Frequency dispersion of the dynamic moduli of elasticity of electrolyte solutions

The frequency dispersion range of the dynamic bulk relaxation modulus K(ω) and shear relaxation modulus µ(ω) of electrolyte solutions has been determined in relation to the nature of stress tensor damping in the momentum and configuration spaces. Numerical calculations have been carried out for an aqueous NaCl solution in wide frequency, temperature, and density ranges using analytical expressions obtained for K(ω) and µ(ω) for the exponential-law damping of the fluxes at a certain molecular interaction potential \(\Phi \left( {\left| {\vec r} \right|} \right)\) and radial distribution function \(g\left( {\left| {\vec r} \right|} \right)\). It has been demonstrated that the frequency dispersion range of K _r (v) and µ(v) for the exponential-law damping of the corresponding fluxes is narrow (～10² Hz).     

Thermo Physical and Spectroscopic Properties of Binary Liquid Systems: Ethanoic Acid/Propanoic Acid/Butanoic Acid with 2-Methylaniline

Densities (ρ), speeds of sound (u), and viscosities (η) are reported for binary mixtures of 2-methylaniline with carboxylic acids (ethanoic acid, propanoic acid and butanoic acid) over the entire composition range of mole fraction at T?=?(303.15–318.15) K and at atmospheric pressure (0.1 MPa). The excess properties such as excess molar volume (V _m ^E ), excess isentropic compressibility (κ _S ^E ) and excess Gibbs energy of activation of viscous flow (G^*E) are calculated from the experimental densities, speeds of sound and viscosities. Excess properties are correlated using the Redlich–Kister polynomial equation. The partial molar volumes, \( \bar{V}_{\text{m,1}} \) and \( \bar{V}_{\text{m,2}} \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}} \) and \( \bar{K}_{\text{s,m,2}} \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{\text{E}} \) and \( \bar{V}_{\text{m,2}}^{\text{E}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{\text{E}} \) and \( \bar{K}_{\text{s,m,2}}^{\text{E}} \), over whole composition range, partial molar volumes, \( \bar{V}_{\text{m,1}}^{ \circ } \) and \( \bar{V}_{\text{m,2}}^{ \circ } \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{ \circ } \) and \( \bar{K}_{\text{s,m,2}}^{ \circ } \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{V}_{{{\text{m}},2}}^{{ \circ {\text{E}}}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{K}_{\text{s,m,2}}^{{ \circ {\text{E}}}} \), of the components at infinite dilution have also been calculated from the analytically obtained Redlich–Kister polynomials. The excess molar volume V^E results are analyzed using the Prigogine–Flory–Patterson theory. Analysis of each of the three contributions viz. interactional V^E(int.), free volume V^E(fv.) and characteristic pressure p* to V^E showed that the interactional contributions are positive for all systems while the free volume and characteristic pressure p* contributions are negative for all the binary mixtures. The results are analyzed in terms of attractive forces between 2-methylaniline and carboxylic acids molecules. Good agreement is obtained between excess quantities and spectroscopic data.     

Blinded predictions of distribution coefficients in the SAMPL5 challenge

In the context of the SAMPL5 challenge water-cyclohexane distribution coefficients for 53 drug-like molecules were predicted. Four different models based on molecular dynamics free energy calculations were tested. All models initially assumed only one chemical state present in aqueous or organic phases. Model A is based on results from an alchemical annihilation scheme; model B adds a long range correction for the Lennard Jones potentials to model A; model C adds charging free energy corrections; model D applies the charging correction from model C to ionizable species only. Model A and B perform better in terms of mean-unsigned error (\(\hbox {MUE}=6.79<6.87<6.95 \log\) D units ? 95 % confidence interval) and determination coefficient \((\hbox {R}^2 = 0.26< 0.27< 0.28)\), while charging corrections lead to poorer results with model D (\(\hbox {MUE}=12.8<12.63<12.98\) and \(\hbox {R}^2 = 0.16<0.17<0.18\)). Because overall errors were large, a retrospective analysis that allowed co-existence of ionisable and neutral species of a molecule in aqueous phase was investigated. This considerably reduced systematic errors (\(\hbox {MUE}=1.87<1.97<2.07\) and \(\hbox {R}^2 = 0.35<0.40<0.45\)). Overall accurate \(\log D\) predictions for drug-like molecules that may adopt multiple tautomers and charge states proved difficult, indicating a need for methodological advances to enable satisfactory treatment by explicit-solvent molecular simulations.     

