Comprehensive quantum calculation of the first dielectric virial coefficient of water

We present a complete calculation, fully accounting for quantum effects and for molecular flexibility, of the first dielectric virial coefficient of water and its isotopologues. The contribution of the electronic polarizability is computed from a state-of-the-art intramolecular potential and polarizability surface from the literature, and its small temperature dependence is quantified. The dipolar polarizability is calculated in a similar manner with an accurate literature dipole-moment surface; it differs from the classical result both due to the different molecular geometries sampled at different temperatures and due to the quantization of rotation. We calculate the dipolar contribution independently from spectroscopic information in the HITRAN2020 database and find that the two methods yield consistent results. The resulting first dielectric virial coefficient provides a complete description of the dielectric constant at low density that can be used in humidity metrology and as a boundary condition for new formulations for the static dielectric constant of water and heavy water.

Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

The four-body nonadditive contribution to the energy of four helium atoms is calculated and fitted for all geometries for which the internuclear distances exceed a small minimum value. The interpolation uses an active learning approach based on Gaussian processes. Asymptotic functions are used to calculate the nonadditive energy when the four helium atoms form distinct subclusters. The resulting four-body potential is used to compute the fourth virial coefficient D(T) for helium, at temperatures from 10 to 2000 K, with a path-integral approach that fully accounts for quantum effects. The results are in reasonable agreement with the limited and scattered experimental data for D(T), but our calculated results have much smaller uncertainties.

Entropy scaling of viscosity for molecular models of molten salts

Entropy scaling relates dynamic and thermodynamic properties by reducing the viscosity to a function of only the residual entropy. Molecular simulations are used to investigate the entropy scaling of the viscosity of three models of sodium chloride and five monovalent salts. Even though the correlation between the potential energy and the virial is weak, entropy scaling applies at liquid densities for all models and salts investigated. At lower densities, entropy scaling breaks down due to the formation of ion pairs and chains. Entropy scaling can be used to develop more extendable correlations for the dynamic properties of molten salts.

An Analysis of the Critical Region of Multiparameter Equations of State

In this work, two classes of defects with multiparameter equations of state are investigated. In the first, it is shown that the critical point provided by equation of state developers often does not exactly meet the criticality conditions based on the first two density derivatives of the pressure being zero at the critical point. Based on the more accurate locations of the critical points given in the first part, the scaling of the densities along the binodal and spinodal in the critical region are investigated, and we find that the vast majority of equations have reasonable behavior but a few do not.

Small Corrections to 1989 NIST Constant-Volume Gas Thermometry Data

Constant-volume gas thermometry data published in 1989 for the difference between the thermodynamic temperature and the International Practical Temperature Scale of 1968 are corrected in two ways. A refined estimate of the thermal expansivity of the material of the gas bulb, published in 1990, increases the thermodynamic temperature by amounts on the order of 1 mK to 3 mK. Better knowledge of the nonideality of helium gas reduces the uncertainty of the nonideality correction to near zero and decreases the thermodynamic temperature by amounts on the order of 0.1 mK to 0.5 mK. The net effect is a small increase in the thermodynamic temperature derived from the 1989 experiments. The magnitude of this increase is approximately 2 mK at 505 K, increasing to 3 mK at temperatures near 700 K, and then diminishing to near 0.5 mK at the highest temperature of the measurements (933 K). These corrections are smaller than the uncertainty of the experiments, but may be of significance for future recommendations for the relationship between the thermodynamic temperature and the consensus scale in this temperature range.

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient C_ɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

First-Principles Diffusivity Ratios for Atmospheric Isotope Fractionation on Mars and Titan

Recent work used the kinetic theory of molecular gases, along with state-of-the-art intermolecular potentials, to calculate from first principles the diffusivity ratios necessary for modeling kinetic fractionation of water isotopes in air. Here, we extend that work to the Martian atmosphere, employing potential-energy surfaces for the interaction of water with carbon dioxide and with nitrogen. We also derive diffusivity ratios for methane isotopes in the atmosphere of Titan by using a high-quality potential for the methane-nitrogen pair. The Mars calculations cover 100 K to 400 K, while the Titan calculations cover 50 K to 200 K. Surprisingly, the simple hard-sphere theory that is inaccurate for Earth's atmosphere is in good agreement with the rigorous results for the diffusion of water isotopes in the Martian atmosphere. A modest disagreement with the hard-sphere results is observed for the diffusivity ratio of CH3D in the atmosphere of Titan. We present temperature-dependent correlations, as well as estimates of uncertainty, for the diffusivity ratios involving HDO, H2 17O, and H2 18O in the Martian atmosphere, and for CH3D and 13CH4 in the atmosphere of Titan, providing for the first time the necessary data to be able to model kinetic isotope fractionation in these environments.

