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.     

Computational Studies on the Mo-Doped Gold Nanoclusters Au<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Mo(<Emphasis Type="Italic">n</Emphasis> = 1–10): Structures,Stabilities and Magnetic Properties

The geometric structures, relative stabilities, magnetic properties of Mo-doped gold clusters Au _n Mo(n = 1–10) have been investigated at the PBE1PBE/def2TZVP level of theory. The results show that molybdenum doping has a significant effect on the geometric structures and electronic properties of Au _n Mo(n = 1–10) clusters. For the lowest energy structures of Au _n Mo(n = 1–10), the two dimensional to three dimensional transition occurs at cluster size n ≥ 8, and their relative stabilities exhibit odd–even oscillation with the change of Au atom number. It is found that charge in corresponding Au _n Mo clusters transfers from Mo atom to Au _n host in the size range n = 1–7, whereas the charge in opposition direction in the size range n = 8–10. In addition, the magnetic properties of Au _n Mo clusters are enhanced after doping single Mo atom into the corresponding gold clusters. Our results are valuable for the design of magnetic material.     

Planar Four-Coordinate Carbon in Star-Like Perlithioannulenes C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Li<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 3–6)

The structure and stability of perlithioannulenes C _n Li _n (n = 3–6) were examined ab initio [MP2(full)/6-311+G**] and in terms of the density functional theory (B3LYP/6-311+G**). The systems with n = 3, 5, and 6 may be stabilized as planar star-like structures with bridging lithium atoms and hypercoordinate carbon atoms. Star-like structures are the most stable isomers of odd-numbered annulenes (n = 3, 5), while the most stable isomers of even-numbered annulenes (n = 4, 6) have less symmetric nonplanar structures.     

The molecular designs and properties of asymmetric heterocycles (HBrBN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1-4)

The structures and properties of asymmetric heterocycles (HBrBN₃) _n (n = 1-4) are systematically studied at the B3LYP/6-31G* level. The molecules (HBrBN₃) _n (n = 2-4) have the core structures of a 2n-membered ring with alternating boron and α-nitrogen atoms. The relationships between geometrical parameters and oligomerization degree n are discussed. The calculated IR spectra have four main characteristic regions. Trends in thermodynamic properties with temperature and oligomerization degree n are discussed. Thermodynamic analysis of the gas-phase oligomerizations shows that formation of the most stable heterocycles (HBrBN₃) _n (n = 2-4) is enthalpy driven in the range of 200-800 K.     

Ionization,atomization, and bond energies as functions of distances in inorganic molecules and crystals

The ionization potentials and dissociation energies of diatomic molecules are determined as functions of bond length, and the atomization energies of metals and crystalline compounds are determined as E = a/d ⁿ functions. In most cases, n ≥ 1; but for a number of metals and compounds, n < 1, as distinct from all known types of interatomic interactions. It is shown that the ratios of the bond energies and bond lengths of Group 1A and 1B metals to the respective molecular parameters have similar values, proving the identical valence states of the atoms of these metals in crystal structures.     

Probing Structure,Thermochemistry, Electron Affinity and Magnetic Moment of Erbium-Doped Silicon Clusters ErSi<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 3–10) and Their Anions with Density Functional Theory

The lowest energy structures and electronic properties of ErSi _n (n = 3–10) and their anions were probed using the ABCluster global search technique combined with the PBE, TPSSh and B3LYP schemes. The lowest energy energies of neutral ErSi _n (n = 3–10) can be regarded as substituting a Si atom of the lowest energy structure of Si_n+1 with a Er atom. The additional electron effects on the geometries are very strong, resulting the lowest energy structures of ErSi _n ^? with n > 6 are different from their neutral counterparts. Starting from n = 7, the potential energy surfaces of ErSi _n ^? are very flat, resulting isomeric arrangements occur and functional dependence of the predicted most stable structures exist. The AEAs, VDEs and simulated PES of ErSi _n (n = 3–10) are reported. Introducing Er to Si cluster can significantly improve photochemical reactivity of the cluster. The 4f electron of Er atom in ErSi₄, ErSi _n ^? (n = 4, 7–10) prefers to take part in bonding. The total magnetic moments of ErSi _n and their anions are mainly provided by the 4f electrons of Er atom. The dissociation energies of Er from ErSi _n and their anions were evaluated to inspect relative stability.     

