hohm_1990b

U. Hohm and K. Kerl, “Interferometric measurements of the dipole polarizability alpha of molecules between 300 K and 1100 K. II. A new method for measuring the dispersion of the polarizability and its application to Ar, H2, and O2”, Mol. Phys. 69, 819 (1990)

Source record · Catalogue · Review register

DOI: 10.1080/00268979000100621

Source kind: measurement

Recorded technique: The Michelson twin interferometer of Part I (hohm_1990; sample cell of length L = l/2 about 0.5 m, quartz glass, 300-1100 K) illuminated simultaneously by four He-Ne lasers of vacuum wavelengths 632.99, 611.97, 594.11 and 543.51 nm. The cell is filled to p_max < 2.5e5 Pa, thermostated 5-10 min and evacuated in 5-15 min while a monochromatic (632.99 nm) and a polychromatic interferogram are recorded (about 20 000 points each). The 632.99 nm absolute measurement gives alpha(lambda_1) and the density of every point (Eq. 17); the Fourier transform of the polychromatic interferogram against density (Eqs. 12-15) has four peaks whose positions give alpha(lambda_k) (Eq. 16). Three to five dispersion measurements per temperature, averaged per wavelength (pp. 820-824).

Materials in structured entries: Ar, H2, O2

Dataset quantities: polarizability, polarizability_derivative

Contents: 26 datasets; 24 formulas.

Curation notes

Part II of Hohm and Kerl. Part I (Mol. Phys. 69, 803, the monochromatic 632.99 nm measurements of the noble gases, H2, N2, O2 and CH4) is hohm_1990; this is the dispersion paper that kerl_1992 cites as ‘Mol. Phys. 69, 819’ (its note b) and hohm_1991 as its ref. [4]. Identity: the first page and the running heads print Molecular Physics 1990, 69:819-831 (the library’s ‘PDF date hint 2016’ is the download date). Page numbers are the journal’s (819-831): pdf page 1 is the publisher’s cover, so p. = pdf page + 817.

REDUCTION (pp. 820-821). (n - 1) = 2 pi N_A alpha rho (Eq. 6, the low-density approximation of Lorentz-Lorenz, (n^2 - 1)/(n^2 + 2) ~ (2/3)(n - 1)); rho = rho_0 [1 - B(T) rho_0], rho_0 = p/RT, with the second thermodynamic virial coefficient B(T) of Kerl 1986 (Eq. 11); the refractivity virial coefficient b_R is neglected (p. 821, and p. 829: ‘no experimental data are available for it at the temperatures used’). So alpha is the free-molecule polarizability volume alpha_SI/(4 pi eps0) (m^3; 10^-30 m^3 = angstrom^3), real-gas reduced, and needs no state. The wavelengths are vacuum wavelengths (p. 819: ‘the vacuum-wavelength range between lambda_1 = 632.99 nm and lambda_4 = 543.51 nm’).

WHAT IS PRINTED. The measured alpha(omega_k, T) themselves are not tabulated here (‘tabulated in [3]’, Hohm’s 1989 Braunschweig dissertation, p. 828: missing). For each temperature the paper prints the fit of the four averaged alpha(omega_k, T) to the single-term Kramers-Heisenberg relation alpha(omega, T) = C0(T)/[C1(T) - omega^2] (Eq. 18), with C0 = f0 e^2/(4 pi eps0 m) and C1 = (E0’/hbar)^2 (Eqs. 19-20) and the same fit in atomic units (Eq. 21: f0, omega0*), the extrapolated static alpha(0, T) = C0/C1, C6 = 3 f0^2/(4 omega0*^3) and the fit’s standard deviation 100 Delta alpha/alpha(0, T) = 0.02-0.08 (Tables 1-3). ‘To reproduce the measured polarizabilities with the given standard deviation, five decimal places have to be used for the fit parameters given in the first four columns’ (p. 824). The fits are the formulas below (one per temperature); evaluated at the four wavelengths they are the measurements to within the stated standard deviation. The static alpha(0, T) are datasets (alpha0_T_<gas>, row = the temperature in K), use = check: a single-term extrapolation from 543.51-632.99 nm to omega = 0, which ‘clearly limits the accuracy’ (p. 826); for H2 and O2 (no infrared activity) the static limit of the electronic polarizability, for Ar the static polarizability. The temperatures carry their own uncertainty in parentheses (‘295.60 (22)’: not transcribed into the row id; in the printed column).

Uncertainty: none stated for alpha itself beyond the fit standard deviation; Part I states |Delta alpha/alpha| < 10^-3 for the method (hohm_1990, p. 809). The Tables 4-5 digits in parentheses (the 0 K extrapolations and alpha’_e) are uncertainties on the last digits, level not stated here (Part I: ‘As usual, standard deviations are given in parentheses’).

TEMPERATURE DEPENDENCE (pp. 826-830). No marked temperature dependence of f0, omega0* or C6 for any gas (p. 827). Ar: alpha(0, T) independent of T; mean alpha(0) = 1.6404(11) x 10^-30 m^3 (p. 828, dataset mean_alpha0_Ar), against Bose and Cole’s 1.64110(24) [19] (bose_1970: 3 A_eps/(4 pi N_A) with A_eps = 4.1397 cm^3/mol is 1.64108, checked) and Kumar and Meath’s DOSD 1.64189 [18]. H2 and O2: the alpha(lambda_k, T) are analysed with Part I’s Eqs. (11)-(12) (rotational stretching only; the vibrational part has no measurable effect), separately at each wavelength, giving the dynamic polarizability extrapolated to T = 0 K and the derivative alpha’_e(lambda) = r_e (d alpha(lambda)/d r)_e (r_e = 0.74144 angstrom for H2, 1.20752 angstrom for O2) (Tables 4-5). H2: alpha(infinity, 0) = 8.0320(57) x 10^-31 m^3 ‘shows a marked agreement’ with Bishop and Cheung’s 8.0306 (p. 828); this work is 0.02-0.06 % above Bishop et al. at every wavelength; mean alpha’_e = 1.06 x 10^-30 m^3 against 0.9 x 10^-30 from light scattering at 400-500 nm (Stansbury, Crawford and Welsh 1953; Knippers, van Helvoort and Stolte 1985) (p. 828); the ratio a1/a2 to Adamov and Evarestov’s calculation is 1.058-1.073 (1.125 at 611.97 nm, which the authors omit). O2: ‘the data of O2 used do not have the same quality as those of H2’ (p. 829); mean alpha’_e = 3 x 10^-30 m^3, ‘considerably higher than the highly reliable one of alpha’_e = 1.76(7) x 10^-30 m^3 given by Buldakov et al.’ (p. 829), since Eq. (11) of Part I neglects the degeneracy of the ground state and the low-lying 1Delta_g level; alpha’’_e neglected. Rijks et al.’s ab initio dynamic polarizabilities are ‘much too low’ and are printed scaled up by 1.0831 to this work’s alpha(infinity, 0) (p. 829), so their static value equals this work’s by construction. The a1/a2 ratios (last column of Tables 4-5) are not extracted.

