Electronic Structure and Relative Stabilities of 10- and 12-Vertex. <Emphasis Type="Italic">Closo</Emphasis>and <Emphasis Type="Italic">Nido</Emphasis>-Heteroborane Clusters of Ga,Ge, and As Elements

A DFT method with the B3LYP functional and the 6-311++G(d,p) diffuse basis set is used to predict geometries, relative stabilities, electronic structures, and the bonding of closo- and nido-Ga_mB_n–mH _n ^2? , Ge_mB_n–mH _n ^m?2 , and As_mB_n–mH _n ^{2 m?2} (n = 10, 12 and m = 1, 2) Clusters are obtained by replacing BH with isolobal GaH, GeH⁺, and AsH²⁺ fragments, keeping the same skeleton electron pairs (SEP). Based on the polyhedral skeletal electron pairs theory (PSEPT), closo and nido structures are predicted and can be of significant interest for experimentalists working in the field of heteroboranes. Different cluster stabilities are studied according to Gimarc′s and Williams′ rules, where our calculations show that the monosubstituted clusters deviate from these rules, giving rise to open structures. As₂B₈H _n ²⁺ as 10-vertex structures lead to nido-type clusters, however, Ge_mB_n–mH _n ^m?2 (n = 10, 12 and m = 1, 2) give rise to closo isomers with close energies. All optimized structures exhibit large HOMO–LUMO gaps suggesting a good kinetic stability, thus predicting their isolation and characterization.     

Theoretical study of stepwise chlorinated aluminide clusters Al<Subscript>13</Subscript>Cl<Stack><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>−</Superscript></Stack> (<Emphasis Type="Italic">n</Emphasis> = 1–9)

The electronic and geometric structures, energy stabilities, normal mode frequencies, and spin density distributions (in radicals) of different stepwise-chlorinated aluminum clusters Al₁₃Cl _n ^? (n = 1–9) are calculated within the B3LYP approximation of the density functional theory using 6-31G* and 6-311+G* basis sets. The results are compared with analogous computation data on hydrides Al₁₃H _n ^? (n = 1–12) obtained at the same level. The general qualitative pattern for related series of hydrides, chlorides, and iodides (as well as fluorides and bromides) turns out to be similar in many respects. For all Al₁₃X _n ^? clusters with different electronegative substituents X, there is a set of a considerable number of low-lying closely spaced inner isomers (with a centered icosahedral cage), marquee isomers, and outer isomers (capped). The effects found by calculations in centered icosahedral isomers—localization of spin density on the trans-Al* atom in radical anions and its associated trans addition rule for an even substituent and the zigzag (odd-even) dependence of the energies D _n (X) of successive addition of substituents X to the metal cage on n described in the framework of the molecular model of the valence states of the Al ₁₃ ^? superatom—should also be shared by many Al₁₃X _n ^? series with different X’s. The differences between hydrides Al₁₃H _n ^? and chlorides Al₁₃Cl _n ^? of the same type are quantitative. For the hydrides, inner isomers are preferable in the first half of the series (n = 1–6); and in the second half (n = 7–12), outer isomers are more favorable. For the chlorides, icosahedral isomers are preferable only at the very beginning of the series. In the other cases, nonicosahedral structures are most favorable, for which the situation becomes very complicated due to the large number of position isomers and the aforementioned simple rules found for centered icosahedral structures are fulfilled to a considerably less extent or not at all.     

Study on the Geometric and Electronic Structures of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Si<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> (n = 3, 4, 5; m = 1, 2, 3, 4) Clusters

Genetic algorithm combined with the semi-empirical Hamitonian AM1/PM3 is used to search the low energy isomers of Al _n Si _m (n = 3, 5, m ≤ 3 and n = 4, m ≤ 4) and the charged clusters with 20 and 28 valence electrons. The candidate structures were optimized by the density functional theory PBE0 and B3LYP models with the triply split basis sets including polarization functions. The electronic structures show that Al–Si binary clusters behave like metal clusters. The molecular orbitals accord with that predicted by the jellium model, and the electron localization function shows the valence electrons are delocalized over the entire clusters. The clusters having 20 and 28 valence electrons exhibit pronounced stabilities and large energy gaps. The 20 valence electrons of Al₄Si₂ and Al₃Si₃ ⁺, Al₅Si^? form closed shells 1S ²1P ⁶2S ²1D ¹⁰. Al₄Si₄ and Al₅Si₃ ^? have oblate structures and the P, D, F levels spilt considerably in these clusters. The electron density distributions suggest that doping silicon in the aluminum clusters enhances the stability considerably.     

