dunmur_1979 =========== D\. A\. Dunmur and N\. E\. Jessup, "The influence of intermolecular interactions on the Kerr effect in gases\. I\. Statistical theory for spherical top molecules", Mol\. Phys\. 37, 697 \(1979\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1080/00268977900103131 `__ **Source kind:** theory **Recorded technique:** Statistical theory of the second and third Kerr virial coefficients B\_K and C\_K of spherical top molecules in terms of irreducible cluster \(pair, triplet\) polarizabilities \(Eqs\. 16, 25\), evaluated with the dipole\-induced\-dipole \(DID\) model for the cluster polarizabilities \(Eqs\. 26\-27\) and a Lennard\-Jones 6\-12 pair potential; the second hyperpolarizability's contribution to B\_K is omitted \(2 % of the DID B\_K for the rare gases, 0\.3 % for SF6, p\. 700\) \(pp\. 697\-708\)\. **Materials in structured entries:** Ar, CH4, Kr, SF6, Xe **Dataset quantities:** kerr\_virial\_coefficient **Contents:** 17 datasets; 0 formulas. Curation notes -------------- PART I ONLY\. This is Part I, the statistical theory\. The requested Part II, Dunmur, Hunt & Jessup, Mol\. Phys\. 37, 713 \(1979\), which reports the measured dc Kerr effect \(A\_K, B\_K, C\_K\) of CH4, SF6 and the other spherical tops, is not in the library \(missing\); its B\_K and C\_K appear here only as Table 2's and Table 4's 'expt \[19\]' comparison values \(reproduced datasets\)\. No A\_K or gamma is given in this paper\. Pages are the journal's \(697\-711\); pdf page 1 is the publisher's cover, so p\. = pdf page \+ 695\. The library's validation warnings concern only the cover's images\. DEFINITIONS \(pp\. 697\-698\)\. mK = lim\_\(E \-\> 0\) 6 n \(n\_par \- n\_perp\) V\_m/\[\(n^2 \+ 2\)^2 \(eps \+ 2\)^2 E^2\] \(Eq\. 1\) = A\_K \+ B\_K V\_m^\-1 \+ C\_K V\_m^\-2 \+ \.\.\. \(Eq\. 2\); for spherical tops A\_K = \(N\_A/\(810 eps0\)\)\[3 gamma\_abab\(\-w; w, 0, 0\) \- gamma\_aabb\(\-w; w, 0, 0\)\] \(Eq\. 3\)\. B\_K in the DID model\: B\_K = \(N\_A^2 alpha\_0^2 a\_0^2/\(90 pi eps0^3 kT\)\) integral R^\-4 g\_0\(R\) dR \(Eq\. 28\), alpha\_0 and a\_0 the static and optical polarizabilities\. The paper's C\_K decomposition \(Table 4\)\: C\_K^\(2\-2\) from the density dependence of g\(R\), C\_K^\(2\-2'\) from pairs within a triplet, C\_K^\(2\-3\) \+ C\_K^\(3\-2\) with the triplet polarizability, and C\_K^\(3\-3\) \(p\. 704\)\. TABLE 1 \(p\. 705\), the inputs \(static alpha, optical a in 10^\-40 C^2 m^2 J^\-1; Lennard\-Jones u0/k, R0 from Hirschfelder, Curtiss & Bird \[41\]\)\: Ar\: alpha = 1\.827 \[7, Orcutt & Cole 1967\], a = 1\.850 \[44, Dalgarno & Kingston 1960\] x 10^\-40 C^2 m^2 J^\-1, u0/k = 119\.8 K, R0 = 0\.3405 nm \[41\]; Kr\: alpha = 2\.764 \[7\], a = 2\.801 \[44\], u0/k = 171 K, R0 = 0\.360 nm \[41\]; Xe\: alpha = 4\.510 \[44\], a = 4\.576 \[44\], u0/k = 221 K, R0 = 0\.410 nm \[41\]; CH4\: alpha = 2\.885 \[45, Bose, Sochanski & Cole 1972\], a = 2\.901 \[48, Landolt\-Bornstein\], u0/k = 148\.2 K, R0 = 0\.382 nm \[41\]; SF6\: alpha = 7\.24 \[47, Buckingham & Raab 1961\], a = 4\.974 \[49, Watson & Ramaswamy 1936\], u0/k = 200\.9 K, R0 = 0\.551 nm \[41\]\. CF4 and neopentane \(C\(CH3\)4\) are also computed throughout\: out of scope, not transcribed\. ACCURACY\. No uncertainties are given; 'the DID model \.\.\. is known to be inaccurate for small intermolecular separations, and so it is not surprising that our calculated values for B\_K and C\_K do not agree with the experimental results' \(p\. 708\); 'The second Kerr virial coefficients calculated for the rare gases are larger than the experimental measurements, while those calculated for polyatomic spherical top molecules are smaller' \(p\. 709\)\. Fig\. 