Density dependence of electric properties of binary mixtures of inert gases

A computational study of the density dependence of the refractivity and dielectric constants, the electric-field induced second harmonic generation (ESHG) hyperpolarizabilities and of the Kerr constants of binary mixtures of helium, neon and argon is presented. Potentials and interaction properties of the homonuclear A₂ and heteronuclear AB dimers (A,?B=He, Ne, Ar) are taken from a previous study [J. López Cacheiro, B. Fernández, D. Marchesan, S. Coriani, C. Hättig, A. Rizzo. Molec. Phys., 102, 101 (2004)]. Dispersion coefficients for the second virial coefficients allow for the determination of the density dependence at any frequency far from the lowest resonance. Fully quantum mechanical results are presented and a comparison with the corresponding classical estimates is discussed. Deep minima are predicted to occur in the ESHG second virial coefficient curve drawn as a function of the molar fraction of one of the components in binary mixtures of He/Ar and Ne/Ar. This phenomenon, observed over a wide range of temperatures, should be easily verifiable experimentally.     

Coupled cluster calculations of the ground state potential and interaction induced electric properties of the mixed dimers of helium,neon and argon

Using augmented polarized correlation consistent basis sets extended with midbond functions, we evaluate the ground state interaction potential and the induced electric dipole polarizabilities and first and second hyperpolarizabilities of the He–Ar, Ne–Ar and He–Ne van der Waals complexes. For the calculation of the potential we resort to the coupled cluster singles and doubles (CCSD) model corrected for triple excitations, CCSD(T), whereas properties are evaluated with CCSD response theory. As a check of the quality of the potential, the rovibrational spectrum and the gas second virial coefficients are evaluated. The rovibrational spectra improve previously available theoretical results, although the dissociation energies are probably still slightly underestimated. For the gas second virial coefficients the agreement with experiment is satisfactory. The frequency dependence of the interaction (hyper)polarizabilities is analysed and a comparison with previous results on the mixed dimers and the pure gases is made.     

Density dependence of the electric-field-gradient induced birefringence of the helium,neon and argon gases

An ab initio investigation of the density dependence of the electric-field-gradient induced birefringence (EFGB) for the noble gases helium, neon and argon is presented. To determine the second coefficient in the virial expansion of the molecular EFGB constant _mQ, the effect of two-body interactions has been studied by computing the internuclear dependence of the molecular quadrupole moment and of the dipole-dipole-quadrupole and dipole-magnetic dipole-dipole hyperpolarizabilities of the van der Waals dimers. A full-configuration-interaction approach as well as the coupled cluster singles and doubles and the coupled cluster singles and doubles plus perturbative triples approximations have been adopted, and extended basis sets including midbond functions have been employed. A semi-classical integration yields the virial coefficients. The effect of density for standard experimental conditions is found to be of the order of a few tens of parts per million for helium and neon, and of the order of a few parts per thousands for argon at low temperatures, and thus not detectable with present apparatus.     

Atomic interactions in neon and helium

The first two quantum corrections to the second virial coefficients of the Smith-Thakkar potential are calculated. Parameters for neon and helium, gases in which quantum effects are important, are then determined by fitting to semiempirical dispersion coefficients and experimental second virial coefficients. Viscosity coefficients for both gases and vibrational energy level spacings for the neon dimer are calculated as independent tests of the potentials. Overall agreement with experiment is excellent for neon and moderate for helium. The previously determined parameters for argon are found to be only very slightly perturbed by the inclusion of quantum corrections in the calculated second virial coefficients.     

Editorial

Using coupled cluster singles and doubles linear response theory and the d-aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions, the interaction induced electric dipole polarisability surface of the CO–Ar van der Waals complex is computed. Combining this surface with accurate intermolecular potential energy and electric dipole surfaces, the pressure and dielectric second virial coefficients of the complex are calculated by a classical statistical approach. Excellent agreement with experimental results (to within the experimental error bars) is obtained for the pressure second virial coefficient over a range of temperatures. No previous experimental or theoretical investigations have been carried out for the dielectric second virial coefficient, B _ε(T), which is estimated to be about 1.9 cm⁶ mol^??1 at room temperature. This value results from a balance of terms due to the interaction induced electric dipole polarisability (predominant at high temperatures) and orientational electric dipole contributions.     

