Ab initio investigation of the lower-energy candidate structures for (H<Subscript>2</Subscript>O)<Subscript>10</Subscript><Superscript>+</Superscript> water cluster

Low-lying structures of water cationic clusters and the compounds with the OH radical have become a hot topic in recent years. We here investigate the cluster \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \) and calculate its ideal structures by the quantum chemical calculation together with the particle swarm optimization method. We analyzed the properties of the obtained lower-energy isomers of \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \). Their energies are further re-optimized and demonstrated at three different methods with two basis sets. Based on our numerical calculations, a new cage-like structure of \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \) with the lowest energy is obtained at MP2/aug-cc-pVDZ level. Our results showed the comparison of energy order at different conditions and demonstrated the influence of temperature on the relative Gibbs energy and IR spectra. Moreover, we also contained the molecule orbitals to discuss the stability of these representative isomers.     

The Radial Distribution of Ions and Electrons in RF Inductively Coupled H<Subscript>2</Subscript>/T<Subscript>2</Subscript>B Plasmas

A glow discharge polymer (GDP) was fabricated using trans-2-butene (T₂B) and hydrogen (H₂) via a plasma-enhanced chemical vapor deposition (PECVD) system. The uniformity of the GDP films was significantly affected by the radial distribution of the H₂/T₂B plasma parameters. The plasma properties while discharging by a multi-carbon gas source of mixed H₂/T₂B were investigated during the GDP deposition process. The main positive ions and ion energy distributions in inductively coupled H₂/T₂B plasmas were analyzed by energy-resolved mass spectrometer (MS), and the electron density and the effective electron temperature were mainly analyzed using a Langmuir probe. The MS results show that the main positive ions in the plasmas are \({\text{C}}_{ 2} {\text{H}}_{ 4}^{ + }\), \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 3}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 8}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 5}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 1 0}^{ + }\), \({\text{C}}_{ 5} {\text{H}}_{ 5}^{ + }\), and \({\text{C}}_{ 5} {\text{H}}_{ 7}^{ + }\) with mass-to-charge ratios (m/e) of 28, 30, 39, 42, 44, 53, 58, 65, and 67, respectively. For a normalized ion intensity, the relative intensities of saturated CH ions increase with increasing radial distance, while the unsaturated CH ions decrease with increasing radial distance. The ion energy distribution of \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\) (m/e = 30) presents a bimodal structure. Additionally, both the electron density and the effective electron temperature decrease with increasing radial distance.     

Thermochemical Properties of Dissolution of Nicotinic Acid C<Subscript>6</Subscript>H<Subscript>5</Subscript>NO<Subscript>2</Subscript>(s) in Aqueous Solution

Nicotinic acid (also known as niacin) was recrystallized from anhydrous ethanol. X-ray crystallography was applied to characterize its crystal structure. The crystal belongs to the monoclinic system, space group P2₍₁₎/c. The crystal cell parameters are a = 0.71401(4) nm, b = 1.16195(7) nm, c = 0.71974(6) nm, α = 90°, β = 113.514(3)°, γ = 90° and Z = 4. Molar enthalpies of dissolution of the compound, at different molalities m/(mol·kg^?1) were measured with an isoperibol solution–reaction calorimeter at T = 298.15 K. The molar enthalpy of solution at infinite dilution was calculated, according to Pitzer’s electrolyte solution model and found to be \( \Delta_{\text{sol}} H_{m}^{\infty } = ( 2 7. 3 \pm 0. 2) \) kJ·mol^?1 and Pitzer’s parameters (\( \beta_{{\text{MX}}}^{{\text{(0)}L}} \), \( \beta_{{\text{MX}}}^{{\text{(1)}L}} \) and \( C_{{\text{MX}}}^{\phi L} \)) were obtained. The values of apparent relative molar enthalpies (\( {}^{\phi }L \)) and relative partial molar enthalpies (\( \overline{{L_{2} }} \) and \( \overline{{L_{1} }} \)) of the solute and the solvent at different molalities were derived from the experimental enthalpy of dissolution values of the compound. Also, the standard molar enthalpy of formation of the anion \( {\text{C}}_{ 6} {\text{H}}_{ 4} \text{NO}_{2}^{-} \) in aqueous solution was calculated to be \( {\Delta_{\text{f}}^{} H}_{\text{m}}^{\text{o}} ({\text{C}}_{ 6} {\text{H}}_{ 4} {\text{NO}}_{2}^{-} \text{,aq}) = - \left( {603.2 \pm 1.2} \right)\;{\text{kJ}}{\cdot}{\text{mol}}^{-1} \).     