INTERNAL CHECKS (2026-09-27, each formula’s check). In every row of Tables 1-3, C0/C1 reproduces the printed alpha(0, T), C0/(e^2/4 pi eps0 m) = C0/253.2638 m^3 s^-2 the printed f0, C1^(1/2) x 2.4188843e-17 s the printed omega0* and 3 f0^2/(4 omega0*^3) the printed C6, each to the last printed digit (1 in the last digit at most), with two exceptions: (1) Ar at 570.48 K prints omega0* = 0.617490 where C1 gives 0.617470; f0/omega0*^2 reproduces the printed alpha(0, T) = 1.64086 with 0.617470 (1.64086) and not with 0.617490 (1.64075): a misprinted omega0*, corrected in the formula (eq18_Ar_570.48); (2) H2 at 1006.72 K prints alpha(0, T) = 0.81227 where C0/C1 = 3.75134e2/4.61631e32 = 0.81263 x 10^-30 m^3, and f0/omega0*^2 (1.48120/0.519712^2 = 5.48388 au = 0.81263) and C6 = 3 alpha*^2 omega0*/4 (11.72 as printed needs 0.81263) agree with C0/C1: a misprinted alpha(0, T), corrected by an erratum. The Eq. (18) fits at 632.99 nm against Part I: Ar 1.66281 (295.60 K) against hohm_1990’s 300-1100 K mean 1.66276(59) (+0.003 %); H2 0.82181 (296.40 K) against hohm_1990’s Eq. (18) at 296.40 K, 0.82187 (-0.007 %); O2 1.59695 (296.78 K) against hohm_1990’s Eq. (20), 1.59618 (+0.05 %).

TABLE 1-3 LITERATURE ROWS (reproduced). ‘With the use of second thermodynamic virial coefficients [15] the given dispersion formulae [8, 16, 17] are converted to non-ideal behaviour’ (p. 825): the rows [8] (K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982), measured 400-700 nm, 293.04-293.05 K), [16] (Cuthbertson and Cuthbertson, Proc. R. Soc. 84, 13 (1910) = cuthbertson_1910, argon, 480-671 nm) and [17] (C. Cuthbertson, Phil. Mag. 25, 592 (1913), H2 and O2; not in the library) are the authors’ re-evaluations of those dispersion formulas at 273.15 K, recorded as reproduced formulas (and their alpha(0, T) as reproduced datasets). The authors find the argon and oxygen values of [8] ‘slightly too high by the same amount’ (p. 825). The rows with only a static value: [18] kumar_1985 (Ar, 11.08 au), [19] bose_1970 (Ar), [20] orcutt_1967 (H2, 0.80515: this corresponds to A_eps = 2.0310 cm^3/mol, not among orcutt_1967’s printed H2 values 2.033(1), 2.0301(8), 2.036(3); unexplained), [21] zeiss_1977 (H2 5.428 au, O2 10.59 au: 0.80435 and 1.56928, checked), [22] bishop_1980 (H2, 0.80524). Bishop and Cheung’s Table 4 column is their J = 0 (v = 0) polarizability, i.e. at T = 0 K: 5.4193 au = 0.80306 (static) and 5.5242 au = 0.81860 at 6328 A (checked; listed here at 632.99 nm); the 611.97, 594.11 and 543.51 nm values (0.81971, 0.82075, 0.82430) are not among bishop_1980’s wavelengths and were presumably interpolated by Hohm and Kerl (not said). Adamov and Evarestov (Opt. Spectrosc. 19, 362 (1965)), Rijks, van Heeringen and Wormer (J. Chem. Phys. 90, 6501 (1989)) and Inoue, Matsushima and Iwata (Mol. Phys. 56, 1097 (1985)) are not in the library.

NOT EXTRACTED (no quantity): C6 (this work 55.98-57.25 a.u. for Ar, 11.44-11.77 for H2, 43.88-44.86 for O2, ‘always lower than the data given in the literature’; literature 64.57 [18] Ar; 12.15 [23] Visser et al. 1985 and 12.11 [21] H2; 50.90 [23] and 62.01 [21] O2), f0 and omega0* beyond the formulas, the fits’ standard deviations (in the formulas’ printed strings), Figs. 1-5 (interferograms, the Fourier spectrum, alpha(lambda) of Ar, H2, O2 at 296 K against [8, 16, 17]).

REPRODUCTIONS ELSEWHERE: kerl_1992’s Eq. (10) fits of Ar, H2 and O2 are fitted to these data (its note b; re-pointed 2026-09-27), and its H2 and O2 alpha(0, 0) (0.80320(57), 1.5658(14)) are this paper’s Table 4-5 extrapolations, digit for digit.

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

Datasets

hohm_1990b/alpha0_T_Ar

{
  "id": "alpha0_T_Ar",
  "material": "Ar",
  "file": "Ar/hohm_1990b__alpha0_T_Ar.csv",
  "table": "tbl_8e74d3a3b9bc",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "parameters": {
    "temperature_range_k": "295.60-1006.48"
  }
}

Table 1 (p. 824), this work: alpha(0, T) = C0/C1 of the Eq. (18) fit to the four measured wavelengths (543.51-632.99 nm), at 295.60-1006.48 K (row = temperature in K). A single-term extrapolation to omega = 0; no temperature dependence (mean 1.6404(11), dataset mean_alpha0_Ar). No uncertainty printed for alpha(0, T); the fit standard deviations are 0.02-0.05 % (printed column).

hohm_1990b/mean_alpha0_Ar

{
  "id": "mean_alpha0_Ar",
  "material": "Ar",
  "table": "text",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  }
}

1 inline points in the source record.

p. 828: ‘The mean value is alpha(0) = 1.6404(11) x 10^-30 m^3’, the mean of alpha0_T_Ar over 295-1006 K (not independent of it). Level of the uncertainty not stated. kerl_1992’s Ar alpha(0,0) is 1.6404(10).

hohm_1990b/kerl_1982_Ar

{
  "id": "kerl_1982_Ar",
  "material": "Ar",
  "file": "Ar/hohm_1990b__kerl_1982_Ar.csv",
  "table": "tbl_8e74d3a3b9bc",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ]
}

Table 1, row ‘293.04 [8]’: C0/C1 of Kerl’s dispersion formula (measured 400-700 nm) converted by Hohm and Kerl to non-ideal behaviour (row = 293.04 K). The authors judge Kerl’s argon values slightly too high (p. 825).

hohm_1990b/cuthbertson_1910_Ar

{
  "id": "cuthbertson_1910_Ar",
  "material": "Ar",
  "file": "Ar/hohm_1990b__cuthbertson_1910_Ar.csv",
  "table": "tbl_8e74d3a3b9bc",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "cuthbertson_1910"
  ]
}

Table 1, row ‘273.15 [16]’: C0/C1 of the Cuthbertsons’ argon dispersion formula (Proc. R. Soc. 84, 13 (1910), measured 480-671 nm) converted by Hohm and Kerl to non-ideal behaviour, 273.15 K.

