Charged Si9 Clusters in Neat Solids and the Detection of [H2 Si9 ]2- in Solution: A Combined NMR, Raman, Mass Spectrometric, and Quantum Chemical Investigation.

Polyanionic silicon clusters are provided by the Zintl phases K4 Si4 , comprising [Si4 ]4- units, and K12 Si17 , consisting of [Si4 ]4- and [Si9 ]4- clusters. A combination of solid-state MAS-NMR, solution NMR, and Raman spectroscopy, electrospray ionization mass spectrometry, and quantum-chemical investigations was used to investigate four- and nine-atomic silicon Zintl clusters in neat solids and solution. The results were compared to 29 Si isotope-enriched samples. 29 Si-MAS NMR and Raman shifts of the phase-pure solids K4 Si4 and K12 Si17 were interpreted by quantum-chemical calculations. Extraction of [Si9 ]4- clusters from K12 Si17 with liquid ammonia/222crypt and their transfer to pyridine yields in a red solid containing Si9 clusters. This compound was characterized by elemental and EDX analyses and 29 Si-MAS NMR and Raman spectroscopy. Charged Si9 clusters were detected by 29 Si NMR in solution. 29 Si and 1 H NMR spectra reveal the presence of the [H2 Si9 ]2- cluster anion in solution.

Zintl Clusters as Wet-Chemical Precursors for Germanium Nanomorphologies with Tunable Composition.

[Ge9](4-) Zintl clusters are used as soluble germanium source for a bottom-up fabrication of Ge nanomorphologies such as inverse opal structures with tunable composition. The method is based on the assembly and oxidation of [Ge9 ](4-) clusters in a template mold using SiCl4 , GeCl4 , and PCl3 leading to Si and P-containing Ge phases as shown by X-ray diffraction, Raman spectroscopy, and energy-dispersive X-ray analysis. [Ge9](4-) clusters are retained using ethylenediamine (en) as a transfer medium to a mold after removal of the solvent if water is thoroughly excluded, but are oxidized to amorphous Ge in presence of water traces. (1)H NMR spectroscopy reveals the oxidative deprotonation of en by [Ge9](4-). Subsequent annealing leads to crystalline Ge. As an example for wet-chemical synthesis of complex Ge nanomorphologies, we describe the fabrication of undoped and P-doped inverse opal-structured Ge films with a rather low oxygen contents. The morphology of the films with regular volume porosity is characterized by SEM, TEM, and grazing incidence small-angle X-ray scattering.

Silicon nanoparticles by the oxidation of [Si4](4-)- and [Si9](4-)-containing Zintl phases and their corresponding yield.

The Zintl phases with nominal compositions Na4Si4, Rb7NaSi8, and A12Si17 (A = K, Rb, Cs) were utilized as precursors in the synthesis of silicon nanoparticles (Si NPs). The present study characterizes and compares the yields of Si NPs synthesized from Na4Si4, Rb7NaSi8, and A12Si17 (A = K, Rb, Cs). Na4Si4 and Rb7NaSi8 Zintl phases consist of anionic silicon tetrahedra stabilized by group I cations. The A12Si17 (A = K, Rb, Cs) Zintl phases that contain [Si9](4-) and [Si4](4-) clusters have been speculated to be more soluble than the A4Si4 (A = Na, Rb, Cs) Zintl phases that contain solely [Si4](4-) clusters due to the lower charge density of the [Si9](4-) cluster. The Zintl phases were reacted with NH4Br in dimethylformamide (DMF) and subsequently capped with allylamine. The Si NPs were characterized by transmission electron microscopy (TEM), energy-dispersive spectroscopy (EDS), UV-vis, and photoluminescence (PL) spectrophotometry. Furthermore, the Si yields were characterized by inductively coupled plasma mass spectrometry (ICP-MS) to evaluate if the reactions of [Si9](4-) cluster containing Zintl phases resulted in higher yields of Si NPs. The yield of Si increased with larger or mixed alkali metal Zintl phases, leading to the conclusion that Coulombic interactions between the cations and anions affect the Zintl phase's reactivity. The size of the Si NPs also increased with larger and mixed alkali metal cations, resulting in similar NP concentrations regardless of the starting material. With respect to ease of synthesis and yield, Na4Si4 remains the most practical precursor for the solution synthesis of Si NPs; however, the larger and mixed alkali metal precursors show promise for further development.

On the formation of intermetalloid clusters: titanocene(III)diammin as a versatile reactant toward nonastannide Zintl clusters.

