kumar_2011_supplement#
A. Kumar and A. J. Thakkar, J. Chem. Phys. 135, 074303 (2011), supplementary material
Source record · Catalogue · Review register
DOI: 10.1063/1.3626523
Source kind: compilation
Recorded technique: Supplementary material (Ref. 43 of the paper, kumar_2011) of Kumar and Thakkar’s constrained dipole oscillator strength distributions of O2 and O3: the integrated DOS (IDOS) per energy interval of the final O2 DOSD (p. 2) and of the five O3 DOSDs A, B1, B2, C, D (pp. 3-4), with the sources of the initial data, and ten-term pseudospectra for O2 and O3 (B1, C) (p. 5). The method (kumar_2011, Sec. II): the Meath constrained least-squares scaling of the photoabsorption data per interval, with an iterated [1/1] Pade high-energy tail (Eq. 9) above 100 keV.
Materials in structured entries: O2, O3
Dataset quantities: interval_oscillator_strength, oscillator_strength
Contents: 7 datasets; 3 formulas.
Curation notes#
Identity checked against the first page of the supplement (PDF page 1): ‘Supplementary material for “Ozone: Unresolved discrepancies for dipole oscillator strength distributions, dipole sums, and van der Waals coefficients” by Ashok Kumar and Ajit J. Thakkar, June 26, 2011’ (the paper is kumar_2011, VALIDATED; the supplement’s own library status is UNVERIFIED). Supplement pages 1-5. ‘The IDOS entries are for the intervals from E(j) to E(j+1) with the last interval ending at infinity. The numbers in parentheses are powers of ten.’ Energies E(j) in eV (the O2 header prints ‘Ej(eV)’; the O3 header ‘E(j)’, the same edges above 36 eV).
REFERENCE NUMBERS: the supplement’s reference numbers for the O3 sources and for the later O2 sources are 9 higher than in the published paper’s list (a preprint numbering): Anderson ‘Ref. 68’ is the paper’s 59, Burrows 76 -> 67, Molina 64 -> 55, Mason 73 -> 64, Tu & Nee 77 -> 68, Cook 62 -> 53, Ogawa & Cook 59 -> 50, Gejo 74 -> 65, Henke 70 -> 61, Chantler 71 -> 62 (the paper’s 68, 76, 64, 73, 77, 62, 59, 74, 70, 71 are Tu & Nee, Maroulis, Mason, Epprecht, Naves, Chantler, Anderson, Cummings, Swift, Hohm). The names are unambiguous; the numbers below are the paper’s.
O3 sources of the initial data (p. 4, page image checked; the line ‘j=14-15: Mason et al.’ is lost from the library’s Markdown and survives as an unclassified block): j = 1-3 (1.313-1.642 eV): Anderson (S. M. Anderson, Geophys. Res. Lett. 20, 1579 (1993), paper Ref. 59; the Wulf band) j = 4-6 (1.642-3.552 eV): Burrows et al. (burrows_1999) j = 7-13 (3.552-6.702 eV): Molina & Molina (J. Geophys. Res. 91, 14501 (1986)) j = 14-15 (6.702-9.501 eV): Mason et al. (mason_1996) j = 16-17 (9.501-12.00 eV): Tu & Nee (Surf. Rev. Lett. 9, 125 (2002)) j = 18 (12.00-20.60 eV): Cook (in Recent Developments in Mass Spectrometry, 1970, pp. 761-764) j = 19 (20.60-23.57 eV): Ogawa & Cook (ogawa_1958) j = 20 (23.57-30.51 eV): 1.9 x O2 DOSD; j = 21 (30.51-36.47): 1.7 x O2 DOSD; j = 22-32 (36.47-524.5 eV): 1.5 x O2 DOSD j = 33-34 (524.5-555.8 eV): Gejo et al. (Chem. Phys. Lett. 277, 497 (1997); the O 1s edge) j = 35-38 (555.8 eV - 100 keV): 1.5 x O2 DOSD; j = 39 (above 100 keV): Eq. (9). The paper’s text (kumar_2011 p. 074303-4) attributes the 12-20.6 eV data to both Ogawa & Cook and Cook (‘the photoabsorption data [50, 53] in the 12-20.6 eV range, which accounts for 28%-34% of S-2, is insufficiently accurate’); the supplement assigns j = 18 (12.00-20.60 eV) to Cook alone and Ogawa & Cook to j = 19.