Path-integral calculation of the fourth virial coefficient of helium isotopes

We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients D(T) of ⁴He and ³He as functions of temperature from 2.6 K to 2000 K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for ⁴He at the temperatures considered, but for ³He, they are necessary for quantitative accuracy below about 4 K. Our results are consistent with previous theoretical work (also with some of the limited and scattered experimental data) for ⁴He; for ³He, there are no experimental values, and this work provides the first values of D(T) calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures, the uncertainties related to the three-body potential and omitted higher-order contributions become dominant.

What the Thermophysical Property Community Should Know about Temperature Scales

Temperature scales have evolved through many decades in order to more accurately represent the thermodynamic temperature. This creates challenges for those who study thermophysical properties, because the temperatures given for literature data may not correspond to the latest international scale. The resulting differences are small, but not necessarily negligible, especially for reference-quality work. Here, we describe the temperature scales that might be encountered in the literature and give guidance for converting them to the International Temperature Scale of 1990 (ITS-90). We pay special attention to the liquid-helium scales used for cryogenic work, where a potentially confusing number of different scales has been used. Advice is given for avoiding common mistakes in dealing with temperature scales in the context of thermophysical property data, including the responsibility of experimentalists to fully document their reported temperatures and the responsibility of modelers to document their handling of any temperature-scale issues.

Reappraising the appropriate calculation of a common meteorological quantity: Potential Temperature

The potential temperature is a widely used quantity in atmospheric science since it is conserved for dry air's adiabatic changes of state. Its definition involves the specific heat capacity of dry air, which is traditionally assumed as constant. However, the literature provides different values of this allegedly constant parameter, which are reviewed and discussed in this study. Furthermore, we derive the potential temperature for a temperature-dependent parameterisation of the specific heat capacity of dry air, thus providing a new reference potential temperature with a more rigorous basis. This new reference shows different values and vertical gradients, in particular in the stratosphere and above, compared to the potential temperature that assumes constant heat capacity. The application of the new reference potential temperature is discussed for computations of the Brunt-Väisälä frequency, Ertel's potential vorticity, diabatic heating rates, and for the vertical sorting of observational data.

Erratum: Improved First-Principles Calculation of the Third Virial Coeffcient of Helium

[This corrects the article on p. 729 in vol. 116.].

First-Principles Diffusivity Ratios for Kinetic Isotope Fractionation of Water in Air

Kinetic isotope fractionation between water vapor and liquid water or ice depends on the ratio of the diffusivities of the isotopic species in air, but there is disagreement as to the values of these ratios and limited information about their temperature dependence. We use state-of-the-art intermolecular potential-energy surfaces for the water-nitrogen and water-oxygen pairs, along with the kinetic theory of molecular gases, to calculate from first principles the diffusivities of water isotopologues in air. The method has sufficient precision to produce accurate diffusivity ratios. For the HDO/H2O ratio, we find that the often used hard-sphere kinetic theory is significantly in error, and confirm the 1978 experimental result of Merlivat. For the ratios involving 17O and 18O, the simple kinetic theory is relatively close to our more rigorous results. We provide diffusivity ratios from 190 K to 500 K, greatly expanding the range of temperatures for which these ratios are available.

Influence of Isotopologue Dipole Moments on Precision Dielectric-Constant Measurements

Measurements of the relative permittivity (static dielectric constant) of fluids such as methane have been interpreted with the assumption of zero dipole moment. This assumption is not strictly true, due to the presence of isotopologues with small, nonzero dipole moments. We investigate the significance of this effect by analyzing the effect of the dipole of CH₃D on the static dielectric constant of methane. It is found that the isotopologue effect is more than two orders of magnitude smaller than the uncertainty of the best existing measurements. Similar estimates for other compounds such as H₂ and CO₂ produce even smaller effects. Therefore, the interpretation of these measurements with a dipole moment of zero remains valid.

Molecular Calculation of the Critical Parameters of Classical Helium

We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol·L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol·L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible; in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.