Stability of molecular form of HCl in water vapor: A computer simulation

The free energy and entropy of the dissociation of HCl molecule into ions in water vapor, HCl(H₂O) _n + mH₂O → H₃O + (H₂O) _n+m -1Cl^?, were calculated. The dependences of various parameters on the interionic distance at 273 K and various vapor pressures were obtained. A detailed model taking into account unpaired covalent-type interactions, polarization interactions, charge transfer effect, and hydrogen bonds was applied. The numerical values of the parameters were reconstructed from the experimental data on the free energy and enthalpy of the first reactions of addition of vapor molecules to ions, and also from the results of quantum-chemical calculations of the energy and geometry of locally stable configurations of clusters HCl(H₂O) _n . Despite lower internal energy of the dissociated state, the molecular form is absolutely stable in clusters of water molecules. The dissociated state is relatively stable. Accumulation of unrecombined ion pairs in clusters is possible with a decrease in the temperature to 200 K.     

Theoretical Study of the Structure and Stability of Stepwise Hydrogenated Aluminum Clusters Al<Subscript>44</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1−24)

The energies and structural and spectroscopic characteristics of a series of model stepwise hydrogenated aluminum clusters Al₄₄H _n (n = 1?24) obtained by successive introduction of hydrogen atoms into various surface positions of the Al₄₄ cluster have been calculated by the density functional theory method (B3LYP). According to these calculations, the [Al₃₉] surface layer of the cage retains a closed “nested doll” shape with a pentaatomic inner core [Al₅]. With increasing n, both the surface layer and the core tend to experience increasing asymmetric distortions. The surface is corrugated and undergoes significant axial and equatorial extensions and contractions, some of the Al?H two-center terminal bonds are transformed into threecenter hydrogen bridges, and some Al atoms are displaced from the surface layer to the outer sphere and are bound to the surface through hydrogen bridges. The inner core [Al₅] at n = 24 loses its bipyramidal shape and shifts to the surface layer so that one or two of its atoms are “built-in” into the concave regions of the surface layer. The calculated average energies of Al?H bonds are within the range ~55.5 ± 2.5 kcal/mol. The averaged energies of the Al₄₄H _n → Al₄₄H_n–2 + Н₂ dissociation reactions with elimination of a hydrogen molecule are on the order of a few kilocalories per mole and are evidence of small exothermicity (or isothermicity) of these reactions. For the Al₄₄H, Al₄₄H₂, and Al₄₄H₆ clusters as an example, the relative stabilities of isomers with terminal Al?H bonds in various nonequivalent positions of the [Al₃₉] surface layer are compared.     

Geometries,stabilities, electronic and magnetic properties of small aluminum cluster anions doped with cobalt: A density functional theory study

The geometrical structures, relative electronic and magnetic properties of small Al_nCo^– (1 ≤ n ≤ 9) clusters are systematically investigated within the framework of density functional theory at the BPW91 level. The single Co doping can dramatically affect the ground state geometries of the 1 Al_n+1^- clusters. At the same time, the resulting geometries show that the lowest energy Al_nCo^– clusters prefer to be three dimensional structures. Here, the relative stabilities are investigated in terms of the calculated average binding energies, fragmentation energies, and second-order energy differences. Moreover, the result of the highest occupiedlowest unoccupied molecular orbital energy gaps indicates that Al₆Co^– clusters have the highest chemical stability for Al_nCo^– (1 ≤ n ≤ 9) clusters. Furthermore, the natural population analysis reveals that the charges in Al_nCo^– clusters transfer from the Al frames to the Co atom. Additionally, the analyses of the local and total magnetic moments of the Al_nCo^– clusters show that the magnetic effect mainly comes from the Co atom.     

