Thermochemical properties of di(N,N-di(2,4,6-trinitrophenyl)amino)-ethylenediamine in dimethyl sulfoxide and N-methyl pyrrolidone

The enthalpies of dissolution for di(N,N-di(2,4,6,-trinitrophenyl)amino)-ethylenediamine (DTAED) in dimethyl sulfoxide (DMSO) and N-methyl pyrrolidone (NMP) were measured using a RD496-2000 Calvet microcalorimeter at 298.15?K. Empirical formulae for the calculation of the enthalpies of dissolution (??_diss H) were obtained from the experimental data of the dissolution processes of DTAED in DMSO and NMP. The linear relationships between the rate (k) and the amount of substance (a) were found. The corresponding kinetic equations describing the two dissolution processes were $ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-0em} {{\rm{d}}t}} = 10^{ - 2.68} \left( {1 - \alpha } \right)^{0.84} $ for the dissolution of DTAED in DMSO, and $ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-0em} {{\rm{d}}t}} = 10^{ - 2.79} \left( {1 - \alpha } \right)^{0.87} $ for the dissolution of DTAED in NMP, respectively.     

The dissolution properties of N-guanylurea-dinitramide (FOX-12) in dimethyl sulfoxide (DMSO)

The enthalpy of dissolution of FOX-12 in dimethyl sulfoxide (DMSO) was measured by means of a RD496-III Calvet microcalorimeter at 298.15 K. Empirical formulae for the calculation of the enthalpy of dissolution ( $ \Updelta_{\text{diss}} H $ ), relative partial molar enthalpy ( $ \Updelta_{\text{diss}} H_{\text{partial}} $ ), and relative apparent molar enthalpy ( $ \Updelta_{\text{diss}} H_{\text{apparent}} $ ) were obtained from the experimental data of the enthalpies of dissolution of FOX-12 in DMSO. The kinetic equation that describes the dissolution process of FOX-12 in DMSO at 298.15 K is determined as $ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 8.5 \times 10^{ - 3} (1 - \alpha )^{0.59} $ .     

Thermochemical properties of the coordination complex of 8-hydroxyquinolinato-bis-(salicylato) praseodymium (III)

