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.     

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.     

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.     

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.     

Thermochemistry of hydroxymethylphenol isomers

The standard (p° = 0.1 MPa) molar enthalpies of formation in the crystalline state of the 2-, 3- and 4-hydroxymethylphenols, $ {{\Updelta}}_{\text{f}} H_{\text{m}}^{\text{o}} ( {\text{cr)}} = \, - ( 3 7 7. 7 \pm 1. 4)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ , $ {{\Updelta}}_{\text{f}} H_{\text{m}}^{\text{o}} ( {\text{cr) }} = - (383.0 \pm 1.4) \, \,{\text{kJ}}\,{\text{mol}}^{ - 1} $ and $ {{\Updelta}}_{\text{f}} H_{\text{m}}^{\text{o}} ( {\text{cr)}} = - (382.7 \pm 1.4)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ , respectively, were derived from the standard molar energies of combustion, in oxygen, to yield CO₂(g) and H₂O(l), at T = 298.15 K, measured by static bomb combustion calorimetry. The Knudsen mass-loss effusion technique was used to measure the dependence of the vapour pressure of the solid isomers of hydroxymethylphenol with the temperature, from which the standard molar enthalpies of sublimation were derived using the Clausius–Clapeyron equation. The results were as follows: $ \Updelta_{\rm cr}^{\rm g} H_{\rm m}^{\rm o} = (99.5 \pm 1.5)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ , $ \Updelta_{\rm cr}^{\rm g} H_{\rm m}^{\rm o} = (116.0 \pm 3.7) \,{\text{kJ}}\,{\text{mol}}^{ - 1} $ and $ \Updelta_{\rm cr}^{\rm g} H_{\rm m}^{\rm o} = (129.3 \pm 4.7)\,{\text{ kJ mol}}^{ - 1} $ , for 2-, 3- and 4-hydroxymethylphenol, respectively. From these values, the standard molar enthalpies of formation of the title compounds in their gaseous phases, at T = 298.15 K, were derived and interpreted in terms of molecular structure. Moreover, using estimated values for the heat capacity differences between the gas and the crystal phases, the standard (p° = 0.1 MPa) molar enthalpies, entropies and Gibbs energies of sublimation, at T = 298.15 K, were derived for the three hydroxymethylphenols.     

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.     

The Formation and Stability of the [FePy3Cl3]· Py Clathrate in the Pyridine–Iron(III) Chloride System: Phase Diagram and Solid–Gas Equilibria Study

The phase diagram of the pyridine–iron(III) chloride system has been studied for the 223–423 K temperature and 0–56 mass-% concentration ranges using differential thermal analysis (DTA) and solubility techniques. A solid with the highest pyridine content formed in the system was found to be an already known clathrate compound, [FePy₃Cl₃]·Py. The clathrate melts incongruently at 346.9 ± 0.3 K with the destruction of the host complex: [FePy₃Cl₃]·Py_(solid)=[FePy₂Cl₃]_(solid) + liquor. The thermal dissociation of the clathrate with the release of pyridine into the gaseous phase (TGA) occurs in a similar way: [FePy₃Cl₃]·Py_(solid)=[FePy2Cl₃]_(solid) + 2 Py_(gas). Thermodynamic parameters of the clathrate dissociation have been determined from the dependence of the pyridine vapour pressure over the clathrate samples versus temperature (tensimetric method). The dependence experiences a change at 327 K indicating a polymorphous transformation occurring at this temperature. For the process ${1 \over 2}[\hbox{FePy}_{3}\hbox{Cl}_{3}]\cdot \hbox{Py}_{\rm (solid)} = {1 \over 2}[\hbox{FePy}_{2}\hbox{Cl}_{3}]_{\rm (solid)} + \hbox{Py}_{\rm (gas)}$ in the range 292–327 K, ΔH $^{0}_{298}$ =70.8 ± 0.8 kJ/mol, ΔS $^{0}_{298}$ =197 ± 3 J/(mol K), ΔG $^{0}_{298}$ =12.2 ± 0.1 kJ/mol; in the range 327–368 K, ΔH $^{0}_{298}$ =44.4 ± 1.3 kJ/mol, ΔS $^{0}_{298}$ =116 ± 4 J/(mol K), ΔG $^{0}_{298}$ =9.9 ± 0.3 kJ/mol.     

