Ab initiopotential energy surface for the nitrogen molecule pair and thermophysical properties of nitrogen gas

Toward the realization of a primary low-pressure standard using a superconducting microwave resonator

We describe a primary gas pressure standard based on the measurement of the refractive index of helium gas using a microwave resonant cavity in the range between 500 Pa and 20 kPa. To operate in this range, the sensitivity of the microwave refractive gas manometer (MRGM) to low-pressure variations is substantially enhanced by a niobium coating of the resonator surface, which becomes superconducting at temperatures below 9 K, allowing one to achieve a frequency resolution of about 0.3 Hz at 5.2 GHz, corresponding to a pressure resolution below 3 mPa at 20 Pa. The determination of helium pressure requires precise thermometry but is favored by the remarkable accuracy achieved by ab initio calculations of the thermodynamic and electromagnetic properties of the gas. The overall standard uncertainty of the MRGM is estimated to be of the order of 0.04%, corresponding to 0.2 Pa at 500 and 8.1 Pa at 20 kPa, with major contributions from thermometry and the repeatability of microwave frequency measurements. A direct comparison of the pressures realized by the MRGM with the reference provided by a traceable quartz transducer shows relative pressure differences between 0.025% at 20 kPa and -1.4% at 500 Pa.

The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids

The NIST REFPROP software program is a powerful tool for calculating thermophysical properties of industrially important fluids, and this manuscript describes the models implemented in, and features of, this software. REFPROP implements the most accurate models available for selected pure fluids and their mixtures that are valid over the entire fluid range including gas, liquid, and supercritical states, with the goal of uncertainties approaching the level of the underlying experimental data. The equations of state for thermodynamic properties are primarily of the Helmholtz energy form; a variety of models are implemented for the transport properties. We document the models for the 147 fluids included in the current version. A graphical user interface generates tables and provides extensive plotting capabilities. Properties can also be accessed through third-party apps or user-written code via the core property subroutines compiled into a shared library. REFPROP disseminates international standards in both the natural gas and refrigeration industries, as well as standards for water/steam.

Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular Potentials

The second to eighth virial coefficients of methane were determined for temperatures up to 1200 K using an existing ab initio-based and empirically fine-tuned two-body potential combined with a new empirical nonadditive three-body potential. Nuclear quantum effects were accounted for by the semiclassical Feynman-Hibbs approach. The numerical evaluation of the high-dimensional integrals through which the virial coefficients are expressed was performed employing the Mayer-sampling Monte Carlo technique. By fitting suitable mathematical functions to the calculated virial coefficients, an analytical eighth-order virial equation of state (VEOS8) was obtained. Pressures p computed as a function of temperature T and density ρ using VEOS8 agree highly satisfactorily with p(ρ, T) values obtained with the experimentally based reference equation of state for methane of Setzmann and Wagner (SWEOS) at state points at which VEOS8 is sufficiently converged. It is shown that it is essential to account for nonadditive three-body interactions in the calculations in order to achieve good agreement with the SWEOS.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor-liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Frenkel Line in Nitrogen Terminates at the Triple Point

Recent studies on supercritical nitrogen revealed clear changes in structural markers and dynamical properties when the coordination number approaches its maximum value. The line in P and T space where these changes occur is referred to as the Frenkel line. Here, we qualitatively reproduce such changes in the supercritical regime using the popular "optimized potential for liquid simulation" (OPLS) classical force field for molecular dynamics. Unfortunately, at 160 K, OPLS nitrogen predicts sublimation rather than producing a liquid phase; therefore, we developed our own force field to achieve quantitative agreement with experimental data. We confirm the asymptotic behavior of the coordination number on crossing the Frenkel line and note an associated change in the diffusion constant, consistent with the non-rigid to rigid liquid-like character of the "transition". The simulations allow us to track the Frenkel line to subcritical temperatures and demonstrate that it terminates at the triple point. This establishes the experimentally measurable changes, which could unequivocally determine the Frenkel line in other systems.

Evaluation of Osmotic Virial Coefficients via Restricted Gibbs Ensemble Simulations, with Support from Gas-Phase Mixture Coefficients

We present a method for computing osmotic virial coefficients in explicit solvent via simulation in a restricted Gibbs ensemble. Two equivalent phases are simulated at once, each in a separate box at constant volume and temperature and each in equilibrium with a solvent reservoir. For osmotic coefficient BN, a total of N solutes are individually exchanged back and forth between the boxes, and the average distribution of solute numbers between the boxes provides the key information needed to compute BN. Separately, expressions are developed for BN as a series in solvent reservoir density ρ₁, with the coefficients of the series expressed in terms of the usual gas-phase mixture coefficients B_ij. Normally, the B_ij are defined for an infinite volume, but we suggest that the observed dependence of B_ij on system size L can be used to estimate L dependence of the BN, allowing them to be computed accurately at L → ∞ while simulating much smaller system sizes than otherwise possible. The methods for N = 2 and 3 are demonstrated for two-component mixtures of size-asymmetric additive hard spheres. The proposed methods are demonstrated to have greater precision than established techniques, for a given amount of computational effort. The ρ₁ series for BN when applied by itself is (for this noncondensing model) found to be the most efficient in computing accurate osmotic coefficients for the solvent densities considered here.

