Ab initio intermolecular potential energy surface and second pressure virial coefficients of methane

A six-dimensional potential energy hypersurface (PES) for two interacting rigid methane molecules was determined from high-level quantum-mechanical ab initio computations. A total of 272 points for 17 different angular orientations on the PES were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory with basis sets of aug-cc-pVTZ and aug-cc-pVQZ qualities. The calculated interaction energies were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites per methane molecule was fitted to the interaction energies. In addition, a semiempirical correction to the analytical potential function was introduced to take into account the effects of zero-point vibrations. This correction includes adjustments of the dispersion coefficients and of a single-parameter within the fit to the measured values of the second virial coefficient B(T) at room temperature. Quantitative agreement was then obtained with the measured B values over the whole temperature range of the measurements. The calculated B values should definitely be more reliable at very low temperatures (T<150 K) than values extrapolated using the currently recommended equation of state.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid neon using a new intermolecular potential from molecular dynamics simulation

A new pair potential energy function of neon has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. The pair potential reproduces the second virial coefficient, viscosity, thermal conductivity, and self-diffusion coefficient of neon in a good accordance with experimental data over wide ranges of temperature and density. We have also performed molecular dynamics simulation to obtain some thermodynamics, transport, and structural properties of fluid neon at different temperatures and densities using our calculated pair potential supplemented by quantum corrections following the Feynman–Hibbs approach. The significance of this work is that the three-body expression of Wang and Sadus (J Chem Phys 125:144509–1, 2006) can be used to improve the prediction of the pressures of neon without requiring an expensive three-body calculation. The molecular dynamics simulation of neon has been also used to determine a new equation of state for neon. Our results are in a good agreement with experiment and literature values.     

Direct determination of pair potential energy function from extended law of corresponding states and calculation of thermophysical properties for H2–He

A new correlation equation for the low-density binary diffusion and viscosity collision integrals of hydrogen–helium over a very large reduced temperature range from 1 to the onset of ionization is obtained. These equations has been inverted directly to give the isotropic reduced intermolecular potential energy curve for H₂–He, corresponding to the viscosity collision integrals and we used these data in conjunction with the second virial coefficient to calculate outer branch of the potential well. Comparison is made between the present MSV interaction potential energy function and the independently known H₂–He potential energy function. The present potential function provides the best overall agreement for the available low-density gas phase thermophysical data, i.e., transport properties in a wide composition and temperature range.     

Collision cross sections, pressure-broadening coefficients and second virial coefficients for the acetylene-argon complex: experiments and calculations on a new potential energy surface

Integral cross sections and pressure-broadening coefficients have been measured by molecular beam scattering and by high-resolution infrared spectroscopy, respectively, for the acetylene-argon system. A new potential energy surface (PES) is proposed to describe structure and dynamical properties of this prototypical weakly bound complex. The PES has been parametrized exploiting a novel atom-bond pairwise additive scheme and has been fitted to the experimental data. Calculations of the scattering cross sections (both differential and integral), pressure-broadening, and second virial coefficients have been performed using both the present and also the most recent ab initio PES available in the literature. Analysis of the new experimental data indicates that the anisotropy of the interaction in the well region should be larger than that obtained in ab initio calculations. This is also in line with previous spectroscopic results.     

Potential energy surface and second virial coefficient of methane-water from ab initio calculations

Six-dimensional intermolecular potential energy surfaces (PESs) for the interaction of CH4 with H2O are presented, obtained from ab initio calculations using symmetry-adapted perturbation theory (SAPT) at two different levels of intramonomer correlation and the supermolecular approach at three different levels of electron correlation. Both CH4 and H2O are assumed to be rigid molecules with interatomic distances and angles fixed at the average values in the ground-state vibration. A physically motivated analytical expression for each PES has been developed as a sum of site-site functions. The PES of the CH4-H2O dimer has only two symmetry-distinct minima. From the SAPT calculations, the global minimum has an energy of -1.03 kcal/mol at a geometry where H2O is the proton donor, HO-H...CH4, with the O-H-C angle of 165 degrees, while the secondary minimum, with an energy of -0.72 kcal/mol, has CH4 in the role of the proton donor (H3C-H...OH2). We estimated the complete basis set limit of the SAPT interaction energy at the global minimum to be -1.06 kcal/mol. The classical cross second virial coefficient B12(T) has been calculated for the temperature range 298-653 K. Our best results agree well with some experiments, allowing an evaluation of the quality of experimental results.     

