margoliash_1978 =============== D\. J\. Margoliash and W\. J\. Meath, J\. Chem\. Phys\. 68, 1426 \(1978\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.435963 `__ **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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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)." } 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\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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)." } 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\_N2O ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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)." } 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\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.