Ion-molecular interactions in solutions of potassium and cadmium thiocyanates in N-methylpyrrolidone at 298.15 k, according to calorimetry and densitometry data

The heat capacity and density of KNCS-N-methylpyrrolidone (MP), Cd(NCS)₂-MP, and KNCS-Cd(NCS)₂-MP solutions at 298.15 K are studied by means of calorimetry and densitometry. Standard partial molar heat capacities and volumes ( $\bar C^\circ _{p,2} $ and $\bar V^\circ _2 $ ) of the studied electrolytes in MP are calculated. Standard values of heat capacity $\bar C^\circ _{p,i} $ and volume $\bar V^\circ _i $ of NCS^? ions in MP at 298.15 K are determined. Values of the heat capacity and volume changes upon the formation of the three-component system KNCS-Cd(NCS)₂-MP from binary solutions are obtained and discussed.     

Clar and Fries numbers for benzenoids

A Kekulé structure of a benzenoid or a fullerene $\Gamma $ Γ is a set of edges $K$ K such that each vertex of $\Gamma $ Γ is incident with exactly one edge in $K$ K . The set of faces in $\Gamma $ Γ that have exactly three edges in $K$ K are called the benzene faces of $K$ K . The Fries number of $\Gamma $ Γ is the maximum number of benzene faces over all possible Kekulé structures for $\Gamma $ Γ . The Clar number is the maximum number of independent benzene faces over all possible Kekulé structures for $\Gamma $ Γ . It is often assumed, but never proved, that some set of independent benzene faces giving the Clar number is a subset of a set of benzene faces giving the Fries number. In Hartung (The Clar structure of fullerenes, Ph.D. Dissertation. Syracuse University, 2012) it is shown that this assumption is false for a large class of fullerenes. In this paper, we prove that this assumption is valid for a large a class of benzenoids.     

Asymptotics (p\rightarrow \infty ) of L_p-norms of hypergeometric orthogonal polynomials

The determination of the weighted $L_p$ norms of the real orthogonal polynomials of hypergeometric type $\left\{ y_n(x)\right\} $ is not only a very important problem per se in the theory of special functions, but also because of their recent entropic characterization and applications in quantum chemistry, quantum physics and information theory. Indeed, they essentially describe the $p$ th-order Rényi and Tsallis entropies of the numerous quantum systems whose wavefunctions are controlled by these polynomials. Moreover, for different values of $p$ , up to a constant factor, these norms characterize various fundamental and experimentally accessible quantities of many-electron systems. As well, the $L_p$ norms have been used to develop and interpret all energy components in the density-functional theory of the ground-state of atoms and molecules. The asymptotics of these quantities when $n \rightarrow \infty $ and $p>0$ have been recently calculated for Hermite polynomials, although not yet for Laguerre and Jacobi polynomials. Here, we determine the asymptotics ( $p\rightarrow \infty $ , $n$ fixed) of the weighted $L_p$ norms for general orthogonal polynomials in terms of the weight function and the coefficients of the second-order hypergeometric differential equation that they satisfy, and we apply it to the three classical families of real orthogonal polynomials. Moreover we analyse and discuss the monotonicity of this asymptotics, and we carry out a detailed numerical study of it.     

Thermodynamic study of metal corrosion and inhibitor adsorption processes in copper/N-1-naphthylethylenediamine dihydrochloride monomethanolate/nitric acid system: part 2

N-1-Naphthylethylenediamine dihydrochloride monomethanolate (N-NEDHME) was tested as a corrosion inhibitor for copper in 2 M HNO₃ solution using the standard gravimetric technique at 303–343 K. N-NEDHME acts as an inhibitor for copper in an acidic medium. Inhibition efficiency increases with increase in concentration of N-NEDHME but decreases with a rise in temperature. Thermodynamic parameters such as adsorption heat ( $ \Updelta H_{\text{ads}}^\circ $ ), adsorption entropy ( $ \Updelta S_{\text{ads}}^\circ $ ) and adsorption free energy ( $ \Updelta G_{\text{ads}}^\circ $ ) were obtained from experimental data of the temperature studies of the inhibition process at five temperatures ranging from 303 to 343 K. Kinetic parameters activation such as $ E_{a} $ , $ \Updelta H_{\text{a}}^\circ $ , $ \Updelta S_{\text{a}}^\circ $ and pre-exponential factors have been calculated and are discussed. Adsorption of N-NEDHME on the copper surface in 2 M HNO₃ follows the Langmuir isotherm model.     

