margoliash_1978#

D. J. Margoliash and W. J. Meath, J. Chem. Phys. 68, 1426 (1978)

Source record · Catalogue · Review register

Source kind: compilation

Recorded technique: Pseudospectral dipole oscillator strength distributions: n pairs (epsilon_i, f_i) reproducing 2n dipole sums S(k) = sum_i epsilon_i^k f_i, k = 0 ... -2n+1 (Eq. (2)), of constrained DOSDs built from photoabsorption, electron-scattering and refractivity data (Refs. 1-4: Zeiss & Meath 1977; Zeiss et al. 1977; Thomas & Meath 1977), by the theory of moments and generalized Gaussian quadrature; ten pseudostates per species listed (up to 19 constructed), Hartree atomic units (p. 1427).

Materials in structured entries: CH4, H2, N2, N2O, O2

Dataset quantities: None recorded.

Contents: 0 datasets; 5 formulas.

Curation notes#

Only the curated species are recorded: H2, N2, O2, N2O and CH4 (Li, N, O, NO, H2O and NH3 are skipped; H and He pseudostates are Johnson, Epstein and Meath’s, not tabulated here). No S(k) are tabulated in this paper: the sums are those of the original DOSDs (zeiss_1977 holds H2, N2, O2 and N2O; CH4’s are in Thomas & Meath 1977, curated since as thomas_1977). The pseudospectra are recorded as oscillator formulas; Tables II and III (C6 and W4 dispersion coefficients) are not refractive-index data.

Table I (p. 1427, JSON only, image checked) prints each number as mantissa(power of ten); the terms are stored in e-notation with the digits unchanged, and tools/extract/margoliash_1978.py asserts that every term equals the library table (it writes no data file).

Accuracy (p. 1429): ‘ten pseudostates reproduce the dynamic polarizabilities alpha(E) for photon energies up to 0.95 and 0.99 E0 with a maximum error of 0.02% and 1.6%, respectively’ (E0: the ultraviolet absorption threshold, Eq. (1)); ‘The DOSDs reproduce accurate experimental refractivities ... to within a few tenths of a percent.’ Checks: the pseudospectra of H2, N2, O2 and N2O reproduce Zeiss et al.’s Table 3 S_k for k = 0 to -14 to 0.05 % or better (the four printed figures; computed 2026-09-25). S_0 is 2.00000, 13.99935, 16.00000, 22.00014 and 9.99999 for H2, N2, O2, N2O and CH4 (N2 alone is off by more than 1e-4 relative).

ERRATUM NOT IN THE LIBRARY: the article’s cover page lists ‘A correction has been published: Erratum: Pseudospectral dipole oscillator strength distributions ...’. It is not in the library; some of Table I may be corrected there.

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#

margoliash_1978/pseudospectrum_H2#

{
  "id": "pseudospectrum_H2",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "0.345800e-1",
      "0.253720e0",
      "0.386589e0",
      "0.332736e0",
      "0.347771e0",
      "0.299819e0",
      "0.209133e0",
      "0.994406e-1",
      "0.308526e-1",
      "0.535865e-2"
    ],
    "E": [
      "0.420131e0",
      "0.446381e0",
      "0.482857e0",
      "0.565092e0",
      "0.689317e0",
      "0.899545e0",
      "0.126909e1",
      "0.202021e1",
      "0.402141e1",
      "0.124531e2"
    ]
  },
  "range_nm": [
    116.8,
    "inf"
  ],
  "material": "H2",
  "equation": "Table I, p. 1427, with Eq. (2); alpha(omega) = sum_i f_i / (epsilon_i^2 - omega^2)",
  "printed": "(epsilon_i, f_i), Hartree atomic units, powers of ten in parentheses: (0.420131(0), 0.345800(-1)); (0.446381(0), 0.253720(0)); (0.482857(0), 0.386589(0)); (0.565092(0), 0.332736(0)); (0.689317(0), 0.347771(0)); (0.899545(0), 0.299819(0)); (0.126909(1), 0.209133(0)); (0.202021(1), 0.994406(-1)); (0.402141(1), 0.308526(-1)); (0.124531(2), 0.535865(-2))",
  "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
  "state": "none (per molecule)",
  "density": "none",
  "range": "photon energies up to 0.95 E0, E0 = 11.18 eV (H2 absorption bands 11.18-14.43 eV, Zeiss et al. 1977, p. 2085): 'ten pseudostates reproduce the dynamic polarizabilities alpha(E) for photon energies up to 0.95 and 0.99 E0 with a maximum error of 0.02% and 1.6%' (p. 1429); range_nm is hc/(0.95 E0) rounded up",
  "check": "Terms equal Table I (asserted by tools/extract/margoliash_1978.py against the library table; image checked). S_0 = 2.00000, S_-2 = 5.4279 against Zeiss et al.'s 2.000 and 5.428; alpha at 632.8 nm 5.5337, 0.13 % below the package's fitted H2 model (5.5409), 0.10 % at 250 nm (computed 2026-09-25)."
}