hohm_1990b/kumar_1985_Ar

{
  "id": "kumar_1985_Ar",
  "material": "Ar",
  "file": "Ar/hohm_1990b__kumar_1985_Ar.csv",
  "table": "tbl_8e74d3a3b9bc",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "kumar_1985"
  ]
}

Table 1, ‘1.64189 [18]’: Kumar and Meath’s DOSD static polarizability (their S(-2) = 11.08 au x 0.14818474 = 1.64189, checked).

hohm_1990b/bose_1970_Ar

{
  "id": "bose_1970_Ar",
  "material": "Ar",
  "file": "Ar/hohm_1990b__bose_1970_Ar.csv",
  "table": "tbl_8e74d3a3b9bc",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bose_1970"
  ],
  "uncertainty": {
    "column": true,
    "level": "3 sigma"
  }
}

Table 1, ‘1.64110 (24) [19]’: Bose and Cole’s measured static value, 3 A_eps/(4 pi N_A) of their A_eps = 4.1397 +- 0.0006 cm^3/mol at 49.7 C (bose_1970/A_eps_Ar; 1.64108 computed, and 0.0006 cm^3/mol is 0.00024: their three-standard-deviation error).

hohm_1990b/alpha0_T_H2

{
  "id": "alpha0_T_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__alpha0_T_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "parameters": {
    "temperature_range_k": "296.40-1006.72"
  }
}

Table 2 (p. 825), this work: alpha(0, T) = C0/C1 of the Eq. (18) fit to the four measured wavelengths (543.51-632.99 nm) at 296.40-1006.72 K (row = temperature in K); normal H2 (not said otherwise). The static limit of the electronic polarizability, rising 0.8 % from 296 to 1007 K. The 1006.72 K value is corrected by an erratum (0.81227 printed, 0.81263 = C0/C1). No uncertainty printed; the fit standard deviations are 0.02-0.08 %.

hohm_1990b/kerl_1982_H2

{
  "id": "kerl_1982_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__kerl_1982_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ]
}

Table 2, row ‘293.05 [8]’: C0/C1 of Kerl’s dispersion formula converted by Hohm and Kerl to non-ideal behaviour (row = 293.05 K).

hohm_1990b/cuthbertson_1913_H2

{
  "id": "cuthbertson_1913_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__cuthbertson_1913_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "C. Cuthbertson, Phil. Mag. 25, 592 (1913)"
  ]
}

Table 2, row ‘273.15 [17]’: C0/C1 of Cuthbertson’s dispersion formula (measured 480-671 nm) converted by Hohm and Kerl to non-ideal behaviour, 273.15 K. The original is not in the library.

hohm_1990b/orcutt_1967_H2

{
  "id": "orcutt_1967_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__orcutt_1967_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "orcutt_1967"
  ]
}

Table 2, ‘0.80515 [20]’ (ref. [20] printed ‘Orcutt and Cole, J. Chem. Phys. 46, 697 (1966)’; the volume is 1967): a static polarizability from Orcutt and Cole’s dielectric measurements. 0.80515 corresponds to A_eps = 2.0310 cm^3/mol, which is none of orcutt_1967’s printed H2 values (2.033 +- 0.001 this work, 2.0301 +- 0.0008, 2.036 +- 0.003 at 322.15 K): how Hohm and Kerl obtained it is not said.

hohm_1990b/zeiss_1977_H2

{
  "id": "zeiss_1977_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__zeiss_1977_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "zeiss_1977"
  ]
}

Table 2, ‘0.80435 [21]’: Zeiss and Meath’s DOSD S(-2) = 5.428 au (x 0.14818474 = 0.80435, checked).

hohm_1990b/bishop_1980_H2

{
  "id": "bishop_1980_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__bishop_1980_H2.csv",
  "table": "tbl_5e447ea27a86",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1980"
  ]
}

Table 2, ‘0.80524 [22]’: Bishop and Cheung’s ab initio static value; their 293 K average is 5.4339 au = 0.80522 and J = 0 5.4193 au = 0.80306 (bishop_1980): 0.80524 matches neither exactly (the 293 K average to 2 in the last digit).

hohm_1990b/alpha0_T_O2

{
  "id": "alpha0_T_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__alpha0_T_O2.csv",
  "table": "tbl_c07dae7af5ae",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "parameters": {
    "temperature_range_k": "296.78-1006.42"
  }
}

Table 3 (p. 825), this work: alpha(0, T) = C0/C1 of the Eq. (18) fit to the four measured wavelengths (543.51-632.99 nm) at 296.78-1006.42 K (row = temperature in K). The O2 data are of lower quality than the H2 data (p. 829). No uncertainty printed; the fit standard deviations are 0.02-0.05 %.

hohm_1990b/kerl_1982_O2

{
  "id": "kerl_1982_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__kerl_1982_O2.csv",
  "table": "tbl_c07dae7af5ae",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ]
}

Table 3, row ‘293.05 [8]’: C0/C1 of Kerl’s dispersion formula converted by Hohm and Kerl to non-ideal behaviour (row = 293.05 K). The authors judge Kerl’s oxygen values slightly too high (p. 825).

hohm_1990b/cuthbertson_1913_O2

{
  "id": "cuthbertson_1913_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__cuthbertson_1913_O2.csv",
  "table": "tbl_c07dae7af5ae",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "C. Cuthbertson, Phil. Mag. 25, 592 (1913)"
  ]
}

Table 3, row ‘273.15 [17]’: C0/C1 of Cuthbertson’s dispersion formula converted by Hohm and Kerl to non-ideal behaviour, 273.15 K.

hohm_1990b/zeiss_1977_O2

{
  "id": "zeiss_1977_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__zeiss_1977_O2.csv",
  "table": "tbl_c07dae7af5ae",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "zeiss_1977"
  ]
}

Table 3, ‘1.56928 [21]’: Zeiss and Meath’s DOSD S(-2) = 10.59 au (x 0.14818474 = 1.56928, checked).

hohm_1990b/alpha_0K_H2

{
  "id": "alpha_0K_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__alpha_0K_H2.csv",
  "table": "tbl_54ded087f133",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "temperature_k": 0
  }
}

Table 4 (p. 828), column dagger: the dynamic polarizability extrapolated to T = 0 K from the alpha(lambda_k, T) at 296-1007 K with Part I’s Eq. (11) (rotational stretching), separately at each wavelength, and its static limit (row inf). The polarizability of H2 in its ground rovibrational state (J = 0, v = 0), 0.02-0.06 % above Bishop and Cheung’s ab initio values (bishop_1980_0K_H2). Parenthesised last digits in the sigma column, level not stated. kerl_1992’s H2 alpha(0,0) reprints the static value.

hohm_1990b/bishop_1980_0K_H2

{
  "id": "bishop_1980_0K_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__bishop_1980_0K_H2.csv",
  "table": "tbl_54ded087f133",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1980"
  ],
  "parameters": {
    "temperature_k": 0
  }
}

