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.     

Virial coefficients of gas monolayers

Second virial coefficients of gas monolayers of two quinone derivatives have been calculated using atom-atom potential functions. The potential parameters were derived from independent data for the corresponding solids. The effects of inter- molecular H bonds on the virial coefficients are dominant. The virial coefficient on one monolayers has been experimentally determined.     

Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures

A sound understanding of any sorption system requires an accurate determination of the enthalpy of adsorption. This is a fundamental thermodynamic quantity that can be determined from experimental sorption data and its correct calculation is extremely important for heat management in adsorptive gas storage applications. It is especially relevant for hydrogen storage, where porous adsorptive storage is regarded as a competing alternative to more mature storage methods such as liquid hydrogen and compressed gas. Among the most common methods to calculate isosteric enthalpies in the literature are the virial equation and the Clausius–Clapeyron equation. Both methods have drawbacks, for example, the arbitrary number of terms in the virial equation and the assumption of ideal gas behaviour in the Clausius–Clapeyron equation. Although some researchers have calculated isosteric enthalpies of adsorption using excess amounts adsorbed, it is arguably more relevant to applications and may also be more thermodynamically consistent to use absolute amounts adsorbed, since the Gibbs excess is a partition, not a thermodynamic phase. In this paper the isosteric enthalpies of adsorption are calculated using the virial, Clausius–Clapeyron and Clapeyron equations from hydrogen sorption data for two materials—activated carbon AX-21 and metal-organic framework MIL-101. It is shown for these two example materials that the Clausius–Clapeyron equation can only be used at low coverage, since hydrogen’s behaviour deviates from ideal at high pressures. The use of the virial equation for isosteric enthalpies is shown to require care, since it is highly dependent on selecting an appropriate number of parameters. A systematic study on the use of different parameters for the virial was performed and it was shown that, for the AX-21 case, the Clausius–Clapeyron seems to give better approximations to the exact isosteric enthalpies calculated using the Clapeyron equation than the virial equation with 10 variable parameters.     

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.     

Second virial coefficients of oxygen—oxygen and carbon—oxygen interactions in different electronic states

Second virial coefficients of oxygen—oxygen and carbon—oxygen interactions in different electronic states have been calculated up to 20000 K. The results show that the virial coefficients of excited states are greater than the corresponding ground state values. The influence of the excited states on the total virial coefficients, calculated by assuming a Botlzmann distribution along the different states, has been found strong (up to 40%) in the carbon—oxygen system, while a minor effect (up to 3%) has been observed for the oxygen—oxygen system.     

Second and third virial coefficients for (methane + nitrogen)

The compression factors Z of (methane  +  nitrogen) of various compositions were measured using a direct method in the temperature range 308.15 K to 333.15 K and at pressures up to 12.0 MPa. Unlike-interaction second virial coefficients were calculated from the data and compared with previous experimental values and values predicted by the Tsonopoulos and GERG equations. Unlike-interaction third virial coefficients were also calculated and compared with estimates provided by both the GERG correlations and the method given by Orbey and Vera.     

Intermolecular potential and second virial coefficient of the water-nitrogen complex

The authors construct a rigid-body (five-dimensional) potential energy surface for the water-nitrogen complex using the systematic intermolecular potential extrapolation routine. The intermolecular potential is then extrapolated to the limit of a complete basis set. An analytic fit of this surface is obtained, and, using this, the global minimum energy is found. The minimum is located in an arrangement in which N2 is near the H atom of H2O, almost collinear with the OH bond. The best estimate of the binding energy is 441 cm-1 (1 cm-1 approximately 1.986 43x10(-23) J). The extrapolated potential is then used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). These calculated second virial coefficients are generally consistent with experimental data, but for the most part the former have smaller uncertainties.     

Comparison of the differential isosteric adsorption enthalpies and entropies calculated from chromatographic data

The differential isosteric enthalpies, -deltaH(ads), and entropies, -deltaS(ads), of adsorption were calculated taking the retention times of the peak maxima and the centres of gravity of peaks into account and compared with the results obtained from the adsorption second virial coefficients. A mathematical link between the -deltaH(ads) and -deltaS(ads) magnitudes and experimental data was derived through the Antoine-type equation which enables the -deltaH(ads) and -deltaS(ads) magnitudes to be found from adsorption second virial coefficients, B2S, calculated on the basis of chromatographically determined adsorption isotherm data. The virial coefficients were calculated employing the values of the Tóth and Unilan equation parameters. There are no significant differences to be found between the isosteric enthalpies obtained, whereas the values of the adsorption entropies were the highest for the centre of peak gravity data.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Estimations of energy of noncovalent bonding from integrals over interatomic zero‐flux surfaces: Correlation trends and beyond

Bonding energies of 50 associates composed by neutral molecules (atoms) and bounded by various weak noncovalent interactions are calculated within the DFT framework using the PBE0/aug‐cc‐pVTZ combination. The electronic virial and electron density values at bond critical points together with their integrals over interatomic surfaces are tested to check their ability to estimate bonding energies. Two correlations schemes dealing with integrals over interatomic surface are suggested to estimate bonding energy of any noncovalent interaction. The physical meaning of explored and several known correlations is discussed. Methods to estimate interatomic surface integrals of electronic virial and electron density are proposed. © 2018 Wiley Periodicals, Inc.     