Synergistic extraction of europium and americium into nitrobenzene by using hydrogen dicarbollylcobaltate and bis(diphenylphosphino)methane dioxide

Extraction of microamounts of europium and americium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B^?) in the presence of bis(diphenylphosphino)methane dioxide (DPPMDO, L) has been investigated. The equilibrium data have been explained assuming that the species $ {\text{HL}}^{ + } $ , $ {\text{HL}}_{2}^{ + } $ , $ {\text{ML}}_{2}^{3 + } $ , $ {\text{ML}}_{3}^{3 + } $ and $ {\text{ML}}_{4}^{3 + } $ (M³⁺ = Eu³⁺, Am³⁺) are extracted into the organic phase. The values of extraction and stability constants of the species in nitrobenzene saturated with water have been determined. It was found that the stability constants of the corresponding complexes $ {\text{EuL}}_{n}^{3 + } $ and $ {\text{AmL}}_{n}^{3 + } $ , where n = 2, 3 and L is DPPMDO, in water–saturated nitrobenzene are comparable, whereas in this medium the stability of the cationic species $ {\text{AmL}}_{4}^{3 + } $ (L = DPPMDO) is somewhat higher than that of $ {\text{EuL}}_{4}^{3 + } $ with the same ligand L.     

Volumetric Properties of the Nucleoside Thymidine in Aqueous Solution at T = 298.15 K and p = (10 to 100) MPa

Sound speeds have been measured for aqueous solutions of the nucleoside thymidine at T = 298.15 K and at the pressures p = (10, 20, 40, 60, 80, and 100) MPa. The partial molar volumes at infinite dilution, $ V_{2}^{\text{o}} $ , the partial molar isentropic compressions at infinite dilution, $ K_{S,2}^{\text{o}} $ , and the partial molar isothermal compressions at infinite dilution, $ K_{T,2}^{\text{o}} $ $ \{ K_{T,2}^{\text{o}} = - (\partial V_{2}^{\text{o}} /\partial p)_{T} \} $ , have been derived from the sound speeds at elevated pressures using methods described in our previous work. The $ V_{2}^{\text{o}} $ and $ K_{T,2}^{\text{o}} $ results were rationalized in terms of the likely interactions between thymidine and the aqueous solvent. The $ V_{2}^{\text{o}} $ results were also compared with those calculated using the revised Helgeson–Kirkham–Flowers (HKF) equation of state.     

Chemical Transfer Energies of Some Homologous Amino Acids and the –CH2– Group in Aqueous DMF: Solvent Effect on Hydrophobic Hydration and Three Dimensional Solvent Structure

Standard transfer Gibbs energies, $ \Updelta_{\text{tr}} G^{^\circ } $ , of a series of homologues α-amino acids have been evaluated by determining the solubility of glycine, alanine, amino butyric acid and norvaline gravimetrically at 298.15 K. Standard entropies of transfer, $ \Updelta_{\text{tr}} S^{^\circ } $ , of the amino acids have also been evaluated by extending the solubility measurement to five equidistant temperatures ranging from 288.15 to 308.15 K. The chemical contributions $ \Updelta_{\text{tr,ch}} G^{^\circ } (i) $ of α-amino acids, as obtained by subtracting theoretically computed contributions to $ \Updelta_{\text{tr}} G^{ \circ } $ due to cavity and dipole–dipole interaction effects from the corresponding experimental $ \Updelta_{\text{tr}} G^{ \circ } $ , are indicative of the superimposed effect of increased basicity and dispersion and decreased hydrophobic hydration (hbh) in DMF–water solvent mixtures as compared to those in water, while, in addition, $ T\Updelta_{\text{tr,ch}} S^{^\circ } (i) $ is guided by structural effects. The computed chemical transfer energies of the –CH₂– group, $ \Updelta_{\text{tr,ch}} P^{^\circ } $ (–CH₂–) [P = G or S] as obtained by subtracting the value of lower homologue from that of immediately higher homologue, are found to change with composition indicating involvement of several opposing factors in the calculation of the chemical interactions. The $ \Updelta_{\text{tr,ch}} G^{^\circ } $ (–CH₂–) values are found to be guided by the decreased hydrophobic effect in DMF–water mixtures, and are indicative of the nature of the three dimensional structure of the aquo-organic solvent system around each solute.     