The product, [Pr(C₇H₅O₃)₂(C₉H₆NO)], which was formed by praseodymium nitrate hexahydrate, salicylic acid (C₇H₆O₃), and 8-hydroxyquinoline (C₉H₇NO), was synthesized and characterized by elemental analysis, UV spectra, IR spectra, molar conductance, and thermogravimetric analysis. In an optimalizing calorimetric solvent, the dissolution enthalpies of [Pr(NO₃)₃·6H₂O(s)], [2 C₇H₆O₃(s) + C₉H₇NO(s)], [Pr(C₇H₅O₃)₂(C₉H₆NO)(s)], and [solution D (aq)] were measured to be, by means of a solution-reaction isoperibol microcalorimeter, $ \begin{gathered}\Updelta_{\text{s}} H_{\text{m}}^{\theta}\left[ {{ \Pr }\left( {{\text{NO}}_{ 3} } \right)_{ 3} \cdot 6{\text{H}}_{ 2} {\text{O}}\left( {\text{s}} \right), 2 9 8. 1 5{\text{ K}}} \right] \, = - ( 20. 6 6 { } \pm \, 0. 29)\,{\text{kJ}}\,{\text{mol}}^{ - 1} , \\\Updelta_{\text{s}} H_{\text{m}}^{\theta } \left[ { 2 {\text{C}}_{7} {\text{H}}_{ 6} {\text{O}}_{ 3} \left( {\text{s}} \right) +{\text{ C}}_{ 9} {\text{H}}_{ 7} {\text{NO}}\left( {\text{s}}\right),{ 298}. 1 5 {\text{ K}}} \right] \, = \, ( 4 2. 2 7 { }\pm \, 0. 3 1)\,{\text{kJ}}\,{\text{mol}}^{ - 1} , \\\Updelta_{\text{s}} H_{\text{m}}^{\theta } \left[ {{\text{solutionD }}\left( {\text{aq}} \right), 2 9 8. 1 5 {\text{ K}}} \right] \,= - \left( { 8 9. 1 5 { } \pm \, 0. 4 3}\right)\,{\text{kJ}}\,{\text{mol}}^{ - 1} , \\\end{gathered} $ Δ s H m θ [ Pr ( NO 3 ) 3 · 6 H 2 O ( s ) , 2 9 8.1 5 K ] = ? ( 20.6 6 ± 0.2 9 ) kJ mol ? 1 , Δ s H m θ [ 2 C 7 H 6 O 3 ( s ) + C 9 H 7 NO ( s ) , 298.1 5 K ] = ( 4 2.2 7 ± 0.3 1 ) kJ mol ? 1 , Δ s H m θ [ solution D ( aq ) , 2 9 8.1 5 K ] = ? ( 8 9.1 5 ± 0.4 3 ) kJ mol ? 1 , and $ \Updelta_{\text{s}} H_{\text{m}}^{\theta } \left\{ {\left[ {{\Pr }\left( {{\text{C}}_{ 7} {\text{H}}_{ 5} {\text{O}}_{ 3} }\right)_{ 2} \left( {{\text{C}}_{ 9} {\text{H}}_{ 6} {\text{NO}}}\right)} \right]\left( {\text{s}} \right),{ 298}. 1 5 {\text{ K}}}\right\} \, = - \left( { 4 1.0 4 { } \pm \, 0. 3 3}\right)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ Δ s H m θ { [ Pr ( C 7 H 5 O 3 ) 2 ( C 9 H 6 NO ) ] ( s ) , 298.1 5 K } = ? ( 4 1.0 4 ± 0.3 3 ) kJ mol ? 1 , respectively. Through an improved thermochemical cycle, the enthalpy change of the designed coordination reaction was calculated to be $\Updelta_{\text{r}} H_{\text{m}}^{\theta} = \, ( 2 1 3. 1 8\pm0. 6 9)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ Δ r H m θ = ( 2 1 3.1 8 ± 0.6 9 ) kJ mol ? 1 , the standard molar enthalpy of the formation was determined as $ \Updelta_{\text{f}} H_{\text{m}}^{\theta} \left\{ {\left[ {{\Pr }\left( {{\text{C}}_{ 7} {\text{H}}_{ 5} {\text{O}}_{ 3} }\right)_{ 2} \left( {{\text{C}}_{ 9} {\text{H}}_{ 6} {\text{NO}}}\right)} \right]\left( {\text{s}} \right), 2 9 8. 1 5 {\text{K}}}\right\} \, = \, - \, ( 1 8 7 5. 4\pm 3.1)\,{\text{kJ}}\,{\text{mol}}^{ - 1} $ Δ f H m θ { [ Pr ( C 7 H 5 O 3 ) 2 ( C 9 H 6 NO ) ] ( s ) , 2 9 8.1 5 K } = ? ( 1 8 7 5.4 ± 3.1 ) kJ mol ? 1 .     