Next-Generation Accurate, Transferable, and Polarizable Potentials for Material Simulations

PHAHST (potentials with high accuracy, high speed, and transferability) intermolecular potential energy functions have been developed from first principles for H₂, N₂, the noble gases, and a metal-organic material, HKUST-1. The potentials are designed from the outset to be transferable to heterogeneous environments including porous materials, interfaces, and material simulations. This is accomplished by theoretically justified choices for all functional forms, parameters, and mixing rules, including explicit polarization in every environment and fitting to high quality electronic structure calculations using methods that are tractable for real systems. The models have been validated in neat systems by comparison to second virial coefficients and bulk pressure-density isotherms. For inhomogeneous applications, our main target, comparisons are presented to previously published experimental studies on the metal-organic material HKUST-1 including adsorption, isosteric heats of adsorption, binding site locations, and binding site energies. A systematic prescription is provided for developing compatible potentials for additional small molecules and materials. The resulting models are recommended for use in complex heterogeneous simulations where existing potentials may be inadequate.

Effective hardness of interaction from thermodynamics and viscosity in dilute gases

The hardness of the effective inverse power law (IPL) potential, which can be obtained from thermodynamics or collision integrals, can be used to demonstrate similarities between thermodynamic and transport properties. This link is investigated for systems of increasing complexity (i.e., the EXP, square-well, Lennard-Jones, and Stockmayer potentials; ab initio results for small molecules; and rigid linear chains of Lennard-Jones sites). These results show that while the two approaches do not yield precisely the same values of effective IPL exponent, their qualitative behavior is intriguingly similar, offering a new way of understanding the effective interactions between molecules, especially at high temperatures. In both approaches, the effective hardness is obtained from a double-logarithmic temperature derivative of an effective area.

The effect of weak intermolecular interactions on the nuclear magnetic resonance shielding constant in N2

Ab initio calculations are applied to examine the influence of the intermolecular interactions on the shielding constant in gaseous nitrogen. An accurate literature potential energy surface and the nuclear magnetic resonance shielding surface of the N₂ -N₂ complex calculated in this work provide results in satisfactory agreement with the available experimental estimates of the effect.

Inelastic rate coefficients based on an improved potential energy surface for N2 + N2 collisions in a wide temperature range

Vibration-to-translation and vibration-to-vibration rate coefficients for N₂–N₂ inelastic scattering are calculated on an improved potential including high temperature regimes.

Entropy Scaling of Viscosity - I: A Case Study of Propane

In this work, a broadly-applicable and simple approach for building high accuracy viscosity correlations is demonstrated for propane. The approach is based on the combination of a number of recent insights related to the use of residual entropy scaling, especially a new way of scaling the viscosity for consistency with the dilute-gas limit. With three adjustable parameters in the dense phase, the primary viscosity data for propane are predicted with a mean absolute relative deviation of 1.38%, and 95% of the primary data are predicted within a relative error band of less than 5%. The dimensionality of the dense-phase contribution is reduced from the conventional two dimensional approach (temperature and density) to a one-dimensional correlation with residual entropy as the independent variable. The simplicity of the model formulation ensures smooth extrapolation behavior (barring errors in the equation of state itself). The approach proposed here should be applicable to a wide range of chemical species. The supporting information includes the relevant data in tabular form and a Python implementation of the model.

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.

Thermophysical Properties of Gaseous H2S–N2 Mixtures from First-Principles Calculations

The cross second virial coefficient and three dilute gas transport properties (shear viscosity, thermal conductivity, and binary diffusion coefficient) of mixtures of hydrogen sulfide (H2S) and nitrogen (N2) were determined with high accuracy at temperatures up to 1200 K using statistical thermodynamics and the kinetic theory of molecular gases, respectively. The required intermolecular potential energy surface (PES) for the H2S–N2 interaction is presented in this work, while the H2S–H2S and N2–N2 PESs were reported previously. All three PESs are based on high-level quantum-chemical ab initio (i.e. first-principles) calculations. There is only very limited experimental information available on the second virial coefficients of H2S–N2 mixtures, and there appear to be no experimental data at all for the transport properties. Thus, the present predictions constitute a substantial increase in our knowledge of the thermophysical properties of this system, which are of practical relevance for modeling sour natural gas.