Determination of the Distribution of Cobalt-Chloro Complexes in Hydrochloric Acid Solutions at 298 K

Knowledge of the distribution of metal-chloro complexes in hydrochloric acid solutions is fundamental for understanding the anion-exchange reaction. Anion-exchange separation allows ultrahigh purification during hydrometallurgical processes. However, at present the exchange reactions are not understood in detail. A more sophisticated purification needs improvement of the anion-exchange separation process. The process is based upon anion-exchange reactions and the distribution of metal-chloro complexes. The present work deals with cobalt-chloro complexes which exhibit a beautiful deep blue color in a concentrated hydrochloric acid solution. The intensity of the absorption attributed to the deep blue color is so strong that it is hard to obtain meaningful results by factor analysis. Another absorption band was chosen to be used in factor analysis and the attempt was successful. The number of cobalt-chloro complexes in hydrochloric acid solutions was determined to be three, and the cumulative formation constants were fitted to absorption spectra decomposed by factor analysis. During the optimization of the cumulative formation constants, a modified Debye–Hückel model for estimation of the activity coefficients of \(\hbox {Cl}^{-}\) was used. It was found that there are three cobalt complexes \([\hbox {Co}^{\mathrm{II}}(\hbox {H}_{2}\hbox {O})_{6}]^{2+}\), \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}(\hbox {H}_{2}\hbox {O})_{5}]^{+}\), and \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}_{4}]^{2-}\), and the two cumulative formation constants were optimized such that \(\log _{10}\beta _{1} = -\,0.861\) and \(\log _{10}\beta _{4} = -\,7.40\). The geometries of the complexes are proposed by assignment of absorption bands using ligand field theory. A qualitative assessment of the relationship between the acquired distribution of cobalt-chloro complexes and the adsorption function of cobalt species from hydrochloric acid solutions to anion-exchange resin was made.     

Preparation of Solid Superacid Catalysts and Oil Oxidative Desulfurization Using K<Subscript>2</Subscript>FeO<Subscript>4</Subscript>

A \(\rm{SO_4^{2-}}\)/MCM-41 superacid catalyst was prepared by impregnation and characterized by various methods. A novel procedure for oxidative desulfurization of simulated light fuel oil using K₂FeO₄ over \(\rm{SO_4^{2-}}\)/MCM-41 was developed. Fourier transform infrared spectroscopy (FTIR) and low-angle X-ray diffractometry (XRD) show that the material synthesized by the precipitation-sol-hydrothermal method is mobil composition of matter no. 41 (MCM-41). Thermogravimetry/differential thermal analysis (TG-DTA) shows that when the calcination temperature is higher than 300°.     

Thermodynamic Study on the Protonation and Na<Superscript>+</Superscript>, Ca<Superscript>2+</Superscript>, Mg<Superscript>2+</Superscript>-Complexation of a Biodegradable Chelant (HEIDA) at Different Ionic Strengths and Temperatures

A potentiometric method has been used for the determination of the protonation constants of N-(2-hydroxyethyl)iminodiacetic acid (HEIDA or L) at various temperatures 283.15?≤?T/K?≤?383.15 and different ionic strengths of NaCl_(aq), 0.12?≤?I/mol·kg^?1?≤?4.84. Ionic strength dependence parameters were calculated using a Debye–Hückel type equation, Specific Ion Interaction Theory and Pitzer equations. Protonation constants at infinite dilution calculated by the SIT model are \( \log_{10} \left( {{}^{T}K_{1}^{\text{H}} } \right) = 8.998 \pm 0.008 \) (amino group), \( \log_{10} \left( {{}^{T}K_{2}^{\text{H}} } \right) = 2.515 \pm 0.009 \) and \( \log_{10} \left( {{}^{T}K_{3}^{\text{H}} } \right) = 1.06 \pm 0.002 \) (carboxylic groups). The formation constants of HEIDA complexes with sodium, calcium and magnesium were determined. In the first case, the formation of a weak complex species, NaL, was found and the stability constant value at infinite dilution is log₁₀K_NaL?=?0.78?±?0.23. For Ca²⁺ and Mg²⁺, the CaL, CaHL, CaL₂ and MgL species were found, respectively. The calculated stability constants for the calcium complexes at T?=?298.15 K and I?=?0.150 mol·dm^?3 are: log₁₀β_CaL?=?4.92?±?0.01, log₁₀β_CaHL?=?11.11?±?0.02 and \( \log_{10} \beta_{\text{Ca{L}}_{2}} \)?=?7.84?±?0.03, while for the magnesium complex (at I?=?0.176 mol·dm^?3): log₁₀β_MgL?=?2.928?±?0.006. Protonation thermodynamic functions have also been calculated and interpreted.     