2 \(argon, eight pair potentials\) shows 'a significant dependence of calculated second Kerr virial coefficients on the potential' \(p\. 706\)\. The C\_K integrals agree with Levine & McQuarrie's to better than 5 % \(truncation errors, p\. 708\)\. TABLE 3 \(p\. 707\), not transcribed\: DID B\_K of the mixtures Ar/Kr and Ar/Xe with the collision\-induced\-dipole terms \(Levine's dispersion dipole and Bar\-Ziv & Weiss's\), 'likely to be negligible'\. Comparisons \(computed here\)\: buckingham\_1969 measured B\_K\(CH4\) = 0\.245 x 10^\-31 C^2 m^8 J^\-2 at 303\.7 K, against this paper's DID 27\.3 x 10^\-33 at 300 K and Part II's 37 x 10^\-33 at 302 K; buckingham\_1968 Table 2 gives B\_K\(Ar\) = 4\.1 \+\- 0\.6 x 10^\-12 e\.s\.u\. \(4\.6 x 10^\-33 C^2 m^8 J^\-2 with Buckingham & Orr's 0\.89876 x 10^21 e\.s\.u\. per S\.I\. unit\) against Part II's 3\.8 x 10^\-33\. The B\_K and C\_K are pair and triplet properties, not hyperpolarizabilities; they bear on the density dependence of dc Kerr data \(the pair term of tammer\_1992's He, buckingham\_1968's quadratic fits\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- dunmur\_1979/table2\_B\_K\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_B_K_Ar", "material": "Ar", "file": "Ar/dunmur_1979__table2_B_K_Ar.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\)\: the second Kerr virial coefficient B\_K of Ar calculated with the dipole\-induced\-dipole pair polarizability and a Lennard\-Jones 6\-12 potential \(Eq\. 28; inputs alpha = 1\.827 \[7, Orcutt & Cole 1967\], a = 1\.850 \[44, Dalgarno & Kingston 1960\] x 10^\-40 C^2 m^2 J^\-1, u0/k = 119\.8 K, R0 = 0\.3405 nm \[41\]\), 250\-330 K\. Theory, no uncertainty stated; the DID model is known to fail at short range \(see the record's notes\)\. The measured value of Part II is table2\_expt\_Ar\. dunmur\_1979/table2\_B\_K\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_B_K_Kr", "material": "Kr", "file": "Kr/dunmur_1979__table2_B_K_Kr.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\)\: the second Kerr virial coefficient B\_K of Kr calculated with the dipole\-induced\-dipole pair polarizability and a Lennard\-Jones 6\-12 potential \(Eq\. 28; inputs alpha = 2\.764 \[7\], a = 2\.801 \[44\], u0/k = 171 K, R0 = 0\.360 nm \[41\]\), 250\-330 K\. Theory, no uncertainty stated; the DID model is known to fail at short range \(see the record's notes\)\. The measured value of Part II is table2\_expt\_Kr\. dunmur\_1979/table2\_B\_K\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_B_K_Xe", "material": "Xe", "file": "Xe/dunmur_1979__table2_B_K_Xe.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\)\: the second Kerr virial coefficient B\_K of Xe calculated with the dipole\-induced\-dipole pair polarizability and a Lennard\-Jones 6\-12 potential \(Eq\. 28; inputs alpha = 4\.510 \[44\], a = 4\.576 \[44\], u0/k = 221 K, R0 = 0\.410 nm \[41\]\), 250\-330 K\. Theory, no uncertainty stated; the DID model is known to fail at short range \(see the record's notes\)\. The measured value of Part II is table2\_expt\_Xe\. dunmur\_1979/table2\_B\_K\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_B_K_CH4", "material": "CH4", "file": "CH4/dunmur_1979__table2_B_K_CH4.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\)\: the second Kerr virial coefficient B\_K of CH4 calculated with the dipole\-induced\-dipole pair polarizability and a Lennard\-Jones 6\-12 potential \(Eq\. 28; inputs alpha = 2\.885 \[45, Bose, Sochanski & Cole 1972\], a = 2\.901 \[48, Landolt\-Bornstein\], u0/k = 148\.2 K, R0 = 0\.382 nm \[41\]\), 250\-330 K\. Theory, no uncertainty stated; the DID model is known to fail at short range \(see the record's notes\)\. The measured value of Part II is table2\_expt\_CH4\. dunmur\_1979/table2\_B\_K\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_B_K_SF6", "material": "SF6", "file": "SF6/dunmur_1979__table2_B_K_SF6.