Lego-like spheres and tori

Given a connected surface \({\mathbb {F}}^2\) with Euler characteristic \(\chi \) and three integers \(b>a\ge 1<k\), an \((\{a,b\};k)\)-\({\mathbb {F}}^2\) is a \({\mathbb {F}}^2\)-embedded graph, having vertices of degree only k and only a- and b-gonal faces. The main case are (geometric) fullerenes (5, 6; 3)-\({\mathbb {S}}^2\). By \(p_a\), \(p_b\) we denote the number of a-gonal, b-gonal faces. Call an \((\{a,b\};k)\)-map lego-admissible if either \(\frac{p_b}{p_a}\), or \(\frac{p_a}{p_b}\) is integer. Call it lego-like if it is either \(ab^f\)-lego map, or \(a^fb\)-lego map, i.e., the face-set is partitioned into \(\min (p_a,p_b)\) isomorphic clusters, legos, consisting either one a-gon and \(f=\frac{p_b}{p_a}\,b\)-gons, or, respectively, \(f=\frac{p_a}{p_b}\,a\)-gons and one b-gon; the case \(f=1\) we denote also by ab. Call a \((\{a,b\};k)\)-map elliptic, parabolic or hyperbolic if the curvature \(\kappa _b=1+\frac{b}{k}-\frac{b}{2}\) of b-gons is positive, zero or negative, respectively. There are 14 lego-like elliptic \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,2)\). No \((\{1,3\};6)\)-\({\mathbb {S}}^2\) is lego-admissible. For other 7 families of parabolic \((\{a,b\};k)\)-\({\mathbb {S}}^2\), each lego-admissible sphere with \(p_a\le p_b\) is \(a^fb\) and an infinity (by Goldberg–Coxeter operation) of \(ab^f\)-spheres exist. The number of hyperbolic \(ab^f\,(\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,3)\) is finite. Such \(a^f b\)-spheres with \(a\ge 3\) have \((a,k)=(3,4),(3,5),(4,3),(5,3)\) or (3, 3); their number is finite for each b, but infinite for each of 5 cases (a, k). Any lego-admissible \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \(p_b=2\le a\) is \(a^f b\). We list, explicitly or by parameters, lego-admissible \((\{a,b\};k)\)-maps among: hyperbolic spheres, spheres with \(a\in \{1,2\}\), spheres with \(p_b\in \{2,\frac{p_a}{2}\}\), Goldberg–Coxeter’s spheres and \((\{a,b\};k)\)-tori. We present extensive computer search of lego-like spheres: 7 parabolic (\(p_b\)-dependent) families, basic examples of all 5 hyperbolic \(a^fb\) (b-dependent) families with \(a\ge 3\), and lego-like \((\{a,b\};3)\)-tori.     

The mass renormalization for the translational Brownian motion

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

Aromaticity of Bare Iridium Trimers and Ir3M0/+ and $$\rm{Ir}_3M_2^{+/3+}$$ (M = Li,Na, K,and Be,Ca) Bimetallic Clusters

The structural stabilities, bonding nature, electronic properties, and aromaticity of bare iridium trimers \(\rm{Ir}_3^{+/-}\) with different geometries and spin multiplicities are studied at the DFT/B3LYP level of theory. The ground state of the \(\rm{Ir}_3^{+}\) cation is found to be the ³A₂ (C_2v) triplet state and the ground state of the \(\rm{Ir}_3^{-}\) anion the ⁵A₂ (C_2v) quintet state. A detailed molecular orbital (MO) analysis indicates that the ground-state \(\rm{Ir}_3^{+}\) ion (C_2v, ³A₂) possesses double (σ and partial δ) aromaticity as well as the ground-state \(\rm{Ir}_3^{-}\) ion (C_2v, ⁵A₂). The multiple d-orbital aromaticity is responsible for the totally delocalized three-center metal-metal bond of the triangular Ir₃ framework. \(\rm{Ir}_3^{-}\) (C_2v, ¹A₁) structure motif is perfectly preserved in pyramidal Ir₃M^0/+ (C_s, ¹A′) and bipyramidal \(\rm{Ir}_3M_2^{+/3+}\) (C_2v, ¹A₁) (M = Li, Na, K and Be, Ca) bimetallic clusters which also possess the corresponding d-orbital aromatic characters.     

Measurement and Calculation the Excess Molar Properties of Binary Mixtures Containing Isobutanol, 1-Amino-2-Propanol,and 1-Propanol at Temperatures of (293.15 to 333.15) K