Quasi-classical trajectory insight into stereodynamics for reaction $$\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}$$ with the improved potential energy surface

In this work, a theoretical study on the detailed vector correlation for the reaction \(\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}~(\hbox {v}, \hbox {j})\) has been carried out at the collision energy of 23.06 kcal/mol with different rotational states of j \(=\) 0–5 and vibrational states v \(=\) 1–5 by use of the quasi-classical trajectory calculation on an improved potential energy surface. The features of \({{\varvec{P}}}\mathbf{(}{\varvec{\theta }}_{{\varvec{r}}}{} \mathbf{)}\) distributions describing k and \(\mathbf{j}^\prime \) correlations were discussed. In addition, in order to get full knowledge of stereodynamics of the system, the distributions of dihedral angle \({{\varvec{P}}}\mathbf{(}{\varvec{\varphi }}_{{\varvec{r}}}{} \mathbf{)}\) and the polarization-dependent differential cross-sections (PDDCSs) were also reported. It has been demonstrated that both product alignment and polarization are sensitive to the reagent vibrational and rotational number. Furthermore, the dynamics behavior of the reaction is independently changed with respect to j under a certain v except for the product alignment effect \(({\varvec{P}}({\varvec{\theta }}_{{\varvec{r}}}))\), while it exhibits a generally regular trend concerning v when j is invariable.     

Crystallization study of Se<Subscript>86</Subscript>Sb<Subscript>14</Subscript> glass

The present study concerns with high-accuracy determination of crystallization activation energy (\(E_{\text{c}}\)), the frequency factor (\(k_{0}\)), the kinetic exponent (n) for Se₈₆Sb₁₄ glass. Different three methods have been used to investigate the \(E_{\text{c}} \,{\text{and}}\,k_{0 }\) values. It was found that the deduced value of k ₀ based on Kissinger’s method is too small compared with the others. Therefore, it can’t be used to investigate k ₀ value. Where \(E_{\text{c}} \,{\text{and}}\,k_{0}\) values are already known, the overall reaction rate \(k = k_{0 } { \exp }\left( { - E_{\text{c}} /\left( {R \cdot T} \right)} \right)\) at any temperature can be calculated. Now, Avrami’s equation (\(\chi = 1 - { \exp }\left( { - \left( {kt} \right)^{\text{n}} } \right)\)) contains only one unknown which is the kinetic exponent (n). This method enables us to determine n value without any approximations. The values’ crystallization fraction \((\chi_{\text{th}} )\) that theoretically calculated is the same as that experimentally investigated \((\chi_{{{ \exp } .}} )\).     

Thermodynamic analysis of the structure of aqueous solutions of C<Subscript>12</Subscript>–C<Subscript>18</Subscript> hydrocarbons

Thermodynamic cycles including the increments \(\Delta G_{CH_2 }^0 , \Delta H_{CH_2 }^0 \), and \(T\Delta S_{CH_2 }^0 \) were constructed for dissolution, evaporation, hydrophobic hydration of C₅–C₉ hydrocarbons, and transfer from vapor (\(\Delta G_{CH_2 }^0 \) = ?0.7 kJ·mol^?1, \(\Delta H_{CH_2 }^0 \) = 2.9 kJ·mol^?1, \(T\Delta S_{CH_2 }^0 \) = 3.6 kJ·mol^?1) and water (\(\Delta G_{CH_2 }^0 \) = ?1.4 kJ·mol^?1, \(\Delta H_{CH_2 }^0 \) = 5.8 kJ·mol^?1, \(T\Delta S_{CH_2 }^0 \) = 7.2 kJ·mol^?1) to micelles of C₁₂–C₁₈ hydrocarbons. The formation of bistable hydrated micelles of C₁₂–C₁₈ is explained by a transition between the order-disorder states in an assembly of small (nano) systems of water. The extensive parameters of small systems and critical phenomena predicted by fluctuation theory are discussed.     