Heat capacity and thermodynamic functions of ferrocenemethanol

The heat capacity (C _{p, m}) of ferrocenemethanol (FM) C₅H₅FeC₅H₄CH₂OH have been measured by the low-temperature adiabatic calorimetry method in the range 6–371 K. The triple point temperature, the enthalpy of fusion, and the purity of the substance under consideration have been determined. The ideal gas thermodynamic functions of FM—absolute entropy S _m(g) ⁰ and change in the enthalpy Δ ₀ ^T H _m at 298.15 K—have been derived from the heat capacity data and the known values of the saturation vapor pressure and enthalpy of sublimation. The ideal gas thermodynamic functions C _{p, m} ⁰ and S _m(g) ⁰ and the enthalpy of formation of FM have been calculated by the empirical difference method at T = 298.15 K. The experimental and calculated values of the thermodynamic functions are consistent within error limits, which proves their reliability.     

Polarization effects in Cl<Superscript>−</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters. Computer simulation

Free energy, enthalpy, equilibrium work of formation from vapor, and structural characteristics of Cl^?(H₂O) _n clusters in models with explicit account for the polarization of particles and many-particle covalent interactions, as well as in their absence, are calculated by the Monte Carlo method in a bicanonical statistical ensemble. The neglect of polarization interactions leads to discrepancies in the experimental values of free energy by up to 4k _B T, even for first addition reactions. Taking into account polarization and many-particle interactions makes it possible to reach an agreement with experimental data on the free energy of hydration with an accuracy of no less than the error of experimental measurements (～0.1k _B T). The account of polarization essentially affects the pattern of the curve of formation work and results in a decrease in the first coordination number of ion by one–two units. Disregard for polarization effects in clusters substantially narrows the region of metastable states of vapor.     

The thermochemical characteristics of solution of DL-α-alanylglycine and DL-α-alanylalanine in water-alcohol mixtures at 298.15 K

The integral enthalpies of solution of DL-α-alanylglycine and DL-α-alanylalanine in water-ethanol, water-n-propanol, and water-isopropanol mixtures were measured calorimetrically at alcohol concentrations x ₂ = 0?0.4 mole fractions. The standard enthalpies of solution (Δ_sol H°) of the peptides and their transfer (Δ_tr H°) from water into the mixed solvents were calculated. The influence of the structure and properties of the solutes and mixture composition on the enthalpy characteristics were considered. The Δ_sol H° = f(x ₂) and Δ_tr H° = f(x ₂) dependences were found to have extrema. The enthalpy coefficients of pair interactions (h _xy ) between the peptide and alcohol molecules were calculated. The coefficients were positive and increased in the series ethanol, n-propanol, isopropanol.     

A density functional study on the aggregation of alumina clusters

A calculation has been performed to explore the mechanism of aggregation reaction between two small molecular clusters [(Al₂O₃) _n1 and (Al₂O₃) _n2] by the density functional theory method. Five pathways of aggregation reactions between two different (Al₂O₃)₁ clusters isomers were identified. The detailed process of (Al₂O₃)₁ interaction with (Al₂O₃)₂ were also obtained. All the products of the aggregation reactions between two cage structures are cage-dimer structures. We calculated the thermodynamic properties of all the aggregate clusters. The Gibbs free energy changes of aggregation reactions in 0–1000 K were negative and increased with the temperature increase. The energy changes of enthalpy and entropy were also obtained.     

First principle study of magnetic and electronic properties of single X (X = Al,Si) atom added to small carbon clusters (C<Subscript> <Emphasis Type="Italic">n</Emphasis> </Subscript>X, <Emphasis Type="Italic">n</Emphasis> = 2–10)

In this paper, the magnetic and electronic properties of single aluminum and silicon atom added to small carbon clusters (C_nX; X = Al, Si; n = 2–10) are studied in the framework of generalized-gradient approximation using density functional theory. The calculations were performed for linear, two dimensional and three dimensional clusters based on full-potential local-orbital (FPLO) method. The total energies, HOMO–LUMO energy gap and total magnetic moments of the most stable structures are presented in this work. The calculations show that C_nSi clusters have more stability compared to C_nAl clusters. In addition, our magnetic calculations were shown that the C_nAl isomers are magnetic objects whereas C_nSi clusters are nonmagnetic objects.     

