thomas_1977#
G. F. Thomas and W. J. Meath, “Dipole spectrum, sums and properties of ground-state methane and their relation to the molar refractivity and dispersion energy constant”, Mol. Phys. 34, 113 (1977)
Source record · Catalogue · Review register
DOI: 10.1080/00268977700101561
Source kind: compilation
Recorded technique: Constrained dipole oscillator strength distribution (DOSD): measured photoabsorption and fast-electron inelastic-scattering data for CH4 above 2.36 nm (Table 1’s references), the mixture rule sigma(CH4) = sigma(C) + 2 sigma(H2) with Henke and Ebisu’s and Millar and Greening’s carbon data below 17.71 nm where CH4 data were missing or unreliable, and the non-relativistic Stobbe formula below 0.05 nm; the initial data, weighted by their errors, adjusted by least squares to satisfy the TRK sum rule S(0) = 10 and the molar refractivity at two wavelengths (0.5462 and 0.2302 um, from the refractivity data of several authors normalised to Watson and Ramaswamy’s at 0.5462 um, with a virial density from Dymond and Smith’s second virial coefficient). The recommended DOSD is the one of least total adjustment. Sums by numerical integration (linear interpolation between data points to 0.05 nm, Gauss-Legendre below) (pp. 115-119).
Materials in structured entries: CH4
Dataset quantities: cauchy_moment, interval_oscillator_strength, polarizability, polarizability_correction
Contents: 13 datasets; 1 formula.
Curation notes#
PDF pages 1 (a download cover sheet) and 2-14 = journal pages 113-125. Identity checked on the first page. Values per molecule; electronic transitions only (the ‘atomic’ (infrared) contribution is excluded from Eqs. (2)-(6), footnote p. 115, and discussed in Section 5).
Dipole sums S(k) = integral of df/dE (E/2R)^k dE (Eq. (4), 2R = 1 hartree), atomic units; S(-2) is the static electronic polarizability in a0^3. Table 2 (p. 120) gives S(-1), S(-2), S(-4) of the recommended DOSD (10.86, 17.27, 62.41) with other DOSDs’ and with S(-2), S(-4) that Thomas and Meath fitted to four sets of normalised refractivity data with the Cauchy series Eq. (3) (the S(-4) spread about +-4 %). The text (p. 121) gives the other sums: S(-6) = 2.983(2), S(-8) = 1.714(3), S(-10) = 1.122(4), S(-12) = 8.064(4), S(-14) = 6.190(5), S(-16) = 4.980(6), S(-3) = 3.140(1) and S(-3/2) = 1.339(1) (mantissa(power of ten)), stored in e-notation with the digits unchanged. S(0) = 10 is the constraint (the Table 1 regions sum to 9.9995). The logarithmic sums L(-2) = -9.374, L(-1) = -3.905, L(0) = 4.259, L(1) = 1.474(2), L(2) = 1.921(4) and the mean excitation energies I_0 = 41.66 eV, I_1 = 497.1 eV, I_2 = 1.087e4 eV, I_-2 = 15.81 eV (pp. 121-122) have no quantity: not extracted. Accuracy (p. 122): for S(k), k >= -8, about 0.5 % (k = 2) to 1 % (k = -8); for k < -8 from about 1.5 % (k = -10) to 4 % (k = -16); L(k) below 1 %; ‘only valid if the refractivity data used to constrain the DOSDs is reliable to a few tenths of a per cent’. So the S(k) are not independent of the refractivity data (as kumar_1985): checks.
Table 1 (p. 118): the recommended DOSD integrated over 17 spectral regions (nm), dataset dosd; threshold to 49.59 nm holds 4.98 (p. 119, checked: 4.982). The ‘unmodified experimental data’ column (several references per cell) is not extracted. Marks: (c) the mixture rule from 10.33 nm down, with the Stobbe formula in the last region; (d) only relative measurements at 4.43-4.08 nm.