Theoretical study of the contribution of physisorption to the low-pressure adsorption of hydrogen on carbon nanotubes

To investigate the contribution of geometry on the adsorption process, we present a theoretical study of the low-pressure physisorption of hydrogen on isolated nanotubes and nanotube bundles through the second virial coefficient, B(AS), computed classically with an uncorrugated adsorption potential. The optimal nanotube bundle geometry at low pressure for a Lennard-Jones adsorption potential is obtained by studying the second virial coefficient, B(AS), for variable radius or bundle lattice constant. The most favorable bundle adsorption sites at low pressures and temperatures are identified for typical bundle structures and the relative contribution of interstitial sites relative to other sites is discussed as a function of temperature and pressure. The Boyle temperature behavior for the B(AS) virial coefficient is also discussed as a function of radius for isolated nanotubes. For a given nanostructure, the maximum pressure of applicability of the B(AS) approach, below which the adsorption isotherm is linear, is estimated as a criterion which depends on temperature.     

Interaction between two star polymers in a good solvent

An off-lattice bead model with a hard-spheres potential is used to characterize the two-body properties of star polymers of functionalities f=4–18 in good solvent conditions through Monte Carlo simulations. The second virial results complement a previous study performed with a Lennard-Jones potential. Some intrinsic viscosity numerical data are also obtained. The second virial coefficient and viscosity data are combined in terms of a single parameter, with apparently anomalous features in terms of the star functionalities which are also observed from existing experimental data. The effective intermolecular potential is compared with a global potential recently proposed.     

The Ne-Ne interatomic potential revisited

The neon-neon interaction has been re-examined in the light of new data, both theoretical and experimental. Because of recent interest in solids at very high pressures, a new accurate potential is presented with particular interest paid to its highly repulsive region. A potential in HFD-B form incorporating the most recent dispersion coefficients was fitted to accurate viscosity data and high-energy scattering beam data. The potential is able to predict a wide range of macroscopic (second virial coefficients, viscosity, thermal conductivity, diffusion and 0 K binding energy) and microscopic properties (spectroscopic differential and high-energy total cross sections). The potential is extended to very short range by extrapolating to united atom perturbation results.     

A Model for Hydration Interactions between Apoferritin Molecules in Solution

We have studied how non-DLVO forces between molecules of the globular protein apoferritin in solution affect its osmotic second virial coefficient. A model explaining the effects of the solution ionic strength and pH on the interprotein interaction is developed, to give a physical interpretation of recently published experimental findings showing that the second virial coefficient of the protein apoferritin, supported by acetate buffer, goes through a minimum as a function of ionic strength. At low ionic strengths, the apoferritin second virial coefficient initially decreases with increasing sodium ion concentration, as DLVO theory predicts. However, non-DLVO hydration forces due to overlapping of the Stern layers of the protein molecules increase the second virial coefficient with further increase of sodium ion concentration, again as found experimentally at higher ionic strengths. The non-DLVO effect arises from ionic exchange between hydrogen and sodium ions at the protein surface. An adsorption shell of hydrated sodium ions forms around the protein molecules with increasing buffer concentration.     

The water-oxygen dimer: first-principles calculation of an extrapolated potential energy surface and second virial coefficients

The systematic intermolecular potential extrapolation routine (SIMPER) is applied to the water-oxygen complex to obtain a five-dimensional potential energy surface. This is the first application of SIMPER to open-shell molecules, and it is the first use, in this context, of asymptotic dispersion energy coefficients calculated using the unrestricted time-dependent coupled-cluster method. The potential energy surface is extrapolated to the complete basis set limit, fitted as a function of intermolecular geometry, and used to calculate (mixed) second virial coefficients, which significantly extend the range of the available experimental data.     

Solution properties and chain conformation characteristics of cellulose tricarbanilate

Fractions of two cellulose tricarbanilate samples were characterized by light-scattering (weight-average molecular weight, second virial coefficient, mean-square radius of gyration), gel permeation chromatography (polydispersity index), and viscometry (intrinsic viscosity) in tetrahydrofuran and acetone. The intrinsic viscosity data were analyzed in terms of the theory developed for the continuous wormlike cylinder model, and the chain parameters (Kuhn statistical segment length λ^?1, chain diameter d, and shift factor M_L) were evaluated. The molecular-weight dependence of the mean-square radius of gyration in tetrahydrofuran was calculated for the Kratky—Porod chain model and compared with the experimental results. Data on the intrinsic viscosity and radii of gyration for other solvents at temperatures from 0 to 100°C were analyzed in the same way, and the effects of solvent and temperature on the statistical segment length were evaluated. Polymer—solvent interaction parameters were estimated from the second virial coefficients.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

Thermodynamic properties of aqueous polyacrylamide solutions as a function of pressure and temperature