A note on the principal measure and distributional ({\varvec{p, q}})-chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction

García Guirao and Lampart in (J Math Chem 48:159–164, 2010) presented a lattice dynamical system stated by Kaneko in (Phys Rev Lett 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction. In this paper, we prove that for any non-zero coupling constant $\varepsilon \in (0, 1)$ , this coupled map lattice system is distributionally $(p, q)$ -chaotic for any pair $0\le p\le q\le 1$ , and that its principal measure is not less than $(1-\varepsilon )\mu _{p}(f)$ . Consequently, the principal measure of this system is not less than $$\begin{aligned} (1-\varepsilon )\left( \frac{2}{3}+\sum \limits _{n=2}^{\infty }\frac{1}{n}\frac{2^{n-1}}{(2^{n}+1) (2^{n-1}+1)}\right) \end{aligned}$$ for any non-zero coupling constant $\varepsilon \in (0, 1)$ and the tent map $\Lambda $ defined by $$\begin{aligned} \Lambda (x)=1-|1-2x|,\quad x\in [0, 1]. \end{aligned}$$      

Thermodynamic Analysis of Homologous α-Amino Acids in Aqueous Potassium Fluoride Solutions at Different Temperatures

Partial molal volumes ( $V_{\phi} ^{0}$ ) and partial molal compressibilities ( $K_{\phi} ^{0}$ ) for glycine, L-alanine, L-valine and L-leucine in aqueous potassium fluoride solutions (0.1 to 0.5?mol?kg^?1) have been measured at T=(303.15,308.15,313.15 and 318.15) K from precise density and ultrasonic speed measurements. Using these data, Hepler coefficients ( $\partial^{2}V_{\phi} ^{0}/\partial T^{2}$ ), transfer volumes ( $\Delta V_{\phi} ^{0}$ ), transfer compressibilities ( $\Delta K_{\phi} ^{0}$ ) and hydration number (n _H) have been calculated. Pair and triplet interaction coefficients have been obtained from the transfer parameters. The values of $V_{\phi} ^{0}$ and $K_{\phi} ^{0}$ vary linearly with increasing number of carbon atoms in the alkyl chain of the amino acids. The contributions of charged end groups ( $\mathrm{NH}_{3}^{+}$ , COO^?), CH₂ group and other alkyl chains of the amino acids have also been estimated. The results are discussed in terms of the solute?Ccosolute interactions and the dehydration effect of potassium fluoride on the amino acids.     

CORAL: QSPRs of enthalpies of formation of organometallic compounds

Available on the Internet the CORAL software gives reasonable good prediction for standard enthalpy of formation for selected organometallic compounds (n = 132). The approach is tested using five random splits of the considered data into the sub-training set (n = 32–49), calibration set (n = 36–51), test set (n = 10–29), and the validation set (n = 22–41). Compounds of the validation set are not involved in building up the models. The average statistical quality of prediction is the following: correlation coefficient ( $\overline{R^{2}} )$ R 2 ¯ ) $0.991\pm 0.005$ 0.991 ± 0.005 and standard error of estimation ( $\overline{s} )$ s ¯ ) $22.9 \pm 5.6$ 22.9 ± 5.6  kJ/mol.     

A CASPT2//CASSCF study of the quartet excited state \tilde{a}^{4}A^{\prime\prime} of the HCNN radical

Complete active space self-consistent field and second-order multiconfigurational perturbation theory methods have been performed to investigate the quartet excited state ${\tilde{a}}^{4}{A^{\prime\prime}}$ potential energy surface of HCNN radical. Two located minima with respective cis and trans structures could easily dissociate to CH $({\tilde{a}}^{4}\Sigma^{-})$ and $N_{2} ({\tilde{X}}^{1}\Sigma_{\rm g}^{+})$ products with similar barrier of about 16.0 kcal/mol. In addition, four minimum energy crossing points on a surface of intersection between ${\tilde{a}}^{4}A^{\prime\prime}$ and X ( $X={\tilde{X}}^{2}A^{\prime\prime}$ and ${\tilde{A}}^{2}A^{\prime}$ ) states are located near to the minima. However, the intersystem crossing ${\tilde{a}}^{4}A^{\prime\prime} \rightarrow X$ is weak due to the vanishingly small spin–orbit interactions. It further indicates that the direct dissociation on the ${\tilde{a}}^{4}{A^{\prime\prime}}$ state is more favored. This information combined with the comparison with isoelectronic HCCO provides an indirect support to the recent experimental proposal of photodissociation mechanism of HCNN.     