A ten-term pseudospectrum fitted (Gaussian quadrature, the theory of moments) to the sums S(0) ... S(-19) of the original DOSD of Zeiss et al. 1977 (zeiss_1977) and Zeiss & Meath 1977 (Refs. 1, 4); the printed mantissa(exponent) values are stored in e-notation, digits unchanged. The original DOSD was constrained to measured refractivities (zeiss_1977 notes), so this model is not independent of them. A published erratum to this paper (J. Chem. Phys., ‘Erratum: Pseudospectral dipole oscillator strength distributions ...’, listed on the article’s cover page) is not in the library: the values may have been corrected.

margoliash_1978/pseudospectrum_N2#

{
  "id": "pseudospectrum_N2",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "0.328825e0",
      "0.527786e0",
      "0.524360e0",
      "0.833046e0",
      "0.135867e1",
      "0.199241e1",
      "0.217348e1",
      "0.189764e1",
      "0.151592e1",
      "0.284721e1"
    ],
    "E": [
      "0.467496e0",
      "0.494570e0",
      "0.550174e0",
      "0.655940e0",
      "0.838536e0",
      "0.114071e1",
      "0.173846e1",
      "0.304633e1",
      "0.944981e1",
      "0.316643e2"
    ]
  },
  "range_nm": [
    104.5,
    "inf"
  ],
  "material": "N2",
  "equation": "Table I, p. 1427, with Eq. (2); alpha(omega) = sum_i f_i / (epsilon_i^2 - omega^2)",
  "printed": "(epsilon_i, f_i), Hartree atomic units, powers of ten in parentheses: (0.467496(0), 0.328825(0)); (0.494570(0), 0.527786(0)); (0.550174(0), 0.524360(0)); (0.655940(0), 0.833046(0)); (0.838536(0), 0.135867(1)); (0.114071(1), 0.199241(1)); (0.173846(1), 0.217348(1)); (0.304633(1), 0.189764(1)); (0.944981(1), 0.151592(1)); (0.316643(2), 0.284721(1))",
  "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
  "state": "none (per molecule)",
  "density": "none",
  "range": "photon energies up to 0.95 E0, E0 = 12.50 eV (N2 bands from 12.50 eV, Zeiss et al. 1977, p. 2086): 'ten pseudostates reproduce the dynamic polarizabilities alpha(E) for photon energies up to 0.95 and 0.99 E0 with a maximum error of 0.02% and 1.6%' (p. 1429); range_nm is hc/(0.95 E0) rounded up",
  "check": "Terms equal Table I (asserted by tools/extract/margoliash_1978.py against the library table; image checked). S_0 = 13.99935 (0.005 % below 14: the only pseudospectrum here off by more than 1e-5; the published erratum, not in the library, may bear on it), S_-2 = 11.7377 against Zeiss et al.'s 11.74; alpha at 632.8 nm 11.8966, +0.01 % from the fitted N2 model, +0.03 % at 250 nm (computed 2026-09-25)."
}

margoliash_1978/pseudospectrum_O2#

{
  "id": "pseudospectrum_O2",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "0.956663e-3",
      "0.296637e-1",
      "0.120254e0",
      "0.571651e-1",
      "0.561433e0",
      "0.160054e1",
      "0.294745e1",
      "0.392044e1",
      "0.277156e1",
      "0.399054e1"
    ],
    "E": [
      "0.257583e0",
      "0.284123e0",
      "0.315624e0",
      "0.389406e0",
      "0.525362e0",
      "0.724304e0",
      "0.111366e1",
      "0.195604e1",
      "0.455412e1",
      "0.307069e2"
    ]
  },
  "range_nm": [
    213.3,
    "inf"
  ],
  "material": "O2",
  "equation": "Table I, p. 1427, with Eq. (2); alpha(omega) = sum_i f_i / (epsilon_i^2 - omega^2)",
  "printed": "(epsilon_i, f_i), Hartree atomic units, powers of ten in parentheses: (0.257583(0), 0.956663(-3)); (0.284123(0), 0.296637(-1)); (0.315624(0), 0.120254(0)); (0.389406(0), 0.571651(-1)); (0.525362(0), 0.561433(0)); (0.724304(0), 0.160054(1)); (0.111366(1), 0.294745(1)); (0.195604(1), 0.392044(1)); (0.455412(1), 0.277156(1)); (0.307069(2), 0.399054(1))",
  "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
  "state": "none (per molecule)",
  "density": "none",
  "range": "photon energies up to 0.95 E0, E0 = 6.12 eV (Schumann-Runge bands from 6.12 eV, Zeiss et al. 1977, p. 2086): 'ten pseudostates reproduce the dynamic polarizabilities alpha(E) for photon energies up to 0.95 and 0.99 E0 with a maximum error of 0.02% and 1.6%' (p. 1429); range_nm is hc/(0.95 E0) rounded up",
  "check": "Terms equal Table I (asserted by tools/extract/margoliash_1978.py against the library table; image checked). S_0 = 16.00000, S_-2 = 10.5901 against Zeiss et al.'s 10.59; alpha at 632.8 nm 10.7769, +0.02 % from the fitted O2 model, +0.04 % at 250 nm (computed 2026-09-25)."
}