CN (<Emphasis Type="Italic">B</Emphasis><Superscript>2</Superscript>Σ<Superscript>+</Superscript> → <Emphasis Type="Italic">X</Emphasis><Superscript>2</Superscript>Σ<Superscript>+</Superscript>) Violet System in a Cold Atmospheric-Pressure Argon Plasma Jet

\( {\text{CN}} (B^{2}\Sigma ^{ + } \to X^{2}\Sigma ^{ + } ) \) violet system was investigated using optical emission spectroscopy in a non-equilibrium microwave atmospheric-pressure plasma jet in argon expanding in air. From the analysis of the emission spectra of the discharge in the range of 380 and 400 nm, the violet system of CN was found to be overlapped with the \( {\text{N}}_{2}^{ + } \left( {B^{2}\Sigma _{u}^{ + } , v = 1 \to X^{2}\Sigma _{g}^{ + } , v = 1} \right) \) and \( {\text{N}}_{2} \left( {C^{3}\Pi _{u} \to B^{3}\Pi _{g} } \right) \) bands, sequence \( \Delta \upsilon = - \;3 \). A numerical disentangle technique, developed in this work, permitted to obtain a well resolved violet system from the different systems observed, namely the nitrogen First Negative and the Second Positive systems. The \( {\text{CN}} (B^{2}\Sigma ^{ + } \to X^{2}\Sigma ^{ + } ) \) band head intensity was determined and analysed as function of discharge powers between 30 and 150 W and fluxes between 2.5 and 10.0 slm. With aid of this numerical approach it was also possible to obtain the rotational temperature, from (1600 ± 100) to (2300 ± 100) K and vibrational temperature between (9000 ± 800) and (14,000 ± 800) K along the plasma jet. The kinetics of \( {\text{CN}} (B^{2}\Sigma ^{ + } ) \) state was analysed as well.     

Mechanism of the electroreduction of Ni (II) ions on mercury electrodes catalyzed by pyridine and its derivatives: nicotinamide, <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-diethylnicotinamide and nicotine: concept of parallel heterogeneous catalytic reactions

The theory of the polarographic catalytic currents (mechanism CE) has been developed for the system: Ni²⁺-L-X^p− where L: pyridine (Py), nicotinamide (NA), N,N-diethylnicotinamide (DEN), nicotine (NC) and X^p−: NO⁻ ₃, AcO⁻, HPO²⁻ ₄ . The theory is based on the kinetic parallel heterogeneous catalytic reactions:

Nested wreath groups and their applications to phylogeny in biology and Cayley trees in chemistry and physics

Nested wreath product groups arise from looped or recursive structures that contain repeated copies of the same structure one within the other. Phylogeny trees in biology, Cayley trees, Bethe lattices, NMR graphs of non-rigid molecules, ammoniated ammonium ions are all examples of structures that exhibit such nested wreath product automorphism groups. We show that the conjugacy classes, irreducible representations and character tables of these nested group structures can be generated using multinomial generating functions cast in terms of matrix types that can be simplified into generalized cycle type polynomials. The nested wreath product groups rapidly increase in orders, for example, a simple wreath product group \(\hbox {S}_{7}[\hbox {S}_{7}]\) consists of \((7!)^{8}\) or \(4.1633\times 10^{23}\) operations, 481,890 conjugacy classes, spanning a 481,891 \(\times \) 481,891 character table that would occupy 232,217,972 pages. We have obtained powerful recursive relations for the conjugacy classes, character tables and the orders of various conjugacy cases of any nested wreath product \(\{[\hbox {S}_{\mathrm{n}}]\}^{\mathrm{m}}\) or \(\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}{\ldots }.[\hbox {S}_{\mathrm{n}}]]{\ldots }.]\) with order \(\left( {n!}\right) ^{a_m},\,\hbox {a}_{\mathrm{m}}=(\hbox {n}^{\mathrm{m}}-1)/(\hbox {n}-1)\). We have obtained the character tables of phylogenetic trees of any order, character tables of Cayley trees of degrees 3 and 4 and for Cayley trees of larger degrees, we have derived exact analytical expressions for the conjugacy classes and IRs for up to \(\{[\hbox {S}_{7}]\}^{\mathrm{m}}\) with order \((7!)^{137257}\) for \(\hbox {m}=7\). Applications to colorings of phylogenic trees in biology are considered.     