Interfacial composition, thermodynamic properties and structural parameters of water-in-oil microemulsions stabilized by 1-pentanol and mixed anionic + polyoxyethylene type nonionic surfactants

The interfacial composition $ \left( {n_a^i} \right) $ , thermodynamic properties and structural parameters of the stable water/(SDS + Brij-58 or Brij-78)/1-pentanol/heptane (or decane or isopropyl myristate) have been evaluated under various physicochemical environments by the dilution method. The results showed $ n_a^i $ values increase with increasing water content (ω?=?[water]/[surfactant]) for all the systems, whereas reverse trend was observed for (SDS/Brij-58)/heptane-derived system. The spontaneity of the transfer process of 1-pentanol from bulk oil to the interface $ \left[ { - \Delta G_t^0} \right] $ decreases with increase in ω for all the systems. The effective binding between 1-pentanol and surfactant(s) at the interface follows the order: SDS/Brij-78/IPM < SDS/Brij-58/IPM < SDS/Brij-78/Hp(or, Dc) < SDS/Brij-58/Hp(or, Dc), which corroborates well with the degree of spontaneity of the transfer process. The Gibbs free energy change $ \left( {\Delta G_t^0} \right) $ , standard enthalpy change $ \left( {\Delta H_t^0} \right) $ and standard entropy change $ \left( {\Delta S_t^0} \right) $ have been found to be dependent on ω, type of nonionic surfactant and its content (X_nonionic), oil and temperature, because of the interdependence of the partition equilibrium of Pn between bulk oil and the interface, and strong adsorption of both surfactants at the interface. Synergism in $ \Delta G_t^0 $ and $ \left[ {{{\left( { - \Delta C_P^0} \right)}_t}} \right] $ (standard specific heat change) is evidenced at equimolar composition of SDS and Brij-58 in both oils at all temperatures and advocates more favorable applications for the synthesis of nanoparticles and the modulation of enzyme activity. The radius of water pool (R_w) was very sensitive to the increment of water content and tuned up by the addition of Brijs, which followed the order with decreasing size: IPM < Dc < Hp.     

Free ions Pr IV (4\text{ f }^{2}) and Tm IV (4\text{ f }^{12}): intermediate versus LS coupling scheme

The intermediate and LS-coupling schemes for the free lanthanide ions $\text{ Pr }^{3+}$ Pr 3 + and $\text{ Tm }^{3+}$ Tm 3 + have been compared by the matrix elements of the tensor operator ${{\varvec{U}}}^{({\varvec{k}})}, \text{ k } = 2, 4, 6$ U ( k ) , k = 2 , 4 , 6 . The necessary eigenvectors and eigenvalues have been computed with the aid of four parameters, $\text{ F }_{2}, \text{ F }_{4}, \text{ F }_{6}$ F 2 , F 4 , F 6 , and $\zeta _{4\mathrm{f}}$ ζ 4 f , known from free-ion spectra of the same ions. It has been found that both coupling types for each ion lead to close values of ${\vert }{{\varvec{U}}}^{({\varvec{k}})}{\vert }^{2}$ | U ( k ) | 2 only for transitions from the ground level to certain lower-lying energy levels within the $4\text{ f }^\mathrm{N}$ 4 f N configuration.     

Photoelectrochemistry of silicon in HF solution

Photoelectrochemical, photoelectrocatalytic, and electrochemical processes of silicon anodic oxidation and hydrogen evolution in aqueous HF solution are discussed in terms of thermodynamic stability of Si, oxides SiO, SiO₂, and Si surface hydrides. It is shown that photoelectrochemical oxidation of n-type low-resistivity silicon to SiO₂ is catalyzed by Si $^{+}$ photo-hole formation, whereas in the case of p-type Si, the feasibility of this reaction is predetermined by p-type conductivity. It is suggested that anodic oxidation of Si goes through the stage of SiO oxide formation and its subsequent oxidation to SiO₂. Such mechanism accounts for chemical inertness of Si phase in HF solutions as well as for selective, anisotropic, and isotropic etching of Si within E ranges from $-0.5$ to 0.35 V, $0.35-0.8~V,$ and $E > 0.8$ V, respectively. Hydrogen evolution reaction on Si surface proceeds at very large overpotential ( $\geq 0.5$ V) through the stage of surface Si hydride formation: $\mathrm {Si + H_{2}O + e^{-} \rightarrow (SiH)_{surf} + OH^{-}}$ (the rate determining step) and $\mathrm {(SiH)_{surf} + H_{2}O + e^{-} \rightarrow Si + H_{2} + OH^{-}}$ . Illumination-related effects of surface reactions relevant to selective and anisotropic etching and nano/micro-structuring of Si surface are discussed.     