margoliash_1978/pseudospectrum_N2O#

{
  "id": "pseudospectrum_N2O",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "0.354715e-4",
      "0.833303e-3",
      "0.424885e-1",
      "0.541260e0",
      "0.897658e0",
      "0.225780e1",
      "0.380666e1",
      "0.516885e1",
      "0.353283e1",
      "0.575172e1"
    ],
    "E": [
      "0.215324e0",
      "0.241027e0",
      "0.313142e0",
      "0.361978e0",
      "0.467336e0",
      "0.648504e0",
      "0.100102e1",
      "0.178454e1",
      "0.412480e1",
      "0.266071e2"
    ]
  },
  "range_nm": [
    244.0,
    "inf"
  ],
  "material": "N2O",
  "equation": "Table I, p. 1427, with Eq. (2); alpha(omega) = sum_i f_i / (epsilon_i^2 - omega^2)",
  "printed": "(epsilon_i, f_i), Hartree atomic units, powers of ten in parentheses: (0.215324(0), 0.354715(-4)); (0.241027(0), 0.833303(-3)); (0.313142(0), 0.424885(-1)); (0.361978(0), 0.541260(0)); (0.467336(0), 0.897658(0)); (0.648504(0), 0.225780(1)); (0.100102(1), 0.380666(1)); (0.178454(1), 0.516885(1)); (0.412480(1), 0.353283(1)); (0.266071(2), 0.575172(1))",
  "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
  "state": "none (per molecule)",
  "density": "none",
  "range": "photon energies up to 0.95 E0, E0 = 5.35 eV (N2O DOSD from 5.35 eV, Zeiss et al. 1977, p. 2088): 'ten pseudostates reproduce the dynamic polarizabilities alpha(E) for photon energies up to 0.95 and 0.99 E0 with a maximum error of 0.02% and 1.6%' (p. 1429); range_nm is hc/(0.95 E0) rounded up",
  "check": "Terms equal Table I (asserted by tools/extract/margoliash_1978.py against the library table; image checked). S_0 = 22.00014, S_-2 = 19.6957 against Zeiss et al.'s 22.00 and 19.70 (read from the table image); alpha at 632.8 nm 20.081, 0.09 % below the default N2O model (He et al.) (computed 2026-09-25)."
}

margoliash_1978/pseudospectrum_CH4#

{
  "id": "pseudospectrum_CH4",
  "material": "CH4",
  "equation": "Table I, p. 1427, with Eq. (2); alpha(omega) = sum_i f_i / (epsilon_i^2 - omega^2)",
  "printed": "(epsilon_i, f_i), Hartree atomic units, powers of ten in parentheses: (0.321135(0), 0.212204(-1)); (0.345902(0), 0.955530(-1)); (0.394321(0), 0.297613(0)); (0.471748(0), 0.998503(0)); (0.583696(0), 0.174261(1)); (0.779898(0), 0.193128(1)); (0.115847(1), 0.176802(1)); (0.204856(1), 0.977037(0)); (0.638403(1), 0.722007(0)); (0.219451(2), 0.144615(1))",
  "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
  "state": "none (per molecule)",
  "density": "none",
  "range": "photon energies up to 0.95 E0 (p. 1429). E0 for CH4 is the threshold of Thomas & Meath's DOSD, 145.86 nm = 8.500 eV (thomas_1977 Table 1), so the stated accuracy holds above hc/(0.95 E0) = 153.6 nm; the formula is still recorded without a form (a model is a decision for review)",
  "check": "Terms equal Table I (asserted by tools/extract/margoliash_1978.py against the library table; image checked). S_0 = 9.99999, S_-2 = 17.2661; alpha at 632.8 nm 17.598, 0.45 % below the default CH4 model (He et al.), 0.40 % at 250 nm (computed 2026-09-25). Against thomas_1977's printed sums (2026-09-27): S_-1 10.858 (10.86), S_-3/2 13.392 (13.39), S_-2 17.266 (17.27), S_-3 31.402 (31.40), S_-4 62.411 (62.41), S_-6 298.28 (298.3), S_-8 1714.1 (1714), S_-10 11223 (11220), S_-12 80641 (80640), S_-14 6.1897e5 (6.190e5), S_-16 4.9804e6 (4.980e6): within 3e-4."
}

A ten-term pseudospectrum fitted (Gaussian quadrature, the theory of moments) to the sums S(0) ... S(-19) of the original DOSD of Thomas & Meath (1977, Ref. 3; thomas_1977); the printed mantissa(exponent) values are stored in e-notation, digits unchanged. The original DOSD was constrained to measured refractivities (zeiss_1977 notes), so this model is not independent of them. A published erratum to this paper (J. Chem. Phys., ‘Erratum: Pseudospectral dipole oscillator strength distributions ...’, listed on the article’s cover page) is not in the library: the values may have been corrected. Recorded without a form because its valid range cannot be stated from the library.

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.