High temperature polymers. I.—Sulfone ether diamines as intermediates for tractable high temperature polymers

A useful synthesis of a series of new aromatic sulfone ether diamines, H₂NC₆H₄O\documentclass{article}\pagestyle{empty}\begin{document}$\hbox{---}\hskip-5pt[\ {\rm C}_{\rm 2} {\rm H}_{\rm 4} {\rm SO}_{\rm 2} {\rm C}_{\rm 6} {\rm H}_{\rm 4} \hbox{--} {\rm ORO}\hbox{---}\hskip-5pt ]_n {\rm OC}_{\rm 6} {\rm H}_{\rm 4} {\rm SO}_{\rm 2} {\rm C}_{\rm 6} {\rm H}_{\rm 4} \hbox{---} {\rm OC}_{\rm 6} {\rm H}_{\rm 4} {\rm NH}_{\rm 2} $\end{document}, where n = 0, 1, 2…, which increases the tractability of polyimides, polyamide-imides, and polyamides, was developed. These diamines were prepared by condensing various proportions of sodium p-aminophenate, sodium bisphenates, and dichlorodiphenyl sulfone. The synthetic procedures are now refined to the point where simply coagulating these diamines into water yields high purity polymer-grade sulfone ether diamines. The latter have good tractability; and in some cases, it is possible to extrude and injection-mold these high temperature polymers.     

The Study of Intermolecular Interactions for <Emphasis Type="SmallCaps">dl</Emphasis>-Alanine and Glycine in Aqueous <Emphasis Type="SmallCaps">l</Emphasis>(+)-Arabinose Solutions at Different Temperatures and Ambient Pressure,Using the Volumetric Approach

Density measurements are used to calculate the apparent molar volumes V_φ, limiting apparent molar volumes \(V_{\varphi }^{0}\), limiting apparent molar volumes of transfer, \(\Delta_{\text{t}} V_{\varphi }^{0}\), limiting apparent molar expansibilities, \(E_{\varphi }^{0}\), and hydration numbers n_H, for dl-alanine and glycine in aqueous solutions of l(+)-arabinose at T?=?293.15 to 313.15 K. To obtain the limiting apparent molar volume, the V_φ values are extrapolated to zero molality using the linear form of the Redlich–Meyer equation. Also, the limiting apparent molar volumes of transfer, \(\Delta_{\text{t}} V_{\varphi }^{0}\), for the amino acids, from water to aqueous l(+)-arabinose solutions, are calculated from the \(V_{\varphi }^{0}\) values. The limiting apparent molar expansibility, \(E_{\varphi }^{0}\), values have been obtained from the first derivative of limiting apparent molar volumes with respect to temperature. Also the hydration number, n_H, for both amino acids in the ternary solutions are estimated. Possible solute–solvent interactions in the studied ternary systems are discussed.     

The First Structurally Characterized Mn(III) Substituted Sandwich-type Polyoxotungstates

The new polyoxotungstates H₂O (1), · 28H₂O (2) and H₂O (3) were synthesized in aqueous solution and characterized by IR and Raman spectroscopy, energy dispersive X-ray fluorescence and single-crystal X-ray analysis. The anions in 1 and 2 are the first structurally characterized sandwich-type polyoxoanions which contain trivalent manganese atoms. The manganese atoms are coordinated by four oxygen atoms of two Keggin fragments and one water molecule, forming a square pyramid. The manganese(II) containing anions in 3 are linked via Mn–O–W-bonds, forming a two-dimensional network.Dedicated to Prof. M.T. Pope on the occasion of his retirement.     

On the structure of discrete spectrum of a non-selfadjoint system of differential equations with integral boundary condition

In this paper, we investigated the spectrum of the operator \(L(\lambda )\) generated in Hilbert Space of vector-valued functions \(L_{2}(\mathbb {R}_{+},C_{2})\) by the system

$$\begin{aligned} iy_{1}^{'}(x,\lambda )+q_{1}(x)y_{2}(x,\lambda )&=\lambda y_{1}(x,\lambda )\\ -iy_{2}^{'}(x,\lambda )+q_{2}(x)y_{1}(x,\lambda )&=\lambda y_{2}(x,\lambda ),x\in \mathbb {R}_{+}:=(0,\infty ), \end{aligned}$$

and the integral boundary condition of the type

$$\begin{aligned} \int _{0}^{\infty }K(x,t)y(t,\lambda ){\mathrm {dt}}+\alpha y_{2}(0,\lambda )-\beta y_{1}(0,\lambda )=0 \end{aligned}$$

where \(\lambda \) is a complex parameter, \(q_{i},\,i=1,2\) are complex-valued functions and \(\alpha ,\beta \in \mathbb {C}\). K(x, t) is vector fuction such that \(K(x,t)=(K_{1}(x,t),K_{2}(x,t)),\,K_{i}(x,t)\in L_{1}(0,\infty )\cap L_{2}(0,\lambda ),\,i=1,2\). Under the condition

$$\begin{aligned} \left| q_{i}(x)\right| \le ce^{-\varepsilon \sqrt{x}},c>0,\varepsilon >0,i=1,2 \end{aligned}$$

we proved that \(L(\lambda )\) has a finite number of eigenvalues and spectral singularities with finite multiplicities.