Densities, ρ, and viscosities, η, of pure isobutanol, 1-amino-2-propanol, and 1-propanol, along with their binary mixtures of {x ₁isobutanol + x ₂1-propanol}, {x ₁1-amino-2-propanol + x ₂1-propanol}, and {x ₁1-amino-2-propanol + x ₂isobutanol} were measured over the entire composition range and at temperatures (293.15–333.15) K at ambient pressure (81.5 kPa). Excess molar properties such as the excess molar volume, V _m ^E , partial molar volumes, \( \bar{V}_{1} \) and \( \bar{V}_{2} \), excess partial molar volumes, \( \bar{V}_{1}^{\text{E}} \) and \( \bar{V}_{2}^{\text{E}} \), thermal expansion coefficient, α, excess thermal expansion coefficient, α ^E, viscosity deviation, Δη, and the excess Gibbs energy of activation, ?G ^E*, for the binary mixtures were calculated from the experimental values of densities and viscosities. The excess values of the binary mixtures are negative in the entire composition range and at all temperatures, and increase with increasing temperature. Viscosity deviations, Δη, are negative over the entire composition range and decrease with increasing temperature. The viscosities of the mixtures were correlated by the models of McAllister, Heric, Hind, Katti, and Nissan. The obtained data were correlated by Redlich–Kister equation and the fitting parameters and standard deviations were determined.     

Deposition Morphology and Magnetism of Co,Pt Adatoms and Small CoPt Adclusters on Ni(100) Substrate

Theoretical calculations of Co\(_{n-x}\)Pt\(_x\) (n = 1–3; \(x \le n\)) clusters on Ni(100) surface for their spin and orbital magnetic moments, as well as the magnetic anisotropy energy (MAE), are performed by using the density-functional theory (DFT) method including a self-consistent treatment of spin–orbit coupling (SOC). The results reveal that the ferromagnetic Co atoms in intra Co\(_{n-x}\)Pt\(_x\) adclusters couple ferromagnetically to their underlayer Ni atoms. The predominant inter-interactions between Co adatoms and Ni surface with the partly filled 3d band, together with the secondary intra-interactions between Co adatoms and Pt adatoms with fully filled 5d band, lead to a strongly quenched orbital moment (\(\mu _{\mathrm{{orb}}}^{\mathrm{{Co}}}\) = 0.18–0.14 \(\mu _B\); \(\mu _{\mathrm{{orb}}}^{\mathrm{{Pt}}} \approx \) 0.24–0.19 \(\mu _B\)) but a less quenched spin moment (\(\mu _{\mathrm{{spin}}}^{\mathrm{{Co}}} \approx \) 2.0 \(\mu _B\); \(\mu _{\mathrm{{spin}}}^{\mathrm{{Pt}}} \approx \) 0.35 \( \mu _B\)). The MAEs of CoPt adclusters exhibit a strong dependence on alloying effect rather than size effect, which is direly proportional to SOC strength and orbital moment anisotropy. The oxidations of CoPt clusters always reduce orbital magnetic moments and consequently decrease the corresponding MAEs.     

Hierarchical enumeration of Kekulé’s benzenes,Ladenburg’s benzenes,Dewar’s benzenes,and benzvalenes by using combined-permutation representations

The group hierarchy for each skeleton of ligancy 6 is formulated to be: point group (PG \({\varvec{G}}_{\sigma }\)) \(\subseteq \) RS-stereoisomeric group (RS-SIG \({\varvec{G}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) stereoisomeric group (SIG \(\widetilde{{\varvec{G}}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) isoskeletomeric group (ISG \(\widetilde{\widetilde{{\varvec{G}}}}_{\sigma \widetilde{\sigma }\widehat{I}}\) = \({\varvec{S}}^{[6]}_{\sigma \widehat{I}}\)), where we start from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{6h}\) for the Kekulé benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{3h}\) for the Ladenburg benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the Dewar benzene skeleton, or from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the benzvalene skeleton. After these groups are constructed as combined-permutation representations, the calculation of the respective cycle indices with chirality fittingness (CI-CFs) and the introduction of ligand-inventory functions are conducted to give generation functions for 3D-based enumerations (for PGs and RS-SIGs) and 2D-based enumerations (for SIGs and ISGs). The enumeration results are discussed by means of isomer-classification diagrams, in which equivalence classes under enantiomerism (for PGs), RS-stereoisomerism (for RS-SIGs), stereoisomerism (for SIGs), and isoskeletomerism (for ISGs) are illustrated schematically. The implicit connotations of the conventional terms “skeletal isomerism”, “positional isomerism”, and “constitutional isomerism” are discussed, where the effects of the concept of isoskeletomerism are emphasized.     

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

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

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

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

Transition-metal dichalcogenide heterostructure solar cells: a numerical study

We evaluate the tunneling short-circuit current density \(J_{TU}\) in a p–i–n solar cell in which the transition metal dichalcogenide heterostructure (\(\hbox {MoS}_2/\hbox {WS}_2\) superlattice) is embedded in the intrinsic i region. The effects of varying well and barrier widths, Fermi energy levels and number of quantum wells in the i region on \(J_{TU}\) are examined. A similar analysis is performed for the thermionic current \(J_{TH}\) that arises due to the escape and recapture of charge carriers between adjacent potential wells in the i-region. The interplay between \(J_{TU}\) and \(J_{TH}\) in the temperature range (300–330 K) is examined. The thermionic current is seen to exceed the tunneling current considerably at temperatures beyond 310 K, a desirable attribute in heterostructure solar cells. This work demonstrates the versatility of monolayer transition metal dichalcogenides when utilized as fabrication materials for van der Waals heterostructure solar cells.     