Table 4, column double dagger, ‘Calculated by Bishop et al. [22]’: bishop_1980’s J = 0 polarizability (static 5.4193 au = 0.80306; 5.5242 au at 6328 A = 0.81860, listed at 632.99 nm; checked). The 611.97, 594.11 and 543.51 nm values are not at bishop_1980’s wavelengths: presumably interpolated by Hohm and Kerl (not said).

hohm_1990b/dalpha_H2

{
  "id": "dalpha_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__dalpha_H2.csv",
  "table": "tbl_54ded087f133",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "component": "mean",
    "mode": "the H-H stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e (r_e = 0.74144 angstrom)"
  }
}

Table 4 (p. 828), ‘alpha’_e(lambda) = a1’ (dagger): alpha’_e = r_e (d alpha(lambda)/d r)_e, the derivative of the mean dynamic polarizability with respect to the internuclear distance at r_e = 0.74144 angstrom, times r_e (10^-30 m^3), fitted to the alpha(lambda, T) with Part I’s Eq. (11); mean 1.06 x 10^-30 m^3 (p. 828). Parenthesised last digits in the sigma column, level not stated. The authors consider the ratio to Adamov and Evarestov’s values (1.058-1.073, except 1.125 at 611.97 nm) more reliable than the absolute values (p. 829).

hohm_1990b/adamov_1965_dalpha_H2

{
  "id": "adamov_1965_dalpha_H2",
  "material": "H2",
  "file": "H2/hohm_1990b__adamov_1965_dalpha_H2.csv",
  "table": "tbl_54ded087f133",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "M. N. Adamov and R. A. Evarestov, Opt. Spectrosc. 19, 362 (1965)"
  ],
  "parameters": {
    "component": "mean",
    "mode": "the H-H stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e"
  }
}

Table 4, column ‘a2’ (section sign), ‘Calculated by Adamov et al. [27]’: the calculated alpha’_e(lambda) = r_e (d alpha/d r)_e of H2 (10^-30 m^3). The original is not in the library; whether Hohm and Kerl interpolated it to these wavelengths is not said.

hohm_1990b/light_scattering_dalpha_H2

{
  "id": "light_scattering_dalpha_H2",
  "material": "H2",
  "table": "text",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "E. J. Stansbury, M. F. Crawford and H. L. Welsh, Can. J. Phys. 31, 954 (1953)",
    "W. Knippers, K. van Helvoort and S. Stolte, Chem. Phys. Lett. 121, 279 (1985)"
  ],
  "parameters": {
    "component": "mean",
    "mode": "the H-H stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e"
  }
}

2 inline points in the source record.

p. 828: ‘the two coinciding values alpha’_e = 0.9 x 10^-30 m^3 given in [28] and [29]’, ‘determined by light scattering experiments in the range between 400 nm and 500 nm’ (no single wavelength given: ‘not stated’). Not in the library.

hohm_1990b/alpha_0K_O2

{
  "id": "alpha_0K_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__alpha_0K_O2.csv",
  "table": "tbl_a1ae6c41a18b",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "temperature_k": 0
  }
}

Table 5 (p. 830), column dagger: the dynamic polarizability of O2 extrapolated to T = 0 K with Part I’s Eq. (11), separately at each wavelength (r_e = 1.20752 angstrom; alpha’’_e neglected), and its static limit (row inf). Less reliable than H2 (p. 829); the model ignores the ground state’s degeneracy and the low 1Delta_g level. Parenthesised last digits in the sigma column, level not stated. kerl_1992’s O2 alpha(0,0) reprints the static value.

hohm_1990b/rijks_1989_0K_O2

{
  "id": "rijks_1989_0K_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__rijks_1989_0K_O2.csv",
  "table": "tbl_a1ae6c41a18b",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "W. Rijks, M. van Heeringen and P. E. S. Wormer, J. Chem. Phys. 90, 6501 (1989)"
  ],
  "parameters": {
    "temperature_k": 0
  }
}

Table 5, column double dagger, ‘Calculated by Rijks et al. [30] and scaled to our alpha(lambda -> infinity, 0)’: the ab initio dynamic polarizabilities multiplied by 1.0831 (p. 829), so the static row equals this work’s by construction; only the dispersion is Rijks et al.’s. The original is not in the library.

hohm_1990b/dalpha_O2

{
  "id": "dalpha_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__dalpha_O2.csv",
  "table": "tbl_a1ae6c41a18b",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "component": "mean",
    "mode": "the O-O stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e (r_e = 1.20752 angstrom)"
  }
}

Table 5 (p. 830), ‘a1’ (dagger): alpha’_e = r_e (d alpha(lambda)/d r)_e of O2 (10^-30 m^3), r_e = 1.20752 angstrom; mean 3 x 10^-30, ‘considerably higher than the highly reliable’ 1.76(7) of Buldakov et al. (p. 829; dataset buldakov_1987_dalpha_O2): the authors attribute this to their model’s neglect of the ground state’s degeneracy and the 1Delta_g level. Parenthesised last digits in the sigma column, level not stated.

hohm_1990b/inoue_1985_dalpha_O2

{
  "id": "inoue_1985_dalpha_O2",
  "material": "O2",
  "file": "O2/hohm_1990b__inoue_1985_dalpha_O2.csv",
  "table": "tbl_a1ae6c41a18b",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "T. Inoue, S. Matsushima and S. Iwata, Mol. Phys. 56, 1097 (1985)"
  ],
  "parameters": {
    "component": "mean",
    "mode": "the O-O stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e"
  }
}

Table 5, column ‘a2’ (section sign), ‘Calculated by Inoue et al. [31]’, not scaled (p. 829). The original is not in the library.

hohm_1990b/buldakov_1987_dalpha_O2

{
  "id": "buldakov_1987_dalpha_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability_derivative",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "M. A. Buldakov, B. V. Korolev, I. I. Matrosov and T. N. Popova, Opt. Spectrosc. 62, 309, 452 (1987)"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "component": "mean",
    "mode": "the O-O stretch",
    "coordinate": "r/r_e: the derivative with respect to the internuclear distance r, times r_e"
  }
}

1 inline points in the source record.

p. 829: ‘the highly reliable one of alpha’_e = 1.76(7) x 10^-30 m^3 given by Buldakov et al. [32]’; wavelength not stated; level of the uncertainty not stated. Not in the library.