Thermodynamic studies on Pr2TeO6

The standard Gibbs energy of formation of Pr₂TeO₆ $ (\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)) $ was derived from its vapour pressure in the temperature range of 1,400–1,480 K. The vapour pressure of TeO₂ (g) was measured by employing a thermogravimetry-based transpiration method. The temperature dependence of the vapour pressure of TeO₂ over the mixture Pr₂TeO₆ (s) + Pr₂O₃ (s) generated by the incongruent vapourization reaction, Pr₂TeO₆ (s) = Pr₂O₃ (s) + TeO₂ (g) + ½ O₂ (g) could be represented as: $ { \log }\left\{ {{{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} \mathord{\left/ {\vphantom {{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} {{\text{Pa}} \pm 0.0 4}}} \right. \kern-0em} {{\text{Pa}} \pm 0.0 4}}} \right\} = 19. 12- 27132\; \left({\rm{{{\text{K}}}}/T} \right) $ . The $ \Updelta_{\text{f}} G^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ could be represented by the relation $ \left\{ {{{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} \mathord{\left/ {\vphantom {{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} \pm 5.0} \right\} = - 2 4 1 5. 1+ 0. 5 7 9 3\;\left(T/{\text{K}}\right) .$ Enthalpy increments of Pr₂TeO₆ were measured by drop calorimetry in the temperature range of 573–1,273 K and heat capacity, entropy and Gibbs energy functions were derived. The $ \Updelta_{\text{f}} H_{{298\;{\text{K}}}}^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ was found to be $ {{ - 2, 40 7. 8 \pm 2.0} \mathord{\left/ {\vphantom {{ - 2, 40 7. 8 \pm 2.0} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} $ .     

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.     

Synthesis and structural characterization of three dinuclear Copper(II) complexes incorporating pyrazolyl-derived ligands

Three new binuclear copper complexes of formulae $ \left[ {{\text{Cu}}_{2}^{\text{II}} {\text{Pz}}_{2}^{\text{Me3}} {\text{Br}}_{ 2} \left( {{\text{PPh}}_{ 3} } \right)_{ 2} } \right] $ (1), $ \left[ {{\text{Cu}}_{ 2}^{\text{II}} {\text{Pz}}_{2}^{\text{Ph2Me}} {\text{Cl}}_{ 2} \left( {{\text{PPh}}_{ 3} } \right)_{ 2} } \right] $ (2) and $ \left[ {{\text{Cu}}_{2}^{\text{II}} \left( {{\text{Pz}}^{\text{PhMe}} } \right)_{ 4} {\text{Cl}}_{ 4} } \right] $ (3) (Pz^Me3?=?3,4,5-trimethylpyrazole, Pz^Ph2Me?=?4-methyl-3,5-diphenylpyrazole and Pz^PhMe?=?3-methyl-5-phenylpyrazole) have been synthesized and characterized by chemical analysis, FTIR and ³¹P NMR spectroscopy and single-crystal X-ray diffraction. Complex 1 is a doubly bromo-bridged dimer, while complexes 2 and 3 are chloro-bridged dimers. The Cu(II) centers are in a distorted tetrahedral geometry for 1 and 2 and a distorted square pyramidal N₂Cl₃ environment for 3.     

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.     

A thermodynamic study of complexation of 18-crown-6 with Zn2+, Tl+, Hg2+ and {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} cations in acetonitrile-dimethylformamide binary media and study the effect of anion on the stability constant of (18C6-Na+) complex in methanol solutions

The equilibrium constants and thermodynamic parameters for complex formation of 18-crown-6(18C6) with Zn²⁺, Tl⁺, Hg²⁺ and $ {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} $ cations have been determined by conductivity measurements in acetonitrile(AN)-dimethylformamide(DMF) binary solutions. 18-crown-6 forms 1:1 complexes [M:L] with Zn²⁺, Hg²⁺ and $ {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} $ cations, but in the case of Tl⁺ cation, a 1:2 [M:L₂] complex is formed in most binary solutions. The thermodynamic parameters ( $ \Delta {\text{H}}^{ \circ }_{{\text{c}}} $ and $ \Delta {\text{S}}^{ \circ }_{{\text{c}}} $ ) which were obtained from temperature dependence of the equilibrium constants show that in most cases, the complexes are enthalpy destabilized but entropy stabilized and a non-monotonic behaviour is observed for variations of standard enthalpy and entropy changes versus the composition of AN/DMF binary mixed solvents. The obtained results show that the order of selectivity of 18C6 ligand for these cations changes with the composition of the mixed solvent. A non-linear relationship was observed between the stability constants (logK_f) of these complexes with the composition of AN/DMF binary solutions. The influence of the $ {\text{ClO}}^{ - }_{{\text{4}}} $ , $ {\text{NO}}^{ - }_{{\text{3}}} $ and $ {\text{Cl}}^{ - } $ anions on the stability constant of (18C6-Na⁺) complex in methanol (MeOH) solutions was also studied by potentiometry method. The results show that the stability of (18C6-Na⁺) complex in the presence of the anions increases in order: $ {\text{ClO}}^{ - }_{{\text{4}}} $  >  $ {\text{NO}}^{ - }_{{\text{3}}} $  >  $ {\text{Cl}}^{ - } $ .     