Thermodynamic Properties of Ternary Ionic Liquid Mixture Containing a Common Ion: Excess Molar Volumes,Excess Isentropic Compressibilities,Excess Molar Enthalpies and Excess Heat Capacities

In the present investigations, the excess molar volumes, \( V_{ijk}^{\text{E}} \), excess isentropic compressibilities, \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), and excess heat capacities, \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \), for ternary 1-butyl-2,3-dimethylimidazolium tetrafluoroborate (i) + 1-butyl-3-methylimidazolium tetrafluoroborate (j) + 1-ethyl-3-methylimidazolium tetrafluoroborate (k) mixture at (293.15, 298.15, 303.15 and 308.15) K and excess molar enthalpies, \( \left( {H^{\text{E}} } \right)_{ijk} \), of the same mixture at 298.15 K have been determined over entire composition range of x _i and x _j . Satisfactorily corrections for the excess properties \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) have been obtained by fitting with the Redlich–Kister equation, and ternary adjustable parameters along with standard errors have also been estimated. The \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) data have been further analyzed in terms of Graph Theory that deals with the topology of the molecules. It has also been observed that Graph Theory describes well \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) values of the ternary mixture comprised of ionic liquids.     

Extending the McClelland formula for total $$\pi $$-electron energy

The McClelland formula, based on the upper bound \(\sqrt{2mn}\), is capable of reproducing over 99.5% of the total \(\pi \)-electron energy (\(E_\pi \)) of a conjugated hydrocarbon, whose molecules possess n carbon atoms and m carbon–carbon bonds. Its weak point is that it predicts equal \(E_\pi \)-values for all isomers. We now show how this failure can be overcome, offering a general strategy for extending McClelland’s formula. By means of one of these extensions, \(E_\pi \) is related with the energy of the highest occupied molecular orbital, and the error of the new formula is diminished by more than \(50\%\) relative to the standard McClelland approximation.     

Additional Aspects of Complexation of Gold(I) with Thiomalate

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

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

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

On the origins of intersecting potential energy surfaces

Techniques developed for investigating nonadiabatic processes in molecular systems are adapted to study the structure and properties of holomorphic and meromorphic functions of a complex variable, \(f(z)=\mathfrak {R}(f)+i\,\mathfrak {I}(f)\). The connection is that \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) are correlated two-dimensional scalar functions, interrelated by the Cauchy–Riemann equations. Exploiting this fact, it is demonstrated that \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) of f can be envisaged in Euclidean \({\mathbb {R}}^{3}\) space as a two-state set of constrained, intersecting two-dimensional potential energy surfaces (PESs), called the graph of f. Importantly, the analytic and algebraic properties of f dictate the geometric structure evinced in the graph of f. This parallels multi-state sets of higher-dimensional, constrained, intersecting PESs linked with correlated electronic eigenstates of the parameterized molecular Hamiltonian operator. In view of this association, the language and mathematical infrastructure devised by chemists for discussing and analyzing intersections in higher-dimensional PESs are suitably modified for f. Notably, an algorithm capable of optimizing roots and poles of f through analysis of the real, two-dimensional \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) functions is derived, which is based on intersection-adapted coordinate and constrained Lagrangian methodologies. As constrained, intersecting PESs are indispensible for conceptualizing and characterizing the physics governing nonadiabatic phenomena, f represents a foundational bridge to these more abstract constructions.     

The heat capacity and density of solutions of barium and tetrabutylammonium iodides in N-methylpyrrolidone at 298.15 K

The heat capacity and density of solutions of barium and tetrabutylammonium iodides in N-methylpyrrolidone (MP) were studied at 298.15 K by calorimetry and densimetry. The standard partial molar heat capacities and volumes (\(\overline {C_{p^2 }^ \circ } \) and \(\overline {V_2^ \circ } \)) of the electrolytes in MP were calculated. The standard heat capacities \(\overline {C_{pi}^ \circ } \) and volumes \(\overline {V_i^ \circ } \) of the Ba²⁺ and (C₄H₉)₄N⁺ ions in solution in MP at 298.15 K were determined. With the tetrabutylammonium ion, these values were in agreement with those calculated on the basis of the tetraphenylarsonium-tetraphenyl borate and tetraphenylphosphonium-tetraphenyl borate assumptions. The results are discussed in relation to the special features of solvation in solutions of the salts studied.