O3 constraints (kumar_2011, pp. 074303-3 and -4): all five use the KRT sum rule S(0) = 24; A no refractivity; B1 Swift et al.’s refractivity at 1.315 um (swift_1988); B2 the Cuthbertsons’ at 546.1 nm (cuthbertson_1914); C and D Swift et al.’s multiplied by 0.95 and 0.90. The scale factors 1 + a_i of the 12-20.6 eV interval are 0.986 (A), 1.34 (B1, B2), 1.18 (C) and 1.012 (D); checked here: the j = 18 IDOS ratios B1/A = 1.359 and D/A = 1.026 reproduce 1.34/0.986 and 1.012/0.986, C/A = 1.193 against 1.197 (0.3 %, the rounding of 1.18). The authors reject A and D (S(-2) below the range 18.55-20.70 of the ab initio values plus the zero-point correction 1.43 of naves_2011) and ignore B2 (within 0.4 % of B1); ‘The true S_k probably lie between the predictions of the B1 and C distributions’ (Table III caption). Interval j = 10 (4.352-5.391 eV, the Hartley band) holds 0.0795 (B1) and 0.0787 (C).
O2 (p. 2, image checked): constraints KRT S(0) = 16 and the refractivities of Smith et al. at 2208.7 A (smith_1976) and Stoll at 9224 A (stoll_1922) (kumar_2011 p. 074303-3). Sources per j (printed): Discrete (Schumann-Runge bands) Bethke (bethke_1959) and Lewis et al.; j = 4, 7-11, 15-17 Chan et al. (Chem. Phys. 170, 99 (1993)); 5-6 Gibson et al.; 12-14 Holland et al.; 18-28 Brion et al. (1979); 29, 32-33 ‘2*O, Henke et al.’ (henke_1993); 30-31 Barrus et al.; 34-35 ‘2*O, Chantler’; 36 Eq. (9). Rows j = 1-3 are not printed (the discrete row).
Checks (2026-09-25): O2 discrete + IDOS = 16.000 (15.99982); O3 IDOS sums 24.0004 (A), 24.0014 (B1), 23.9991 (B2), 24.0006 (C), 24.0016 (D) = S(0) = 24 to the rounding; the pseudospectra reproduce kumar_2011’s Tables I and III (formulas’ checks).
Not independent of the refractivity data used as constraints: the IDOS and the pseudospectra are checks against those data, not fits to them (as kumar_2010_supplement). FORMAT NEED (as kumar_2010_supplement): an interval-integrated oscillator strength has no quantity of its own; oscillator_strength at the lower edge E_j (eV) is used, row = j.
kumar_2011’s notes say ‘The DOSDs themselves are supplementary material, not in the library’: they now are (this record).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
kumar_2011_supplement/idos_C#
{
"id": "idos_C",
"material": "O3",
"file": "O3/kumar_2011_supplement__idos_C.csv",
"table": "tbl_4d1cc5fd6d9e",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "check"
}
Distribution C (KRT and 0.95 x Swift’s refractivity), the authors’ compromise. Integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 1-39, abscissa E_j (eV, the lower edge; 1.313 eV - 100 keV). Not a line: an interval integral (format need). Constrained to refractivity data (source notes): a check.
kumar_2011_supplement/idos_B1#
{
"id": "idos_B1",
"material": "O3",
"file": "O3/kumar_2011_supplement__idos_B1.csv",
"table": "tbl_4d1cc5fd6d9e",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "check"
}
Distribution B1 (KRT and Swift’s refractivity at 1.315 um), the other bound of the recommended range. Integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 1-39, abscissa E_j (eV, the lower edge; 1.313 eV - 100 keV). Not a line: an interval integral (format need). Constrained to refractivity data (source notes): a check.
kumar_2011_supplement/idos_B2#
{
"id": "idos_B2",
"material": "O3",
"file": "O3/kumar_2011_supplement__idos_B2.csv",
"table": "tbl_4d1cc5fd6d9e",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "check"
}
Distribution B2 (KRT and the Cuthbertsons’ refractivity at 546.1 nm), within 0.4 % of B1 and ignored by the authors. Integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 1-39, abscissa E_j (eV, the lower edge; 1.313 eV - 100 keV). Not a line: an interval integral (format need). Constrained to refractivity data (source notes): a check.