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\)\: the second Kerr virial coefficient B\_K of SF6 calculated with the dipole\-induced\-dipole pair polarizability and a Lennard\-Jones 6\-12 potential \(Eq\. 28; inputs alpha = 7\.24 \[47, Buckingham & Raab 1961\], a = 4\.974 \[49, Watson & Ramaswamy 1936\], u0/k = 200\.9 K, R0 = 0\.551 nm \[41\]\), 250\-330 K\. Theory, no uncertainty stated; the DID model is known to fail at short range \(see the record's notes\)\. The measured value of Part II is table2\_expt\_SF6\. dunmur\_1979/table2\_expt\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_expt_Ar", "material": "Ar", "file": "Ar/dunmur_1979__table2_expt_Ar.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\), row 'expt \[19\]'\: the measured B\_K of Ar from Part II \(Dunmur, Hunt & Jessup 1979, not in the library\) at 305 K \('Temperatures given in brackets below results'\)\. The wavelength of the measurement is not stated here\. No uncertainty printed\. dunmur\_1979/table2\_expt\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_expt_Kr", "material": "Kr", "file": "Kr/dunmur_1979__table2_expt_Kr.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\), row 'expt \[19\]'\: the measured B\_K of Kr from Part II \(Dunmur, Hunt & Jessup 1979, not in the library\) at 303 K \('Temperatures given in brackets below results'\)\. The wavelength of the measurement is not stated here\. No uncertainty printed\. dunmur\_1979/table2\_expt\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_expt_Xe", "material": "Xe", "file": "Xe/dunmur_1979__table2_expt_Xe.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\), row 'expt \[19\]'\: the measured B\_K of Xe from Part II \(Dunmur, Hunt & Jessup 1979, not in the library\) at 302 K \('Temperatures given in brackets below results'\)\. The wavelength of the measurement is not stated here\. No uncertainty printed\. dunmur\_1979/table2\_expt\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_expt_CH4", "material": "CH4", "file": "CH4/dunmur_1979__table2_expt_CH4.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\), row 'expt \[19\]'\: the measured B\_K of CH4 from Part II \(Dunmur, Hunt & Jessup 1979, not in the library\) at 302 K \('Temperatures given in brackets below results'\)\. The wavelength of the measurement is not stated here\. No uncertainty printed\. dunmur\_1979/table2\_expt\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_expt_SF6", "material": "SF6", "file": "SF6/dunmur_1979__table2_expt_SF6.csv", "table": "tbl_02b495d28eaa", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-33, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 2 } } Table 2 \(p\. 705\), row 'expt \[19\]'\: the measured B\_K of SF6 from Part II \(Dunmur, Hunt & Jessup 1979, not in the library\) at 303 K \('Temperatures given in brackets below results'\)\. The wavelength of the measurement is not stated here\. No uncertainty printed\. dunmur\_1979/table4\_C\_K\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_C_K_Ar", "material": "Ar", "file": "Ar/dunmur_1979__table4_C_K_Ar.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), 'Third Kerr virial coefficients at 300 K'\: C\_K^TOTAL of Ar, DID model and Lennard\-Jones potential\. The contributions C\_K^\(2\-2\), C\_K^\(2\-2'\), C\_K^\(2\-3\) \+ C\_K^\(3\-2\), C\_K^\(3\-3\)\: \-0\.59, \-42, \-4\.06, 0\.000018 \(total \-47\) x 10^\-38 C^2 m^11 J^\-2 \(their sum reproduces the total, checked\)\. Theory, no uncertainty stated\. dunmur\_1979/table4\_C\_K\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_C_K_Kr", "material": "Kr", "file": "Kr/dunmur_1979__table4_C_K_Kr.