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 `__ · :doc:`Catalogue ` · :doc:`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 -------- No datasets are recorded. Formulas -------- No formulas are recorded. Corrections ----------- No dataset errata are recorded in this source record. Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register ` for the checks and decisions.