Valence basis sets for lanthanide 4f-in-core pseudopotentials adapted for crystal orbital ab initio calculations

Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets have been derived for calculating periodic bulk materials containing trivalent lanthanide ions modeled with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Koeln variety. The calibration calculations of crystalline A-type Pm₂O₃ using different segmented contraction schemes (4s4p3d)/[2s2p2d], (4s4p3d)/[3s3p2d], (5s5p4d)/[2s2p2d], (5s5p4d)/[3s3p3d], (5s5p4d)/[4s4p3d], (6s6p5d)/[2s2p2d], (6s6p5d)/[3s3p3d] and (6s6p5d)/[4s4p4d] are discussed at both Hartree–Fock (HF) and density functional theory (DFT) levels for the investigation of basis set size effects. Applications to the geometry optimization of A-type Ln₂O₃ (Ln = La-Pm) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d] and the standard set 6-311G* for oxygen. The corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for describing neutral lanthanide atoms were applied to calculate atomic energies of free lanthanide atoms for the evaluation of cohesive energies for A-Ln₂O₃ within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes.     

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.     

Preparation and electrochemical properties of {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} cathode materials for intermediate-temperature solid oxide fuel cells

Cathodic materials $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ (x?=?0.5, 0.6, 0.8, 1.0) with K₂NiF₄-type structure, for use in intermediate-temperature solid oxide fuel cells (IT-SOFCs), have been prepared by the glycine?Cnitrate process and characterized by XRD, SEM, AC impedance spectroscopy, and DC polarization measurements. The results have shown that no reaction occurs between an $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ electrode and an Sm_0.2Gd_0.8O_1.9 electrolyte at 1,200?°C, and that the electrode forms a good contact with the electrolyte after sintering at 1,000?°C for 2?h. In the series $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ (x?=?0.5, 0.6, 0.8, 1.0), the composition $ {\hbox{N}}{{\hbox{d}}_{{{1}.0}}}{\hbox{S}}{{\hbox{r}}_{{{1}.0}}}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ shows the lowest polarization resistance and cathodic overpotential, 2.75????cm² at 700?°C and 68?mV at a current density of 24.3?mA?cm^?2 at 700?°C, respectively. It has also been found that the electrochemical properties are remarkably improved the increasing Sr content in the experimental range.     

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 .     

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.     

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.     

Indecomposable representations and boson realizations of the nonlinear deformed angular momentum algebra of Witten’s first type

In this paper indecomposable representations and boson realizations of the nonlinear angular momentum algebra $\mathcal{R}_{q,p}^{c_1,c_2,c_3}$ of Witten’s first type are investigated in a purely algebraic manner. Explicit form of the master representation of $\mathcal{R}_{q,p}^{c_1,c_2,c_3}$ on the space of its universal enveloping algebra is given. Then, from this master representation, other indecomposable representations are obtained in explicit form. Various kinds of single-boson, single inverse boson, and double-boson realizations of $\mathcal{R}_{q,p}^{c_1,c_2,c_3}$ are respectively obtained by generalizing the Holstein–Primakoff realization, the Dyson realization, and the Jordan–Schwinger realization of the Lie algebras SU(2) and SU(1,1). For each kind, the unitary realization, the nonunitary realization, and their connection by the corresponding similarity transformation are respectively discussed. Using a kind of double-boson realizations, the irreducible representation of $\mathcal{R}_{q,p}^{c_1,c_2,c_3}$ in the angular momentum basis is given.     

Thermochemical properties of hydrazinium dipicrylamine in N-methyl pyrrolidone and dimethyl sulfoxide

The enthalpies of dissolution for Hydrazinium Dipicrylamine (HDPA) in N-methyl pyrrolidone (NMP) and dimethyl sulfoxide (DMSO) were measured using a RD496-2000 Calvet microcalorimeter at 298.15 K. Empirical formulae for the calculation of the enthalpies of dissolution (Δ_diss H) were obtained from the experimental data of the dissolution processes of HDPA in NMP and DMSO. 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 $ {{\text{d}\alpha } \mathord{\left/ {\vphantom {{\text{d}\alpha} {\text{d}t}}} \right. \kern-0pt} {\text{d}t}} = 10^{ - 2.71}\left( {1 - \alpha } \right)^{1.23} $ d α / d t = 10 ? 2.71 ( 1 ? α ) 1.23 for the dissolution of HDPA in NMP, and $ {{\text{d}\alpha } \mathord{\left/ {\vphantom {{\text{d}\alpha} {\text{d}t}}} \right. \kern-0pt} {\text{d}t}} = 10^{ - 2.58}\left( {1 - \alpha } \right)^{0.81} $ d α / d t = 10 ? 2.58 ( 1 ? α ) 0.81 for the dissolution of HDPA in DMSO, respectively.     

