borysow_2019#
J. Borysow, T. Capek, C. Mazzoleni and M. Moraldi, “Corrections to the Raman fundamental band of N2 and O2 due to molecular non-rigidity: computations and experiment”, Mol. Phys. 118, e1663287 (2020) (published online 11 September 2019)
Source record · Catalogue · Review register
DOI: 10.1080/00268976.2019.1663287
Source kind: measurement
Recorded technique: Spontaneous vibrational Raman spectra of the fundamental band of N2 and O2 in room air (about 20 C), CW 10 W single-mode fibre laser at 532 nm in a 40-pass two-mirror cell (about 400 W at the focus), 90-degree collection through a Dove prism and a 535 nm long-pass filter into a 0.5 m imaging spectrograph with a CCD at -50 C; configuration II (laser polarized in the scattering plane: depolarized light only) for the intensities, 15 exposures of 60 s, lines integrated over fixed widths (8 cm-1 N2, 10 cm-1 O2) after baseline and spectral-response corrections (pp. 2-6 of the article). The ratio Z^2(j) of the squared anisotropy matrix elements of the S and O lines from the same j, from their intensities (Eqs. 2, 5), fitted by Hamaguchi, Suzuki and Buckingham’s third-order perturbative formula (Eqs. 16-18) for b0 = beta_e/(r_e beta_e’).
Materials in structured entries: N2, O2
Dataset quantities: None recorded.
Contents: 0 datasets; 2 formulas.
Curation notes#
PDF page n is the article’s page n - 1 (PDF page 1 is the publisher’s cover); page numbers below are the article’s. Identity checked on the first page (DOI, authors).
NOTHING IS EXTRACTED AS A DATASET: no quantity of the vocabulary holds these values honestly (a second curator’s decision; see the formulas). - Z^2(j) (Tables 1-2) is a ratio of squared matrix elements of the polarizability anisotropy, <0 j|beta|1 j+2>^2/<0 j|beta|1 j-2>^2 (Eq. 15), from the S/O intensity ratio corrected for the frequency factor and the Clebsch-Gordan coefficients (Eqs. 2, 5): not a cross-section ratio (the Clebsch-Gordan factors are divided out), not a transition polarizability (a ratio of two), and not a derivative. A quantity such as a ‘Raman matrix-element ratio’ against j would hold it. - b0 = beta_e/(r_e beta_e’) (Eq. 1) is a dimensionless ratio of the equilibrium anisotropy to r_e times its first derivative, and b2 = beta_e’’ r_e/beta_e’ another: neither is a polarizability derivative (the list of requested papers’ reading of Table 3 as ‘the polarizability derivative’ does not hold). With an independent beta_e (e.g. from wahlstrand_2012 or a polarizability_anisotropy dataset) and r_e, beta_e’ = beta_e/(r_e b0): a modelling step, not a value of this paper. The fits are recorded as the formulas z2_N2 and z2_O2; the tables are quoted here (CSV cells checked against the table images).
TABLE 1 (p. 9), ‘Z^2 values for oxygen’, j: Z^2 +- error: 5: 0.917 +- 0.013; 7: 0.902 +- 0.004; 9: 0.869 +- 0.004; 11: 0.850 +- 0.004; 13: 0.826 +- 0.012; 15: 0.797 +- 0.013. For O2, j is the nuclear rotational quantum number (N, the paper’s k; odd only for 16O2), the intensity of each k -> k’ triplet summed (Eqs. 11-14). TABLE 2 (p. 9), ‘Z^2 values for nitrogen’: 4: 0.940 +- 0.005; 8: 0.901 +- 0.004; 10: 0.873 +- 0.004; 12: 0.846 +- 0.005; 14: 0.817 +- 0.014; 16: 0.790 +- 0.015 (even j only: the odd lines overlap their neighbours; j = 6 omitted, overlapped by the Q branch of another isotopologue; p. 5). ‘The errors shown in column 3 of Tables 1 and 2 are maximum errors’, 3 x the square root of the photo-electron count plus 1 % for isotopologue overlap at N2 j = 14, 16 and O2 j = 5, 13, 15 (p. 9). Only j <= 16 is used because the perturbative formula matches Langhoff’s non-perturbative Z^2 to < 0.5 % there (p. 8). The measurements are ‘at a temperature of about 20 C but the results are independent on the temperature’ (p. 9).
