kerl_1992 ========= K\. Kerl, U\. Hohm and H\. Varchmin, "Polarizability alpha\(omega, T, rho\) of small molecules in the gas phase", Ber\. Bunsenges\. Phys\. Chem\. 96, 728 \(1992\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1002/bbpc\.19920960517 `__ **Source kind:** fit **Recorded technique:** A review of the Braunschweig group's interferometric refractive\-index measurements \(Michelson twin interferometer, 300\-1100 K, visible He\-Ne and Hg lines; the apparatus and methods of their refs\. \[27, 28\]\) with one new product\: the polarizability of the free molecule fitted to Eq\. \(10\), a one\-term Kramers\-Heisenberg dispersion times a quadratic in temperature \(Table 1\)\. **Materials in structured entries:** Ar, CH4, CO2, H2, N2, O2 **Dataset quantities:** None recorded. **Contents:** 0 datasets; 6 formulas. Curation notes -------------- Page numbers are the journal's \(728\-733; pdf page 1 = p\. 728\)\. The last pdf page is the start of an unrelated communication \(Behrisch, on DD fusion\)\. Reduction \(Eqs\. 1\-3, pp\. 728\-729\)\: \(n^2 \- 1\)/\(n^2 \+ 2\)/rho\_0 = sum\_j A\_j rho\_0^\(j\-1\), rho\_0 = p/RT; A\_1 = \(4/3\) pi N\_A alpha\(omega, T\), alpha the volume polarizability of the free molecule, 'with a precision of about 0\.03%' \(p\. 729\)\. Eq\. \(10\) \(p\. 730\)\: alpha\(omega, T\) = alpha\(0, 0\)/\(1 \- omega^2/omega\_0^2\) \(1 \+ b T \+ c T^2\), from Eq\. \(5\) \(one effective oscillator, 'may be used also for careful extrapolations to other frequency ranges within the accuracy of our measurements'\) and Eq\. \(8\) \(Bell and Buckingham's rotation\-vibration averaging, zero\-point vibration included in alpha\(omega, 0\)\)\. 'This equation is sufficient to represent our experimental results for simple atoms and small molecules with a mean uncertainty of about 0\.1%' \(p\. 730\)\. 'As usual standard deviations are given in parenthesis'; 'additional figures are given to some numbers, which otherwise are not significant' \(p\. 730\)\. Table 1 note a\: 'The uncertainty of omega\_0 is usually less than 0\.5%'\. alpha\(0, 0\) is an extrapolation to omega = 0 and T = 0 of electronic \(optical\) data\: it excludes the vibrational \(atomic\) polarizability \(p\. 731, of Fig\. 3\), so it is not a static polarizability\. Sources of the fitted data \(Table 1 notes\)\: b \[35\] Hohm and Kerl, Mol\. Phys\. 69, 819 \(1990\) \(Ar, H2, O2; hohm\_1990b, in the library since 2026\-09\-27\); c N2, the temperature dependence from \[23\] \(hohm\_1990\) and the dispersion from \[19\] \(K\. Kerl, Z\. Phys\. Chem\. NF 129, 129 \(1982\)\), e 'Dispersion only determined at 298 K'; d CH4 \[26\] \(U\. Hohm and K\. Kerl, Ber\. Bunsenges\. Phys\. Chem\. 95, 36 \(1991\) = hohm\_1991\), f 'Dispersion only determined between 128 K and 296 K'; CO2 no reference; g 'Given high statistical weight for fit in T to keep the occurring \[misspelt in print\] and physically wrong negative slope at lower T small' \(H2, O2, CH4, air; footnotes f and g are garbled in the library's text, read from the image, p\. 731\)\. A negative b gives a spurious weak minimum of alpha\(T\), suppressed in Fig\. 2 \(p\. 