The Zero-Density Limit of the Residual Entropy Scaling of Transport Properties

The modified residual entropy scaling approach has been shown to be a successful means of scaling dense phase transport properties. In this work, we investigate the dilute-gas limit of this scaling. This limit is considered for model potentials and highly accurate results from calculations with ab initio pair potentials for small molecules. These results demonstrate that with this approach, the scaled transport properties of noble gases can be collapsed without any empirical parameters to nearly their mutual uncertainties and that the scaled transport properties of polyatomic molecules are qualitatively similar, and for sufficiently high temperatures they agree with "universal" values proposed by Rosenfeld in 1999. There are significant quantitative differences between the model potentials and real fluids in these scaled coordinates, but this study provides a thorough coverage of model fluids and simple real fluids, providing the basis for further study. In the supporting information we provide the collected calculations with ab initio pair potentials from the literature, as well as code in the Python language implementing all aspects of our analysis.

Anomaly in the Virial Expansion of IAPWS-95 at Low Temperatures

In the standard reference equation of state for the thermodynamic properties of water, known as IAPWS-95, the fourth virial coefficient D(T) becomes abnormally large in magnitude at temperatures below approximately 300 K. At conditions where a virial expansion using only second and third virial coefficients should be essentially exact (such as vapors at pressures near 100 Pa or 1000 Pa), such a truncated expansion may miss on the order of 2 % of the deviation from ideal-gas behavior in the compressibility factor or the fugacity. The term in IAPWS-95 that causes this issue is identified, and suggestions are made for future equation-of-state development.

Measured relationship between thermodynamic pressure and refractivity for six candidate gases in laser barometry

Laser refractometers are approaching accuracy levels where gas pressures in the range 1 Pa < p < 1 MPa inferred by measurements of gas refractivity at a known temperature will be competitive with the best existing pressure standards and sensors. Here, the authors develop the relationship between pressure and refractivity p = c 1 ⋅ ( n - 1 ) + c 2 ⋅ ( n - 1 ) 2 + c 3 ⋅ ( n - 1 ) 3 + ⋯ , via measurement at T = 293.1529(13) K and λ = 632.9908(2) nm for p ≤ 500 kPa. The authors give values of the coefficients c 1, c 2, c 3 for six gases: Ne, Ar, Xe, N2, CO2, and N2O. For each gas, the resulting molar polarizabilityA R ≡ 2 R T 3 c 1 has a standard uncertainty within 16 × 10-6·A R . In these experiments, pressure was realized via measurements of helium refractivity at a known temperature: for He, the relationship between pressure and refractivity is known through calculation much more accurately than it can presently be measured. This feature allowed them to calibrate a pressure transducer in situ with helium and subsequently use the transducer to accurately gage the relationship between pressure and refractivity on an isotherm for other gases of interest.

Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials

Path-Integral Monte Carlo methods were applied to calculate the second, B(T), and the third, C(T), virial coefficients for water. A fully quantum approach and state-of-the-art flexible-monomer pair and three-body potentials were used. Flexible-monomer potentials allow calculations for any isotopologue; we performed calculations for both H2O and D2O. For B(T) of H2O, the quantum effect contributes 25% of the value at 300 K and is not entirely negligible even at 1000 K, in accordance with recent literature findings. The effect of monomer flexibility, while not as large as some claims in the literature, is significant compared to the experimental uncertainty. It is of opposite sign to the quantum effect, smaller in magnitude than the latter below 500 K, and varies from 2% at 300 K to 10% at 700 K. When monomer flexibility is accounted for, results from the CCpol-8sf pair potential are in excellent agreement with the available experimental data and provide reliable B(T) values at temperatures outside the range of experimental data. The flexible-monomer MB-pol pair potential yields B(T) values that are slightly too high compared to experiment. For C(T), our calculations confirm earlier findings that the use of three-body potential is necessary for meaningful predictions. However, due to various uncertainties of the potentials used, especially the three-body ones, we were not able to establish benchmark values of C(T), although our results are in qualitative agreement with available experimental data. The quantum effect, never before included for water, reduces the magnitude of the classical value for H2O by a factor of 2.5 at 300 K and is not entirely negligible even at 1000 K.