RESULT, Eq. (19), p. 10: b0(O2) = 0.49 +- 0.01, b0(N2) = 0.48 +- 0.01, with b2 = b3 = 0, a1 = -2.716, a2 = 4.412 for N2 (Hamaguchi et al. [5]) and a1 = -2.99, a2 = 5.61 for O2 (Herzberg [26]); chi^2/DOF (DOF = 5) 0.5 (O2) and 1.0 (N2). The error is stated as ‘about 2%’ (p. 10). DOUBT: the conclusions (p. 11) give ‘For 14N2, the b0 parameter inferred from our experiment (0.49 +- 0.01)’; the refit below gives 0.479, so Eq. (19)’s 0.48 is the fitted value and the conclusions’ 0.49 a slip.
REFIT (2026-09-26, scratch; a second curator’s check of Eqs. 16-18): weighted least squares of Eq. (16) to Tables 1-2 with the stated a1, a2 and b2 = b3 = 0. O2: epsilon = 2 B_e/omega_e with B_e = 1.445611834 and omega_e = 1579.833 cm-1 (Hajigeorgiou 2013, in the library, p. 014309-4) gives b0 = 0.486 +- 0.009, chi^2/DOF = 0.50 (paper 0.49 +- 0.01, 0.5). N2: B_e = 1.998232 cm-1 (Bendtsen 1974 Table IX, in the library) and omega_e = 2358.57 cm-1 (QUOTED FROM MEMORY, Huber and Herzberg, for this check only; no library source found) give b0 = 0.479 +- 0.009, chi^2/DOF = 1.03 (paper 0.48 +- 0.01, 1.0). Eq. (16) at b0 = 0.48 gives Z^2(N2) = 0.943, 0.895, 0.872, 0.849, 0.828, 0.807 at j = 4-16 against the printed 0.940, 0.901, 0.873, 0.846, 0.817, 0.790. Eq. (17) as printed reproduces the paper’s fits: no misprint found.
TABLE 3 (p. 10), ‘Historical values of b0 for O2 and N2’ (all reproduced, ‘derived from measurements of Raman scattering cross sections apart the result taken from Ref. [3] which is derived from ab initio calculations’): O2 0.339 +- 0.040, b2 = 2.5 +- 1.0 (Buldakov [27]); O2 0.23 +- 0.07 (Rosenblatt [7] = Asawaroengchai and Rosenblatt, J. Chem. Phys. 72, 2664 (1980)); O2 0.42 (Klemperer [2] = James and Klemperer, J. Chem. Phys. 31, 130 (1959)); N2 0.33, b2 = 1.2 (Langhoff [3] (th), Langhoff, Bauschlicher and Chong, J. Chem. Phys. 78, 5287 (1983)); N2 0.318 +- 0.043, b2 = 1 +- 2 (Buldakov [27] = Buldakov et al., J. Mol. Spectrosc. 217, 1 (2003) and Spectrochim. Acta 52A, 995 (1996)); N2 0.45 +- 0.09, b2 = 0.42 (Rosenblatt [7]); N2 0.4 (Klemperer [2]); N2 0.380 +- 0.042 (‘Buckingham [6]’ = Hamaguchi, Buckingham and Jones, Mol. Phys. 43, 1311 (1981)). No level is stated for the +-. None of the cited works is in the library.
For review (the Herman-Wallis correction of the fundamental): Z^2 < 1 means the S lines of the fundamental are weaker, and the O lines stronger, than the rigid-rotor values: to first order 1 - Z^2 ~ 8 b0 epsilon (2j + 1) in the S/O ratio (C ~ -4 b0 epsilon), 6 % at j = 4 and 21 % at j = 16 for N2; the per-line factor is in the formulas.
ISOTOPOLOGUES: the measurements are 14N2 and 16O2 in air; 14N15N (abundance 0.0075 of 14N2) and 16O18O (0.0038 of 16O2) overlap some lines and enter the error budget (pp. 6-7); their spectra (Figs. 12-13) are computed, not measured. Figures 3-13 are spectra and Z^2 plots (digitised values of Rosenblatt’s, Fig. 10-11): nothing digitised here.