Accurate second Kerr virial coefficient of rare gases from the state-of-the-art ab initio potentials and (hyper)polarizabilities

The second Kerr virial coefficient of rare gases is studied in this work using the best ab initio potentials and (hyper)polarizabilities in the literature. The second Kerr virial coefficient of helium-4, helium-3, neon, argon, and krypton and its polarizability component of xenon are computed by the semi-classical method together with the Padé approximant over a wide temperature range. In addition, the uncertainty of second Kerr virial coefficient is estimated from the uncertainties of the ab initio interaction-induced properties. The experimental and theoretical data in the literature is compared with our calculated values to examine the quality of this work. It is shown that our computed values in the supplementary materials are as accurate as the literature data at medium and high temperatures and are more reliable at low temperatures.     

Effect of collisions on the resonance vibrational polarizability of gaseous SF<Subscript>6</Subscript> and CF<Subscript>4</Subscript> molecules

The density dependences of the absorption cross sections and refractivity are experimentally studied for the SF₆ and CF₄ molecules in pure gases in the region of their ν₃ infrared vibrational-rotational antisymmetric modes. The dispersions of the refractive index are determined for both compounds by the Kramers-Kronig transformation of the spectral data obtained, and, for the SF₆ isotopomers, they are also measured by the method of two-color interferometry. Strong nonlinear dependences of optical parameters and their dispersions on the gas density are observed. The values of second optical virial coefficient B _R (ν) obtained for pure SF₆ are more than an order of magnitude greater than the values found earlier for mixtures of SF₆ with buffer rare gases. The results of calculations of the second virial coefficients of the absorption cross section and refractivity in terms of the DID model of interacting dipoles are in agreement with the experimental data in the band wings. Correlations between the behavior of the spectral dependence of functions B _R (ν) and the parameters of model intermolecular potentials used in the calculations are found.     

Density expansion of the magnetic susceptibility

The pressure of a system may be expanded as a power series in the density, whose coefficients are the virial coefficients. In this paper, the magnetic susceptibility of a $\text{spin}\text{-}\text{1}\text{2}$ fermion system is also expanded in powers of density. This process explicitly separates the temperature and density dependence of the magnetic susceptibility. The coefficients of this series are shown to be related to certain virial coefficients. The first (previously established) and second corrections to Curie's law are explicitly expressed in terms of second and third virial coefficients. These corrections to Curie's law are small for temperatures above 4K, but become important below that temperature. The first correction has been previously measured. Given a set of second and third virial coefficients, the importance of the second correction can be calculated immediately at any density of interest.     

Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ⁴, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ³, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.     

Collision-induced vibrational polarizability and mixed second refractivity virial coefficients B ab R: an experimental study of the SF6—rare gas mixtures

Mixed second refractivity virial coefficients B ^ab _R (ω) are determined in the infrared spectral range from the analysis of the buffer gas-induced intensity redistribution in the ν₃ absorption band at ω ? 930 cm^?1 of ³⁴SF₆ perturbed by the rare gases Ar, Kr, and Xe at relative densities up to 140 Amagat. The values of the refractivity virial coefficients are found to be several orders of magnitude greater than those observed in the spectral regions far removed from single-photon resonances. The undamped dynamic dipole—induced-dipole (DID) model is shown to qualitatively correctly reproduce the observed unusual dispersion of the B ^ab _R (ω) functions. A new estimate of the integrated band intensity S(ν₃) of SF₆ is also obtained.     

Ab initio intermolecular potential energy surface of Ne···NCCN van der Waals complex: effect of the place of midbond function on the interaction

The intermolecular potential energy surface of Ne···NCCN van der Waals complex was evaluated in the framework of the counterpoise-corrected supermolecular approach using CCSD(T) level and aug-cc-pVDZ basis set extended with a set of midbond (3s3p2d1f1g) functions. The effect of the place of midbond function on the accuracy of the calculated potential energy surface was examined and the optimised position for placing midbond function was determined. The calculated potential energy surface was fitted by an analytical function. The analytical function of intermolecular potential energy surface of Ne···NCCN demonstrated a global minimum energy of ?12.024 meV related to the T-shape geometry at the distance between Ne and the centre of mass of NCCN of 3.28 Å. Finally, the interaction second virial coefficients (B₁₂) of Ne and NCCN were calculated and used to calculate the second virial coefficients for the mixture of neon and cyanogen gases at different mole fractions of Ne gas.     