Positive ions of SiH4: Jahn-Teller-like distortions for {{\rm SiH}_{4}^{+}} and eventually molecular collapse on further ionisation.

We have recently studied by quantum-chemical calculations some fifteen tetrahedral and octahedral molecules. These seemingly disparate numerical tabulations were, it was demonstrated, pulled together by comparison with model semiclassical scaling laws for (i) nuclear–nuclear repulsion energy at the equilibrium geometry and (ii) total energies likewise. Here, we again appeal to such model scaling predictions, but now for positive ions of SiH₄. We then report Hartree-Fock equilibrium geometries and MP2 corrections. For ${{\rm SiH}_{4}^{+}}$ , we assumed the symmetry to be C_2v , by analogy with ${{\rm CH}_{4}^{+}}$ for which experimental confirmation of this symmetry is available. Larger distortions, but still for C_2v symmetry, are found from our quantum-chemical studies in the case of ${{\rm SiH}_{4}^{2+}}$ . But for ${{\rm SiH}_{4}^{3+}}$ there is a marked tendency to return to a configuration quite close to tetrahedral symmetry. But non-convergence is found for ${{\rm SiH}_{4}^{4+}}$ . Finally relations to the admittedly simplistic semiclassical geometry scaling predictions of Lawes and March are conjectured.     

Characteristics of an oxa-diamide–HNO3 extractant in the supercritical fluid extraction of uranium

An extractant is required in the recovery process to drive the uranium to a stage that enables it to be extracted using the extraction solvent. This paper proposes the composition of a composite extractant, N,N,N′,N′-tetrabutyl-3-oxapentane-diamide–HNO₃ (TBODA–HNO₃) as an extractant, to successfully achieve the objective using supercritical carbon dioxide (sc-CO₂). The composite TBODA–HNO₃ extractant has a chemical composition of TBODA(HNO₃)_1.0(H₂O)_1.5. The U(IV) in the UO₂ containing solid phase is directly oxidized to U(VI) in the form of $ {\rm UO}_{2}^{2 + } $ in sc-CO₂, which contains a CO₂-soluble TBODA–HNO₃ extractant at 200 atm and 50 °C. The resulting $ {\rm UO}_{2}^{2 + } $ /TBODA complex can be consequently extracted using acetone-modified sc-CO₂. The chemical composition of the $ {\rm UO}_{2}^{2 + } $ /TBODA complex, which can be extracted by nonpolar sc-CO₂, is proposed in the form of an ion pair: [UO₂(TBODA)₂]²⁺–2( $ {\rm NO}_{3}^{ - } $ ).     

Molecular Interactions in 1-Ethyl-3-Methylimidazolim Tetrafluoroborate + Amide Mixtures: Excess Molar Volumes, Excess Isentropic Compressibilities and Excess Molar Enthalpies

The densities, ρ ₁₂, and speeds of sound, u ₁₂, of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + N-methylformamide or N,N-dimethylformamide (2) binary mixtures at (293.15. 298.15. 303.15, 308.15 K), and excess molar enthalpies, $ H_{12}^{\text{E}} $ H 12 E , of the same mixtures at 298.15 K have been measured over the entire mole fraction range using a density and sound analyzer (Anton Paar DSA-5000) and a 2-drop microcalorimeter, respectively. Excess molar volume, $ V_{12}^{\text{E}} $ V 12 E , and excess isentropic compressibility, $ \left( {\kappa_{S}^{\text{E}} } \right)_{12} $ ( κ S E ) 12 , values have been calculated by utilizing the measured density and speed of sound data. The observed data have been analyzed in terms of: (i) Graph theory and (ii) the Prigogine–Flory–Patterson theory. Analysis of the $ V_{12}^{\text{E}} $ V 12 E data in terms of Graph theory suggest that: (i) in pure 1-ethyl-3-methylimidazolium tetrafluoroborate, the tetrafluoroborate anion is positioned over the imidazoliun ring and there are interactions between the hydrogen atom of (C–H{edge}) and proton of the –CH₃ group (imidazolium ring) with fluorine atoms of tetrafluoroborate anion, and (ii) (1 + 2) mixtures are characterized by ion–dipole interactions to form a 1:1 molecular complex. Further, the $ V_{12}^{\text{E}} $ V 12 E , $ H_{12}^{\text{E}} $ H 12 E and $ \left( {\kappa_{S}^{\text{E}} } \right)_{12} $ ( κ S E ) 12 values determined from Graph theory compare well with their measured experimental data.     