A Systematic Search for Structures and Stabilities of Asymmetric Clusters (HfInN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1-6)

In order to find single source precursors (SSP), the structures, relative stabilities, and IR spectra of small asymmetric clusters (HFInN₃) _n (n = 1–6) are systematically investigated by means of the density functional theory at the B3LYP level. The obtained geometries show that the frameworks of clusters (HFInN₃) _n (n = 2–6) prefer to be 2n-membered ring with alternating indium and α-nitrogen atoms. The averaged binding energies reveal that all of asymmetric clusters (HFInN₃) _n (n = 1–6) can continue to gain energy as the cluster size n increasing. The second-order difference of energy (Δ₂E) and the HOMO-LUMO energy gap (E_gap) as a function of the cluster size n both exhibit a pronounced even-odd alternation phenomenon. The influences of cluster size n and temperature T on the thermodynamic properties of clusters are discussed. Judged by enthalpies and Gibbs free energies, the formations of the most stable clusters (HFInN₃) _n (n = 2–6) from the monomer are thermodynamically favorable in the range of 200–800 K.     

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.     

On bicriticality of (3,6)-fullerene graphs

A (3,6)-fullerene is a plane cubic graph whose faces are only triangles and hexagons. A connected graph G with at least \(2n+2\) vertices is said to be n-extendable if it has n independent edges and every set of n independent edges extends to a perfect matching of G. A graph G is said to be bicritical if for every pair of distinct vertices u and v, \(G-u-v\) has a perfect matching. It is known that every (3,6)-fullerene is 1-extendable, but not 2-extendable. In this short paper, we show that a (3,6)-fullerene G is bicritical if and only if G has the connectivity 3 and is not isomorphic to one graph (2,4,2). As a surprising consequence we have that a (3,6)-fullerene is bicritical if and only if each hexagonal face is resonant.     

Random packing of monoatomic structures

The dependence of the first coordination number k _n on the packing factor k _y is obtained for four cubic structures: fcc, bcc, simple cubic, and diamond. The k _n (k _y ) dependence is described by a third-degree polynomial k _n = ?71.76782 + 467.78914 k _y ? 925.48451 k _y ² + 603.01146 k _y ³ with the confidence factor R _d = 1. The k _n (k _y ) function has an N loop with a maximum at k _n = 6.32; k _y = 0.454 and a minimum at k _n = 5.84; k _y = 0.573. The tangents intersect the k _n (k _y ) curve at extrema at k _y = 0.4 and k _y = 0.625. Around the N loop, i.e., at 5.84 ≤ k _n ≤ 6.32 and 0.4 ≤ k _y ≤ 0.625, two or three packing factors correspond to a certain value of the coordination number. Therefore, this range of the k _n and k _y values can be defined as a “random packing” region. Estimations presented here agree well with the results of calculations, both geometric and numerical. For monoatomic solids with the random packing parameters, the difference between the specific volumes of the solid and liquid phases is insignificant. The dilatancy effect is possible in the region where ?k _n / ?k _y ≤ 0.     

When does a diblock copolymer probe the interfacial rheological effect?

Lateral diffusion of diblock copolymer residing on the interfaces between two immiscible liquids is investigated at single molecular level. Fluorescence correlation spectroscopy was used to study the diffusion of fluorescence-labeled diblock copolymer, polystyrene-b-polyisoprene, at the interface formed between two immiscible liquids. The interfaces are formed between N,N-dimethylformamide (DMF) and a few immiscible liquids, n-alkane and polyisoprene. Interfacial diffusion coefficient of the diblock copolymer probe is found to decrease monotonously with the increase of the molecular length of the interface constituting liquids. The decrease of diffusion coefficient follows the prediction by Einstein relation using the viscosity of the constituting liquids as the variables only for interfaces between DMF and very small n-alkanes. For interfaces formed between DMF and bigger alkanes and especially between DMF and polyisoprene, the diffusion coefficient is much higher than the calculated value, indicating that the probe molecule starts to probe the much less viscous interfacial region because the interfacial width gets larger, whose thickness is comparable to the molecule size of the liquids.     

Spatial Structure,Electron Energy Spectrum,and Growth of HfSi<Stack><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>−</Superscript></Stack> Clusters (<Emphasis Type="Italic">n</Emphasis> = 6–20)

The optimized spatial structure and calculated electronic spectra of anionic clusters HfSi _n ^? (n = 6–20) are presented. The calculations have been performed by the density functional theory method. By comparing the calculated and available experimental data, the spatial structures of the clusters detected in the experiment have been determined. It has been established that the formation of endohedral structures begins with n = 12, when a stable structure of a prism encapsulating a hafnium atom is formed. Clusters with n = 12 and 16 have increased stability and are basic for the construction of clusters with a close number of silicon atoms.     

Description of the even-odd alternation of the clearing temperatures over homologous series of mesogens by second-order differential equations

It is shown for liquid crystals of various chemical classes that the nematic-isotropic transition temperatures in homologous series of compounds undergoing enantiotropic transitions are described by secondorder inhomogeneous recurrent equations with constant coefficients: T(n + 2) = aT(n + 1) + bT(n) + c (n is the number of alkyl carbon atoms). Solutions of the corresponding differential equations as T(n) functions allow reproduction of the even-odd alternation of the clearing temperatures.     