731\)\. Checks \(2026\-09\-26\), Eq\. \(10\) in angstrom^3 against Hohm's measurements \(hohm\_1994b, hohm\_1993; 1 au = 0\.1481847 angstrom^3\) at their temperatures\: Ar \-0\.026 % \(633 nm\) and \-0\.011 % \(543\.5 nm\); CH4 \-0\.016 %, \-0\.015 %; O2 \-0\.275 %, \-0\.246 %; CO2 \+0\.208 %, \+0\.211 %; H2 \+0\.02 % against hohm\_1994/input\_H2 \(whose temperature is not stated, taken as 293\-296 K\)\. Against hohm\_1990's alpha\(T\) formulas at 632\.99 nm \(the same group\)\: Ar \+0\.018 % \(1\.66306 against 1\.66276\), N2 \+0\.002 % at 300 K, CH4 \-0\.014 %, O2 \-0\.035 %, H2 \-0\.10 % at 300 K\. The fits' rise from 0 to 1000 K\: H2 1\.34 %, CH4 1\.14 %, O2 0\.63 %, N2 0\.18 %, Ar 0 \(hohm\_1990\: 1\.4, 1\.2, 0\.7, 0\.2 %\)\. The O2 and CO2 offsets from hohm\_1994b exceed the stated 0\.1 %\. Not transcribed\: air \(not a curated species; alpha\(0,0\) = 1\.6970\(13\) angstrom^3, omega\_0 = 2\.47044e16 s^\-1, b = \-1\.765\(3\.0\)e\-6 K^\-1, c = 7\.909\(3\.7\)e\-9 K^\-2, 296\-985 K, dispersion at 298 K only\); the neopentane, CH3OH and CF2Cl2 discussion \(b\_R of CH3OH 3160\(25\) cm^3/mol, dimerisation; not curated species\); Figs\. 1\-4\. **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 -------- kerl\_1992/eq10\_Ar ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_Ar", "material": "Ar", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "alpha(omega, T) = alpha(0,0)/(1 - omega^2/omega_0^2) (1 + b T + c T^2); Ar: 10^30 alpha(0,0)/m^3 = 1.6404(10), 10^-16 omega_0/s^-1 = 2.54932, 10^6 b/K = 0.0, 10^9 c/K^2 = 0.0", "variable": "omega: angular frequency in s^-1 (2 pi c over the vacuum wavelength); T: temperature in K; alpha: polarizability volume in 1e-30 m^3", "range": "295-1007 K, 543.51-632.99 nm", "coefficients": { "alpha00": "1.6404", "alpha00_sigma": "0.0010", "omega0": "2.54932e16", "b": "0.0", "c": "0.0", "unit": "1e-30 m^3" }, "check": "At 632.99 nm gives 1.66306 angstrom^3 (hohm_1990's mean 1.66276(59): +0.018 %); against hohm_1994b/alpha_Ar at 296.82 K -0.026 % (633 nm), -0.011 % (543.5 nm). Checked 2026-09-26." } Data of Hohm and Kerl, Mol\. Phys\. 69, 819 \(1990\) \(note b\) = hohm\_1990b \(re\-pointed 2026\-09\-27\)\: a fit to its Ar data, so not independent of hohm\_1990b's formulas and alpha0\_T\_Ar \(fit one or the other\)\. alpha\(0,0\) = 1\.6404\(10\) is hohm\_1990b's mean static value, printed there 1\.6404\(11\)\. No temperature dependence \(b = c = 0\)\. kerl\_1992/eq10\_H2 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_H2", "material": "H2", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "as eq10_Ar; H2: 10^30 alpha(0,0)/m^3 = 0.80320(57) (note g), 10^-16 omega_0/s^-1 = 2.13987, 10^6 b/K = 5.87(1.6), 10^9 c/K^2 = 7.544(2.0)", "variable": "as eq10_Ar", "range": "296-1007 K, 543.51-632.99 nm", "coefficients": { "alpha00": "0.80320", "alpha00_sigma": "0.00057", "omega0": "2.13987e16", "b": "5.87e-6", "b_sigma": "1.6e-6", "c": "7.544e-9", "c_sigma": "2.0e-9", "unit": "1e-30 m^3" }, "check": "Against hohm_1994/input_H2 (5.53900 au at 632.99 nm, temperature not stated) +0.02 % at 293-296 K; against hohm_1990's Eq. (18) -0.10 % at 300 K, and the 0-1000 K rise is 1.34 % (hohm_1990: 1.4 %). Checked 2026-09-26." } Data of Hohm and Kerl, Mol\. Phys\. 69, 819 \(1990\) \(note b\) = hohm\_1990b \(re\-pointed 2026\-09\-27; not independent of it\)\. alpha\(0,0\) = 0\.80320\(57\) is hohm\_1990b's Table 4 extrapolation to 0 K \(alpha\_0K\_H2, static row\), digit for digit\. Normal H2 \(the paper does not say otherwise\)\. Note g\: alpha\(0,0\) given high statistical weight to keep the spurious low\-T slope small\. The measured alpha\(T\) agrees with Bishop and Pipin's ab initio values \(Fig\. 2, p\. 731\)\. kerl\_1992/eq10\_N2 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_N2", "material": "N2", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "as eq10_Ar; N2: 10^30 alpha(0,0)/m^3 = 1.7406(14), 10^-16 omega_0/s^-1 = 2.60490, 10^6 b/K = 1.8(1.1), 10^9 c/K^2 = -", "variable": "as eq10_Ar", "range": "295-1089 K; 400-700 nm, the dispersion at 298 K only (note e)", "coefficients": { "alpha00": "1.7406", "alpha00_sigma": "0.0014", "omega0": "2.60490e16", "b": "1.8e-6", "b_sigma": "1.1e-6", "unit": "1e-30 m^3" }, "check": "At 632.99 nm and 300 K gives 1.76457 angstrom^3, hohm_1990's Eq. (19) 1.76453 (+0.002 %); +0.18 % from 0 to 1000 K (hohm_1990: 0.2 %). Checked 2026-09-26." } The temperature dependence from hohm\_1990 \(\[23\]\), the dispersion from Kerl 1982 \(\[19\], Z\. Phys\. Chem\. NF 129, 129; not in the library\), note c\. c is printed '\-' \(no quadratic term\)\. kerl\_1992/eq10\_O2 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_O2", "material": "O2", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "as eq10_Ar; O2: 10^30 alpha(0,0)/m^3 = 1.5658(14) (note g), 10^-16 omega_0/s^-1 = 2.18010, 10^6 b/K = -2.369(1.2), 10^9 c/K^2 = 8.687(1.6)", "variable": "as eq10_Ar", "range": "297-1006 K, 543.51-632.99 nm", "coefficients": { "alpha00": "1.5658", "alpha00_sigma": "0.0014", "omega0": "2.18010e16", "b": "-2.369e-6", "b_sigma": "1.2e-6", "c": "8.687e-9", "c_sigma": "1.6e-9", "unit": "1e-30 m^3" }, "check": "Against hohm_1994b/alpha_O2 at 292.06 K: -0.275 % (633 nm), -0.246 % (543.5 nm), beyond the stated 0.1 %; against hohm_1990's Eq. (20) -0.035 % at 300 K, and +0.63 % from 0 to 1000 K (hohm_1990: 0.7 %). Checked 2026-09-26." } Data of Hohm and Kerl, Mol\. Phys\. 69, 819 \(1990\) \(note b\) = hohm\_1990b \(re\-pointed 2026\-09\-27; not independent of it\)\. alpha\(0,0\) = 1\.5658\(14\) is hohm\_1990b's Table 5 extrapolation to 0 K \(alpha\_0K\_O2, static row\), digit for digit\. Note g as for H2\. Fig\. 3 extrapolates the O2 polarizability surface far outside the measured \(hatched\) region; the authors warn that it neglects the atomic polarizability at low frequencies \(p\. 731\)\. kerl\_1992/eq10\_CH4 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_CH4", "material": "CH4", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "as eq10_Ar; CH4: 10^30 alpha(0,0)/m^3 = 2.5548(18) (note g), 10^-16 omega_0/s^-1 = 2.14600, 10^6 b/K = -1.637(1.6), 10^9 c/K^2 = 13.048(2.1)", "variable": "as eq10_Ar", "range": "128-890 K; 543.51-632.99 nm, the dispersion between 128 and 296 K only (note f)", "coefficients": { "alpha00": "2.5548", "alpha00_sigma": "0.0018", "omega0": "2.14600e16", "b": "-1.637e-6", "b_sigma": "1.6e-6", "c": "13.048e-9", "c_sigma": "2.1e-9", "unit": "1e-30 m^3" }, "check": "Against hohm_1993/alpha_CH4 at 294.47 K: -0.016 % (633 nm), -0.015 % (543.5 nm); against hohm_1990's Eq. (20) -0.014 % at 300 K, and +1.14 % from 0 to 1000 K (hohm_1990: 1.2 %). Checked 2026-09-26." } Data of Hohm and Kerl, Ber\. Bunsenges\. Phys\. Chem\. 95, 36 \(1991\) \(note d\) = hohm\_1991 \(re\-pointed 2026\-09\-27; with hohm\_1990's 300\-1100 K data, not independent of either\)\. Note g as for H2\. kerl\_1992/eq10\_CO2 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq10_CO2", "material": "CO2", "equation": "Eq. (10) with Table 1, pp. 730-731", "printed": "as eq10_Ar; CO2: 10^30 alpha(0,0)/m^3 = 2.5891(35), 10^-16 omega_0/s^-1 = 2.33357, 10^6 b/K = 10.6(5.0), 10^9 c/K^2 = -", "variable": "as eq10_Ar", "range": "220-360 K, 543.51-632.99 nm", "coefficients": { "alpha00": "2.5891", "alpha00_sigma": "0.0035", "omega0": "2.33357e16", "b": "10.6e-6", "b_sigma": "5.0e-6", "unit": "1e-30 m^3" }, "check": "Against hohm_1994b/alpha_CO2 at 293.80 K: +0.208 % (633 nm), +0.211 % (543.5 nm), beyond the stated 0.1 %. Checked 2026-09-26." } No reference is given for the CO2 data \(the only row without a note\)\. c is printed '\-'\. 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.