kumar_2011_supplement/idos_A#
{
"id": "idos_A",
"material": "O3",
"file": "O3/kumar_2011_supplement__idos_A.csv",
"table": "tbl_4d1cc5fd6d9e",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "excluded"
}
Distribution A (KRT only, no refractivity): rejected by the authors (its S(-2) = 17.54 is below the plausible range; kumar_2011 p. 074303-4). Its 12-20.6 eV interval is the least rescaled (1 + a = 0.986). Integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 1-39, abscissa E_j (eV, the lower edge; 1.313 eV - 100 keV). Not a line: an interval integral (format need)..
kumar_2011_supplement/idos_D#
{
"id": "idos_D",
"material": "O3",
"file": "O3/kumar_2011_supplement__idos_D.csv",
"table": "tbl_4d1cc5fd6d9e",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "excluded"
}
Distribution D (KRT and 0.90 x Swift’s refractivity): rejected by the authors with A. Integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 1-39, abscissa E_j (eV, the lower edge; 1.313 eV - 100 keV). Not a line: an interval integral (format need). Constrained to refractivity data (source notes).
kumar_2011_supplement/idos_O2#
{
"id": "idos_O2",
"material": "O2",
"file": "O2/kumar_2011_supplement__idos_O2.csv",
"table": "tbl_528da2c47d04",
"quantity": "interval_oscillator_strength",
"abscissa_unit": "eV",
"columns": {
"x_upper": "eV"
},
"use": "check"
}
The final O2 DOSD (p. 2): integrated oscillator strength over [E_j, E_j+1] (the last to infinity), rows j = 4-36, abscissa E_j (eV, the lower edge; 7.081 eV - 100 keV), 33 intervals. Constrained to Smith et al.’s and Stoll’s refractivities (source notes): a check.
kumar_2011_supplement/discrete_O2#
{
"id": "discrete_O2",
"material": "O2",
"file": "O2/kumar_2011_supplement__discrete_O2.csv",
"table": "tbl_528da2c47d04",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check"
}
p. 2 row ‘Discrete’: 2.862(-4), the summed strength of the discrete Schumann-Runge bands of the O2 DOSD (Bethke; Lewis et al.), index abscissa. A check.
Formulas#
kumar_2011_supplement/pseudospectrum_O2#
{
"id": "pseudospectrum_O2",
"form": "oscillator",
"energy_unit": "hartree",
"terms": {
"f": [
"2.48350e-3",
"5.53116e-2",
"1.15386e-1",
"2.30683e-1",
"1.32524e+0",
"2.61887e+0",
"4.04473e+0",
"3.47869e+0",
"3.96222e+0",
"1.66385e-1"
],
"E": [
"2.62667e-1",
"2.91727e-1",
"3.25561e-1",
"4.72601e-1",
"6.35974e-1",
"9.54410e-1",
"1.69855e+0",
"3.91164e+0",
"2.59273e+1",
"3.27630e+2"
]
},
"range_nm": [
191.0,
"inf"
],
"material": "O2",
"equation": "Ten-term pseudospectrum, supplement page 5, tbl_2c21978e4d0b",
"printed": "O2: E f; 2.62667E-1 2.48350E-3; 2.91727E-1 5.53116E-2; 3.25561E-1 1.15386E-1; 4.72601E-1 2.30683E-1; 6.35974E-1 1.32524E+0; 9.54410E-1 2.61887E+0; 1.69855E+0 4.04473E+0; 3.91164E+0 3.47869E+0; 2.59273E+1 3.96222E+0; 3.27630E+2 1.66385E-1",
"variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
"state": "none (per molecule)",
"density": "none",
"range": "A pseudospectrum 'suitable for input to a computer program' (for the dipole sums and C6 coefficients) representing the constrained DOSD; its lowest pole is at 0.262667 hartree (173.46 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-191), not the paper's. It carries no absorption: below that bound, and wherever the real spectrum absorbs, it is not a dispersion model.",
"check": "S(k) = sum f_i E_i^k reproduces kumar_2011's Table I 'This work' for every integer k from 2 to -8 to 4e-4 (the table's rounding): S(0) = 16.0000, S(-2) = 10.594 against 10.59 (checked 2026-09-25)."