Formulas

hohm_1990b/eq18_Ar_295.60

{
  "id": "eq18_Ar_295.60",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 295.60(22) K: 10^-3 C0/(m^3 s^-2) = 1.04163, 10^-32 C1/s^-2 = 6.35283, f0 = 4.11283, omega0*/a.u. = 0.609675; 10^30 alpha(0, T)/m^3 = 1.63964, C6/a.u. = 55.98, 100 Delta alpha/alpha(0, T) = 0.03",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.04163e3",
    "C1": "6.35283e32",
    "f0": "4.11283",
    "omega0_au": "0.609675"
  },
  "check": "C0/C1 = 1.63963e-30 m^3 (printed alpha(0, T) 1.63964); f0 = C0/(e^2/4 pi eps0 m) = 4.11283 (printed 4.11283); omega0* = C1^(1/2) x 2.4188843e-17 = 0.609675 (printed 0.609675); C6 = 3 f0^2/(4 omega0*^3) = 55.98 (printed 55.98). alpha(632.99 nm) = 1.66281, alpha(543.51 nm) = 1.67123 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_Ar_570.48

{
  "id": "eq18_Ar_570.48",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 570.48(89) K: 10^-3 C0/(m^3 s^-2) = 1.06923, 10^-32 C1/s^-2 = 6.51630, f0 = 4.22181, omega0*/a.u. = 0.617490; 10^30 alpha(0, T)/m^3 = 1.64086, C6/a.u. = 56.78, 100 Delta alpha/alpha(0, T) = 0.03",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.06923e3",
    "C1": "6.51630e32",
    "f0": "4.22181",
    "omega0_au": "0.617490"
  },
  "check": "C0/C1 = 1.64085e-30 m^3 (printed alpha(0, T) 1.64086); f0 = C0/(e^2/4 pi eps0 m) = 4.22180 (printed 4.22181); omega0* = C1^(1/2) x 2.4188843e-17 = 0.617470 (printed 0.617490); C6 = 3 f0^2/(4 omega0*^3) = 56.78 (printed 56.78). alpha(632.99 nm) = 1.66346, alpha(543.51 nm) = 1.67167 angstrom^3. Checked 2026-09-27.",
  "corrections": [
    {
      "term": "omega0_au",
      "printed": "0.617490",
      "corrected": "0.617470",
      "reason": "omega0* = (C1)^(1/2) in atomic units (Eqs. 20-21): (6.51630e32)^(1/2) x 2.4188843e-17 = 0.617470, and only 0.617470 reproduces the printed alpha(0, T) = 1.64086 through alpha* = f0/omega0*^2 (0.617490 gives 1.64075). Every other row of Tables 1-3 satisfies both relations to the last digit.",
      "evidence": "The table image (tbl_8e74d3a3b9bc.jpg) prints 0.617490 (not a mis-extraction); the correction follows from the row's own C1, f0 and alpha(0, T) (checked 2026-09-27)."
    }
  ]
}

The printed omega0* = 0.617490 is inconsistent with the row’s C1 (0.617470) and with its alpha(0, T): f0/omega0*^2 = 4.22181/0.617470^2 = 11.0731 au = 1.64086e-30 m^3 as printed, while 0.617490 gives 1.64075. Corrected below; C0 and C1, which define the fit, are unaffected.

hohm_1990b/eq18_Ar_667.37

{
  "id": "eq18_Ar_667.37",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 667.37(75) K: 10^-3 C0/(m^3 s^-2) = 1.06897, 10^-32 C1/s^-2 = 6.51935, f0 = 4.22077, omega0*/a.u. = 0.617614; 10^30 alpha(0, T)/m^3 = 1.63969, C6/a.u. = 56.71, 100 Delta alpha/alpha(0, T) = 0.04",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.06897e3",
    "C1": "6.51935e32",
    "f0": "4.22077",
    "omega0_au": "0.617614"
  },
  "check": "C0/C1 = 1.63969e-30 m^3 (printed alpha(0, T) 1.63969); f0 = C0/(e^2/4 pi eps0 m) = 4.22078 (printed 4.22077); omega0* = C1^(1/2) x 2.4188843e-17 = 0.617614 (printed 0.617614); C6 = 3 f0^2/(4 omega0*^3) = 56.71 (printed 56.71). alpha(632.99 nm) = 1.66227, alpha(543.51 nm) = 1.67046 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_Ar_760.80

{
  "id": "eq18_Ar_760.80",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 760.80(17) K: 10^-3 C0/(m^3 s^-2) = 1.08457, 10^-32 C1/s^-2 = 6.60512, f0 = 4.28238, omega0*/a.u. = 0.621664; 10^30 alpha(0, T)/m^3 = 1.64202, C6/a.u. = 57.25, 100 Delta alpha/alpha(0, T) = 0.03",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.08457e3",
    "C1": "6.60512e32",
    "f0": "4.28238",
    "omega0_au": "0.621664"
  },
  "check": "C0/C1 = 1.64201e-30 m^3 (printed alpha(0, T) 1.64202); f0 = C0/(e^2/4 pi eps0 m) = 4.28237 (printed 4.28238); omega0* = C1^(1/2) x 2.4188843e-17 = 0.621664 (printed 0.621664); C6 = 3 f0^2/(4 omega0*^3) = 57.25 (printed 57.25). alpha(632.99 nm) = 1.66433, alpha(543.51 nm) = 1.67243 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_Ar_864.64

{
  "id": "eq18_Ar_864.64",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 864.64(27) K: 10^-3 C0/(m^3 s^-2) = 1.05826, 10^-32 C1/s^-2 = 6.45675, f0 = 4.17849, omega0*/a.u. = 0.614642; 10^30 alpha(0, T)/m^3 = 1.63900, C6/a.u. = 56.39, 100 Delta alpha/alpha(0, T) = 0.02",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.05826e3",
    "C1": "6.45675e32",
    "f0": "4.17849",
    "omega0_au": "0.614642"
  },
  "check": "C0/C1 = 1.63900e-30 m^3 (printed alpha(0, T) 1.63900); f0 = C0/(e^2/4 pi eps0 m) = 4.17849 (printed 4.17849); omega0* = C1^(1/2) x 2.4188843e-17 = 0.614642 (printed 0.614642); C6 = 3 f0^2/(4 omega0*^3) = 56.39 (printed 56.39). alpha(632.99 nm) = 1.66179, alpha(543.51 nm) = 1.67007 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_Ar_1006.48

{
  "id": "eq18_Ar_1006.48",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 1006.48(18) K: 10^-3 C0/(m^3 s^-2) = 1.07380, 10^-32 C1/s^-2 = 6.54390, f0 = 4.23985, omega0*/a.u. = 0.618776; 10^30 alpha(0, T)/m^3 = 1.64092, C6/a.u. = 56.91, 100 Delta alpha/alpha(0, T) = 0.05",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.07380e3",
    "C1": "6.54390e32",
    "f0": "4.23985",
    "omega0_au": "0.618776"
  },
  "check": "C0/C1 = 1.64092e-30 m^3 (printed alpha(0, T) 1.64092); f0 = C0/(e^2/4 pi eps0 m) = 4.23985 (printed 4.23985); omega0* = C1^(1/2) x 2.4188843e-17 = 0.618776 (printed 0.618776); C6 = 3 f0^2/(4 omega0*^3) = 56.91 (printed 56.91). alpha(632.99 nm) = 1.66343, alpha(543.51 nm) = 1.67160 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_kerl_1982_Ar

