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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/borysow_2019.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1080/00268976\.2019\.1663287 <https://doi.org/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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.