A new approach to maturity of molecules by rationality of finite groups

These two concepts, maturity in chemistry and rationality in group theory were discovered by a chemist, Fujita. In the present study, we introduce a new approach to maturity and immaturity of simple groups, using the deep theorem (Feit and Seitz in Ill J Math 33:101–131, 1988). Additionally, we prove that 1,3,5-trimethyl-2,4,6-trinitrobenzene are always unmatured and tetra platinum(II) with point group $D_{2n}$ , dihedral group of order $2n$ , is unmatured if $n\ne 1,2,3,4,6$ . Also, we compute integer-valued characters of the simple sporadic group $Ly$ .     

Short- and long-range behavior of the inner and outer densities

We report the short- and long-range behavior of the inner $ \rho_<(r) $ and outer $ \rho_>(r) $ densities, which result from a rigorous partitioning of the spherically averaged one-electron density $ \rho(r) $ in many-electron atoms. It is found that for a small r, $ \rho_<(r) $ has one-electron nature but $ \rho_>(r) $ has two-electron nature. For a large r, however, the opposite is true.     

Transport of Water by Group 1 and 2 Ions with t-Butyl Alcohol as Reference Substance: Comparison with Raffinose and Dioxan

Measurement of the transport of water with respect to the second solvent component in a binary aqueous mixture gives the Washburn number, $ w_{\text{W}} = (n_{\text{W}} )_{ + } t_{ + } - (n_{\text{W}} )_{ - } t_{ - } $ , in a transport number determination, where the ions move in opposite directions, and give the Erdey–Grúz number, $ \Upsigma n_{\text{W}} = (n_{\text{W}} )_{ + } + (n_{\text{W}} )_{ - } $ , in a diffusion experiment, where the ions move in the same direction. Here n _W and t are the number of water molecules and transport number, respectively, of the anion or cation. Combination of the results of these two experiments allows unambiguous determination of values for the solvent transport numbers, $ n_{\text{W}} $ , of the individual ions. While the values of $ n_{\text{W}} $ depend on the cosolvent, at high dilutions of the second component the highest value of $ n_{\text{W}} $ found, $ N_{\text{W}} $ , should approach the number of water molecules transported by the ion in pure water, $ N_{\text{W}}^{0} $ . New data for alkali-metal, alkaline-earth metal, hydrogen and halide ions in dilute mixtures of t-butyl alcohol with water are presented. Values of $ N_{\text{W}} $ rounded to whole numbers thus found are: 12 (Li⁺), 10 (Na⁺), 6 (K⁺), 5 (Rb⁺), 5 (Cs⁺), 1 (H⁺), 13 (Ca²⁺), 16 (Sr²⁺) and 15 (Ba²⁺). Factors influencing preferential solvation are briefly discussed. Detailed recalculations of $ n_{\text{W}} $ in the raffinose–water system from literature data also allows resolution of a problem with the Onsager Relations.     

Three–step method to determine the eutectic composition of binary and ternary mixtures

A three-step method to determine the eutectic composition of a binary or ternary mixture is introduced. The method consists in creating a temperature–composition diagram, validating the predicted eutectic composition via differential scanning calorimetry and subsequent T-History measurements. To test the three-step method, we use two novel eutectic phase change materials based on \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\mathrm O}\) and \(\mathrm{NH}_4\mathrm{NO}_3\)   respectively \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\hbox {O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) with equilibrium liquidus temperatures of 12.4 and 3.9  \(\,^{\circ }\mathrm {C}\) respectively with corresponding melting enthalpies of 135 J \(\mathrm{g}^{-1}\) (237 J \(\mathrm{cm}^{-3}\) ) respectively 133 J \(\mathrm{g}^{-1}\) (225 J \(\mathrm{cm}^{-3}\) ). We find eutectic compositions of 75/25 mass% for \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) and 73/27 mass% for \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) . Considering a temperature range of 15 K around the phase change, a maximum storage capacity of about 172 J \(\mathrm{g}^{-1}\) (302 J \(\mathrm{cm}^{-3}\) ) respectively 162 J \(\mathrm{g}^{-1}\) (274 J \(\mathrm{cm}^{-3}\) ) was determined for \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) respectively \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) .     

