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.     

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.     

Determination of unlike-pair potential parameters from second virial coefficient data

Using available interaction virial coefficient data for forty-five non-polar binary systems, potential parameters for unlike interactions have been obtained by an analytical procedure for the Lennard—Jones (12-6) and Kihara intermolecular potentials.     

Calculation of the binary diffusion second virial coefficient

Calculations of the first density correction to the binary diffusion coefficient are presented for several mixtures. These calculations are based on the classical kinetic theory for mixtures developed by Bennett and Curtiss. The theoretical predictions agree well with experimental data.     

Methane-water cross second virial coefficient with quantum corrections from an ab initio potential

We present our calculations of the cross second virial coefficient (B12) and of a related quantity, phi 12 = B12-TdB12/dT, for the methane-water system in the temperature range T = 200-1000 K. These calculations were performed using one of the ab initio potentials developed in previous work [Akin-Ojo and Szalewicz, J. Chem. Phys. 123, 134311 (2005)]. Quantum corrections of order variant Planck's over 2pi(2) were added to the computed classical values. We have estimated the uncertainties in our computed B12 and phi 12(T). This allowed evaluation of the quality of the experimental data to which we compare our results. We also provide an analytical expression for B12(T) as a function of the temperature T obtained by fitting the calculated values. This formula also predicts values of phi12(T) consistent with the directly calculated values.     

Influence of polymolecularity on the second virial coefficient of polymers

Scaling theory is applied to derive expressions describing the influence of polymolecularity on the second virial coefficient, A₂, as obtained from osmotic pressure and light scattering measurements. Numerical values of polymolecularity correction factors are calculated for Schulz-Zimm and logarithmic normal distributions of the molecular weight, different qualities of the solvent and several ratios of the weight-average and the number-average molecular weights M̄_w/M̄_n. It is found that in the equation $ A_2 = K_{A_2 } \cdot M_{{\rm av}}^{a_{A_2 } } $ the weight-average molecular weight is a good approximation for M_av if A₂ is measured via light scattering, while the number-average molecular weight can be inserted for M_av if A₂ stems from osmotic pressure measurements.     

The second virial coefficient of argon at low temperatures

We present experimental data of second virial coefficients of argon at temperatures of 77.3, 87.2 and 90.2 K. The results are in excellent agreement with theoretical values.     

Pressure dependence of the second virial coefficient of dilute polystyrene solutions

The pressure derivatives of the second virial coefficients [dA₂/dP; 0.1 ≤ P (MPa) ≤ 35.0] for dilute polystyrene (PS) solutions in good, θ, and poor solvents were measured with static light scattering. The solvent quality improved (dA₂/dP > 0) in the good and poor solvents that we investigated (toluene, chloroform; and methylcyclohexane) but deteriorated (dA₂/dP < 0) in θ solvents (cyclohexane and 50‐50 cis,trans‐decalin). The effects of temperature [22 < T (°C) < 45] and molecular weight [25 × 10³ < weight‐average molecular weight (amu mol^?1) < 900 × 10³] on dA₂/dP for PS/cyclohexane solutions were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3070–3076, 2003     

Interdependence of enthalpic and entropic contributions to the second osmotic virial coefficient

The interdependence of the enthalpic contribution A_{2, H} and the entropic contribution A_{2, s} to the second osmotic virial coefficient for a given polymer-solvent system has been investigated from the experimental and the theoretical point of view. Experimentally, the following common facts were observed for various systems at temperatures and pressures below the critical values for the solvent. Both the isobaric and isothermal dependences can be approximated over relatively wide ranges of A_{2, H} by linear relations with a slope deviating only slightly, but in a characteristic manner from a value of ?1. When the temperature is increased at constant pressure one moves along an isobar towards higher A_{2, H}; when the pressure is increased at constant temperature, one moves along an isotherm in the opposite direction, i.e., towards lower A₂, _H. Theoretically this behavior can be described in a qualitative manner, starting from a relation derived by Patterson and Delmas on the basis of the Prigogine corresponding-states theory. The reasons for the lack of quantitative agreement are discussed.     