{
  "id": "eq18_kerl_1982_Ar",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 293.04 K, row [8]: 10^-3 C0/(m^3 s^-2) = 1.12389, 10^-32 C1/s^-2 = 6.82947, f0 = 4.43764, omega0*/a.u. = 0.632133; 10^30 alpha(0, T)/m^3 = 1.64565, C6/a.u. = 58.47",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.12389e3",
    "C1": "6.82947e32",
    "f0": "4.43764",
    "omega0_au": "0.632133"
  },
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ],
  "check": "C0/C1 = 1.64565e-30 m^3 (printed alpha(0, T) 1.64565); f0 = C0/(e^2/4 pi eps0 m) = 4.43763 (printed 4.43764); omega0* = C1^(1/2) x 2.4188843e-17 = 0.632133 (printed 0.632133); C6 = 3 f0^2/(4 omega0*^3) = 58.47 (printed 58.47). alpha(632.99 nm) = 1.66727, alpha(543.51 nm) = 1.67511 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_cuthbertson_1910_Ar

{
  "id": "eq18_cuthbertson_1910_Ar",
  "material": "Ar",
  "equation": "Eqs. (18)-(21) with Table 1, p. 824",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 273.15 K, row [16]: 10^-3 C0/(m^3 s^-2) = 1.10212, 10^-32 C1/s^-2 = 6.71488, f0 = 4.35167, omega0*/a.u. = 0.626808; 10^30 alpha(0, T)/m^3 = 1.64131, C6/a.u. = 57.67",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "1.10212e3",
    "C1": "6.71488e32",
    "f0": "4.35167",
    "omega0_au": "0.626808"
  },
  "reproduced_from": [
    "cuthbertson_1910"
  ],
  "check": "C0/C1 = 1.64131e-30 m^3 (printed alpha(0, T) 1.64131); f0 = C0/(e^2/4 pi eps0 m) = 4.35167 (printed 4.35167); omega0* = C1^(1/2) x 2.4188843e-17 = 0.626808 (printed 0.626808); C6 = 3 f0^2/(4 omega0*^3) = 57.67 (printed 57.67). alpha(632.99 nm) = 1.66324, alpha(543.51 nm) = 1.67120 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_296.40

{
  "id": "eq18_H2_296.40",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 296.40(13) K: 10^-2 C0/(m^3 s^-2) = 3.66354, 10^-32 C1/s^-2 = 4.54644, f0 = 1.44653, omega0*/a.u. = 0.515764; 10^30 alpha(0, T)/m^3 = 0.80580, C6/a.u. = 11.44, 100 Delta alpha/alpha(0, T) = 0.02",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.66354e2",
    "C1": "4.54644e32",
    "f0": "1.44653",
    "omega0_au": "0.515764"
  },
  "check": "C0/C1 = 0.80580e-30 m^3 (printed alpha(0, T) 0.80580); f0 = C0/(e^2/4 pi eps0 m) = 1.44653 (printed 1.44653); omega0* = C1^(1/2) x 2.4188843e-17 = 0.515764 (printed 0.515764); C6 = 3 f0^2/(4 omega0*^3) = 11.44 (printed 11.44). alpha(632.99 nm) = 0.82181, alpha(543.51 nm) = 0.82767 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_571.19

{
  "id": "eq18_H2_571.19",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 571.19(54) K: 10^-2 C0/(m^3 s^-2) = 3.65765, 10^-32 C1/s^-2 = 4.52926, f0 = 1.44420, omega0*/a.u. = 0.514788; 10^30 alpha(0, T)/m^3 = 0.80756, C6/a.u. = 11.47, 100 Delta alpha/alpha(0, T) = 0.05",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.65765e2",
    "C1": "4.52926e32",
    "f0": "1.44420",
    "omega0_au": "0.514788"
  },
  "check": "C0/C1 = 0.80756e-30 m^3 (printed alpha(0, T) 0.80756); f0 = C0/(e^2/4 pi eps0 m) = 1.44421 (printed 1.44420); omega0* = C1^(1/2) x 2.4188843e-17 = 0.514788 (printed 0.514788); C6 = 3 f0^2/(4 omega0*^3) = 11.47 (printed 11.47). alpha(632.99 nm) = 0.82366, alpha(543.51 nm) = 0.82956 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_664.69

{
  "id": "eq18_H2_664.69",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 664.69(25) K: 10^-2 C0/(m^3 s^-2) = 3.82998, 10^-32 C1/s^-2 = 4.73424, f0 = 1.51225, omega0*/a.u. = 0.526308; 10^30 alpha(0, T)/m^3 = 0.80899, C6/a.u. = 11.77, 100 Delta alpha/alpha(0, T) = 0.08",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.82998e2",
    "C1": "4.73424e32",
    "f0": "1.51225",
    "omega0_au": "0.526308"
  },
  "check": "C0/C1 = 0.80900e-30 m^3 (printed alpha(0, T) 0.80899); f0 = C0/(e^2/4 pi eps0 m) = 1.51225 (printed 1.51225); omega0* = C1^(1/2) x 2.4188843e-17 = 0.526308 (printed 0.526308); C6 = 3 f0^2/(4 omega0*^3) = 11.76 (printed 11.77). alpha(632.99 nm) = 0.82442, alpha(543.51 nm) = 0.83005 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_760.59

{
  "id": "eq18_H2_760.59",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 760.59(2) K: 10^-2 C0/(m^3 s^-2) = 3.69837, 10^-32 C1/s^-2 = 4.56628, f0 = 1.46028, omega0*/a.u. = 0.516888; 10^30 alpha(0, T)/m^3 = 0.80993, C6/a.u. = 11.58, 100 Delta alpha/alpha(0, T) = 0.05",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.69837e2",
    "C1": "4.56628e32",
    "f0": "1.46028",
    "omega0_au": "0.516888"
  },
  "check": "C0/C1 = 0.80993e-30 m^3 (printed alpha(0, T) 0.80993); f0 = C0/(e^2/4 pi eps0 m) = 1.46028 (printed 1.46028); omega0* = C1^(1/2) x 2.4188843e-17 = 0.516888 (printed 0.516888); C6 = 3 f0^2/(4 omega0*^3) = 11.58 (printed 11.58). alpha(632.99 nm) = 0.82595, alpha(543.51 nm) = 0.83181 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_864.99

{
  "id": "eq18_H2_864.99",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 864.99(25) K: 10^-2 C0/(m^3 s^-2) = 3.63044, 10^-32 C1/s^-2 = 4.48175, f0 = 1.43346, omega0*/a.u. = 0.512081; 10^30 alpha(0, T)/m^3 = 0.81005, C6/a.u. = 11.48, 100 Delta alpha/alpha(0, T) = 0.03",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.63044e2",
    "C1": "4.48175e32",
    "f0": "1.43346",
    "omega0_au": "0.512081"
  },
  "check": "C0/C1 = 0.81005e-30 m^3 (printed alpha(0, T) 0.81005); f0 = C0/(e^2/4 pi eps0 m) = 1.43346 (printed 1.43346); omega0* = C1^(1/2) x 2.4188843e-17 = 0.512081 (printed 0.512081); C6 = 3 f0^2/(4 omega0*^3) = 11.48 (printed 11.48). alpha(632.99 nm) = 0.82638, alpha(543.51 nm) = 0.83236 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_H2_1006.72