The reactivity of TiCp2Cl2 (d(0)) towards Zintl clusters was studied in liquid ammonia (Cp = cyclopentadienyl). Reduction of Ti(IV)Cp2Cl2 and ligand exchange led to the formation of [Ti(III)Cp2(NH3)2](+), also obtainable by recrystallization of [CpTi(III)Cl]2. Upon reaction with [K4Sn9], ligand exchange leads to [TiCp2(η(1)-Sn9)(NH3)](3-). A small variation of the stoichiometry led to the formation of [Ti(η(4)-Sn8)Cp](3-), which cocrystallizes with [TiCp2(NH3)2](+) and [TiCp2(η(1)-Sn9)(NH3)](3-). Finally, the large intermetalloid cluster anion [Ti4Sn15Cp5](n-) (n = 4 or 5) was obtained from the reaction of K12Sn17 and TiCp2Cl2 in liquid ammonia. The isolation of three side products, [K([18]crown-6)]Cp, [K([18]crown-6)]Cp(NH3), and [K([2.2]crypt)]Cp, suggests a stepwise elimination of the Cl(-) and Cp(-) ligands from TiCp2Cl2 and thus gives a hint to the mechanism of the product formation in which [Ti(η(4+2)-Sn8)Cp](3-) has a key role.

Reactivity of liquid ammonia solutions of the Zintl phase K12Sn17 towards mesitylcopper(I) and phosphinegold(I) chloride.

To gain more insight into the reactivity of intermetalloid clusters, the reactivity of the Zintl phase K12 Sn17 , which contains [Sn4 ](4-) and [Sn9 ](4-) cluster anions, was investigated. The reaction of K12 Sn17 with gold(I) phosphine chloride yielded K7 [(η(2) -Sn4 )Au(η(2) -Sn4 )](NH3 )16 (1) and K17 [(η(2) -Sn4 )Au(η(2) -Sn4 )]2 (NH2 )3 (NH3 )52 (2), which both contain the anion [(Sn4 )Au(Sn4 )](7-) (1 a) that consists of two [Sn4 ](4-) tetrahedra linked through a central gold atom. Anion 1 a represents the first binary AuSn polyanion. From this reaction, the solvate structure [K([2.2.2]crypt)]3 K[Sn9 ](NH3 )18 (3; [2.2.2]crypt=4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8]hexacosane) was also obtained. In the analogous reaction of mesitylcopper with K12 Sn17 in the presence of [18]crown-6 in liquid ammonia, crystals of the composition [K([18]crown-6)]2 [K([18]crown-6)(MesH)(NH3 )][Cu@Sn9 ](thf) (4) were isolated ([18]crown-6=1,4,7,10,13,16-hexaoxacyclooctadiene, MesH=mesitylene, thf=tetrahydrofuran) and featured a [Cu@Sn9 ](3-) cluster. A similar reaction with [2.2.2]crypt as a sequestering agent led to the formation of crystals of [K[2.2.2]crypt][MesCuMes] (5). The cocrystallization of mesitylene in 4 and the presence of [MesCuMes](-) (5 a) in 5 provides strong evidence that the migration of a bare Cu atom into an Sn9 anion takes place through the release of a Mes(-) anion from mesitylcopper, which either migrates to another mesitylcopper to form 5 a or is subsequently protonated to give MesH.

A quantitative test of Hamilton's rule for the evolution of altruism.

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.

Mixed Si/Ge nine-atom Zintl clusters: ESI mass spectrometric investigations and single-crystal structure determination of paramagnetic [Si(9-x)Ge(x)]3-.

Mixed Si/Ge compounds are of special interest as potential materials for photovoltaic applications. In order to evaluate the usage of soluble precursor compounds, we investigated the synthesis of heteroatomic nine-atom clusters that consist of Si and Ge atoms through dissolution of the ternary Zintl phases K12Si(17-x)Ge(x) (x = 9, 12) and Rb12Si(17-x)Ge(x) (x = 9). Electrospray ionization (ESI) mass spectrometry demonstrates the presence of mixed Si(9-x)Ge(x) clusters in acetonitrile solution. From ammonia solutions of the ternary phases, four compounds that contain 3-fold negatively charged [Si(9-x)Ge(x)](3-) clusters are obtained. The paramagnetic behavior is confirmed by EPR spectroscopy. [E9](3-) Zintl clusters are considered as intermediate structures in the stepwise oxidation of [E9](4-) clusters to novel element allotropes (E = Si-Pb). The structure of Rb[Rb-crypt]2[Si2.3(1)Ge6.7(1)](NH3)7 and the isostructural structures of [Rb-crypt]3[Si2.2(1)Ge6.8(1)](NH3)8, [K-crypt]3[Si2.4(1)Ge6.6(1)](NH3)8.5, and [K-crypt]3[Si4.6(1)Ge4.4(1)](NH3)8.5 are investigated by single-crystal X-ray diffraction (crypt = 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8]-hexacosane). The Si/Ge ratio of the products correlates with the composition of the ternary precursor phases.

Soluble Zintl phases A14ZnGe16 (A = K, Rb) featuring [(η3-Ge4)Zn(η2-Ge4)]6- and [Ge4]4- clusters and the isolation of [(MesCu)2(η3,η3-Ge4)]4-: the missing link in the solution chemistry of tetrahedral group 14 element Zintl clusters.