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.     

To determine the half-life for gemcitabine hydrochloride using microcalorimetry

The enthalpies of dissolution of gemcitabine hydrochloride in 0.9 % normal saline (medical) and citric acid solution were measured using a microcalorimeter at 309.65 K under atmospheric pressure. The differential enthalpy $ \left( {\Updelta_{\text{dif}} H_{\text{m}}^{{{\theta}}} } \right) $ and molar enthalpy $ \left( {\Updelta_{\text{sol}} H_{\text{m}}^{{{\theta}}} } \right) $ of dissolution were determined, respectively. The corresponding kinetic equation described the dissolution were elucidated to be da/dt = 10^?3.84(1 ? a)^0.92 and da/dt = 10^?3.80(1 ? a)^1.21. Besides, the half-life, $ \Updelta_{\text{sol}} H_{\text{m}}^{{{\theta}}} ,\;\Updelta_{\text{sol}} G_{\text{m}}^{{{\theta}}} $ and $ \Updelta_{\text{sol}} S_{\text{m}}^{{{\theta}}} $ of the dissolution were also obtained. Obviously, it will provide a simple and reliable method for the clinical application of gemcitabine hydrochloride.     

Correlation between C-H and C-C spin-spin coupling constants and s character of hybrids calculated by the maximum overlap method

For some thirty hydrocarbons the s character of hybrids obtained by the application of the maximum overlap method have been correlated with C-H and C-C spin-spin coupling constants. The following relationships were obtained: $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} = 1079a_{{\text{CH}}}^{\text{2}} /(1 + S_{{\text{CH}}}^{\text{2}} ) - 54.9$$ , $$J_{{\text{C}}_{\text{1}}^{{\text{13}}} - {\text{C}}_{\text{2}}^{{\text{13}}} } = 1020.5a_{{\text{C}}_{\text{1}} }^2 a_{{\text{C}}_{\text{2}} }^{\text{2}} /(1 + S_{{\text{CC}}}^{\text{2}} ) - 8.2$$ . Here the coupling constants are expressed in cps units. In the calculation of the maximum overlap hybrids either the experimental bond lengths or a standard bond lengths were used. For the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) and \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}} \) coupling constants the standard deviations are 0.9 cps and 1.9 cps respectively. It has been suggested that the large additive constant in the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) correlation may be attributed to the ionic character of C-H bonds. A good agreement with the experimental data strongly supports the idea that the Fermi contact term and the hybridization are dominant factors in determining carbon-hydrogen and carbon-carbon spin-spin coupling constants across one bond, at least in hydrocarbons.     

Effect of size of tetraalkylammonium counterions on the temperature dependent micellization of AOT in aqueous medium