Eq. (8) (p. 121): the recommended eight-term Cauchy formula for the molar refractivity (formula cauchy_molar_refractivity), R(lambda) in m^3/mol; ‘For the spectral region lambda > 0.2 um the results for R(lambda) obtained from the DOSD and (2) are reproduced to within approximately 5.4, 1.7, 0.61, 0.24, 0.10, 0.04 and 0.02 per cent, respectively, if from two to eight terms are retained’.
Section 5 (pp. 122-123): C6(CH4-CH4) = 129.6 hartree bohr^6 (Table 3, with eight approximate formulas, 106.7-152.2), and combination-rule C6(CH4-B) for H2, N2, O2, NH3, H2O, NO, N2O, He = 39.6, 97.0, 89.0, 107.4, 76.6, 94.7, 154.7, 13.2: no quantity (dispersion coefficients), not extracted. The infrared (atomic) polarizability from band intensities, minimum 3.304e-32 and maximum 4.467e-32 m^3, against 3.17e-32 m^3 from Watson and Ramaswamy’s electronic 2.5590e-30 m^3 and Watson, Rao and Ramaswamy’s total 2.5907e-30 m^3 (p. 123; datasets). A footnote (p. 123) notes CH4’s centrifugal-distortion dipole moment (about 1e-36 C m), assumed zero here.
REPRODUCTIONS: margoliash_1978’s CH4 pseudospectrum is fitted to this DOSD’s sums; olney_1997 (thomas_1977_CH4) and zhao_2026 quote its S(k) (see those records). Olney et al. print S(-6) = 289.3 for this DOSD; the original prints 2.983(2) = 298.3 (p. 121).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
thomas_1977/dosd#
{
"id": "dosd",
"material": "CH4",
"file": "CH4/thomas_1977__dosd.csv",
"table": "tbl_df5a5473a0a4",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "nm",
"columns": {
"x_upper": "nm"
},
"use": "check"
}
Table 1 ‘Recommended oscillator strengths’: the constrained DOSD integrated over each spectral region, from the threshold (145.86 nm) to 0.00 nm, 17 regions; x the long-wavelength edge, x_upper the short one (nm, as printed; the last region’s 0.00 nm edge is infinite photon energy); row = the region. Constrained to the TRK sum and two refractivities (source notes): a check. Sums to 9.9995 (S(0) = 10).
thomas_1977/moments#
{
"id": "moments",
"material": "CH4",
"file": "CH4/thomas_1977__moments.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "check",
"uncertainty": {
"relative": 0.01,
"level": "not stated"
}
}
Table 2 ‘Calculated using (4) and the recommended DOSD’: S(-1) = 10.86, S(-2) = 17.27, S(-4) = 62.41 (rows k), atomic units. Estimated accuracy about 1 % for these k (p. 122), given reliable refractivity constraints: not independent of those data, a check.
thomas_1977/moments_text#
{
"id": "moments_text",
"material": "CH4",
"table": "text",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "check",
"uncertainty": {
"relative": 0.01,
"level": "not stated",
"relative_rows": {
"-10": 0.015,
"-12": 0.04,
"-14": 0.04,
"-16": 0.04
}
}
}
8 inline points in the source record.
p. 121: S(-6) = 2.983(2), S(-8) = 1.714(3), S(-10) = 1.122(4), S(-12) = 8.064(4), S(-14) = 6.190(5), S(-16) = 4.980(6), S(-3) = 3.140(1), S(-3/2) = 1.339(1) (mantissa(power of ten); rows k, -1.5 for -3/2). Accuracy (p. 122): about 1 % to k = -8, about 1.5 % at k = -10 rising to 4 % at k = -16 (k = -12, -14 stored at 4 %, the stated upper end). A check, as moments.
