Dielectric virial coefficients

Clausius-Mossotti equation). The AE, BE,. .., are the first, second,. .., dielectric virial coefficients, given by... 

At very low temperatures Eq. (1-250) is no longer valid, and one has to use the exact quantum-statistical expression. The quantum equivalent of Eq. (1-250) has been developed in Ref. (317) from the general relation between the second dielectric virial coefficient and the ordinary (thermodynamic) second virial coefficient of an atomic gas in a uniform electric field317,... 

Equation (1-251) can also be used to derive the semiclassical expansion of the second dielectric virial coefficient. Indeed, one may hope that at intermediate temperatures an expansion of Be(T) as a power series in h2 will give sufficiently accurate results, making full quantum-statistical calculations unnecessary. Thus, one can approximate Be(T) as,... 

A quantum expression and a semi-classical expansion can be derived328, as in the case of the dielectric virial coefficient. We wish to end this short section by saying that recently Rizzo and collaborators reported a general virial expansion of various properties of atomic gases322. 

Before comparing theory and experiment let us discuss the convergence of the semiclassical expansion of the dielectric second virial coefficient. In Table 1-15 the classical dielectric virial coefficient the first and second quantum corrections, and the full quantum result are reported. An inspection of this table shows that the quantum effects are small for temperatures larger than 100 K, and /it(/) can be approximated by the classical expression with an error smaller than 2.5%. At lower temperatures the dielectric virial coefficient of 4He starts to deviate from the classical value. Still, for T > 50 K the quantum effects can be efficiently accounted for by the sum of the first and second quantum corrections. Indeed, for T = 50, 75, and 100 K the series (7) + lli 1 (7) + (7) reproduces the exact results with errors... 

Table 1-15. Second dielectric virial coefficient of 4He (in cm6mol 2) as function of the temperature (in K)...

The comparison of the theoretical and experimental values of the second dielectric virial coefficient can serve as a further check of the accuracy of the ab initio trace polarizability. An example of such a comparison is shown on Figure 1-25, where the theoretical and experimental second dielectric virial coefficients for the 4He gas at various temperatures are reported. 

Figure 1-25. Theoretical (full line) and experimental second dielectric virial coefficients of the He gas at various temperatures...

Moszynski R, Heijmen TGA, Wormer PES, Van der Avoird A (1996) Ab initio collision-induced polarizability, polarized and depolarized Raman spectra, and second dielectric virial coefficient of the helium diatom. J Chem Phys 104 6997-7007... 

Moszynski R, Heijmen TGA, van der Avoird A (1995) Second dielectric virial coefficient of helium gas quantum-statistical calculations from an ab initio interaction-induced polarizability. Chem Phys Lett 247 440- 146... 

Huot J, Bose TK (1991) Experimental determination of the dielectric virial coefficients of atomic gases as a function of temperature. J Chem Phys 95 2683-2687... 

Be for Mixtures. The values of the dielectric virial coefficients of a mixture are determined in the same way as those of a pure gas. For a two-component mixture we can, in the absence of reaction, write... 

Table 3 Selected values of dielectric virial coefficients of dipolar gases ...

The order of accuracy required in measurements of the molar volume and the electric po mittivity for dielectric virial coefficient determinations may... 

In an effort to determine the higher dielectric virial coefficients without determining fin. Cole and co-workers have adapted the Burnett expansion technique to dielectric measurements. A schematic figure of their apparatus is shown [Figure 1(a) ]. Initially the system is filled with gas, the valve closed and Cr measured. Volume B is then evacuated, the gas from cell A allowed to expand into B, the valve closed and Sg measured again. The process is repeated a number of times giving a series of... 

H. B. Levine and D. A. McQuarrie. Second and third ordinary and dielectric virial coefficients for nonpolar axial molecules. J. Chem. Phys., 44 3500-3505 (1966). 

D. E. Logan and P. A. Madden. On the second dielectric virial coefficients of methane and the inert gases. Molec. Phys., 46 1195-1211 (1982). 

The present status of symmetry-adapted perturbation theory applied to intermolecular potentials and interaction-induced properties is presented, and illustrated by means of applications to the calculations of the collision-induced Raman spectra, rovibrational spectra of weakly bound dimers, and second (pressure and dielectric) virial coefficients. 

Recently, a detailed study of the importance of the quantum effects and of the applicability of the semiclassical expansion has been reported (46). This study started from the ab initio SAPT trace polarizability (32) and it involved semiclassical and full quantum calculations of the second dielectric virial coefficient for the 4He gas at various temperatures. Illustrative results of these calculations are presented in Table 2. 

Comparison of the at initio and experimental second dielectric virial coefficients of 4He at various temperatures. The solid line represents the second dielectric virial coefficients generated from the at initio polarizability trace of Ref. (32), and the empirical potential of Ref. (58). Crosses label the indirect measurements from Refs. (51, 55, 56, 57), open circles and squares the measurements from Refs. (54), and (49), respectively, and filled circles and squares represent experimental data from Refs. (50) and (52, 53). 

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