Synthesis,characterization, antimicrobial activity and ultrastructure of the affected bacteria of new quinoline compounds

The reaction on 8-hydroxy quinoline-7-aldehyde azo compounds (HL _n ) (where n = 1–5) with 4-amino-1,2-dihydro-2,3-dimethyl-1-phenylpyrazol-5-one to obtain HL _n (where n = 6–10) have been characterized by means of TLC, melting point and spectral data, such as IR, ¹H NMR, mass spectra and thermal studies. The X-ray diffraction patterns of two starting materials 8-hydroxy quinoline-7-aldehyde (start 1), 4-amino-1,2-dihydro-2,3-dimethyl-1-phenylpyrazol-5-one (start 2) and the ligands (HL_5,10) are investigated in powder form. All the ligands have been screened for their antimicrobial activity against four local bacterial species, two Gram-positive bacteria (Bacillus cereus and Staphylococcus aureus) and two Gram-negative bacteria (Escherichia coli and Klebsiella pneumoniae) as well as against four local fungi; Aspergillus niger, Alternaria alternata, Penicillium italicum and Fusarium oxysporium. The results show that the azo ligands (HL _n ) (where n = 1–5) have no antimicrobial activity against bacteria and fungi while most azomethine ligands (HL _n ) (where n = 6–10) are good antibacterial agents against E. coli and K. pneumoniae as well as antifungal agents against P. italicum and A. alternata. The results were compared to standard substances (start 1) and (start 2). Among the azomethine ligands, HL₁₀ was the most effective against the most microorganisms tested. The size of clear zone was ordered as p-(OCH₃ < CH₃ < H < Cl < NO₂) as expected from Hammett’s constant (σ ^R ). Also, the ultrastructure study of the affected bacteria confirmed that HL₈ is good antibacterial agent against E. coli and S. aureus.     

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.     

DFT study of small aluminum and boron hydrides: isomeric composition and physical properties

The structure, energetics, and physical properties, including rotational constants, characteristic vibrational temperatures, dipole moment, static polarizability, HOMO-LUMO gap, formation enthalpy and collision diameter of different isomeric forms of atomic Al _n H _m and B _n H _m clusters with n = 1..4 and all feasible m numbers are studied within the density functional theory framework. The search of isomer structures has been accomplished using multistep hierarchical algorithm. Temperature dependences of thermodynamic functions (enthalpy, entropy and specific heat capacity) have been calculated both for the individual isomers and for the ensemble of isomers with equilibrium composition for each class of clusters, taking into account the anharmonicity of cluster vibrations and the contribution of excited electronic states. The prospects of the application of small atomic Al _n H _m and B _n H _m clusters as the components of energetic and hydrogen storage materials are also discussed.     

Theoretical investigation on the geometries and electronic properties of cesium–silicon CsSi<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2–12) clusters

The structures, relative stabilities, and electronic properties of pure Si _n and Cs-doped silicon clusters (n = 2–12) are systematically investigated using the density functional theory at the B3LYP level. The optimized structures indicated that the lowest-energy structures of CsSi _n are similar to those of pure Si _n clusters and prefer the 3-dimensional configuration for n = 3–12. The relative stabilities of CsSi _n clusters are analyzed based on the averaged binding energy, fragmentation energy, second-order energy difference, and HOMO–LUMO energy gap. It is found that CsSi₆ and CsSi₉ are the magic clusters, and the doping of Cs atom reduces the chemical stabilities of Si _n frame. The Mulliken population analysis pointed out that the charges in the corresponding CsSi _n clusters always transfer from Cs atom to Si _n host in the range of 0.80–0.91 electron. In addition, the partial density of states, infrared, and Raman spectra is discussed.     

Crystalline hydrates of calix[4]arene-<Emphasis Type="Italic">para</Emphasis>-sulfonic acid with <Emphasis Type="Italic">n</Emphasis> (<Emphasis Type="Italic">n</Emphasis> = 6–16) water molecules: a structure modeling

The structures of crystalline hydrates of calix[4]arene-para-sulfonic acid with n (n = 6–16) water molecules and the activation barriers to surface proton migration were calculated within the framework of the density functional theory (DFT) using the PBE gradient-corrected functional, the "hard" basis set of projector-augmented waves (PAW), a corresponding pseudopotential, periodic boundary conditions, and the VASP program package. The energies of formation of crystalline hydrates from calix[4]arene-para-sulfonic acid and n water molecules calculated per water molecule are in the range of 0.4–0.9 eV and depend on n. The adsorption energy of water on the surface is in the range of 0.5–0.7 eV. The activation barriers to proton transfer across the surface calculated for the most stable crystal (n = 8) are close to experimental data and depend on the number of superstoihiometric water molecules, being equal to ~0.2 eV provided three superstoihiometric water molecules per surface SO₃H group.