thomas_1977/platzman_1962#
{
"id": "platzman_1962",
"material": "CH4",
"file": "CH4/thomas_1977__platzman_1962.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"R. L. Platzman, Vortex 23, 372 (1962)"
]
}
Table 2: dipole sums (rows k) of another source; a DOSD, apparently TRK-normalised (p. 121).
thomas_1977/santar_1969#
{
"id": "santar_1969",
"material": "CH4",
"file": "CH4/thomas_1977__santar_1969.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"I. Santar and J. Bednář, Collect. Czech. Chem. Commun. 34, 1 (1969)"
]
}
Table 2: dipole sums (rows k) of another source; a DOSD; its S(-1) is about 15 % below the present value (p. 121).
thomas_1977/fit_watson_1936#
{
"id": "fit_watson_1936",
"material": "CH4",
"file": "CH4/thomas_1977__fit_watson_1936.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"watson_1936"
]
}
Table 2: S(-2) and S(-4) (rows k) obtained by Thomas and Meath by least-squares fitting the Cauchy series Eq. (3) to the (normalised, virial-density) refractivities of Watson and Ramaswamy (printed ‘Ramasawamy’), the reference set to which the others were normalised at 0.5462 um: derived from that source’s data, not printed by it.
thomas_1977/fit_cuthbertson_1920#
{
"id": "fit_cuthbertson_1920",
"material": "CH4",
"file": "CH4/thomas_1977__fit_cuthbertson_1920.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"cuthbertson_1920"
]
}
Table 2: S(-2) and S(-4) (rows k) obtained by Thomas and Meath by least-squares fitting the Cauchy series Eq. (3) to the (normalised, virial-density) refractivities of Cuthbertson and Cuthbertson: derived from that source’s data, not printed by it.
thomas_1977/fit_friberg_1927#
{
"id": "fit_friberg_1927",
"material": "CH4",
"file": "CH4/thomas_1977__fit_friberg_1927.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"S. Friberg, Z. Phys. 41, 378 (1927)"
]
}
Table 2: S(-2) and S(-4) (rows k) obtained by Thomas and Meath by least-squares fitting the Cauchy series Eq. (3) to the (normalised, virial-density) refractivities of Friberg: derived from that source’s data, not printed by it.
thomas_1977/fit_frivold_1939#
{
"id": "fit_frivold_1939",
"material": "CH4",
"file": "CH4/thomas_1977__fit_frivold_1939.csv",
"table": "tbl_010d4e4faeeb",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"O. E. Frivold, O. Hassel and E. Hetland, Phys. Z. 40, 29 (1939)"
]
}
Table 2: S(-2) and S(-4) (rows k) obtained by Thomas and Meath by least-squares fitting the Cauchy series Eq. (3) to the (normalised, virial-density) refractivities of Frivold et al.: derived from that source’s data, not printed by it.
thomas_1977/infrared_polarizability#
{
"id": "infrared_polarizability",
"material": "CH4",
"table": "text",
"quantity": "polarizability_correction",
"unit": "angstrom3",
"scale": 0.01,
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"part": "vibrational"
}
}
2 inline points in the source record.
p. 123: ‘Using the IR experimental band intensities one can also estimate a minimum and a maximum value for the atomic (IR) polarizability of CH4, namely alpha_A = 3.304 x 10^-32 m^3 and alpha_A = 4.467 x 10^-32 m^3 respectively’ (rows min, max; polarizability volumes, printed mantissa times 10^-32 m^3 = 10^-2 A^3, the scale). The static vibrational (infrared) polarizability; bounds, not a value with an uncertainty.
thomas_1977/infrared_polarizability_watson#
{
"id": "infrared_polarizability_watson",
"material": "CH4",
"table": "text",
"quantity": "polarizability_correction",
"unit": "angstrom3",
"scale": 0.01,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"watson_1936",
"H. E. Watson, G. G. Rao and K. L. Ramaswamy, Proc. R. Soc. A 143, 558 (1934)"
],
"parameters": {
"part": "vibrational"
}
}
1 inline points in the source record.