Various contributions to the osmotic second virial coefficient in protein-water-cosolvent solutions

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water-protein-cosolvent mixtures is developed. The Kirkwood-Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water-protein-cosolvent mixtures. These properties can be divided into two groups: (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water-cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions: (1) one due to the protein-solvent interactions B2(p-s), which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B2(p-p)), and (3) a third one representing an ideal mixture contribution (B2(id)). The cosolvent composition dependencies of these three contributions were examined for several water-protein-cosolvent mixtures using experimental data regarding the OSVC and the preferential binding parameter. For the water-lysozyme-arginine mixture, it was found that OSVC exhibits the behavior of an ideal mixture and that B2(id) provides the main contribution to the OSVC. For the other mixtures considered (water-Hm MalDH-NaCl, water-Hm MalDH-(NH4)2SO4, and water-lysozyme-NaCl mixtures), it was found that the contribution of the protein-solvent interactions B2(p-s) is responsible for the composition dependence of the OSVC on the cosolvent concentration, whereas the two remaining contributions (B2(p-p)) and B2(id)) are almost composition independent.     

The scaling behavior of the second virial coefficient of linear and ring polymer

The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer(θ_L) is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U(r) between two ring polymers as well as the second virial coefficient A_2 of ring polymers at θ_L, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A_2 of ring polymers at θ_L: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.     

Influence of polymolecularity on the second virial coefficient of polymers, 2

It is shown that the recently developed scaling theory for the second virial coefficient, A₂, of dilute solutions of polymers with non-uniform molecular weight distributions in a good solvent is able to explain in principle all seemingly contradictory observations reported in the literature, in contrast to all other theories proposed so far.     

Chain length effects in the second virial coefficient of linear polymer molecules

A generalized perturbation theory is presented for the second virial coefficient of linear and branched polymer systems. Results have been computed for linear chains having two to five hundred statistical segments. These are found to differ significantly from the long-chain asymptotic results of Zimm. A semi-empirical modification of the Flory--Orofino theory is also suggested.     

Classical and quantal calculations of the dimerization constant and second virial coefficient for argon

Summary Computations of the second virial coefficient and thermodynamic equilibrium constant for the dimerization of argon are reported. These are based on accurate analytic representations of the Ar-Ar interaction energy. Calculations have been made using classical and quantal statistical mechanics and for the second virial coefficient the JWKB series as well.     

Influence of second virial coefficient and persistence length on dilute solution polymer conformation

The effect of different types of short- and long-range intrachain interactions along the polymeric backbone on the persistence length of a polymer, as well as on other properties such as solvation (characterized by the second virial coefficient), dilute solution conformation, specific refractive index increment, and intrinsic viscosity, were studied using multi-detector size-exclusion chromatography and off-line techniques. The polymers in this study, namely, polystyrene (PS), poly(vinyl chloride) (PVC), and poly(p-vinylbenzyl chloride) (PpVBC), were chosen based on intrachain interactions specific to each, intrachain repulsion in PVC, attraction in PS, and hindered attraction in PpVBC, and also based on a coincidence in molar mass averages and distributions between the polymers. The latter allowed polymeric properties of the three polymers to be compared to each other at the same molar mass and/or degree of polymerization. From the comparisons emerged the effects of intrachain repulsion between consecutive monomers and of the second virial coefficient on chain stiffness and solvation. The increase in the second virial coefficient corresponded to an increase in both polymer solvation and rigidity, while increased intrachain repulsion between consecutive monomers increased polymer solvation while decreasing chain rigidity.

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.     

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.     

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

The segment-cloud model of the second virial coefficient of polymer solutions: effects of chain length and branching

The segment-cloud model for polymer molecules has been used, and the second virial coefficient A₂ obtained as a function of the interaction parameter z for linear and branched chains having different values of n. It is observed that the chain length effect, though much smaller than in the perturbation theory, increases as the degree of branching increases. Also, the branching parameter g is found to be a better correlating parameter than the segment density distribution for A₂. This is in contrast to earlier results for the perturbation theory of the excluded volume.