Thermodynamic investigations of 1-ethyl-3-methylimidazolium tetrafluoroborate and cycloalkanone mixtures

The densities, ρ, speeds of sound, u, and heat capacities, (C _P)_mix, for binary 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + cyclopentanone or cyclohexanone (2) mixtures within temperature range (293.15–308.15 K) and excess molar enthalpies, H ^E, at 298.15 K have been measured over the entire composition range. The excess molar volumes, V ^E, excess isentropic compressibilities, \( \kappa_{\text{S}}^{\text{E}}, \) and excess heat capacities, \( C_{\text{P}}^{\text{E}}, \) have been computed from the experimental results. The V ^E, \( \kappa_{\text{S}}^{\text{E}} \) , H ^E, and \( C_{\text{P}}^{\text{E}} \) values have been calculated and compared with calculated values from Graph theory. It has been observed that V ^E, \( \kappa_{\text{S}}^{\text{E}} \) , H ^E, and \( C_{\text{P}}^{\text{E}} \) values were predicted by Graph theory compare well with their experimental values. The V ^E, \( \kappa_{\text{S}}^{\text{E}}, \) and H ^E thermodynamic properties have also been analyzed in terms of Prigogine–Flory–Patterson theory.     

Excess Molar Volumes and Excess Isentropic Compressibilities of o-Toluidine + Tetrahydropyran with Pyridine or Benzene or Toluene Ternary Mixtures at 298.15, 303.15 and 308.15 K

The densities, ρ ₁₂₃, and speeds of sound, u ₁₂₃, of ternary o-toluidine (OT, 1) + tetrahydropyran (THP, 2) + pyridine (Py) or benzene or toluene (3) mixtures have been measured as a function of composition at 298.15, 303.15 and 308.15 K. Values of the excess molar volumes, $ V_{123}^{\text{E}} , $ and excess isentropic compressibilities, $ (\kappa_{\text{S}}^{\text{E}} )_{123} , $ of the studied mixtures have been determined by employing the measured experimental data. The observed thermodynamic properties were fitted with the Redlich–Kister equation to determine adjustable ternary parameters and standard deviations. The $ V_{123}^{\text{E}} $ and $ (\kappa_{\text{S}}^{\text{E}} )_{123} $ values were also analyzed in terms of Graph theory. It was observed that Graph theory correctly predicts the sign as well as magnitude of $ V_{123}^{\text{E}} $ and $ (\kappa_{\text{S}}^{\text{E}} )_{123} $ values of the investigated mixtures. Analysis of the data suggests strong interactions and a more close packed arrangement in OT (1) + THP (2) + Py (3) mixtures as compared to those of the OT (1) + THP (2) + benzene (3) or toluene (3) mixtures. This may be due to the presence of a nitrogen atom in Py which results in stronger interactions for the OT:THP molecular entity as compared to those with benzene or toluene.     

Thermodynamic properties of non-electrolyte solutions

Experimental densities (ρ) and ultrasonic sound velocities (u) for the binary mixtures of toluene, o-chlorotoluene, m-chlorotoluene, and p-chlorotoluene with 1-octanol were measured over the entire composition range at T = (298.15, 303.15, and 308.15) K and at a pressure of 0.1 MPa. Excess volumes (V ^E), isentropic compressibilities $ (\kappa_{\text{s}} ) $ , and excess isentropic compressibilities $ (\kappa_{\text{s}}^{\text{E}} ) $ were calculated using the measured experimental densities and ultrasonic sound velocities of the pure liquids and their mixtures. The experimental data were discussed in terms of intermolecular interactions between component molecules. The measured excess properties were correlated with the Redlich–Kister polynomial equation.     

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.     