Thermochemical Properties of n-Undecylammonium Bromide Monohydrate C11H28BrNO(s)

The crystal structure of n-undecylammonium bromide monohydrate was determined by X-ray crystallography. The crystal system of the compound is monoclinic, and the space group is P2₁/c. Molar enthalpies of dissolution of the compound at different concentrations m/(mol·kg^?1) were measured with an isoperibol solution–reaction calorimeter at T = 298.15 K. According to the Pitzer’s electrolyte solution model, the molar enthalpy of dissolution of the compound at infinite dilution ( $ \Updelta_{\text{sol}} H_{\text{m}}^{\infty } $ ) and Pitzer parameters ( $ \beta_{\text{MX}}^{(0)L} $ and $ \beta_{\text{MX}}^{(1)L} $ ) were obtained. Values of the apparent relative molar enthalpies ( $ {}^{\Upphi }L $ ) of the title compound and relative partial molar enthalpies ( $ \bar{L}_{2} $ and $ \bar{L}_{1} $ ) of the solute and the solvent at different concentrations were derived from experimental values of the enthalpies of dissolution.     

Volumetric Properties of l-Alanine and l-Serine in Aqueous N,N-Dimethylformamide Solutions at 298.15 K

The densities of l-alanine and l-serine in aqueous solutions of N,N-dimethylformamide (DMF) have been measured at 298.15 K with an Anton Paar Model 55 densimeter. Apparent molar volumes $ (V_{\phi } ) $ ( V ? ) , standard partial molar volumes $ (V_{\phi }^{0} ) $ ( V ? 0 ) , standard partial molar volumes of transfer $ (\Updelta_{\text{tr}} V_{\phi }^{0} ) $ ( Δ tr V ? 0 ) and hydration numbers have been determined for the amino acids. The $ \Updelta_{\text{tr}} V_{\phi }^{0} $ Δ tr V ? 0 values of l-serine are positive which suggest that hydrophilic–hydrophilic interactions between l-serine and DMF are predominant. The –CH₃ group of l-alanine has much more influence on the volumetric properties and the $ \Updelta_{\text{tr}} V_{\phi }^{0} $ Δ tr V ? 0 have smaller negative values. The results have been interpreted in terms of the cosphere overlap model.     

Spectroscopic Studies on the Thermodynamics of the Complexation of Trivalent Curium with Propionate in the Temperature Range from 20 to 90 °C

The thermodynamics of the stepwise complexation reaction of Cm(III) with propionate was studied by time resolved laser fluorescence spectroscopy (TRLFS) and UV/Vis absorption spectroscopy as a function of the ligand concentration, the ionic strength and temperature (20–90 °C). The molar fractions of the 1:1 and 1:2 complexes were quantified by peak deconvolution of the emission spectra at each temperature, yielding the log₁₀ $ K_{n}^{\prime } $ values. Using the specific ion interaction theory (SIT), the thermodynamic stability constants log₁₀ $ K_{n}^{0} (T) $ were determined. The log₁₀ $ K_{n}^{0} (T) $ values show a distinct increase by 0.15 (n = 1) and 1.0 (n = 2) orders of magnitude in the studied temperature range, respectively. The temperature dependency of the log₁₀ $ K_{n}^{0} (T) $ values is well described by the integrated van’t Hoff equation, assuming a constant enthalpy of reaction and $ \Updelta_{\text{r}} C^\circ_{{p,{\text{m}}}} = 0, $ yielding the thermodynamic standard state $ \left( {\Updelta_{\text{r}} H^\circ_{\text{m}} ,\Updelta_{\text{r}} S^\circ_{\text{m}} ,\Updelta_{\text{r}} G^\circ_{\text{m}} } \right) $ values for the formation of the $ {\text{Cm(Prop)}}_{n}^{3 - n} $ , n = (1, 2) species.     