New carborane-containing acids and amines

Alkylation of nido-carborane methyl sulfide derivative [9-MeS-7,8-C₂B₉H₁₁]^– was used to synthesize a series of new carborane-containing acids 9-HOOC(CH₂) _n (Me)S-7,8-C₂B₉H₁₁ (n = 1—4) and amines 9-H₂N(CH₂) _n (Me)S-7,8-C₂B₉H₁₁ (n = 2, 3). The compounds obtained can be used for the development of BNCT agents.     

Vapor pressure and heat capacities of perfluoro-<Emphasis Type="Italic">N</Emphasis>-(4-methylcyclohexyl)piperidine

Heat capacities of perfluoro-N-(4-methylcyclohexyl)piperidine (PMCP) have been measured by low-temperature adiabatic calorimetry. The purity of the compound, its triple-point temperature, and its enthalpy and entropy of fusion have been determined. The saturated vapor pressure was determined by comparative ebulliometry as a function of temperature in the 6.2–101.6 kPa pressure range and 374.2–460.9 K temperature range. The calorimetric enthalpy of vaporization at T = 298.15 K has been measured. The following thermodynamic properties were calculated for PMCP: normal boiling temperature, enthalpy of vaporization Δ_vap H _m ⁰ (T) as a function of temperature, and critical parameters. The enthalpies of vaporization at 298.15 K obtained experimentally and by calculation methods match within their error limits, which validates their adequacy and the adequacy of the Δ_vap H _m ⁰ = f(T) equation as an extrapolation.     

Bismuth aluminoborate Bi<Subscript>0.96</Subscript>Al<Subscript>2.37</Subscript>(B<Subscript>4</Subscript>O<Subscript>10</Subscript>)O: Synthesis and crystal structure

The crystal structure of a new bismuth aluminoborate Bi_0.96Al_2.37(B₄O₁₀)O is studied by single-crystal X-ray diffraction. The Bi_0.96Al_2.37(B₄O₁₀)O single crystals are hexagonal (space group \(P\bar 6\) 2m). The unit cell parameters are as follows: a = b = 4.587(4) Å, c = 2.253(9) Å, α = β = 90°, γ = 120°, V = 168.60 ų, Z = 1.     

Study on the Mixed ZnO Clusters and Ring-Like ZnO Ions

The pure Zn_m (m?=?2–10), mixed Zn_mO_m (m?=?1–10), Zn_mO_10??m (m?=?1–9) clusters and the univalent and divalent ring-like Zn_mO_m (m?=?2–10) cluster ions are systematically investigated by using Amsterdam density functional (ADF) program with Triple-zeta with two polarization functions basis set in conjunction with self-consistent field. Our calculated results show that the Zn₄ and Zn₇ clusters are the magic clusters. The structures of the Zn_mO_m (m?=?1–10) clusters evolve from two-dimension to three-dimension after m?=?8. For the Zn_mO_10??m (m?=?1–9) clusters, the Zn-rich structures evolve gradually from three-dimension to plane with an increase in the O ratios. The Zn₅O₅ cluster with equal ratio has a two dimensional structure. In the O-rich clusters, the O dimers can be easily detached from them. The O and Zn atoms partly adopt sp² and sp hybridization, respectively, in the ring-like Zn_mO_m (m?=?2–10) clusters and their ions. Gain and loss charge would affect the degree of hybridization and change their geometries. Their structural changes can be explained by valence bond theory.     

Thermodynamic study of nanoclusters of lead (Pb<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>, <Emphasis Type="Italic">n</Emphasis> = 1–6): adsorption of small molecules on the Pb<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters

Nanoclusters of lead (Pb _n , n = 1–6) were studied theoretically employing MP2 and M062X methods. Structural and thermodynamic properties as well as ionization energies and electron affinities of two isomers of Pb₃, six isomers of Pb₄, seven isomers of Pb₅ and seven isomers of Pb₆ were obtained at 298 K. Rhombic, pyramidal and octagonal structures were the most stable forms of the Pb₄, Pb₅ and Pb₆ clusters, respectively. Proton affinities of the Pb _n clusters were computed, which were in the range of 200–250 kcal/mol. Adsorption of C₂H₂, C₂H₄, CO, CO₂, CH₂O, HNO, O₃, NO, N₂O, NO₂, N₂O₄ and N₂O₅ on the Pb _n clusters was studied. O₃ showed the strongest interaction with the Pb _n clusters with adsorption enthalpies of 80–130 kcal/mol. HNO, O₃, N₂O, N₂O₄ and N₂O₅ were dissociated after adsorption on the Pb _n clusters. N₂O decomposes to adsorbed O atom and a free N₂ molecule, while N₂O₄ and N₂O₅ release a NO₂ molecule.     