}
Columns as printed, ‘E f’ (energies in hartree, then strengths; not swapped, unlike kumar_2010_supplement): the f column sums to the electron number and only this reading reproduces the moments (check). Page image checked, every entry. Not independent of the Smith et al. and Stoll refractivities (a constraint): a check against those data, not a fit to them.
kumar_2011_supplement/pseudospectrum_O3_B1#
{
"id": "pseudospectrum_O3_B1",
"form": "oscillator",
"energy_unit": "hartree",
"terms": {
"f": [
"7.41571e-8",
"1.43124e-6",
"1.68656e-5",
"1.74042e-2",
"7.86667e-2",
"5.50351e-1",
"5.01340e+0",
"9.88258e+0",
"7.84581e+0",
"6.11764e-1"
],
"E": [
"5.07265e-2",
"6.08058e-2",
"7.54526e-2",
"1.60064e-1",
"1.86956e-1",
"3.82425e-1",
"7.27457e-1",
"1.69425e+0",
"1.15789e+1",
"2.13921e+2"
]
},
"range_nm": [
988.0,
"inf"
],
"material": "O3",
"equation": "Ten-term pseudospectrum, supplement page 5, tbl_2c21978e4d0b",
"printed": "O3 B1: E f; 5.07265E-2 7.41571E-8; 6.08058E-2 1.43124E-6; 7.54526E-2 1.68656E-5; 1.60064E-1 1.74042E-2; 1.86956E-1 7.86667E-2; 3.82425E-1 5.50351E-1; 7.27457E-1 5.01340E+0; 1.69425E+0 9.88258E+0; 1.15789E+1 7.84581E+0; 2.13921E+2 6.11764E-1",
"variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
"state": "none (per molecule)",
"density": "none",
"range": "A pseudospectrum 'suitable for input to a computer program' (for the dipole sums and C6 coefficients) representing the constrained DOSD; its lowest pole is at 0.0507265 hartree (898.2 nm; its strength 7.4e-8 stands for the Wulf band). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-191), not the paper's. It carries no absorption: below that bound, and wherever the real spectrum absorbs, it is not a dispersion model.",
"check": "S(k) reproduces kumar_2011's Table III B1 column for every integer k from 2 to -6 to 2.6e-4: S(0) = 24.0000, S(-2) = 19.671 against 19.67 (checked 2026-09-25)."
}
Columns as printed, ‘E f’ (energies in hartree, then strengths; not swapped, unlike kumar_2010_supplement): the f column sums to the electron number and only this reading reproduces the moments (check). Page image checked, every entry. Not independent of Swift et al.’s refractivity at 1.315 um (a constraint): a check against those data, not a fit to them.
kumar_2011_supplement/pseudospectrum_O3_C#
{
"id": "pseudospectrum_O3_C",
"form": "oscillator",
"energy_unit": "hartree",
"terms": {
"f": [
"7.40909e-8",
"1.42844e-6",
"1.68551e-5",
"1.67624e-2",
"7.82596e-2",
"5.14881e-1",
"4.73919e+0",
"9.90383e+0",
"8.08862e+0",
"6.58437e-1"
],
"E": [
"5.07251e-2",
"6.07987e-2",
"7.54443e-2",
"1.59826e-1",
"1.86755e-1",
"3.80107e-1",
"7.35051e-1",
"1.70972e+0",
"1.18711e+1",
"2.08524e+2"
]
},
"range_nm": [
988.0,
"inf"
],
"material": "O3",
"equation": "Ten-term pseudospectrum, supplement page 5, tbl_2c21978e4d0b",
"printed": "O3 C: E f; 5.07251E-2 7.40909E-8; 6.07987E-2 1.42844E-6; 7.54443E-2 1.68551E-5; 1.59826E-1 1.67624E-2; 1.86755E-1 7.82596E-2; 3.80107E-1 5.14881E-1; 7.35051E-1 4.73919E+0; 1.70972E+0 9.90383E+0; 1.18711E+1 8.08862E+0; 2.08524E+2 6.58437E-1",
"variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
"state": "none (per molecule)",
"density": "none",
"range": "A pseudospectrum 'suitable for input to a computer program' (for the dipole sums and C6 coefficients) representing the constrained DOSD; its lowest pole is at 0.0507251 hartree (898.2 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-191), not the paper's. It carries no absorption: below that bound, and wherever the real spectrum absorbs, it is not a dispersion model.",
"check": "S(k) reproduces kumar_2011's Table III C column for every integer k from 2 to -6 to 2.3e-4: S(0) = 24.0000, S(-2) = 18.684 against 18.68 (checked 2026-09-25)."
}
Columns as printed, ‘E f’ (energies in hartree, then strengths; not swapped, unlike kumar_2010_supplement): the f column sums to the electron number and only this reading reproduces the moments (check). Page image checked, every entry. Not independent of 0.95 x Swift et al.’s refractivity at 1.315 um (a constraint): a check against those data, not a fit to them.
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.