Inversion of the classical second virial coefficient

It is shown that, on the basis of some weak assumptions regarding the nature of the intermolecular pair potential, the classical second virial coefficient determines the potential uniquely.Research supported by NSF Grant GP-19881.     

Evaluation of second and third dielectric virial coefficients for non-polarisable molecular models

The dielectric constant, ε, of a dilute vapour can be estimated from the dielectric virial equation of state (VEOS), but the long-ranged nature of the electrostatic interactions complicates the evaluation of coefficients of this series. We propose a formulation of the second and third dielectric coefficients of a general non-polarisable molecular model that permits their reliable calculation using Mayer sampling Monte Carlo. We demonstrate for three models: dipolar hard spheres, dipolar Lennard–Jones, and TIP4P water. The coefficients are used to compute ε for each model as a function of density, which are compared to molecular-simulation data. The form of the VEOS relating ε to density depends on the dielectric constant ε′ of the embedding medium. Three choices are examined: vacuum (ε′ = 1), self-consistent (ε′ = ε) and tin foil (ε′ = ∞). The vacuum-boundary form is found to be unreliable, losing accuracy at low density and yielding divergent results for ε at moderate densities. In contrast, the series formulated using the tin-foil boundary produces accurate and stable values of ε for almost all conditions and models examined here, even when truncated at second order (which itself is shown to be a large improvement over the first-order Clausius–Mossotti–Debye formula).     

Explicit and implicit finiteness corrections of virial coefficients

The equation of state of finite systems deviates from thermodynamic limit. The corresponding finiteness corrections of virial coefficients are studied. Most calculations are based on the canonical ensemble with periodic boundary conditions.Explicit andimplicit finiteness corrections occur. They are displayed up to the eighth virial coefficient. These results are applied to hard spheres in one, two, and three dimensions.     

第二位力系数与体积关系的理论证明

用参数变换方法,研究了位形配分函数对体积的一次导数,得到了第二位力系数,从而证明了第二位力系数与体积无关,并对现有教材所给出的条件加以补充。     

On the inversion of the classical second virial coefficient

For a large class of intermolecular potentials, the values of the second virial coefficient at a discrete set of temperature points in an arbitrarily small neighborhood of the origin determine the potential uniquely.     

Delta-function expansion of Mayer function with application to virial coefficients

The Mayer cluster integrals of a fluid with smooth, repulsive interactions are expanded in orders of a well-defined softness parameter. To first but not second order in softness, all virial coefficients are given by their hard-sphere forms with an effective diameter. A closed asymptotic expression is derived for the third virial coefficient which gives excellent results for the inverse power and exponential potentials.     

A general analytical method for evaluation of the thermodynamic properties of matters using virial coefficients with Morse potential at high temperature

In this paper, we established an analytical formula for the second virial coefficient (SVC) with Morse potential without using any numerical methods, and the obtained formula is applied to the calculation of the speed of sound of some matter at high temperature. This approach is based on the series expansion formula and special functions, which allows the exact evaluations of any thermodynamic properties of matter using the SVC. As an application, the obtained analytical formula is used for evaluation of the SVC with Morse potential for high‐temperature gas and the plasma region of the intermolecular interactions of neutral atom gases of B, Si, Zn, H₂, N₂, O₂, NO, CO, He, Ne, Ar, Kr , and Xe . Based on the obtained formula of SVC, the speed of sound for gases of N₂, Ar , and Zn are also determined analytically. A specific maximum temperature is chosen for every gas to ensure that there are still neutral atoms in the gas, and low temperatures are avoided due to quantum effects. The results are compared with numerical data and another analytical data from the literature. The new analytical solution is shown to be in good agreement with the compared data and is verified to supply proper thermodynamic data.     

An alternative formulation of the virial expansion for simple fluids

A new analytical formulation of the virial expansion for simple fluids is presented. Starting from the usual expression of the partition function of a set of identical molecules, a Fourier transformation is performed. Then a systematic procedure formally allowing the computation of the virial coefficients in the reciprocal space is presented; the coefficients are finally expressed as multiple integral expressions in the reciprocal space, and focus is on the simple case of hard sphere fluids. Finally, an approximate recursion relation is proposed that allows an estimation to be obtained of those coefficients without having to actually perform the integrations; a comparison of the results is made with the equation of state by Carnahan and Starling and with the recent numerical results by Clisby and Mc Coy.     