Reconstruction of the potential of an intermolecular interaction on the basis of the virial coefficients

Some formulations of the problem of reconstructing the potential of the two-body interaction from the temperature dependence of the second virial coefficient are considered. For three-parameter potential models (Morse and Kihara) the formalism of the Fisher matrix is used to calculate the coefficients of the amplification of the errors in the determination of each of the parameters. For the general case of the nonparametric approach a scheme of formal linearization of the problem is given and conditions for unique solution of it found. The example of the reconstruction of the potential of Maxwellian molecules is given. Some new possibilities are noted for the unique reconstruction on the basis of the temperature dependences of the transport coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 30–33, June, 1980.     

Interpolation of virial coefficients

The paper presents a method for interpolation of the temperature dependence of the coefficients appearing in the virial equation of state. Regression of available data for a virial coefficient at high and low temperatures is used to formulate an approximant that captures the order-of-magnitude behaviour in these extremes. This behaviour is factored out of the data, and the resulting residual is subject to spline interpolation. The value of the virial coefficient at an interpolated temperature is recovered by multiplying by the approximant evaluated at the temperature of interest. The scheme is demonstrated through application to virial data for several model systems, and is shown to provide much more reliable results than direct interpolation performed on the unscaled virial-coefficient data.     

Ab initio potential energy curve for the neon atom pair and thermophysical properties for the dilute neon gas. II. Thermophysical properties for low-density neon

A neon–neon interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation (R. Hellmann, E. Bich, and E. Vogel, Molec. Phys. 106, 133 (2008)) was used in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of neon governed by two-body and three-body interactions. The second and third pressure virial coefficients as well as the viscosity and thermal conductivity coefficients, the last two in the so-called limit of zero density, were calculated for natural Ne from 25 to 10,000 K. Comparison of the calculated viscosity and thermal conductivity with the most accurate experimental data at ambient temperature shows that these values are accurate enough to be applied as standard values for the complete temperature range of the calculations characterized by an uncertainty of about ±0.1% except at the lowest temperatures.     

Critical temperature of infinitely long chains from Wertheim's perturbation theory

Wertheim's theory is used to determine the critical properties of chains formed by m tangent spheres interacting through the pair potential u(r). It is shown that within Wertheim's theory the critical temperature and compressibility factor reach a finite non-zero value for infinitely long chains, whereas the critical density and pressure vanish as m ^-1.5. Analysing the zero density limit of Wertheim's equation or state for chains it is found that the critical temperature of the infinitely long chain can be obtained by solving a simple equation which involves the second virial coefficient of the reference monomer fluid and the second virial coefficient between a monomer and a dimer. According to Wertheim's theory, the critical temperature of an infinitely long chain (i.e. the Θ temperature) corresponds to the temperature where the second virial coefficient of the monomer is equal to 2/3 of the second virial coefficient between a monomer and dimer. This is a simple and useful result. By computing the second virial coefficient of the monomer and that between a monomer and a dimer, we have determined the Θ temperature that follows from Wertheim's theory for several kinds of chains. In particular, we have evaluated Θ for chains made up of monomer units interacting through the Lennard-Jones potential, the square well potential and the Yukawa potential. For the square well potential, the Θ temperature that follows from Wertheim's theory is given by a simple analytical expression. It is found that the ratio of Θ to the Boyle and critical temperatures of the monomer decreases with the range of the potential.     

Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids

Mayer-sampling Monte Carlo (MSMC) has enabled computation of higher-order virial coefficients than previously possible for a variety of potential models, but it is not required for computation of the entire virial coefficient for models that are spherically symmetric: approximations that result from the hypernetted-chain (HNC) or Percus–Yevick (PY) integral-equation theories in conjunction with the compressibility equation (c) or virial equation (v) can be computed quickly by fast Fourier transforms. For the fourth and fifth virial coefficients of the Lennard–Jones potential (with parameters σ and ε), we demonstrate that the corrections to each of the four approximations (HNC(c), HNC(v), PY(c), and PY(v)) are faster to compute to a desired precision by MSMC than the full coefficient itself, with the exception of the PY(v) correction at fifth order, and that the optimal decomposition with regard to precision can be identified using a fraction of the steps required to obtain precise virial coefficients. At reduced temperatures kT/ε greater than 4, the PY(c) correction is fastest to compute by MSMC at both fourth and fifth orders. For lower temperatures, the HNC(v) decomposition is most efficient at fourth order, while the HNC(c) decomposition is most efficient at fifth order. These results are specific to the Lennard–Jones potential, but the method for determining the optimal decomposition is applicable to any spherically symmetric potential.     

Interatomic interactions and the Cotton—Mouton effect for helium

We report calculations of the interaction-induced polarizability (δα^anis), magnetizability (δξ^anis;) and hypermagnetizability (δη^anis) anisotropies for the helium gas as a function of the interatomic separation. From these data we determine the virial coefficients for the Cotton—Mouton effect and the hypermagnetizability anisotropy of helium. We also find the mean polarizability and magnetizability as a function of the interatomic separation and the virial coefficients for these properties. The results for the Cotton—Mouton effect indicate that pressure affects the Cotton—Mouton constant to the same extent as it does the second hyperpolarizability (γ) and the virial coefficient b^CME(ω, T) lies in the range of ?1.6 to ?1.8 cm³ mol^?1. This means that pressure effects for the Cotton-Mouton constant could be detected with modern experimental techniques. All calculations were carried out using the full configuration interaction technique and large basis sets of London atomic orbitals. The polarizability calculations were performed both for relevant optical frequencies as well as the static case.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

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

A four-dimensional potential energy hypersurface (PES) for the interaction of two rigid nitrogen molecules was determined from high-level quantum-chemical ab initio computations. A total of 408 points for 26 distinct angular configurations were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and basis sets up to aug-cc-pV5Z supplemented with bond functions. The calculated interaction energies were extrapolated to the complete basis set limit and complemented by corrections for core–core and core–valence correlations, relativistic effects and higher coupled-cluster levels up to CCSDT(Q). An analytical site–site potential function with five sites per nitrogen molecule was fitted to the interaction energies. The PES was validated by computing second and third pressure virial coefficients as well as shear viscosity and thermal conductivity in the dilute-gas limit. An improved PES was obtained by scaling the CCSDT(Q) corrections for all 408 points by a constant factor, leading to quantitative agreement with the most accurate experimental values of the second virial coefficient over a wide temperature range. The comparison with the best experimental data for shear viscosity shows that the values computed with the improved PES are too low by about 0.3% between 300 and 700?K. For thermal conductivity large systematic deviations are found above 500?K between the calculated values and most of the experimental data.     

Evaluating virial coefficients for multicomponent mixtures: hard sphere mixtures and flexible chains

A new algorithm to compute the virial coefficients of multicomponent mixtures is proposed. The number of graphs that must be evaluated increases dramatically in a multicomponent mixture so that it becomes difficult to enumerate and compute all possible graphs. However, once all of them are known and evaluated, the virial coefficient of the mixture can be evaluated for any composition. If one is interested in the virial coefficient of a mixture of a certain composition, then a simpler approach can be followed. Starting from the graphs of a pure fluid, we assign a random chemical identity to each of the molecules of the graph. The probability of assigning a given chemical identity is taken from the composition of the mixture. In this way composition is treated as a random variable within the Monte Carlo procedure which determines the virial coefficient. The algorithm is checked by comparison with the virial coefficients of binary hard spheres mixtures which are well known. Good agreement is found. The procedure is then extended to multicomponent mixtures of hard spheres. Finally the procedure is applied to the determination of the virial coefficients of a flexible molecule. For flexible molecules the possible configurations of the molecules are treated as different components of the mixture. In this way we present what appears to be the first determination of the third and fourth virial coefficients of polymers in the continuum.