p. 123: ‘the experimental value of alpha_A = 3.17 x 10^-32 m^3 obtained by using the results of Watson and Ramaswamy [69] ... and Watson et al. [110] for the electric and total polarizabilities of methane’, i.e. the total (dielectric) 2.5907e-30 minus the electronic (optical) 2.5590e-30 m^3; the minimum IR estimate is ‘within 4 per cent (and therefore within the experimental error)’ of it.
thomas_1977/polarizability_watson#
{
"id": "polarizability_watson",
"material": "CH4",
"table": "text",
"quantity": "polarizability",
"unit": "angstrom3",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"watson_1936"
]
}
1 inline points in the source record.
p. 123: the electronic polarizability of methane from Watson and Ramaswamy’s refractivities, alpha_e = 2.5590 x 10^-30 m^3 (a polarizability volume; 10^-30 m^3 = 1 A^3). How it was obtained from their data (extrapolation to infinite wavelength, density) is not stated here.
thomas_1977/polarizability_total_watson_1934#
{
"id": "polarizability_total_watson_1934",
"material": "CH4",
"table": "text",
"quantity": "polarizability",
"unit": "angstrom3",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"H. E. Watson, G. G. Rao and K. L. Ramaswamy, Proc. R. Soc. A 143, 558 (1934)"
]
}
1 inline points in the source record.
p. 123: the total (static dielectric: electronic plus infrared) polarizability of methane, alpha_T = 2.5907 x 10^-30 m^3, from Watson, Rao and Ramaswamy’s dielectric measurements (a polarizability volume). Not the electronic polarizability: it includes the vibrational part.
Formulas#
thomas_1977/cauchy_molar_refractivity#
{
"id": "cauchy_molar_refractivity",
"material": "CH4",
"equation": "Eq. (8), p. 121",
"printed": "R(lambda) x 10^6 = 6.454 + 4.843 x 10^-2/lambda^2 + 4.805 x 10^-4/lambda^4 + 5.733 x 10^-6/lambda^6 + 7.792 x 10^-8/lambda^8 + 11.62 x 10^-10/lambda^10 + 18.52 x 10^-12/lambda^12 + 30.94 x 10^-14/lambda^14",
"variable": "lambda: wavelength in um (vacuum, as the DOSD's photon energies); R(lambda) the molar refractivity in m^3 mol^-1 (the printed left side is R x 10^6)",
"state": "none (per mole of molecules: R = (4 pi/3) N_A alpha(lambda), Eq. (2))",
"density": "none",
"range": "lambda > 0.2 um (p. 121: the eight-term series reproduces the DOSD's R(lambda) there to about 0.02 %)",
"coefficients": {
"c0": "6.454",
"c1": "4.843e-2",
"c2": "4.805e-4",
"c3": "5.733e-6",
"c4": "7.792e-8",
"c5": "11.62e-10",
"c6": "18.52e-12",
"c7": "30.94e-14"
},
"check": "Each coefficient is (4 pi/3) N_A a0^3 S(-2l) (hc/(2R))^(2(l-1)) x 10^6 with the paper's S(-2l) (Eq. (3)): with 2018 constants the eight terms come out 6.4556, 4.8432e-2, 4.8057e-4, 5.7325e-6, 7.7904e-8, 11.624e-10, 18.523e-12, 30.938e-14, within 3.3e-4 of the printed ones (the paper used 1973 constants). R(0.5462 um) = 6.622e-6 m^3/mol, against 6.620e-6 from watson_1936's (n - 1) = 405.90e-6 at 25 C and 760 mm with the ideal-gas density (Thomas and Meath used a virial density) (computed 2026-09-27)."
}
The recommended Cauchy formula built from the DOSD’s S(-2) ... S(-16); the electronic molar refractivity only (no infrared part). Not independent of the refractivity data that constrain the DOSD.
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.