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#
borysow_2019/z2_N2#
{
"id": "z2_N2",
"material": "N2",
"equation": "Eqs. (16)-(18), pp. 9-10; fitted b0 Eq. (19), p. 10",
"printed": "Z^2(j) = [1 + C m(j, j+2) + D m(j, j+2)^2] / [1 + C m(j, j-2) + D m(j, j-2)^2]; C = (epsilon/G) (b0 (-4 - 12 epsilon - 15 a1 epsilon + 9 a2 epsilon - (41/4) a1^2 epsilon) + ((13/2) a1 + 3/2) epsilon - b2 epsilon); D = (C/2)^2 - (epsilon^2/G) ((3/2) a1 + 3/2 - 2 b2); G = 1 + (11/16) a1^2 epsilon - (3/4) a2 epsilon - (5/4) b2 a1 epsilon + (1/4) b3 epsilon; m(j, j') = (1/2) (j'(j'+1) - j(j+1)); epsilon = 2 B_e/omega_e",
"variable": "j: the rotational quantum number of the initial level (v = 0) of the S and O lines; Z^2 = <0 j|beta|1 j+2>^2/<0 j|beta|1 j-2>^2",
"state": "none (a molecular property; measured at about 20 C)",
"density": "unknown",
"range": "j = 4-16 (the data fitted, even j, j = 6 omitted)",
"coefficients": {
"b0": "0.48",
"a1": "-2.716",
"a2": "4.412",
"b2": "0",
"b3": "0"
},
"check": "Refit of Table 2 (2026-09-26): b0 = 0.479 +- 0.009, chi^2/DOF = 1.03, against the printed 0.48 +- 0.01 and 1.0, with epsilon = 2 x 1.998232/2358.57 (B_e from Bendtsen 1974 Table IX; omega_e quoted from memory for the check only). Eq. (16) at b0 = 0.48 differs from Table 2 by up to 1.5 times the stated error (j = 8: 0.895 against 0.901 +- 0.004; j = 16: 0.807 against 0.790 +- 0.015)."
}
Hamaguchi, Suzuki and Buckingham’s formula [5] (Mol. Phys. 43, 963 (1981)), third-order perturbation theory (p. 8); b0 = beta_e/(r_e beta_e’) the fitted parameter (+- 0.01, ‘about 2%’), b2 = b3 = 0 assumed (the second and third derivatives of the anisotropy neglected), a1 and a2 the Dunham anharmonic coefficients of Hamaguchi et al. [5]. B_e and omega_e (epsilon) are not printed in the paper. The conclusions (p. 11) print b0(14N2) = 0.49 +- 0.01, inconsistent with Eq. (19)’s 0.48, which the refit confirms. Isotopologue 14N2.
borysow_2019/z2_O2#
{
"id": "z2_O2",
"material": "O2",
"equation": "Eqs. (16)-(18), pp. 9-10; fitted b0 Eq. (19), p. 10",
"printed": "Z^2(j) as for z2_N2 (the same Eqs. 16-18)",
"variable": "j: the nuclear rotational quantum number N (the paper's k) of the initial level, odd; the intensity of each k -> k' triplet summed over the spin components (Eqs. 11-14)",
"state": "none (a molecular property; measured at about 20 C)",
"density": "unknown",
"range": "j = 5-15 (the data fitted, odd j)",
"coefficients": {
"b0": "0.49",
"a1": "-2.99",
"a2": "5.61",
"b2": "0",
"b3": "0"
},
"check": "Refit of Table 1 (2026-09-26): b0 = 0.486 +- 0.009, chi^2/DOF = 0.50, against the printed 0.49 +- 0.01 and 0.5, with epsilon = 2 x 1.445611834/1579.833 (B_e and omega_e of Hajigeorgiou 2013, p. 014309-4, in the library). Eq. (16) at b0 = 0.49 gives 0.924, 0.897, 0.872, 0.847, 0.824, 0.801 at j = 5-15 against the printed 0.917, 0.902, 0.869, 0.850, 0.826, 0.797."
}
As z2_N2, with a1 and a2 for O2 from Herzberg [26]. Isotopologue 16O2 X 3Sigma_g-. The paper’s b0(O2) is twice Asawaroengchai and Rosenblatt’s 0.23 +- 0.07 and 45 % above Buldakov et al.’s 0.339 +- 0.040 (Table 3).
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.