A mathematical approach to chemical equilibrium theory for gaseous systems—III: \hbox {Q}_\mathrm{p}, \hbox {Q}_\mathrm{c}, and \hbox {Q}_{\mathrm{x}}

The reaction quotient Q can be expressed in partial pressures as $\hbox {Q}_\mathrm{P}$ or in mole fractions as $\hbox {Q}_{\mathrm{x}}$ . $\hbox {Q}_\mathrm{P}$ is ostensibly more useful than $\hbox {Q}_{\mathrm{x}}$ because the related $\hbox {K}_{\mathrm{x}}$ is a constant for a chemical equilibrium in which T and P are kept constant while $\hbox {K}_{\mathrm{P}}$ is an equilibrium constant under more general conditions in which only T is constant. However, as demonstrated in this work, $\hbox {Q}_{\mathrm{x}}$ is in fact more important both theoretically and technically. The relationships between $\hbox {Q}_{\mathrm{x}}$ , $\hbox {Q}_\mathrm{P}$ , and $\hbox {Q}_{\mathrm{C}}$ are discussed. Four examples of applications are given in detail.     

Volumetric and Viscometric Studies in Binary Liquid Mixtures of 2-Methyl-2-propanol with Some Ketones at Different Temperatures

Densities, ??, and viscosities, ??, of binary mixtures of 2-methyl-2-propanol with acetone (AC), ethyl methyl ketone (EMK) and acetophenone (AP), including those of the pure liquids, were measured over the entire composition range at 298.15, 303.15 and 308.15?K. From these experimental data, the excess molar volume $V_{\mathrm{m}}^{\mathrm{E}}$ , deviation in viscosity ????, partial and apparent molar volumes ( $\overline{V}_{\mathrm{m},1}^{\,\circ }$ , $\overline{V}_{\mathrm{m},2}^{\,\circ }$ , $\overline{V}_{\phi ,1}^{\,\circ}$ and $\overline{V}_{\phi,2}^{\,\circ} $ ), and their excess values ( $\overline{V}_{\mathrm{m},1}^{\,\circ \mathrm{E}}$ , $\overline{V}_{\mathrm{m,2}}^{\,\circ \mathrm{ E}}$ , $\overline {V}_{\phi \mathrm{,1}}^{\,\circ \mathrm{ E}}$ and $\overline{V}_{\phi \mathrm{,2}}^{\,\circ \mathrm{ E}}$ ) of the components at infinite dilution were calculated. The interaction between the component molecules follows the order of AP > AC > EMK.     

Spin correlation in Pr IV and Tm IV free ions

The coefficients \(c_{k}\) (k = 2, 4, 6) that pertain to spin-correlated matrix elements of the tensor operator \({{\varvec{U}}}^{{\varvec{(k)}}}\) have been evaluated by means of the differences \({{\varvec{U}}}^{{\varvec{(k)}}}\) (intermediate) \(-\) \({{\varvec{U}}}^{{\varvec{(k)}}}\) (LS) and the reduced matrix elements of the operator \({{\varvec{V}}}^{{\varvec{(1k)}}}\) . Only spin-allowed transitions have been considered from each ground level to the excited energy levels within the \(4\hbox {f}^{2}\) and \(4\hbox {f}^{12}\) configurations of the free ions Pr (3+) and Tm (3+), respectively. The values of the coefficients \(c_{k}\) thus found correspond in most cases by sign and order of magnitude to those determined in other sources as corrections to lanthanide (3+) crystal-field parameters.     

Towards a definition of almost–equienergetic graphs

The energy $E(G)$ of a graph $G$ , a quantity closely related to total $\pi $ -electron energy, is equal to the sum of absolute values of the eigenvalues of $G$ . Two graphs $G_a$ and $G_b$ are said to be equienergetic if $E(G_a)=E(G_b)$ . In 2009 it was discovered that there are pairs of graphs for which the difference $E(G_a)-E(G_b)$ is non-zero, but very small. Such pairs of graphs were referred to as almost equienergetic, but a precise criterion for almost–equienergeticity was not given. We now fill this gap.     

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.