Candidates to Replace R-12 as a Radiator Gas in Cherenkov Detectors

Dichlorodifluoromethane (R-12) has been widely used as a radiator gas in pressure threshold Cherenkov detectors for high-energy particle physics. However, that compound is becoming unavailable due to the Montreal Protocol. To find a replacement with suitably high refractive index, we use a combination of theory and experiment to examine the polarizability and refractivity of several non-ozone-depleting compounds. Our measurements show that the fourth-generation refrigerants R-1234yf (2,3,3,3-tetrafluoropropene) and R-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) have sufficient refractivity to replace R-12 in this application. If the slight flammability of these compounds is a problem, two nonflammable alternatives are R-218 (octafluoropropane), which has a high Global Warming Potential, and R-13I1 (trifluoroiodomethane), which has low Ozone Depletion Potential and Global Warming Potential but may not be sufficiently inert.

Accuracy of Approximations to the Poynting Correction for Ice and Liquid Water

Rigorous calculation of the Poynting correction, which describes the effect of pressure on the fugacity of a condensed phase, requires time-consuming evaluation of a thermodynamic potential such as the International Association for the Properties of Water and Steam (IAPWS-95) formulation for water. Simplifying approximations are used in many applications, but the error introduced by the approximations is seldom evaluated. In this work, first-order and second-order approximations were developed for the Poynting correction for both ice and liquid water (including supercooled liquid water), and their errors were evaluated by comparison to the full thermodynamic potentials. The range of conditions covered is from -100 °C to 200 °C at pressures to 20 MPa. Some implications for the calculation of the enhancement factor used in humidity metrology are discussed.

Correlations for the Dielectric Constants of H2S, SO2, and SF6

A new method is developed for correlating the static dielectric constant of polar fluids over wide ranges of conditions where few experimental data exist. Molecular dynamics simulations are used to establish the temperature and density dependence of the Kirkwood g-factor, and also the functional form for the increase of the effective dipole moment with density. Most parameters in the model are obtained entirely from simulation; a single proportionality constant is adjusted to obtain agreement with the limited experimental data. The method is applied to hydrogen sulfide (H₂S) and sulfur dioxide (SO₂), both of which are important in geochemistry but have only a few dielectric data available. The resulting correlations agree well with the available liquid data, obey physical boundary conditions at low density and at high temperature, and interpolate in density and temperature in a physically reasonable manner. In addition, we present a more conventional correlation for the dielectric constant of sulfur hexafluoride, SF₆, where more data are available.

All-dimensional H2-CO potential: Validation with fully quantum second virial coefficients

We use a new high-accuracy all-dimensional potential to compute the cross second virial coefficient B₁₂(T) between molecular hydrogen and carbon monoxide. The path-integral method is used to fully account for quantum effects. Values are calculated from 10 K to 2000 K and the uncertainty of the potential is propagated into uncertainties of B₁₂. Our calculated B₁₂(T) are in excellent agreement with most of the limited experimental data available, but cover a much wider range of temperatures and have lower uncertainties. Similar to recently reported findings from scattering calculations, we find that the reduced-dimensionality potential obtained by averaging over the rovibrational motion of the monomers gives results that are a good approximation to those obtained when flexibility is fully taken into account. Also, the four-dimensional approximation with monomers taken at their vibrationally averaged bond lengths works well. This finding is important, since full-dimensional potentials are difficult to develop even for triatomic monomers and are not currently possible to obtain for larger molecules. Likewise, most types of accurate quantum mechanical calculations, e.g., spectral or scattering, are severely limited in the number of dimensions that can be handled.

Metrological challenges for measurements of key climatological observables, Part 4: Atmospheric relative humidity

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest "greenhouse" gas, and non-equilibrium relative humidity at the air-sea interface drives evaporation and latent heat export from the ocean. In this paper, we examine the climatologically relevant atmospheric relative humidity, noting fundamental deficiencies in the definition of this key observable. The metrological history of this quantity is reviewed, problems with its current definition and measurement practice are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, (BIPM), in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organisations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for this long standing metrological problem, such as are suggested here.

Metrological challenges for measurements of key climatological observables: Oceanic salinity and pH, and atmospheric humidity. Part 1: Overview

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest "greenhouse" gas, and non-equilibrium relative humidity at the air-sea interface drives evaporation and latent heat export from the ocean. On climatic time scales, melting ice caps and regional deviations of the hydrological cycle result in changes of seawater salinity, which in turn may modify the global circulation of the oceans and their ability to store heat and to buffer anthropogenically produced carbon dioxide. In this paper, together with three companion articles, we examine the climatologically relevant quantities ocean salinity, seawater pH and atmospheric relative humidity, noting fundamental deficiencies in the definitions of those key observables, and their lack of secure foundation on the International System of Units, the SI. The metrological histories of those three quantities are reviewed, problems with their current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, BIPM, in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organisations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems in climatology.