{
  "id": "eq18_H2_1006.72",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 1006.72(10) K: 10^-2 C0/(m^3 s^-2) = 3.75134, 10^-32 C1/s^-2 = 4.61631, f0 = 1.48120, omega0*/a.u. = 0.519712; 10^30 alpha(0, T)/m^3 = 0.81227, C6/a.u. = 11.72, 100 Delta alpha/alpha(0, T) = 0.07",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.75134e2",
    "C1": "4.61631e32",
    "f0": "1.48120",
    "omega0_au": "0.519712"
  },
  "check": "C0/C1 = 0.81263e-30 m^3 (printed alpha(0, T) 0.81227); f0 = C0/(e^2/4 pi eps0 m) = 1.48120 (printed 1.48120); omega0* = C1^(1/2) x 2.4188843e-17 = 0.519712 (printed 0.519712); C6 = 3 f0^2/(4 omega0*^3) = 11.72 (printed 11.72). alpha(632.99 nm) = 0.82852, alpha(543.51 nm) = 0.83434 angstrom^3. Checked 2026-09-27."
}

The printed alpha(0, T) = 0.81227 disagrees with C0/C1 = 0.81263 and with f0, omega0* and C6, which all agree with C0/C1: a misprint in the alpha(0, T) column, corrected by the erratum on alpha0_T_H2 (row 1006.72). The fit itself (C0, C1) is as printed.

hohm_1990b/eq18_kerl_1982_H2

{
  "id": "eq18_kerl_1982_H2",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 293.05 K, row [8]: 10^-2 C0/(m^3 s^-2) = 4.09565, 10^-32 C1/s^-2 = 5.06462, f0 = 1.61715, omega0*/a.u. = 0.544363; 10^30 alpha(0, T)/m^3 = 0.80868, C6/a.u. = 12.16",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "4.09565e2",
    "C1": "5.06462e32",
    "f0": "1.61715",
    "omega0_au": "0.544363"
  },
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ],
  "check": "C0/C1 = 0.80868e-30 m^3 (printed alpha(0, T) 0.80868); f0 = C0/(e^2/4 pi eps0 m) = 1.61715 (printed 1.61715); omega0* = C1^(1/2) x 2.4188843e-17 = 0.544363 (printed 0.544363); C6 = 3 f0^2/(4 omega0*^3) = 12.16 (printed 12.16). alpha(632.99 nm) = 0.82307, alpha(543.51 nm) = 0.82832 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_cuthbertson_1913_H2

{
  "id": "eq18_cuthbertson_1913_H2",
  "material": "H2",
  "equation": "Eqs. (18)-(21) with Table 2, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 273.15 K, row [17]: 10^-2 C0/(m^3 s^-2) = 3.95934, 10^-32 C1/s^-2 = 4.89888, f0 = 1.56333, omega0*/a.u. = 0.535382; 10^30 alpha(0, T)/m^3 = 0.80821, C6/a.u. = 11.94",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "3.95934e2",
    "C1": "4.89888e32",
    "f0": "1.56333",
    "omega0_au": "0.535382"
  },
  "reproduced_from": [
    "C. Cuthbertson, Phil. Mag. 25, 592 (1913)"
  ],
  "check": "C0/C1 = 0.80821e-30 m^3 (printed alpha(0, T) 0.80821); f0 = C0/(e^2/4 pi eps0 m) = 1.56333 (printed 1.56333); omega0* = C1^(1/2) x 2.4188843e-17 = 0.535382 (printed 0.535382); C6 = 3 f0^2/(4 omega0*^3) = 11.94 (printed 11.94). alpha(632.99 nm) = 0.82309, alpha(543.51 nm) = 0.82853 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_296.78

{
  "id": "eq18_O2_296.78",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 296.78(53) K: 10^-2 C0/(m^3 s^-2) = 7.43615, 10^-32 C1/s^-2 = 4.74503, f0 = 2.93613, omega0*/a.u. = 0.526908; 10^30 alpha(0, T)/m^3 = 1.56714, C6/a.u. = 44.20, 100 Delta alpha/alpha(0, T) = 0.02",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.43615e2",
    "C1": "4.74503e32",
    "f0": "2.93613",
    "omega0_au": "0.526908"
  },
  "check": "C0/C1 = 1.56714e-30 m^3 (printed alpha(0, T) 1.56714); f0 = C0/(e^2/4 pi eps0 m) = 2.93613 (printed 2.93613); omega0* = C1^(1/2) x 2.4188843e-17 = 0.526908 (printed 0.526908); C6 = 3 f0^2/(4 omega0*^3) = 44.20 (printed 44.20). alpha(632.99 nm) = 1.59695, alpha(543.51 nm) = 1.60784 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_568.32

{
  "id": "eq18_O2_568.32",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 568.32(27) K: 10^-2 C0/(m^3 s^-2) = 7.43490, 10^-32 C1/s^-2 = 4.74321, f0 = 2.93564, omega0*/a.u. = 0.526807; 10^30 alpha(0, T)/m^3 = 1.56748, C6/a.u. = 44.21, 100 Delta alpha/alpha(0, T) = 0.02",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.43490e2",
    "C1": "4.74321e32",
    "f0": "2.93564",
    "omega0_au": "0.526807"
  },
  "check": "C0/C1 = 1.56748e-30 m^3 (printed alpha(0, T) 1.56748); f0 = C0/(e^2/4 pi eps0 m) = 2.93563 (printed 2.93564); omega0* = C1^(1/2) x 2.4188843e-17 = 0.526807 (printed 0.526807); C6 = 3 f0^2/(4 omega0*^3) = 44.21 (printed 44.21). alpha(632.99 nm) = 1.59730, alpha(543.51 nm) = 1.60821 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_665.48

{
  "id": "eq18_O2_665.48",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 665.48(5) K: 10^-2 C0/(m^3 s^-2) = 7.63013, 10^-32 C1/s^-2 = 4.86265, f0 = 3.01272, omega0*/a.u. = 0.533398; 10^30 alpha(0, T)/m^3 = 1.56913, C6/a.u. = 44.86, 100 Delta alpha/alpha(0, T) = 0.05",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.63013e2",
    "C1": "4.86265e32",
    "f0": "3.01272",
    "omega0_au": "0.533398"
  },
  "check": "C0/C1 = 1.56913e-30 m^3 (printed alpha(0, T) 1.56913); f0 = C0/(e^2/4 pi eps0 m) = 3.01272 (printed 3.01272); omega0* = C1^(1/2) x 2.4188843e-17 = 0.533398 (printed 0.533398); C6 = 3 f0^2/(4 omega0*^3) = 44.86 (printed 44.86). alpha(632.99 nm) = 1.59824, alpha(543.51 nm) = 1.60887 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_761.78