Different tetraalkylammonium, viz. N⁺(CH₃)₄, N⁺(C₂H₅)₄, N⁺(C₃H₇)₄, N⁺(C₄H₉)₄ along with simple ammonium salts of bis (2-ethylhexyl) sulfosuccinic acid have been prepared by ion-exchange technique. The critical micelle concentration of surfactants with varied counterions have been determined by measuring surface tension and conductivity within the temperature range 283–313 K. Counterion ionization constant, α, and thermodynamic parameters for micellization process viz., $\Delta G_m^{\text{0}} $ , $\Delta H_m^{\text{0}} $ , and $\Delta S_m^{\text{0}} $ and also the surface parameters, Γ_max and A_min, in aqueous solution have been determined. Large negative $\Delta G_m^{\text{0}} $ of micellization for all the above counterions supports the spontaneity of micellization. The value of standard free energy, $\Delta G_m^{\text{0}} $ , for different counterions followed the order $${\text{N}}^{\text{ + }} \left( {{\text{CH}}_{\text{3}} } \right)_4 >{\text{NH}}_{\text{4}}^{\text{ + }} >{\text{Na}}^{\text{ + }} >{\text{N}}^{\text{ + }} \left( {{\text{C}}_{\text{2}} {\text{H}}_5 } \right)_{\text{4}} {\text{ $>$ N}}^{\text{ + }} \left( {{\text{C}}_{\text{3}} {\text{H}}_{\text{7}} } \right)_4 >{\text{N}}^{\text{ + }} \left( {{\text{C}}_{\text{4}} {\text{H}}_{\text{9}} } \right)_4 $$ , at a given temperature. This result can be well explained in terms of bulkiness and nature of hydration of the counterion together with hydrophobic and electrostatic interactions.     

Symmetry-itemized enumeration of RS-stereoisomers of allenes. I. The fixed-point matrix method of the USCI approach combined with the stereoisogram approach

After the RS-stereoisomeric group \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) of order 16 has been defined by starting point group \(\mathbf{D}_{2d}\) of order 8, the isomorphism between \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) and the point group \(\mathbf{D}_{4h}\) of order 16 is thoroughly discussed. The non-redundant set of subgroups (SSG) of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) is obtained by referring to the non-redundant set of subgroups of \(\mathbf{D}_{4h}\) . The coset representation for characterizing the orbit of the four positions of an allene skeleton is clarified to be \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) , which is closely related to the \(\mathbf{D}_{4h}(/\mathbf{C}_{2v}^{\prime \prime \prime })\) . According to the unit-subduced-cycle-index (USCI) approach (Fujita, Symmetry and combinatorial enumeration of chemistry. Springer, Berlin 1991), the subduction of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) is examined so as to generate unit subduced cycle indices with chirality fittingness (USCI-CFs). Then, 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 \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) . After the subgroups of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) are categorized into types I–V, type-itemized enumeration of quadruplets is conducted to illustrate the versatility of the stereoisogram approach.     

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.     

Assessment of the global and range-separated hybrids for computing the dynamic second-order hyperpolarizability of solution-phase organic molecules

A comparison is presented of uncontracted multireference singles and doubles configuration interaction (MRCI) and internally contracted MRCI potential energy surfaces for the reaction ${\text{H}}\left( {^{2} {\text{S}}} \right) + {\text{O}}_{2} \left( {^{3} \sum\nolimits_{g}^{ - } {} } \right) \to {\text{HO}}_{2} \left( {^{2} {\text{A}}^{{\prime \prime }} } \right)$ . It is found that internal contraction leads to significant differences in the reaction kinetics relative to the uncontracted calculations.     

Bounds for the Kirchhoff index via majorization techniques

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of ${\mathbb{R}^{n}}$ , we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that $$K(G) \geq \frac{n}{d_{1}} \left[ \frac{1}{1+\frac{\sigma}{\sqrt{n-1}}} + \frac{(n-2)^{2}}{n-1-\frac{\sigma}{\sqrt{n-1}}}\right] ,$$ where d ₁ is the largest degree among all vertices in G, $$\sigma ^{2} = \frac{2}{n} \sum_{(i, j) \in E} \frac{1}{d_{i}d_{j}} = \left( \frac{2}{n}\right) R_{-1}(G),$$ and R _?1(G) is the general Randi? index of G for ${\alpha =-1}$ . Also we show that $$K(G) \leq \frac{n}{d_{n}}\left( \frac{n-k-2}{1-\lambda _{2}}+\frac{k}{2}+\frac{1}{\theta}\right) ,$$ where d _n is the smallest degree, ${\lambda _{2}}$ is the second eigenvalue of the transition probability of the random walk on G, $$k = \left \lfloor \frac{\lambda _{2} \left( n-1\right) +1}{\lambda _{2}+1}\right\rfloor {\rm and}\quad\theta = \lambda _{2} \left( n-k-2\right) -k+2.$$      

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.     