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.     

The calculation of the detection efficiency in the calibration of gross alpha–beta systems

This paper presents a method for efficiency calibration of a measuring alpha–beta system PROTEAN ORTEC, MPC-2000-DP, using standard radioactive sources. The system is used to measure gross alpha–beta activity concentrations in environmental samples. The calculated efficiencies of detection were subsequently introduced in the system for two working geometries: measuring geometry—gross alpha–beta $ \varepsilon_{\alpha }^{g} $  = 31,37 ± 0.25 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{g} $  = 44.94 ± 0.69 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{g} $  = 25.59 ± 0.50 (%) and measuring geometry up alpha–beta $ \varepsilon_{\alpha }^{u} $  = 36.23 ± 0.29 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{u} $  = 48.53 ± 0.74 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{u} $  = 31.08 ± 0.60 (%).     

Symmetry-itemized enumeration of quadruplets of RS-stereoisomers: I—the fixed-point matrix method of the USCI approach combined with the stereoisogram approach

The RS-stereoisomeric group $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ is examined to characterize quadruplets of RS-stereoisomers based on a tetrahedral skeleton and found to be isomorphic to the point group $\mathbf{O}_{h}$ of order 48. The non-redundant set of subgroups (SSG) of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ is obtained by referring to the non-redundant SSG of $\mathbf{O}_{h}$ . The coset representation for characterizing the orbit of the four positions of the tetrahedral skeleton is clarified to be $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{3v\widetilde{\sigma }\widehat{I}})$ , which is closely related to the $\mathbf{O}_{h}(/\mathbf{D}_{3d})$ . According to the unit-subduced-cycle-index (USCI) approach (Fujita in Symmetry and combinatorial enumeration in chemistry. Springer, Berlin, 1991), the subdution of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{3v\widetilde{\sigma }\widehat{I}})$ is examined so as to generate unit subduced cycle indices with chirality fittingness (USCI-CFs). The fixed-point matrix method of the USCI approach is applied to the USCI-CFs. Thereby, the numbers of quadruplets are calculated in an itemized fashion with respect to the subgroups of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ . After the subgroups of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ are categorized into types I–V, type-itemized enumeration of quadruplets is conducted to illustrate the versatility of the stereoisogram approach.     

Theoretical study of N–H· · ·O hydrogen bonding properties and cooperativity effects in linear acetamide clusters

We investigated geometry, energy, ${\nu_{{\text{N--H}}}}$ harmonic frequencies, ¹⁴N nuclear quadrupole coupling tensors, and ${n_{\rm O}\to \sigma _{{\text{N--H}}}^\ast}$ charge transfer properties of (acetamide) _n clusters, with n = 1 ? 7, by means of second-order Møller-Plesset perturbation theory (MP2) and DFT method. Dependency of dimer stabilization energies and equilibrium geometries on various levels of theory was examined. B3LYP/6-311++G** calculations revealed that for acetamide clusters, the average hydrogen-bonding energy per monomer increases from ?26.85 kJ mol^?1 in dimer to ?35.12 kJ mol^?1 in heptamer; i.e., 31% cooperativity enhancement. The n-dependent trend of ${\nu_{{\text{N--H}}}\,{and}\,^{14}}$ N nuclear quadrupole coupling values were reasonably correlated with cooperative effects in ${r_{{\text{N--H}}}}$ bond distance. It was also found that intermolecular ${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$ charge transfer plays a key role in cooperative changes of geometry, binding energy, ${\nu_{{\text{N--H}}}}$ harmonic frequencies, and ¹⁴N electric field gradient tensors of acetamide clusters. There is a good linear correlation between ¹⁴N quadrupole coupling constants, C _Q (¹⁴N), and the strength of Fock matrix elements (F _ij ). Regarding the ${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$ interaction, the capability of the acetamide clusters for electron localization, at the N–H· · ·O bond critical point, depends on the cluster size and thereby leads to cooperative changes in the N–H· · ·O length and strength, N–H stretching frequencies, and ¹⁴N quadrupole coupling tensors.