The number of Zintl phases containing polyhedral clusters of tetrel elements that are accessible for chemical reactions of the main-group element clusters is rather limited. The synthesis and structural characterization of two novel ternary intermetallic phases A(14)ZnGe(16) (A = K, Rb) are presented, and their chemical reactivity is investigated. The compounds can be rationalized as Zintl phases with 14 alkali metal cations A(+) (A = K, Rb), two tetrahedral [Ge(4)](4-) Zintl anions, and one anionic heterometallic [(Ge(4))Zn(Ge(4))](6-) cluster per formula unit. The Zn-Ge cluster comprises two (Ge(4)) tetrahedra which are linked by a Zn atom, with one (Ge(4)) tetrahedron coordinating with a triangular face (η(3)) and the other one with an edge (η(2)). [(η(3)-Ge(4))Zn(η(2)-Ge(4))](6-) is a new isomer of the [(Ge(4))Zn(Ge(4))](6-) anion in Cs(6)ZnGe(8). The phases dissolve in liquid ammonia and thus represent rare examples of soluble Zintl compounds with deltahedral units of group 14 element atoms. Compounds with tetrahedral [E(4)](4-) species have previously been isolated from solution for E = Si, Sn, and Pb, and the current investigation provides the "missing link" for E = Ge. Reaction of an ammonia solution of K(14)ZnGe(16) with MesCu (Mes = 2,4,6-(CH(3))(3)C(6)H(2)) in the presence of [18]-crown-6 (1,4,7,10,13,16-hexaoxacyclooctadecane) yielded crystals of the salt [K([18]-crown-6)](2)K(2)[(MesCu)(2)Ge(4)](NH(3))(7.5) with the polyanion [(MesCu)(2)Ge(4)](4-). This MesCu-stabilized tetrahedral [Ge(4)](4-) cluster also completes the series of [(MesCu)(2)Si(4-x)Ge(x)](4-) clusters, which have previously been isolated from solution for x = 0 and 0.7, as the end member with x = 4. The electronic structures of [(Ge(4))Zn(Ge(4))](6-) and [(MesCu)(2)Ge(4)](4-) were investigated in terms of a molecular orbital description and analyses of the electron localization functions. The results are compared with band structure calculations for the A(14)ZnGe(16) phases (A = K, Rb).

Division of labour and colony efficiency in social insects: effects of interactions between genetic architecture, colony kin structure and rate of perturbations.

The efficiency of social insect colonies critically depends on their ability to efficiently allocate workers to the various tasks which need to be performed. While numerous models have investigated the mechanisms allowing an efficient colony response to external changes in the environment and internal perturbations, little attention has been devoted to the genetic architecture underlying task specialization. We used artificial evolution to compare the performances of three simple genetic architectures underlying within-colony variation in response thresholds of workers to five tasks. In the 'deterministic mapping' system, the thresholds of individuals for each of the five tasks is strictly genetically determined. In the second genetic architecture ('probabilistic mapping'), the genes only influence the probability of engaging in one of the tasks. Finally, in the 'dynamic mapping' system, the propensity of workers to engage in one of the five tasks depends not only on their own genotype, but also on the behavioural phenotypes of other colony members. We found that the deterministic mapping system performed well only when colonies consisted of unrelated individuals and were not subjected to perturbations in task allocation. The probabilistic mapping system performed well for colonies of related and unrelated individuals when there were no perturbations. Finally, the dynamic mapping system performed well under all conditions and was much more efficient than the two other mapping systems when there were perturbations. Overall, our simulations reveal that the type of mapping between genotype and individual behaviour greatly influences the dynamics of task specialization and colony productivity. Our simulations also reveal complex interactions between the mode of mapping, level of within-colony relatedness and risk of colony perturbations.

[(η2-(Si/Ge)4)Zn(η2-(Si/Ge)4)](6-)- novel Zintl clusters with mixed Si/Ge tetrahedra bridged by a Zn atom.

The solubility of the ternary Zintl phase K(12)Si(17-x)Ge(x) (x = 5), containing mixed group 14 element clusters, was investigated. Novel dimeric tetrahedral Zintl clusters [(η(2)-E(4))Zn(η(2)-E(4))](6-) with mixed site occupation (E = Si/Ge) were obtained through reaction with (C(6)H(6))(2)Zn in ammonia solutions and investigated by means of X-ray single crystal diffraction.

Measures of diversity for populations and distances between individuals with highly reorganizable genomes.

In this paper we address the problem of defining a measure of diversity for a population of individuals whose genome can be subjected to major reorganizations during the evolutionary process. To this end, we introduce a measure of diversity for populations of strings of variable length defined on a finite alphabet, and from this measure we derive a semi-metric distance between pairs of strings. The definitions are based on counting the number of substrings of the strings, considered first separately and then collectively. This approach is related to the concept of linguistic complexity, whose definition we generalize from single strings to populations. Using the substring count approach we also define a new kind of Tanimoto distance between strings. We show how to extend the approach to representations that are not based on strings and, in particular, to the tree-based representations used in the field of genetic programming. We describe how suffix trees can allow these measures and distances to be implemented with a computational cost that is linear in both space and time relative to the length of the strings and the size of the population. The definitions were devised to assess the diversity of populations having genomes of variable length and variable structure during evolutionary computation runs, but applications in quantitative genomics, proteomics, and pattern recognition can be also envisaged.