{
  "id": "eq18_O2_761.78",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 761.78(10) K: 10^-2 C0/(m^3 s^-2) = 7.52548, 10^-32 C1/s^-2 = 4.78657, f0 = 2.97139, omega0*/a.u. = 0.529210; 10^30 alpha(0, T)/m^3 = 1.57221, C6/a.u. = 44.68, 100 Delta alpha/alpha(0, T) = 0.02",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.52548e2",
    "C1": "4.78657e32",
    "f0": "2.97139",
    "omega0_au": "0.529210"
  },
  "check": "C0/C1 = 1.57221e-30 m^3 (printed alpha(0, T) 1.57221); f0 = C0/(e^2/4 pi eps0 m) = 2.97140 (printed 2.97139); omega0* = C1^(1/2) x 2.4188843e-17 = 0.529209 (printed 0.529210); C6 = 3 f0^2/(4 omega0*^3) = 44.68 (printed 44.68). alpha(632.99 nm) = 1.60184, alpha(543.51 nm) = 1.61267 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_866.79

{
  "id": "eq18_O2_866.79",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 866.79(57) K: 10^-2 C0/(m^3 s^-2) = 7.47779, 10^-32 C1/s^-2 = 4.75567, f0 = 2.95257, omega0*/a.u. = 0.527498; 10^30 alpha(0, T)/m^3 = 1.57239, C6/a.u. = 44.55, 100 Delta alpha/alpha(0, T) = 0.04",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.47779e2",
    "C1": "4.75567e32",
    "f0": "2.95257",
    "omega0_au": "0.527498"
  },
  "check": "C0/C1 = 1.57239e-30 m^3 (printed alpha(0, T) 1.57239); f0 = C0/(e^2/4 pi eps0 m) = 2.95257 (printed 2.95257); omega0* = C1^(1/2) x 2.4188843e-17 = 0.527498 (printed 0.527498); C6 = 3 f0^2/(4 omega0*^3) = 44.55 (printed 44.55). alpha(632.99 nm) = 1.60223, alpha(543.51 nm) = 1.61314 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_O2_1006.42

{
  "id": "eq18_O2_1006.42",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 1006.42(12) K: 10^-2 C0/(m^3 s^-2) = 7.26667, 10^-32 C1/s^-2 = 4.62392, f0 = 2.86921, omega0*/a.u. = 0.520140; 10^30 alpha(0, T)/m^3 = 1.57154, C6/a.u. = 43.88, 100 Delta alpha/alpha(0, T) = 0.04",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.26667e2",
    "C1": "4.62392e32",
    "f0": "2.86921",
    "omega0_au": "0.520140"
  },
  "check": "C0/C1 = 1.57154e-30 m^3 (printed alpha(0, T) 1.57154); f0 = C0/(e^2/4 pi eps0 m) = 2.86921 (printed 2.86921); omega0* = C1^(1/2) x 2.4188843e-17 = 0.520140 (printed 0.520140); C6 = 3 f0^2/(4 omega0*^3) = 43.88 (printed 43.88). alpha(632.99 nm) = 1.60222, alpha(543.51 nm) = 1.61345 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_kerl_1982_O2

{
  "id": "eq18_kerl_1982_O2",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 293.05 K, row [8]: 10^-2 C0/(m^3 s^-2) = 7.97115, 10^-32 C1/s^-2 = 5.04901, f0 = 3.14737, omega0*/a.u. = 0.543523; 10^30 alpha(0, T)/m^3 = 1.57876, C6/a.u. = 46.27",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.97115e2",
    "C1": "5.04901e32",
    "f0": "3.14737",
    "omega0_au": "0.543523"
  },
  "reproduced_from": [
    "K. Kerl, Z. Phys. Chem. Frankf. Ausg. 129, 129 (1982)"
  ],
  "check": "C0/C1 = 1.57876e-30 m^3 (printed alpha(0, T) 1.57876); f0 = C0/(e^2/4 pi eps0 m) = 3.14737 (printed 3.14737); omega0* = C1^(1/2) x 2.4188843e-17 = 0.543523 (printed 0.543523); C6 = 3 f0^2/(4 omega0*^3) = 46.27 (printed 46.27). alpha(632.99 nm) = 1.60694, alpha(543.51 nm) = 1.61723 angstrom^3. Checked 2026-09-27."
}

hohm_1990b/eq18_cuthbertson_1913_O2

{
  "id": "eq18_cuthbertson_1913_O2",
  "material": "O2",
  "equation": "Eqs. (18)-(21) with Table 3, p. 825",
  "printed": "alpha(omega, T) = C0(T)/[C1(T) - omega^2]; T = 273.15 K, row [17]: 10^-2 C0/(m^3 s^-2) = 7.93784, 10^-32 C1/s^-2 = 5.05482, f0 = 3.13422, omega0*/a.u. = 0.543836; 10^30 alpha(0, T)/m^3 = 1.57035, C6/a.u. = 45.81",
  "variable": "omega: angular frequency 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha: polarizability volume in m^3 (C0 in m^3 s^-2, C1 in s^-2). Eq. (21) is the same fit in atomic units: alpha*(omega*) = f0/(omega0*^2 - omega*^2), omega* = 2.4188843e-17 omega/s^-1 (p. 824).",
  "range": "543.51-632.99 nm (the four fitted wavelengths; the static limit is an extrapolation)",
  "coefficients": {
    "C0": "7.93784e2",
    "C1": "5.05482e32",
    "f0": "3.13422",
    "omega0_au": "0.543836"
  },
  "reproduced_from": [
    "C. Cuthbertson, Phil. Mag. 25, 592 (1913)"
  ],
  "check": "C0/C1 = 1.57035e-30 m^3 (printed alpha(0, T) 1.57035); f0 = C0/(e^2/4 pi eps0 m) = 3.13422 (printed 3.13422); omega0* = C1^(1/2) x 2.4188843e-17 = 0.543836 (printed 0.543836); C6 = 3 f0^2/(4 omega0*^3) = 45.81 (printed 45.81). alpha(632.99 nm) = 1.59835, alpha(543.51 nm) = 1.60857 angstrom^3. Checked 2026-09-27."
}

Corrections

[
  {
    "dataset": "alpha0_T_H2",
    "row": "1006.72",
    "column": "value",
    "printed": "0.81227",
    "corrected": "0.81263",
    "reason": "Table 2 defines alpha(0, T) = C0/C1 (p. 824), and the same row's C0 and C1 give 3.75134e2/4.61631e32 = 0.81263e-30 m^3, not the printed 0.81227 (-0.044 %). The row's other columns agree with C0/C1: f0/omega0*^2 = 1.48120/0.519712^2 = 5.48388 au = 0.81263e-30 m^3, and the printed C6 = 11.72 a.u. = 3 alpha*^2 omega0*/4 needs alpha* = 5.4839 au (the printed alpha gives 11.71). Every other row of Tables 1-3 reproduces alpha(0, T) = C0/C1 to 1 in the last digit.",
    "evidence": "The table image (tbl_5e447ea27a86.jpg) prints 0.81227 (not a mis-extraction); the correction follows from the row's own C0, C1, f0, omega0* and C6 (checked 2026-09-27)."
  }
]

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.