The second dielectric virial coefficient of a dipolar sticky hard sphere fluid

We calculate the second dielectric virial coefficient, B _?, of a fluid whose molecules are sticky hard spheres with embedded central point dipoles. The effect of stickiness is to increases B _? markedly.     

Quantum second virial coefficient paradox

The quantum second virial coefficient vanishes when we apply directly Moller operators. We analyze such a paradox, giving an answer: Usual scattering formulas fail in some cases.     

Third virial coefficient of hard spheroids

The third virial coefficient B ₃ of a fluid of spheroids is calculated by direct integration using the method of 2-point measures of convex body geometry. Calculations are performed for aspect ratios up to 10 for both prolate and oblate spheroids. The infinite set of 2-point measures has five indices. The three numerical ones, L, Lι and m, are standard quantities in the theory of the rotation group. These new calculations use truncation at the L = L = 2 level. The results show dramatic improvement over previous results at the L = Lι = 1 level and are in excellent agreement with existing Monte Carlo calculations of B ₃.     

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.     

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.     

The second virial coefficient of quadrupolar dumbells

To study the effect of the shape of molecules on properties of polar fluids, the second pressure virial coefficient,B(T), of quadrupolar hard homonuclear dumbells is investigated both numerically and analytically. Convergence of the expansion ofB(T) about the hard dumbell reference is examined and a simple approximate analytic formula is derived which provides a good estimate ofB(T) for temperatures higher than the Boyle temperature,T _B. BelowT _B the examined expansion methods break down. Independently of the calculations ofB(T), an approximate analytic expression of the average Boltzmann factor of the model considered has been also derived.     

Second virial coefficient of homonuclear two-centre Lennard-Jones molecules

A semiempirical expression based on numerical values of the second virial coefficient of the two-centre Lennard-Jones molecules and on the theoretical expression for hard dumbells is given. The resulting expression possesses the form developed formerly for the second virial coefficient of the Kihara non-spherical molecules and reproduces fairly well the correct limits at high temperatures. It allows the prediction of the second virial coefficient at reduced temperatures T*≧0·5.     

S matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S matrix is meromorphic. It may be expressed in terms of its poles, and then the quantum mechanical second virial coefficient of a neutral gas may be calculated. This paper takes another look at this approach, and discusses the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the ‘pole’ expansion and the physical significance of the ‘higher’ poles.     

Second virial coefficient and mechanical moduli of metallic glasses

The relationship between the bulk, shear moduli and second virial coefficient of amorphous materials is derived according to their dependences with the radial distribution function. Lennard-Jones–Gaussian potential is used to investigate the relationship between second virial coefficient and temperature, where Lennard-Jones potential represents interactions with the nearest neighbor atoms, and Gaussian potential is responsible for the multi-atom interactions including the next nearest neighbor atoms and heterogeneous structures for a metallic glass. The results show that deep potential well formed by Gaussian potential causes a large second virial coefficient at low temperatures, which is very obvious for the larger fragility glasses. The quadratic form relationship of shear modulus and compositions is proposed, and confirmed by the experimental results of Pd_xNi_100−x−20P₂₀ alloy.     

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.     

Fifth virial coefficient for a system of hard disks

The most accurate value of the fitth virial coefficient B₅ for a system of hard disks has been (0.3338±0.0005) B⁴₂ until now, where B₂ is the second virial coefficient. The present work describes methods of calculation and gives the improved value B₅ = 0.3335561 B⁴₂, the last digit being uncertain.     

RESEARCH NOTE Fifth virial coefficient of hard sphere mixtures

New calculations of the fifth virial coefficient are presented for binary hard sphere mixtures. These improve on, and in some cases correct, previous results. A polynomial fit is used to extend the results to all diameter ratios, with an accuracy better than 1.05%. It is confirmed that the fifth virial coefficient is positive for all diameter ratios and mole fractions.     

Second surface virial coefficient for nitrogen adsorbed on graphite

We present the results of calculations of the second surface virial coefficient for nitrogen adsorbed on graphite. The three-dimensional calculations are confronted with those resulting from a two-dimensional model of adsorption.     

Third virial coefficient for hard spheres with embedded dipoles

The doublet stability of the SCF solutions for the allyl radical is re-examined for various ab-initio model hamiltonians, based on the minimum, double-zeta and double-zeta plus polarization atomic orbital basis sets in the LCAO scheme. The calculations are carried out for a wide range of the C-C bond lengths (1.3 Å to 2·0 Å). In all cases the critical bond length, separating regions of stability and instability, is found to be shorter than the corresponding equilibrium C-C bond length (1·36 Å versus 1·44 Å, respectively, for the minimum basis set). In contrast to the results of McKelvey and Berthier we find that the doublet-stability problem yields at most one negative eigenvalue in the whole range of the C-C bond lengths studied, this implying only one possible (other than spin) symmetry breaking, in complete agreement with the semi-empirical PPP model results for this system. The basis dependence of the doublet instability is also re-examined and the generality of this phenomenon is firmly established for the system studied : while the actual values of the energy lowering due to the symmetry breakdown and the critical value of the C-C bond length for the onset of instability will of course depend on the basis and approximations used, there is no doubt about the general occurrence of doublet instability in this system for large enough C-C internuclear separations, and about the implied non-analytic behaviour of the potential energy hypersurface in this region, for any basis. Finally, a simple physically and chemically plausible source of the doublet instability of allyl RHF solutions is pointed out.