Thermodynamic Properties of Binary Liquid Mixtures of n-Dodecane with an Alkan-1-ol or an Alkan-2-ol at 298.15 K: A Comparative Study

Experimental densities (ρ), viscosities (η), and speeds of sound (u) of the binary mixtures of n-dodecane with an alkan-1-ol (hexan-1-ol, heptan-1-ol, octan-1-ol) or an alkan-2-ol (hexan-2-ol, heptan-2-ol and octan-2-ol) were measured over the whole mixture composition range at T = 298.15 K. From these data, the excess molar volume ( $ V_{\text{m}}^{\text{E}} $ V m E ), deviations in viscosity (Δη), and excess isentropic compressibility ( $ \kappa_{S}^{\text{E}} $ κ S E ) have been calculated. The results were fitted by means of the Redlich–Kister equation, in order to estimate the binary coefficients and standard errors. Differences among these binary systems are ascribed to the different association abilities of the alkan-1-ols and alkan-2-ols. Experimental data on the constituted binaries were analyzed using McAllister’s multi-body interaction model, the Jouyban–Acree model, the Prigogine–Flory–Patterson theory, and the Bloomfield and Dewan model. The experimental and calculated quantities are used to study the nature of mixing behavior among the mixtures.     

Densities and Viscosities for Binary and Ternary Mixtures of 2-Methylbutan-2-ol (1) + Trichloroethylene (2) + Acetonitrile (3) at 298.15 K and at Ambient Pressure (81.5 kPa)

Densities (ρ) and viscosities (η) of ternary mixtures of 2-methylbutan-2-ol (1) + trichloroethylene (2) + acetonitrile (3) and the related binary mixtures of {2-methylbutan-2-ol (1) + trichloroethylene (2)}, {2-methylbutan-2-ol (1) + acetonitrile (3)}, and {trichloroethylene (2) + acetonitrile (3)} have been measured over the whole composition range at 298.15 K and at ambient pressure (81.5 kPa). Excess molar volumes $ V_{\text{m}}^{\text{E}} $ , viscosity deviations Δη, and excess Gibbs energies of activation ΔG ^*E were derived from the experimental data. The binary and ternary data of $ V_{\text{m}}^{\text{E}} $ , Δη, and ΔG ^*E for the binary and ternary mixtures were correlated as functions of the mole fraction by using the Redlich–Kister and the Cibulka equations. Kinematic viscosities of the binary mixtures were correlated by means of several semi-empirical equations to determine the fitting parameters and the SDs. The experimental results are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

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.     

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.     

Excess parameters for binary mixtures of alkyl benzoates with 2-propanol at different temperatures

Density (ρ), viscosity (η), and speed of sound (U) values for the binary mixture systems of methyl benzoate + 2-propanol and ethyl benzoate + 2-propanol including those of pure liquids were measured over the entire mole fraction range at five different temperatures (303.15, 308.15, 313.15, 318.15, and 323.15) K. From these experimentally determined values, various thermo-acoustic parameters such as excess isentropic compressibility $ \left( {K_{\text{s}}^{\text{E}} } \right) $ , excess molar volume (V ^E) and excess free length $ \left( {L_{\text{f}}^{\text{E}} } \right) $ , excess Gibb’s free energy (ΔG ^*E), and excess enthalpy (H ^E) have been calculated. The excess functions have been fitted to the Redlich–Kister type polynomial equation. The deviations for excess thermo-acoustic parameters have been explained on the basis of the intermolecular interactions present in these binary mixtures. The theoretical values of speed of sound in the mixtures have been evaluated using various theories and have been compared with experimentally determined speed of sound values in order to check the applicability of such theories to the liquid mixture systems under study. Viscosity data have been used to test the applicability of standard viscosity models of Grunberg–Nissan, Hind–Mc Laughlin, Katti–Chaudhary, Heric and Brewer, Frenkel, Tamura and Kurata at various temperatures for the binary liquid systems under study.     