The equation of state of hard hyperspheres in nine dimensions for low to moderate densities

The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or singularities on or near the negative density axis, in qualitative agreement with the recently solved Percus-Yevick equation of state in nine dimensions.     

Calculation of the second virial coefficients of alkali metals by modified Peng–Robinson equation

In this work, the Peng–Robinson (P–R) equation of state has been modified by proposing a new α function for calculating the second virial coefficients of alkali metals. The relationship between α^0.5 and (1???T _r ^0.5 ) is a nonlinear function. The correlation between the second virial coefficient and P–R equation was presented by expanding the P–R equation into its Taylor series form. For P–R equation, the linear correlation between parameters C₁ and C₂ of α function and acentric factors \( \omega \) of alkali metals was proposed. The new α function and its first, second and third derivatives are continuous. The average standard deviations of compressibility factor which calculated by modified P–R equation are less than 4.3%. The second virial coefficients of alkali metals were calculated over the temperature range 600–3000 K by using the modified P–R equation. Comparison with literature data, the new equation provides more reliable and accurate second virial coefficient predictions for alkali metals than the original P–R equation. It is useful to guide and improve calculation of the second virial coefficients of other metal vapors for design and operation of separation processes in vacuum metallurgy.     

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.     

Calculation of one-electron properties of diatomic molecules using the SCF-Xα scattered-wave method

Some one-electron properties of LiH, BH, CO. LiF, NaF, KF and RbF are calculated within the framework of the overlapping atomic sphere model, using wavefunctions of the SCF-Xα scattered-wave method. The influence of the functional form of the wavefunction in the intersphere region on the values of the calculated properties is investigated and the dependence of these values on various approximations of the method is demonstrated. It is shown that the virial theorem must be the criterion for optimizing the degree of overlap of the spheres in calculations of one-electron properties of molecules by the SCF-Xα scattered-wave method.     

Calculation of the force between surfaces coated with grafted molecules by molecular simulation

We discuss the calculation of the force between surfaces coated with anchored molecules. This force is related to the pressure and can therefore be calculated by the usual means: either by summing over all surface-particle forces or from the virial. However, we argue that the grafting of the molecule must be included by means of a restraining potential-otherwise, nonphysical results can be obtained, such as the appearance of a net force even when the particles are spaced very far away. Bond-stretching potentials are also required if the virial is employed.     

On the apparent molar volumes of nonelectrolytes in water

Apparent molar volumes of aqueous solutions of argon and xenon have been calculated using a previously developed comprehensive equation of state for nonelectrolyte systems. The equation consists of a virial expansion truncated after the fourth virial coefficient and a closed-form term approximating higher coefficients. Mixing rules are based on the composition dependence of virial coefficients, which is known from statistical mechanics. The equation accurately represents vapor-liquid and gas-gas equilibria for the Ar+H₂O and Xe+H₂O systems over wide ranges of pressure and temperature using two binary parameters. With the binary parameters determined from phase equilibrium data, the equation accurately predicts apparent molar volumes V in the near-critical and far-from-critical regions. Apart from reproducing experimental V data, the equation reveals remarkable maxima of V as a function of pressure and temperature in the near-critical region. The implications of this equation with respect to the Ar–H₂O potential are discussed via the second virial coefficient.     

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.     

Electron density and localizability in BH

Three partitioning methods are compared for the molecule BH. They are by minimum fluctuations, intersections of isodensity contours for localized molecular orbitals, and the virial partitioning method. The first two methods were found to partition BH very similarly, such that the centroids of charge can be calculated for these loges defined by minimum fluctuation and using the localized molecular orbitals.     

Interface effects in nematic liquid-crystalline structures of polymer solutions

A solution of long semirigid linear macromolecules was considered. The liquid-crystalline nematic ordering in the solution was analyzed theoretically using an Onsager-type approach. The orientation entropy was calculated in the frameworks of Lifshits' approach, successfully developed for this system originally by Khokhlov and Semenov. For homogeneous liquid-crystalline phase using the third virial approximation for intersegmental steric interaction the orientation distribution function, the free energy density, the isotropic-nematic coexistence and the spinodal conditions were computed numerically for two types of polymer flexibility mechanism: persistent chains and chains of freely joint segments. For the asymptotically exact second virial approximation the applicability region was analyzed. We considered the general equations, which describe the concentration and orientational segment distribution for a semirigid persistent polymer chain at a surface (or interface) of any shape and orientation. These equations were numerically solved for the case when the nematic director axis was perpendicular to a planar interface boundary between the real coexisting nematic and isotropic phases. The coordinate-dependencies of the polymer concentration and of the order-parameter take the smooth two-steps form in the interface region.