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), 'Third Kerr virial coefficients at 300 K'\: C\_K^TOTAL of Kr, DID model and Lennard\-Jones potential\. The contributions C\_K^\(2\-2\), C\_K^\(2\-2'\), C\_K^\(2\-3\) \+ C\_K^\(3\-2\), C\_K^\(3\-3\)\: \-8\.70, \-229, \-40\.2, 0\.00019 \(total \-278\) x 10^\-38 C^2 m^11 J^\-2 \(their sum reproduces the total, checked\)\. Theory, no uncertainty stated\. dunmur\_1979/table4\_C\_K\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_C_K_Xe", "material": "Xe", "file": "Xe/dunmur_1979__table4_C_K_Xe.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), 'Third Kerr virial coefficients at 300 K'\: C\_K^TOTAL of Xe, DID model and Lennard\-Jones potential\. The contributions C\_K^\(2\-2\), C\_K^\(2\-2'\), C\_K^\(2\-3\) \+ C\_K^\(3\-2\), C\_K^\(3\-3\)\: \-19\.6, \-1731, \-586, 0\.0019 \(total \-2337\) x 10^\-38 C^2 m^11 J^\-2 \(their sum reproduces the total, checked\)\. Theory, no uncertainty stated\. dunmur\_1979/table4\_C\_K\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_C_K_CH4", "material": "CH4", "file": "CH4/dunmur_1979__table4_C_K_CH4.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), 'Third Kerr virial coefficients at 300 K'\: C\_K^TOTAL of CH4, DID model and Lennard\-Jones potential\. The contributions C\_K^\(2\-2\), C\_K^\(2\-2'\), C\_K^\(2\-3\) \+ C\_K^\(3\-2\), C\_K^\(3\-3\)\: \-8\.72, \-260, \-44\.0, 0\.00014 \(total \-313\) x 10^\-38 C^2 m^11 J^\-2 \(their sum reproduces the total, checked\)\. Theory, no uncertainty stated\. dunmur\_1979/table4\_C\_K\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_C_K_SF6", "material": "SF6", "file": "SF6/dunmur_1979__table4_C_K_SF6.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), 'Third Kerr virial coefficients at 300 K'\: C\_K^TOTAL of SF6, DID model and Lennard\-Jones potential\. The contributions C\_K^\(2\-2\), C\_K^\(2\-2'\), C\_K^\(2\-3\) \+ C\_K^\(3\-2\), C\_K^\(3\-3\)\: \-152, \-5171, \-2187, 0\.0015 \(total \-7510\) x 10^\-38 C^2 m^11 J^\-2 \(their sum reproduces the total, checked\)\. Theory, no uncertainty stated\. dunmur\_1979/table4\_expt\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_expt_CH4", "material": "CH4", "file": "CH4/dunmur_1979__table4_expt_CH4.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), column 'Expt\. \[19\]'\: the measured third Kerr virial coefficient C\_K of CH4 from Part II \(not in the library\), \-450 x 10^\-38 C^2 m^11 J^\-2, listed under the table's '300 K' \(the measurement's temperature is not stated here\)\. 'Experimental measurements of the third Kerr virial coefficient are rather limited and imprecise' \(p\. 709\)\. No uncertainty printed\. dunmur\_1979/table4\_expt\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_expt_SF6", "material": "SF6", "file": "SF6/dunmur_1979__table4_expt_SF6.csv", "table": "tbl_63fdb7ad5cff", "quantity": "kerr_virial_coefficient", "unit": "C2 m11 J-2", "scale": 1e-38, "abscissa": "temperature", "abscissa_unit": "K", "use": "reproduced", "reproduced_from": [ "dunmur_1979b" ], "uncertainty": { "level": "not stated" }, "parameters": { "order": 3 } } Table 4 \(p\. 708\), column 'Expt\. \[19\]'\: the measured third Kerr virial coefficient C\_K of SF6 from Part II \(not in the library\), \-10000 x 10^\-38 C^2 m^11 J^\-2, listed under the table's '300 K' \(the measurement's temperature is not stated here\)\. 'Experimental measurements of the third Kerr virial coefficient are rather limited and imprecise' \(p\. 709\)\. No uncertainty printed\. 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.