Theoretical Study of Electronic Structure and Stability of Mixed AlmBn−mH n 2− and CmBn−mH n 2−m (n = 6, 10, 12 and m = 1, 2) Clusters

Density functional theory (DFT) method with B3LYP functional and 6-311++G(d,p) basis set has been used to predict the geometries, relative stabilities, electronic structures and bonding analysis of Mixed Al_mB_n?mH _n ^2? and C_mB_n?mH _n ^2?m (n = 6, 10, 12 and m = 1, 2) clusters; being compared to the B_nH _n ^2? ones. Therefore, the DFT results suggest that the replacing of boron by aluminium or carbon is governed by Natural net charges following Gimar’s and Williams’s rules. The Al_mB_n?mH _n ^2? structures are relatively distorted compared to those of B_nH _n ^2? and C_mB_n?mH _n ^2?m . In Al_mB_n?mH _n ^2? structures Al atoms prefer the adjacent sites, however for the C₂B_n?2H_n cluster cages, the carbon atoms are positioned at diametrically opposed sites. The large HOMO–LUMO gaps show that the predicted clusters have chemical stabilities, principally, those of Al_mB_n?mH _n ^2? ones, which are not experimentally isolated. The optimized geometries obtained through boron substitution by Al and C lead to compactness and to contracted structures, respectively, where B–B bonds are the shortest in mono- and di-carbaboranes.     

Thermochemistry of the Dissolution of Dipeptides Containing DL-α-Alanine in Aqueous Solutions of Sodium Dodecyl Sulfate at 298.15 K

Enthalpies of the dissolution of DL-α-alanylglycine (AlaGly), DL-α-alanyl-DL-α-alanine (AlaAla), DL-α-alanyl-DL-α-valine (AlaVal), and DL-α-alanyl-DL-norleucine (AlaNln) in an aqueous solution of sodium dodecyl sulfate (SDS) at SDS concentration of m = 0–0.07 mol kg^?1 and temperature Т = 298.15 K are measured via calorimetry. The standard values of the enthalpy of dissolution (Δ_solH ^m ) and the transfer of dipeptides (Δ_trH ^m ) from water to aqueous SDS solutions are calculated using the experimental data. The dependences of Δ_solH ^m and Δ_trH ^m the SDS concentration at a constant concentration of dipeptide are established. Thermochemical characteristics of the transfer of AlaGly, AlaAla, AlaVal, and AlaNln in the investigated range of SDS concentrations are compared. The results are interpreted by considering ion–ion, ion–polar, and hydrophobic–hydrophobic interactions between SDS and dipeptide molecules.     

The enthalpy of solution of DL-α-alanyl-DL-α-valine depending on the composition of water-alcohol binary solvents at 298.15 K

The integral enthalpies of solution of DL-α-alanyl-DL-α-valine in water-ethanol, water-n-propanol, and water-isopropanol mixtures at alcohol concentrations x ₂ = 0–0.4 mole fractions were measured calorimetrically. The enthalpies of solution of the peptide Δ_sol H° and transfer from water to a mixed solvent Δ_tr H° were calculated. The effect of the structure and properties of the peptide and mixture composition on the enthalpy characteristics of the peptide are discussed. The enthalpy coefficients of pair interactions h _xy of DL-α-alanyl-DL-α-valine with alcohol molecules were calculated. It was found that they were positive and increased in the series ethanol, n-propanol, isopropanol. An analysis of the results allows the general features of changes in the thermodynamic parameters of solution of peptides of the DL-α-alanine series with different amino acid residues in water-alcohol mixtures to be established.