     

The mass renormalization for the translational Brownian motion

The damped harmonic oscillator is modeled as a local mode X with mass m and frequency \(\omega _{0}\) immersed in a phonon bath with spectral density function \(j_{0}(\omega \)). This function behaves as \(\omega ^{s}\, (s= 1,2,3,\ldots )\) when \(\omega \rightarrow 0\). The limit \(\omega _{0} = 0\) represents translational (free) Brownian motion. The earlier work (Hakim and Ambegaokar in Phys Rev A 32:423, 1985) concluded that the so defined limit transition is prohibited for spectral densities with \(s<2\). In the present study we demonstrate that a specially constructed preliminary excitation changing the original bath spectrum as \(j_{0}(\omega ) \rightarrow j(\omega )\) allows for treating the free damped motion of X with no restriction for the initial spectrum dimensionality. This procedure validates the finite mass renormalization (i.e. \(m\rightarrow M\) when \(\omega _{0}\rightarrow 0)\) for the conventional bath spectra with \(s=1,2\). We show that the new spectral density \(j(\omega )\) represents the momentum bilinear interaction between mode X and the environmental modes, whereas the conventional function \(j_{0}(\omega )\) is inherent to the case of bilinear coordinate interaction in terms of the same variables. The translational damping kernel is derived based on the new spectral density.     

Additional Aspects of Complexation of Gold(I) with Thiomalate

Some equilibria involving gold(I) thiomalate (mercaptosuccinate, TM) complexes have been studied in the aqueous solution at 25 °C and I?=?0.2 mol·L^?1 (NaCl). In the acidic region, the oxidation of TM by \( {\text{AuCl}}_{4}^{ - } \) proceeds with the formation of sulfinic acid, and gold(III) is reduced to gold(I). The interaction of gold(I) with TM at n_TM/n_Au?≤?1 leads to the formation of highly stable cyclic polymeric complexes \( {\text{Au}}_{m} \left( {\text{TM}} \right)_{m}^{*} \) with various degrees of protonation depending on pH. In general, the results agree with the tetrameric form of this complex proposed in the literature. At n_TM/n_Au?>?1, the processes of opening the cyclic structure, depolymerization and the formation of \( {\text{Au}}\left( {\text{TM}} \right)_{2}^{*} \) occur: \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au}}_{ 4} ( {\text{TM)}}_{5}^{11 - } \), log₁₀ K₄₅?=?10.1?±?0.5; 0.25 \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au(TM)}}_{2}^{5 - } \), log₁₀ K₁₂?=?4.9?±?0.2. The standard potential of \( {\text{Au(TM)}}_{2}^{5 - } \) is \( E_{1/0}^{ \circ } = -0. 2 5 5\pm 0.0 30{\text{ V}} \). The numerous protonation processes of complexes at pH?<?7 were described with the use of effective functions.     

Density functional theoretical study of A series of pentazolide compounds \hbox{A}_{\it n}(\hbox{N}_5)_{\rm 6-{\it n}}^{\it q} (A = B, Al, Si, P, and S; n = 1–3; q = +1, 0, −1, −2, and −3)

The structure and the stability of pentazolide compounds $\hbox{A}_{\it n}(\hbox{N}_5)_{\rm 6-{\it n}}^{\it q}$ (A = B, Al, Si, P, and S; n= 1–3; q = +1, 0, ?1, ?2, and ?3), as high energy-density materials (HEDMs), have been investigated at the B3LYP/6-311+G* level of theory. The natural bond orbital analysis shows that the charge transfer plays an important role when the $\hbox{A}_{\it n}(\hbox{N}_5)_{\rm 6-{\it n}}^{\it q}$ species are decomposed to $\hbox{A}_{\it n}(\hbox{N}_5)_{\rm 5-{\it n}}\hbox{N}_3^{\it q}$ and N₂. The more negative charges are transferred from the N₂ molecule after breaking the N₅ ring, the more stable the systems are with respect to the decomposition. Moreover, the conclusion can be drawn that ${\hbox{Al}(\hbox{N}_5)_5^{2-}}$ and ${\hbox{Al}_2(\hbox{N}_5)_4^{2-}}$ are predicted to be suitable as potential HEDMs.