Sixth,seventh and eighth virial coefficients of the Lennard-Jones model

We report values of the virial coefficients B _n of the Lennard-Jones (LJ) model, as computed by the Mayer Sampling Monte Carlo method. For n = 4 and 5, values are reported for 103 temperatures T = 0.62 to 40.0 (in LJ units); for n = 6, 31 values are reported for T = 0.625 to 20.0; for n = 7, 15 values are reported from T = 0.625 to 10; and for n = 8, four values are reported from T = 0.75 to 10. Data are used to estimate the location of the LJ critical point, and the critical temperature estimated this way is given to within 0.8% of the established value, while the critical density is too low by 10%. Data derived from the virial equation of state (VEOS) are compared to pressures and internal energies calculated by Monte Carlo simulation. Simulations of systems ranging from 125 to 30,000 particles are extrapolated to infinite system size, and it is shown that the VEOS–when applied at densities where the series has reached convergence–provides results closer to the infinite-system values than obtained by any of the finite-system simulations. For n = 6, convergence of VEOS (within a 1% tolerance) is obtained for densities up to the spinodal for subcritical temperatures and up to ρ = 0.4 (in LJ units) in the vicinity of the critical temperature; the range of applicability of VEOS increases with temperature, reaching for example densities of 0.65 for T = 5.0 and 0.8 for T = 8.0 when truncated at n = 6.     

RESEARCH NOTE A method for predicting the virial coefficients of hard linear homonuclear molecules

This paper proposes a simple method for predicting the virial coefficients, up to the fifth, for hard linear homonuclear molecules. The method uses the virial coefficients for hard spherocylinders and hard linear tangent spheres to obtain the virial coefficients of linear fused hard spheres. The results are in very good agreement with the known values for the latter kind of molecules. Thus the method is suitable for predictive purposes when virial coefficients are not known, which makes it useful for the derivation of certain equations of state.     

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.     

线型分子势能函数及第二维里系数计算

本文以两中心的Lennard—Jones（2CLJ）流体为研究对象,通过引入与温度相关的势能参数,提出了改进型的2CLJDQP势能函数模型。应用此模型计算了乙烷（C2H6）、六氟乙烷（C2F6）、氟甲烷（CH3F）、氯甲烷（CH3C1）、1,1,1-三氟乙烷（CH3CF3）、二氟乙烷（CH3CHF2）的第二维里系数,较...     

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.     

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.     

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

A helium–helium interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation considering relativistic retardation effects (R. Hellmann, E. Bich, and E. Vogel, Molec. Phys. (in press)) was used in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions. The second pressure virial coefficient as well as the viscosity and thermal conductivity coefficients, the last two in the so-called limit of zero density, were calculated for ³He and ⁴He from 1 to 10 000 K and the third pressure virial coefficient for ⁴He from 20 to 10 000 K. The transport property values can be applied as standard values for the complete temperature range of the calculations characterized by an uncertainty of ±0.02% for temperatures above 15 K. This uncertainty is superior to the best experimental measurements at ambient temperature.     

二值噪声驱动下二阶线性系统的随机共振

研究了二值噪声驱动下二阶线性系统的随机共振问题. 采用平均法推导出系统输出幅值增益的表达式,考察了幅值增益与系统频率、输入信号频率、噪声强度和噪声相关时间的关系,发现系统输出幅值增益随这些参量呈单峰共振变化. 另外,二值噪声的非对称性对共振峰值具有很大影响. 关键词： 随机共振 幅值增益 二值噪声 二阶线性系统     

New method for the evaluation of the RKR potential-integrals for diatomic molecules

We present a new method for the evaluation of the RKR potential-integrals for diatomic molecules. This method is straightforward and fast, and the calculations can be performed to an accuracy better than any other method.     

A convergent nonequilibrium statistical mechanical theory for dense gases. III. Transport coefficients to second order in the density

The purpose of this paper is to obtain general expressions for the second-order terms of the transport coefficients of a dense gas. These expressions are obtained using the convergent kinetic theory proposed recently by Braun and Flores.     

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

A recent argon–argon interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation [B. Jäger, R. Hellmann, E. Bich, and E. Vogel, Mol. Phys. 107, 2181 (2009); 108, 105 (2010)] was used to calculate the most important thermophysical properties of argon governed by two-body interactions. Second pressure, acoustic, and dielectric virial coefficients as well as viscosity and thermal conductivity in the limit of zero density were computed for natural argon from 83 to 10,000?K. The calculated values for the different thermophysical properties are compared with available experimental data and values computed for other argon–argon potentials. This extensive analysis shows that the proposed potential is superior to all previous ones and that the calculated thermophysical property values are accurate enough to be applied as standard values for the complete temperature range of the calculations.