Thermal analysis, phase transitions and molecular reorientations in [Sr(OS(CH3)2)6](ClO4)2

Thermal analysis (TG/DTG/QMS), performed for [Sr(OS(CH₃)₂)₆](ClO₄)₂ in a flow of argon and in temperature range of 295–585 K, indicated that the compound is completely stable up to ca. 363 K, and next starts to decompose slowly, and in the temperature at ca. 492 K looses four (CH₃)₂SO molecules per one formula unit. During further heating [Sr(DMSO)₂](ClO₄)₂ melts and simultaneously decomposes with explosion. Differential scanning calorimetry (DSC) measurements performed in the temperature range of 93–370 K for [Sr(DMSO)₆](ClO₄)₂ revealed existence of the following phase transitions: glass ? crystal phase Cr5 at T _g  ≈ 164 K (235 K), phase Cr5 → phase Cr4 at $ T_{\text{c6}}^{\text{h}} $  ≈ 241 K, phase Cr4 → phase Cr3 at $ T_{\text{c5}}^{\text{h}} $  ≈ 255 K, phase Cr3 → phase Cr2 at $ T_{\text{c4}}^{\text{h}} $  ≈ 277 K, phase Cr2 ? phase Cr1 at $ T_{\text{c3}}^{\text{h}} $  ≈ 322 K and $ T_{\text{c3}}^{\text{c}} $  ≈ 314 K, phase Cr1 ? phase Rot2 at $ T_{\text{c2}}^{\text{h}} $  ≈ 327 K and $ T_{\text{c2}}^{\text{c}} $  ≈ 321 K and phase Rot2 ? phase Rot1 at $ T_{\text{c1}}^{\text{h}} $  ≈ 358 K and $ T_{\text{c1}}^{\text{c}} $  ≈ 347 K. Entropy changes values of the phase transitions at $ T_{\text{c1}}^{\text{h}} $ and $ T_{\text{c2}}^{\text{h}} $ (?S ≈ 79 and 24 J mol^?1 K^?1, respectively) indicated that phases Rot1 and Rot2 are substantially orientationally disordered. The solid phases (Cr1–Cr5) are more or less ordered phases (?S ≈ 7, 10, 4 and 3 J mol^?1 K^?1, respectively). Phase transitions in [Sr(DMSO)₆](ClO₄)₂ were also examined by Fourier transform middle infrared spectroscopy (FT-MIR). The characteristic changes in the FT-MIR absorption spectra of the low- and high-temperature phases observed at the phase transition temperatures discovered by DSC allowed us to relate these phase transitions to the changes of the reorientational motions of DMSO ligands and/or to the crystal structure changes.     

Exploring antibiotic resistance based on enzyme hydrolysis by microcalorimetry

In an effort to understand the reactions of antibiotics hydrolysis with metallo-β-lactamases (MβLs), the thermokinetic parameters of cefazolin hydrolysis with B1 subclass MβL CcrA from Bacteroides fragilis were determined by microcalorimetric method. The values of activation free energy $ \Updelta G_{ \ne }^{\theta } $ are 88.032 ± 0.038, 89.075 ± 0.025, 90.095 ± 0.034, and 91.261 ± 0.044 kJ mol^?1 at 293.15, 298.15, 303.15, and 308.15 K, respectively, the activation enthalpy $ \Updelta H_{ \ne }^{\theta } $ is 25.278 ± 0.005 kJ mol^?1, the activation entropy $ \Updelta S_{ \ne }^{\theta } $ is ?213.99 ± 0.14 J mol^?1 K^?1, the apparent activation energy E is 27.776 kJ mol^?1, and the reaction order is 1.4. The results indicated that the cefazolin hydrolysis with CcrA is an exothermic and spontaneous reaction. An association between the thermokinetic and kinetic parameters was revealed, which is that the catalytic constant K _cat increase with increase in $ \Updelta H_{ \ne }^{\theta } $ .     

Thermodynamic properties of polymorphic forms of theophylline. Part II: The enthalpies of solution in water at 298.15 K

The enthalpies of solution $ \Updelta_{sol}^{{}} H_{m}^{{}} $ of polymorphic forms I and II of theophylline in water at 298.15 K using the isoperibol solution calorimeter have been determined in the range of concentration (0.311–1.547) · 10^?3 /mol · kg^?1. The enthalpies of hydration $ \Updelta_{hyd}^{{}} H_{m}^{o} $ were determined from the experimentally obtained the enthalpies of solution for aqueous solutions and previously determined enthalpies of sublimation $ \Updelta_{s}^{g} H_{m}^{o} . $      

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.     

