buckingham_1955

A. D. Buckingham and J. A. Pople, “The Dielectric Constant of an Imperfect Non-Polar Gas”, Trans. Faraday Soc. 51, 1029 (1955)

Source record · Catalogue · Review register

DOI: 10.1039/tf9555101029

Source kind: theory

Recorded technique: Theory: classical statistical mechanics of the Clausius-Mossotti function of a non-polar gas, expanded in inverse molar volume, giving the second dielectric virial coefficient as a configuration integral over a pair’s excess polarizability and field-free dipole, with estimates from a point-dipole (dipole-induced-dipole) model and a Lennard-Jones potential, compared with measured values (Table 1).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Identity VALIDATED_WITH_WARNINGS by the library. Printed pages 1029-1035 = pdf pages 1-7. The library’s text gives the second author as ‘POPLLE’ and fuses Table 1’s reference superscripts into the values (‘119.7514’ is 119.75 with ref. 14, ‘25 +- 73’ is 25 +- 7 with ref. 3); the printed Eq. (3.7) has a mismatched brace.

THE RESULT (Eqs. 2.12 and 3.1, p. 1031, Gaussian units, checked by a reader against the page images, 2026-09-30): B = (4 pi N^2 / 3 Omega) integral {[1/2 d(mu_1 + mu_2)/ dE_0 . e - alpha] + (1/6kT)(mu_1 + mu_2)^2} exp(-u_12/kT) dtau_2, the expansion (Eq. 2.6) being of the Clausius-Mossotti function times the molar volume. For atoms, averaged over field directions, the first bracket is 1/2 (the pair’s mean polarizability - 2 alpha), so B = (2 pi N^2/3) integral Delta alpha exp(-u/kT) d^3r; in SI, with alpha_G = alpha_SI/(4 pi eps0), B = N_A^2/(6 eps0) integral Delta alpha exp(-U/kT) d^3R, the form of OEP 4 (§4.1), Delta alpha being one third of the trace. Garberoglio and Harvey’s classical limit (their Eq. 13) matches it.

THE TERMS: (i) the change of the mean polarizability with separation (p. 1031), unknown and set to zero in the estimates; (ii) dipole-induced-dipole, 2 alpha^3 r^-6 per molecule (Eqs. 3.5-3.6, p. 1032), which with a Lennard-Jones potential gives Eq. (3.8) (reproduces Table 1’s argon value, 1.99 cm^6/mol^2 at 25 C); molecular anisotropy enters only here, alpha^3 -> (1/9)(sum alpha_i)(sum alpha_i^2) (p. 1033); (iii) the orientational term (1/6kT) <(mu_1 + mu_2)^2> of a pair’s field-free dipole, identically zero for like atoms by symmetry (p. 1032), from quadrupole-induced dipoles for quadrupolar molecules (Eq. 3.18, p. 1035; for CO2 at 50 C, 38 of 46 cm^6/mol^2). At high frequencies (iii) vanishes, since ‘the molecules do not have time to orient themselves’ (p. 1035): the optical coefficient keeps (i) + (ii) only. The boundary polarization is ‘proportional to 1/V_m^2’ (p. 1031), so there is no separate local-field term.

SCOPE: a single gas of identical molecules (p. 1029, Eq. 2.5). For a mixture the pair count gives B_mix = sum x_s x_t B_st; an unlike atom pair carries an interaction-induced dipole, so its static cross coefficient has a term (iii) that its optical one lacks. Classical by construction; nothing on quantum corrections. Nothing transcribed.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

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Formulas

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Corrections

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Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.