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.     

The Statistical Description of Precision Conductivity Data for Aqueous Sodium Chloride

Published precise data for NaCl in the temperature range 0?C50?°C were assembled, corrected to current standards and analyzed by weighted least-squares regression. There was a notable paucity of data at 0?°C. Data were analyzed as specific conductivity to avoid violation of the statistical independence assumption. The regression model was a polynomial in $\sqrt{c}$ , with an added transcendental term. Powers of $\sqrt{c}$ were added to published equations to extend the range of c fitted. Temperature dependency of the coefficients was individually modeled by cubic functions in the Celsius temperature. Criteria for an acceptable model included lack of bias, similarity to published theoretical equations, and extrapolation to infinite dilution consistent with literature values. The predictive equation chosen was of the form: $$\kappa = \varLambda _{0}c - Sc^{3/2} + Ec^{2}\ln c + J_{1}c^{2} + J_{2}c^{5/2} + J_{3}c^{3} + J_{4}c^{7/2} + J_{5}c^{4} + J_{6}c^{9/2} $$ and fit the data without bias but with high precision (±0.33 ??S?cm^?1) for the full range of published concentrations (up to 5.4?mol?L^?1), over the temperature range 0?C50?°C, something not previously achieved. All coefficients but J ₅ and J ₆ were temperature dependent; the latter terms were required for an unbiased fit at higher concentrations (>1 mol?L^?1). Solution of the equation for infinite dilution matched published values closely. The use of separate empirical temperature dependency for the equation coefficients may provide an independent means of validating theoretical treatments of conductivity data.     

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)}} $ .     

The Effect of Organic Modifiers on Electrospray Ionization Charge-State Distribution and Desorption Efficiency for Oligonucleotides

The chemical composition of the solution has a critical impact on the electrospray desorption efficiency of oligonucleotides. Several physiochemical properties of various organic modifiers were investigated with respect to their role in the desorption process of oligonucleotides. The Henry’s Law Constant, which reflects the volatility of alkylamines, was found to have a prominent effect on both the electrospray charge state distribution and desorption efficiency of oligonucleotides. Alkylamines with higher $ \mathrm{k}_{\mathrm{H,cc}}\left( {\mathrm{aq}/\mathrm{gas}} \right) $ values such as hexylamine, piperidine, and imidazole reduced the charge state distribution by forming complexes with the oligonucleotide and dissociating from it in the gas phase, while alkylamines with extremely low $ \mathrm{k}_{\mathrm{H,cc}}\left( {\mathrm{aq}/\mathrm{gas}} \right) $ values reduced the electrospray charge state distribution by facilitating ion emission at an earlier stage of the electrospray desorption process. Ion-pairing agents with moderate $ \mathrm{k}_{\mathrm{H,cc}}\left( {\mathrm{aq}/\mathrm{gas}} \right) $ values do not alter the electrospray charge state distribution of oligonucleotides and their ability to enhance oligonucleotide ionization followed the order of decreasing $ \mathrm{k}_{\mathrm{H,cc}}\left( {\mathrm{aq}/\mathrm{gas}} \right) $ values. The Henry’s Law Constant also correlated to the impact of the acidic modifiers on oligonucleotide ionization efficiency. Ionization enhancement effects were observed with hexafluoroisopropanol, and this effect was attributed to its low $ \mathrm{k}_{\mathrm{H,cc}}\left( {\mathrm{aq}/\mathrm{gas}} \right) $ and moderate acidity. The comprehensive effects of both alkylamine and hexafluoroisoproapnol on the electrospray ionization desorption of oligonucleotides were also evaluated, and acid-base equilibrium was found to play a critical role in determining these effects.      

Calculation of molecular g-tensors using the zeroth-order regular approximation and density functional theory: expectation value versus linear response approaches

Density functional theory (DFT) calculations of molecular g-tensors were implemented as a second derivative property within the two-component relativistic zeroth-order regular approximation (ZORA). g-tensors were computed for systems ranging from light atomic radicals to molecules with heavy d and f block elements. For comparison, computations were also performed with a ZORA first-order derivative approach and with a second derivative method based on the Pauli Hamiltonian. In each set of computations, Slater-type basis sets have been used. The new ZORA implementation allows for non-hybrid and hybrid DFT calculations. A comparison of the PBE non-hybrid and the PBE0 hybrid functional yielded mixed results for our test set. For the lanthanide complex $[\hbox{Ce}(\hbox{DPA})_3]^{3-}$ (DPA = pyridine-2,6-dicarboxylate), calculations of the g-tensor were used to estimate paramagnetic NMR pseudocontact shifts for protons and carbon atoms in the ligands. The results are in reasonable agreement with experimental data.     

Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of ${\gamma = 1.4 a_{0}^{-1}}$ can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated.     

Prediction and correlations between the stability constants of mono- and polynuclear chromium(III) and iron(III) complexes

Correlations between the experimentally determined stability constants of mono- and polynuclear chromium(III) and iron(III) complexes are discussed. An equation to evaluate the stability constants of mono- and polynuclear chromium(III) complexes is obtained: \(\log \beta [Cr_p^{3 + } (L_i )_{q_i } ] = 0.84\log \beta [Fe_p^{3 + } (L_i )_{q_i } ]\) .     

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.     

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.     

Isosaccharinate Complexes of Fe(III)

Prior to this study there were no thermodynamic data for isosaccharinate (ISA) complexes of Fe(III) in the environmental range of pH (>~4.5). This study was undertaken to obtain such data in order to predict Fe(III) behavior in the presence of ISA. The solubility of Fe(OH)₃(2-line ferrihydrite), referred to as Fe(OH)₃(s), was studied at 22?±?2?°C in: (1) very acidic (0.01?mol·dm^?3 H⁺) to highly alkaline conditions (3?mol·dm^?3 NaOH) as a function of time (11?C421?days), and fixed concentrations of 0.01 or 0.001?mol·dm^?3 NaISA; and (2) as a function of NaISA concentrations ranging from approximately 0.0001 to 0.256?mol·dm^?3 and at fixed pH values of approximately 4.5 and 11.6 to determine the ISA complexes of Fe(III). The data were interpreted using the SIT model that included previously reported stability constants for $ {{\text{Fe(ISA}})_{n}}^{3 - n} $ (with n varying from 1 to 4) and Fe(III)?COH complexes, and the solubility product for Fe(OH)₃(s) along with the values for two additional complexes (Fe(OH)₂(ISA)(aq) and $ {\text{Fe(OH)}}_{ 3} ( {{\text{ISA}})_{2}}^{2 - } $ ) determined in this study. These extensive data provided a log₁₀ K ⁰ value of 1.55?±?0.38 for the reaction $ ({\text{Fe}}^{ 3+ } + {\text{ISA}}^{-} + 2 {\text{H}}_{ 2} {\text{O}} \rightleftarrows {\text{Fe(OH}})_{ 2} {\text{ISA(aq}}) + 2 {\text{H}}^{ + } ) $ and a value of ?3.27?±?0.32 for the reaction $ ({\text{Fe}}^{ 3+ } + 2 {\text{ISA}}^{-} + 3 {\text{H}}_{ 2} {\text{O}} \rightleftarrows {\text{Fe(OH)}}_{ 3} ( {\text{ISA}})_{2}^{2 - } + 3 {\text{H}}^{ + } ) $ and show that ISA forms strong complexes with Fe(III) which significantly increase the Fe(OH)₃(s) solubility at pH?<~12. Thermodynamic calculations show that competition of Fe(III) with tetravalent ions for ISA does not significantly affect the solubilities of tetravalent hydrous oxides (e.g., Th and Np(IV)) in ISA solutions.     

Thermal properties of Na2TeO4(s) and TiTe3O8(s)

Molar heat capacity measurement on Na₂TeO₄(s) and TiTe₃O₈(s) were carried out using differential scanning calorimeter. The molar heat capacity values were least squares analyzed and the dependence of molar heat capacity with temperature for Na₂TeO₄(s) and TiTe₃O₈(s) can be given as, $$ \begin{gathered} {\text{C}}^{\text{o}}_{{{\text{p}},{\text{m}}}} \left\{ {{\text{Na}}_{ 2} {\text{TeO}}_{ 4} \left( {\text{s}} \right)} \right\} \,={159}.17 { } + 1.2\,\times\,10^{-4}T-{55}.34\,\times\,10^{5}/T^{2};\hfill \\ C^{\text{o}}_{{{\text{p}},{\text{m}}}} \left\{ {{\text{TiTe}}_{ 3} {\text{O}}_{ 8} \left( {\text{s}} \right)} \right\}\,=\,{ 275}.22{ }+{4}.0\,\times\, 10^{-5}T-{58}.28\,\times\,10^{5}/T^{2};\hfill \\ \end{gathered} $$ From this data, other thermodynamic functions were evaluated.