Experimental and DFT study on complexation of Eu3+ with a macrocyclic lactam receptor

From extraction experiments and $ \gamma $ -activity measurements, the extraction constant corresponding to the equilibrium $ {\text{Eu}}^{ 3+ } \left( {\text{aq}} \right) + 3 {\text{A}}^{ - } \left( {\text{aq}} \right) + {\mathbf{1}}\left( {\text{nb}} \right) \Leftrightarrow {\mathbf{1}} \cdot {\text{Eu}}^{ 3+ } \left( {\text{nb}} \right) + 3 {\text{A}}^{ - } \left( {\text{nb}} \right) $ taking place in the two-phase water–nitrobenzene system ( $ {\text{A}}^{ - } = \text {CF}_{3} \text{SO}_{3}^{ - } $ ; 1 = macrocyclic lactam receptor—see Scheme 1; aq = aqueous phase, nb = nitrobenzene phase) was evaluated as $ { \log } K_{{{\text{ex}} }} ({\mathbf{1}} \cdot {\text{Eu}}^{ 3+ } ,{\text{ 3A}}^{ - } )\; = \; - 4. 9 \pm 0. 1 $ . Further, the stability constant of the 1·Eu³⁺ cationic complex in nitrobenzene saturated with water was calculated for a temperature of 25 °C: $ { \log } \beta_{{{\text{nb}} }} ({\mathbf{1}} \cdot {\text{Eu}}^{ 3+ } ) \; = \; 8. 2 \pm 0. 1 $ . Finally, using DFT calculations, the most probable structure of the cationic complex species 1·Eu³⁺ was derived. In the resulting 1·Eu³⁺ complex, the “central” cation Eu³⁺ is bound by five bond interactions to two ethereal oxygen atoms and two carbonyl oxygens, as well as to one carbon atom of the corresponding benzene ring of the parent macrocyclic lactam receptor 1 via cation-π interaction.

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.     

Acid–Base Properties of the \mathrm{Fe}(\mathrm{CN})_{6}^{3-}/\mathrm{Fe}(\mathrm{CN})_{6}^{4-} Redox Couple in the Presence of Various Background Mineral Acids and Salts

The acid?Cbase behavior of $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ was investigated by measuring the formal potentials of the $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}$ / $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ couple over a wide range of acidic and neutral solution compositions. The experimental data were fitted to a model taking into account the protonated forms of $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ and using values of the activities of species in solution, calculated with a simple solution model and a series of binary data available in the literature. The fitting needed to take account of the protonated species $\mathrm{HFe}(\mathrm{CN})_{6}^{3-}$ and $\mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-}$ , already described in the literature, but also the species $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}$ (associated with the acid?Cbase equilibrium $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}\rightleftharpoons \mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-} + \mathrm{H}^{+}$ ). The acidic dissociation constants of $\mathrm{HFe}(\mathrm{CN})_{6}^{3-}$ , $\mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-}$ and $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}$ were found to be $\mathrm{p}K^{\mathrm{II}}_{1}= 3.9\pm0.1$ , $\mathrm{p}K^{\mathrm{II}}_{2} = 2.0\pm0.1$ , and $\mathrm{p}K^{\mathrm{II}}_{3} = 0.0\pm0.1$ , respectively. These constants were determined by taking into account that the activities of the species are independent of the ionic strength.