isomers. When there is at least one closo fragment it has 12-vertexes. Without any closo fragment the most stable macropolyhedral borane has a nido 10-vertex cluster fragment.

Age-related alterations in oxidatively damaged proteins of mouse skeletal muscle mitochondrial electron transport chain complexes

Age-associated mitochondrial dysfunction is a major source of reactive oxygen species (ROS) and oxidative modification to proteins. Mitochondrial electron transport chain (ETC) complexes I and III are the sites of ROS production and we hypothesize that proteins of the ETC complexes are primary targets of ROS-mediated modification which impairs their structure and function. The pectoralis, primarily an aerobic red muscle, and quadriceps, primarily an anaerobic white muscle, have different rates of respiration and oxygen-carrying capacity, and hence, different rates of ROS production. This raises the question of whether these muscles exhibit different levels of oxidative protein modification. Our studies reveal that the pectoralis shows a dramatic age-related decline in almost all complex activities that correlates with increased oxidative modification. Similar complex proteins were modified in the quadriceps, at a significantly lower level with less change in enzyme and ETC coupling function. We postulate that mitochondrial ROS causes damage to specific ETC subunits which increases with age and leads to further mitochondrial dysfunction. We conclude that physiological characteristics of the pectoralis vs quadriceps may play a role in age-associated rate of mitochondrial dysfunction and in the decline in tissue function.

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.

Structural Paradigms in Macropolyhedral Boranes

Macropolyhedral borane clusters are concave polyhedra constituting fused convex simple polyhedra. They are formally obtained by condensation of simple polyhedral boranes under elimination of between one and four BH(3) or isoelectronic units. The number of eliminated vertexes from simple polyhedra equals the number of shared vertexes in macropolyhedral boranes. For each of the eight classes with general formulae ranging from B(n)H(n-4) to B(n)H(n+10), more than one structure type is possible, differing in the number of shared vertexes and in the types of the two combined cluster fragments. However, only one type of "potential structures" is represented by experimentally known examples and is found to be favored by theoretical calculations. A sophisticated system exists among the favored macropolyhedral borane structures. For each class of macropolyhedral boranes, the number of skeletal electron pairs is directly related to the general formula, the number of shared vertexes and the type of fused cluster fragments. In order to predict the distribution of vertexes among the fused fragments, we propose the concept of preferred fragments. Preferred fragments are those usually present in the thermodynamically most stable structure of a given class of macropolyhedral boranes and are also frequently observed in the experimentally known structures. This allows us to completely predict the cluster framework of the thermodynamically most stable macropolyhedral borane isomers.

Effects of halogen substitution on the properties of eight- and nine-vertex closo-boranes

The symmetry constrained geometries of the eight- and nine-vertex polyhedral boranes and haloboranes BnXnz (n = 8 and 9; X = H, F and Cl; z = -2, -1 and 0) were optimized at the B3LYP/6-311+G(d) level and their nucleus-independent chemical shifts (NICS) were calculated using the GIAO method with Kohn-Sham orbitals. Substitution of halogens on borane cages was found to significantly impact not only the geometric but also magnetic properties. Multiple fluorine substituents cause a deviation from the Wade-Mingos skeletal electron rules in B8F8(2-), resulting in a distortion from the expected D2d bisdisphenoid to a C2v nido type bicapped trigonal prism. However, all of the nine-vertex cages B9X9z retain the D3h tricapped trigonal prismatic structure of B9H9(2-). The presence of halogen substituents was found to enhance the three-dimensional diatropic ring currents within the dianionic borane cages B8X8(2-) and B9X9(2-). For the neutral structures the NICS values indicate BnFn to be aromatic, BnCln to be essentially non-aromatic, and BnHn to be antiaromatic (n = 8, 9).

Beyond the Wade-Mingos Rules in Bare 10- and 12-Vertex Germanium Clusters: Transition States for Symmetry Breaking Processes.

The lowest energy structures of bare Gen(z) clusters (n = 10, 12; z = -6, 0, +2, +4) obtained using density functional theory (DFT) at the hybrid B3LYP level often are relatively low-symmetry polyhedra not readily recognizable by the Wade-Mingos rules. However, such optimized structures may arise from higher symmetry transition states through symmetry breaking processes. Thus the lowest energy structures for the Ge10(6)(-) and Ge12(6)(-) clusters with hyperelectronic arachno 2n + 6 skeletal electron counts are derived from pentagonal and hexagonal prism transition states, respectively, and retain the pentagonal and hexagonal faces of the prisms upon symmetry-breaking optimization. In addition, a variety of capped cube, prism, and antiprism transition states are found for the hypoelectronic Ge10(4+), Ge12, and Ge12(4+) clusters, which go to low-energy low-symmetry optimized structures, typically Cs or Ci, upon following the normal modes of the imaginary vibrational frequencies.

Na9K16Tl~25: A New Phase Containing Naked Icosahedral Cluster Fragments Tl9 9−

The phase Na9K16Tl25.25(2) was synthesized by fusion of the elements in sealed Ta containers followed by quenching and annealing at 250°C. The structure established by single crystal X-ray diffraction means (P63/m, Z = 2, a = 19.376(3) A, c = 11.480(2) A) features Tl99− clusters. These are well separated by cations that bridge between, faces, edges, and vertices of the clusters; sodium appears to be essential in this role. This is the third compound known to contain Tl9 clusters, but here two of nine sites are partially occupied, which can be interpreted as a 70:30 mixture of Tl9 and Tl7 units in the same cavity. This Tl9 example also displays lower symmetry (Cs) but requires the same 2n skeletal electrons. EHTB electronic structure calculations indicate that the Fermi level intersects a finite densities-of-states (DOS), and only some bonds are optimized at EF, giving some insight regarding the site of Tl deficiency. Direct geometric relationships are found among Tl13, Tl9, Tl7 and Tl5 clusters through systematic removal of vertices.