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.     

Crystal structure and thermodynamic properties of dipotassium diiron(III) hexatitanium oxide

In the present work, the temperature dependence of heat capacity of dipotassium diiron(III) hexatitanium oxide has been measured for the first time in the range from 10 to 300 K by means of precision adiabatic vacuum calorimetry. The experimental data were used to calculate standard thermodynamic functions, namely the heat capacity $ C_{p}^{ \circ } (T) $ , enthalpy $ H^{ \circ } (T) - H^{ \circ } (0) $ , entropy $ S^{ \circ } (T) - S^{ \circ } (0), $ and Gibbs function $ G^{ \circ } (T) - H^{ \circ } (0) $ for the range from T → 0 to 300 K. The structure of K₂Fe₂Ti₆O₁₆ is refined by the Rietveld method: space group I4/m, Z = 1, a = 10.1344(2) Å, c = 2.97567(4) Å, V = 305.618(7) Å³. The high-temperature X-ray diffraction was used for the determination of coefficients of thermal expansion.     

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.     

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.

Density functional study on structures, stabilities, and electronic properties of size-selected Pd n Si q (n = 1–7 and q = 0, +1, −1) clusters

The density functional theory (DFT) calculations within the framework of generalized gradient approximation have been employed to systematically investigate the geometrical structures, stabilities, and electronic properties of Pd _n Si ^q (n = 1–7 and q = 0, +1, ?1) clusters and compared them with the pure ${\text{Pd}}_{n + 1}^{q}$ (n = 1–7 and q = 0, +1, ?1) clusters for illustrating the effect of doping Si atom into palladium nanoclusters. The most stable configurations adopt a three-dimensional structure for both pure and Si-doped palladium clusters at n = 3–7. As a result of doping, the Pd _n Si clusters adopt different geometries as compared to that of Pd _n+1. A careful analysis of the binding energies per atom, fragmentation energies, second-order difference of energies, and HOMO–LUMO energy gaps as a function of cluster size shows that the clusters ${\text{Pd}}_{4}^{ + }$ , ${\text{Pd}}_{4}$ , ${\text{Pd}}_{8}^{ - }$ , ${\text{Pd}}_{5} {\text{Si}}^{0, + , - }$ , and ${\text{Pd}}_{7} {\text{Si}}^{0, + , - }$ possess relatively higher stability. There is enhancement in the stabilities of palladium frameworks due to doping with an impurity atom. In addition, the charge transfer has been analyzed to understand the effect of doped atom and compared further.     

Use of auxiliary functions {Q_{ns}^q} and {G_{-ns}^q} in evaluation of multicenter integrals over integer and noninteger n-Slater type orbitals arising in Hartree–Fock–Roothaan equations for molecules

With the help of expansion relations for the two-center Slater type orbitals (STOs) charge densities established by the author from the use of complete orthonormal sets of Ψ ^α -exponential type orbitals (Ψ ^α -ETOs), where α = 1, 0, ? 1, ? 2, . . . , a large number of series expansion formulas for the multicenter integrals of integer and noninteger n-STOs (ISTOs and NISTOs) occurring in Hartree–Fock–Roothaan (HFR) equations for molecules is derived through the auxiliary functions ${Q_{ns}^q}$ and ${G_{-ns}^q}$ , and one- and two-center basic integrals of ISTOs. The analytical relations for basic integrals are presented. As an example of application, the calculations have been performed for the ground state of electronic configuration of ${{\it CH}_4((1a_1)^{2}(2a_1)^{2}(1t_{2x})^{2} (1t_{2y})^{2} (1t_{2z})^{2},{}^1A_1)}$ using combined HFR theory suggested by the author.     

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.