The viscosities of dilute aqueous solutions of polyacrylamide were measured at temperatures from 20 to 60.4° and pressures up to 150 MPa using a falling-body viscometer. The viscosity coefficient, ν, increases exponentially with increasing pressure at a given temperature and concentration. The rate of increase of the apparent energy of activation. E≠, with pressure becomes more rapid as the concentration of the solutions increases. Intrinsic viscosity, [ν], increases with increasing pressure at a given temperature but almost levels off at pressures above 100 MPa while the Huggins constant, k_H, decreases. The Flory-Huggins interaction parameter, _X1, decreases at a greater rate with increasing pressure as the temperature decreases indicating that the effect of pressure on improving the compatability between the polymer and solvent is greater near the θ-temperature. The second virial coefficient, A₂, was calculated from the intrinsic viscosity data and compared with the results obtained by light scattering technique.     

Intermolecular potential energy surface and second virial coefficients for the water-CO2 dimer

A five-dimensional potential energy surface is calculated for the interaction of water and CO(2), using second-order M?ller-Plesset perturbation theory and coupled-cluster theory with single, double, and perturbative triple excitations. The correlation energy component of the potential energy surface is corrected for basis set incompleteness. In agreement with previous studies, the most negative interaction energy is calculated for a structure with C(2v) symmetry, where the oxygen atom of water is close to the carbon atom of CO(2). Second virial coefficients for the water-CO(2) pair are calculated for a range of temperatures, and their uncertainties are estimated. The virial coefficients are shown to be in close agreement with the available experimental data.     

SOLVENT QUALITY AND SOLUTION BEHAVIOR OF NYLON 12

The refractive index increment,dynamic and static laser light scattering,intrinsic viscosity[η]and Huggins constant(K_H)of nylon 12 have been measured in m-cresol and sulphuric acid/water system at 10-60℃.The intrinsic viscosity,R_H,R_g,A_2,and(~2)~(1/2)(calculated from viscosity data)and"a"values of nylon 12 are found to be higher in m-cresol than in sulphuric acid.All these parameters decrease with the increase in water contents in sulphuric acid.The refractive index increment,K_H and activation energy show an opposite trend to that of[η].The intrinsic viscosity,R_H,R_g,A_2, and(~2)~(1/2) have maximum values around 30-40℃in sulphuric acid/water system,whereas in m-cresol they fall at about 20℃.It has been concluded that the variation in size,interaction parameter(second virial coefficient),[η]and K_H of the polymer solutions with the alteration in solvent composition and temperature are the out come of change in thermodynamic quality of solvents,selective adsorption,hydrogen bonding and conformational transitions.It has also been concluded that the increase in temperature first enhances the quality of the solvent,encourages hydrogen bonding and specific adsorption, and then deteriorates,bringing conformational transitions in the polymer molecules.However,the addition of water to sulphuric acid continuously deteriorates the solvent quality.This characteristic of the solvent system brings conformational changes in the polymer especially at low temperatures.     

Ab initio calculation of structure and transport properties of He…X (X = Zn, Cd, Hg) van der Waals complexes

The ground state ab initio CCSD(T) potential curves using various basis sets (aug-cc-pVXZ-PP (X = D, T, Q, 5)) is obtained for the dimers of helium with IIb group metals. The effect of the position of the (mid) bond-functions on the interaction energy is discussed. A Symmetry Adapted Perturbation Theory decomposition of the interaction energy is provided and the trends in the dimer stabilizing and destabilizing contributions are depicted. The spline fitted potential curves are applied together with rigorous statistical formulae in order to obtain the transport coefficients (viscosity coefficients, diffusion coefficients) and the second virial coefficient both for pure constituents and mixtures. The obtained theoretical results are compared with available experimental data. Molecular dynamics is used to obtain reliable values of the diffusion coefficients for all the systems under study.     

Vapor pressure studies of hydrophobic association. Thermodynamics of fluorobenzene in dilute aqueous solution

An automated vapor pressure apparatus has been used to obtain measurements of the vapor pressure of aqueous solutions of fluorobenzene at temperatures of 15, 25, 35, and 45°C, and in the concentration range 0 to 0.011M. The results have been interpreted to infer the dimerization constant of fluorobenzene in very dilute aqueous solutions, equivalent to the second virial coefficient of interaction between fluorobenzene molecules. The hydrophobic association of fluorobenzene molecules is thermodynamically quite similar to that of benzene at comparable temperatures and concentrations. A dimerization constant of fluorobenzene of 0.56 M^–1 at 30°C and an endothermic enthalpy of association equal to 3.9 kcal-mol^–1 are calculated from the measurements.     

Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections.