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 · Catalogue · Review register
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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.