Impact of change of knee prosthesis on early clinical outcomes in a large volume arthroplasty centre

Introduction

The aim of our study was to investigate the effect of changing the default knee prosthesis in a high volume dedicated arthroplasty unit from DePuy’s PFC® Sigma® to Smith & Nephew’s Genesis™ II.

Methods

A retrospective analysis was performed of prospective data on primary total knee replacements (TKRs) from January 2009 until December 2011. This provided information on the operative time, length of stay, pain at mobilisation, radiography analysis, any complications, and readmission at 30 and 60 days.

Results

The total numbers of primary TKRs using the PFC® and Genesis™ II prostheses were 1,061 and 1,268 respectively. The results showed a slight increase (maximum of five minutes) in the operative time for all the surgeons except one surgeon, whose operative time reduced by an average of seven minutes. There was no significant adverse outcome after the change in the knee implant. There was no clinically significant increase in the length of stay, pain at mobilisation or complication rates. There was a twofold increase in the wastage of the implant in the Genesis™ II group in the initial learning period.

Conclusions

Through a competitive process of implant tendering, we have successfully introduced a new implant into a large elective orthopaedic unit. This has resulted in significant financial savings without adversely affecting our clinical practice or patient outcome.

Impact of change of knee prosthesis on early clinical outcomes in a large volume arthroplasty centre

INTRODUCTION

The aim of our study was to investigate the effect of changing the default knee prosthesis in a high volume dedicated arthroplasty unit from DePuy's PFC(®) Sigma(®) to Smith & Nephew's Genesis™ II.

METHODS

A retrospective analysis was performed of prospective data on primary total knee replacements (TKRs) from January 2009 until December 2011. This provided information on the operative time, length of stay, pain at mobilisation, radiography analysis, any complications, and readmission at 30 and 60 days.

RESULTS

The total numbers of primary TKRs using the PFC(®) and Genesis™ II prostheses were 1,061 and 1,268 respectively. The results showed a slight increase (maximum of five minutes) in the operative time for all the surgeons except one surgeon, whose operative time reduced by an average of seven minutes. There was no significant adverse outcome after the change in the knee implant. There was no clinically significant increase in the length of stay, pain at mobilisation or complication rates. There was a twofold increase in the wastage of the implant in the Genesis™ II group in the initial learning period.

CONCLUSIONS

Through a competitive process of implant tendering, we have successfully introduced a new implant into a large elective orthopaedic unit. This has resulted in significant financial savings without adversely affecting our clinical practice or patient outcome.

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

A seven-dimensional potential energy surface is calculated for the interaction of water and carbon monoxide using second-order Moller-Plesset theory, coupled-cluster theory, and extrapolated intermolecular perturbation theory. The effects of stretching the CO molecule and bending the water molecule are included. The minimum energy structure of the water-CO dimer changes from an H-C hydrogen bond to an H-O hydrogen bond when the CO bond length increases by less than 10 pm from its equilibrium value. Second virial coefficients for the water-CO interaction are calculated for a wide range of temperatures and compared with the limited experimental data. Allowing the CO bond length and water bond angle to vary has little effect on the second virial coefficients.

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.

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.

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.

Intermolecular potential and second virial coefficient of the water–hydrogen complex

We construct a rigid-body (five-dimensional) potential-energy surface for the water-hydrogen complex using scaled perturbation theory (SPT). An analytic fit of this surface is obtained, and, using this, two minima are found. The global minimum has C2v symmetry, with the hydrogen molecule acting as a proton donor to the oxygen atom on water. A local minimum with Cs symmetry has the hydrogen molecule acting as a proton acceptor to one of the hydrogen atoms on water, where the OH bond and H2 are in a T-shaped configuration. The SPT global minimum is bound by 1097 microEh (Eh approximately 4.359744 x 10(-18) J). Our best estimate of the binding energy, from a complete basis set extrapolation of coupled-cluster calculations, is 1076.1 microEh. The fitted surface is used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). Three complementary methods are used to quantify quantum statistical mechanical effects that become significant at low temperatures. We compare our results with experimental data, which are available over a smaller temperature range (230-700 K). Generally good agreement is found, but the experimental data are subject to larger uncertainties.