Intermolecular potential energy surface and thermophysical properties of propane

A six-dimensional potential energy surface (PES) for the interaction of two rigid propane molecules was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations level of theory for 9452 configurations. An analytical site-site potential function with 14 sites per molecule was fitted to the calculated interaction energies. To validate the analytical PES, the second virial coefficient and the dilute gas shear viscosity and thermal conductivity of propane were computed. The dispersion part of the potential function was slightly adjusted such that quantitative agreement with the most accurate experimental data for the second virial coefficient at room temperature was achieved. The adjusted PES yields values for the three properties that are in very good agreement with the best experimental data at all temperatures.

Reference Correlation for the Viscosity of Carbon Dioxide

A comprehensive database of experimental and computed data for the viscosity of carbon dioxide (CO2) was compiled and a new reference correlation was developed. Literature results based on an ab initio potential energy surface were the foundation of the correlation of the viscosity in the limit of zero density in the temperature range from 100 K to 2000 K. Guided symbolic regression was employed to obtain a new functional form that extrapolates correctly to T → 0 K and to 10 000 K. Coordinated measurements at low density made it possible to implement the temperature dependence of the Rainwater-Friend theory in the linear-in-density viscosity term. The residual viscosity could be formulated with a scaling term ργ /T the significance of which was confirmed by symbolic regression. The final viscosity correlation covers temperatures from 100 K to 2000 K for gaseous CO2, and from 220 K to 700 K with pressures along the melting line up to 8000 MPa for compressed and supercritical liquid states. The data representation is more accurate than with the previous correlations, and the covered pressure and temperature range is significantly extended. The critical enhancement of the viscosity of CO2 is included in the new correlation.

Calculation of the thermal conductivity of low-density CH4-N2 gas mixtures using an improved kinetic theory approach

The thermal conductivity of low-density CH4-N2 gas mixtures has been calculated by means of the classical trajectory method using state-of-the-art intermolecular potential energy surfaces for the CH4-CH4, N2-N2, and CH4-N2 interactions. Results are reported in the temperature range from 70 K to 1200 K. Since the thermal conductivity is influenced by the vibrational degrees of freedom of the molecules, which are not included in the rigid-rotor classical trajectory computations, a new correction scheme to account for vibrational degrees of freedom in a dilute gas mixture is presented. The calculations show that the vibrational contribution at the highest temperature studied amounts to 46% of the total thermal conductivity of an equimolar mixture compared to 13% for pure nitrogen and 58% for pure methane. The agreement with the available experimental thermal conductivity data at room temperature is good, within ±1.4%, whereas at higher temperatures, larger deviations up to 4.5% are observed, which can be tentatively attributed to deteriorating performance of the measuring technique employed. Results are also reported for the magnitude and temperature dependence of the rotational collision number, Z(rot), for CH4 relaxing in collisions with N2 and for N2 relaxing in collisions with CH4. Both collision numbers increase with temperature, with the former being consistently about twice the value of the latter.

Influence of a magnetic field on the viscosity of a dilute gas consisting of linear molecules

The viscomagnetic effect for two linear molecules, N2 and CO2, has been calculated in the dilute-gas limit directly from the most accurate ab initio intermolecular potential energy surfaces presently available. The calculations were performed by means of the classical trajectory method in the temperature range from 70 K to 3000 K for N2 and 100 K to 2000 K for CO2, and agreement with the available experimental data is exceptionally good. Above room temperature, where no experimental data are available, the calculations provide the first quantitative information on the magnitude and the behavior of the viscomagnetic effect for these gases. In the presence of a magnetic field, the viscosities of nitrogen and carbon dioxide decrease by at most 0.3% and 0.7%, respectively. The results demonstrate that the viscomagnetic effect is dominated by the contribution of the jj¯ polarization at all temperatures, which shows that the alignment of the rotational axes of the molecules in the presence of a magnetic field is primarily responsible for the viscomagnetic effect.

A high-level ab initio study of the N2 + N2 reaction channel

A new six-dimensional (6D) global potential energy surface (PES) is proposed for the full range description of the interaction of the N2(1Σg+)+N2(1Σg+) system governing collisional processes, including N atom exchange. The related potential energy values were determined using high-level ab initio methods. The calculations were performed at a coupled-cluster with single and double and perturbative triple excitations level of theory in order to have a first full range picture of the PES. Subsequently, in order to accurately describe the stretching of the bonds of the two interacting N2 molecules by releasing the constraints of being considered as rigid rotors, for the same molecular geometries higher level of theory multi reference calculations were performed. Out of the calculated values a 6D 4-atoms global PES was produced for use in dynamical calculations. The ab initio calculations were made possible by the combined use of High Throughput Computing and High Performance Computing techniques within the frame of a computing grid empowered molecular simulator.