kumar_2010_supplement ===================== A\. Kumar and A\. J\. Thakkar, J\. Chem\. Phys\. 132, 074301 \(2010\), supplementary material `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.3315418 `__ **Source kind:** compilation **Recorded technique:** Supplementary material \(EPAPS, Ref\. 84 of the paper\) of Kumar and Thakkar's constrained dipole oscillator strength distributions \(the paper is kumar\_2010\)\: the integrated DOS of the adopted DOSDs per energy interval \(Table I, p\. 2\) and the ten\-term pseudospectra {f\_i, E\_i} reproducing the dipole sums \(p\. 3\)\. **Materials in structured entries:** Ar, Kr, Ne, Xe **Dataset quantities:** interval\_oscillator\_strength, oscillator\_strength **Contents:** 8 datasets; 4 formulas. Curation notes -------------- The library record is UNVERIFIED and untitled; the first page names it\: 'Supplementary material for the paper "Dipole oscillator strength distributions with improved high\-energy behavior\. Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited" by Ashok Kumar and Ajit J\. Thakkar' \(kumar\_2010; file name KumarMeathSupplementary\.pdf\)\. 'The reference numbers are the same as in the paper\.' Table I \(IDOS\)\: E\_j in eV; the IDOS entries are for \[E\_j, E\_j\+1\], the last interval ending at infinity; the 'Discrete' row sums 17, 20, 25 and 28 discrete transitions for Ne, Ar, Kr, Xe \(note e; initial data from Refs\. 50, 51, 74, 78, 83 and Natali et al\., unpublished\)\. Datasets 'idos\_\' \(rows j, abscissa E\_j the LOWER edge of the interval; FORMAT NEED\: an integrated oscillator strength over an interval has no quantity of its own, so oscillator\_strength at the lower edge is used\) and 'discrete\_\' \(index abscissa\)\. Check \(2026\-09\-25\)\: discrete \+ IDOS sums to 9\.99956 \(Ne\), 18\.0006 \(Ar\), 35\.9994 \(Kr\), 53\.9990 \(Xe\), the electron numbers \(S\(0\) = N\)\. Constraints and initial data \(Table I notes a\-d; Refs\. of kumar\_2010\)\: Ne\: initial DOSD from Refs\. 50 \(Chan et al\. 1992, neon = chan\_1992\_neon\), 58 \(Samson and Stolte 2002\), 73 \(Marr and West 1976\), 60 \(Suzuki and Saito 2003\), 71 \(Veigele 1973\), 56 \(Chantler 1995\), above E\_48 Eq\. \(9\) with b = 3\.373\(6\); scaling spread 100 a\-bar = 0\.451, 100 s = 0\.601; refractivity constraints at 302\.2 and 546\.2 nm from Ref\. 79 \(Cuthbertson and Cuthbertson 1932 = cuthbertson\_1932\)\. Ar\: Refs\. 51 \(Chan et al\. 1992 = chan\_1992\), 73, 58, 61 \(Suzuki and Saito 2005\), 69 \(Watson 1972\), 71; Eq\. \(9\) above E\_47 with b = \-1\.710\(7\), 100 a\-bar = 0\.337, 100 s = 0\.512; refractivity at 325\.1 and 633\.0 nm from Ref\. 62 \(Hohm 1994, not in the library\)\. Kr\: Refs\. 51, 72 \(Lang and Watson 1975\), 59 \(Suzuki and Saito 2002\), 52 \(Henke et al\. 1993 = henke\_1993\), 56; Eq\. \(9\) above E\_54 with b = \-2\.594\(9\), 100 a\-bar = 0\.147, 100 s = 0\.262; refractivity at 177\.1 and 263\.2 nm from Ref\. 81 \(Smith et al\. 1976 = smith\_1976\)\. Xe\: Refs\. 51, 58, 60, 71; Eq\. \(9\) above E\_60 with b = \-2\.702\(10\), 100 a\-bar = 0\.255, 100 s = 0\.342; refractivity at 170\.2 and 253\.7 nm from Ref\. 82 \(Bideau\-Mehu et al\. 1981 = bideau\_mehu\_1981\)\. The constraint values themselves are not printed\. So the DOSDs \(and the pseudospectra and kumar\_2010's S\_k\) are tied to those refractivities at two wavelengths each\: use as checks, not beside those data in a fit \(as kumar\_2010, TC\-72\)\. Pseudospectra \(p\. 3, 'in a form suitable for cut\-and\-paste'\)\: recorded as oscillator formulas\. The columns are headed 'f' and 'E' \('The symbols f and E stand for f and epsilon respectively', p\. 1\), but the 'f' column holds the energies and the 'E' column the strengths \(see the formulas' notes and TC\-119\)\. The Kr list is not a library table \(the extraction turned it into a line of text on page 3\); its numbers were checked against the pdf page image\. Energies are in hartree\: S\(k\) with the energies in hartree reproduces kumar\_2010's moments\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- kumar\_2010\_supplement/idos\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "idos_Ne", "material": "Ne", "file": "Ne/kumar_2010_supplement__idos_Ne.csv", "table": "tbl_8fedf8f12d10", "quantity": "interval_oscillator_strength", "abscissa_unit": "eV", "columns": { "x_upper": "eV" }, "use": "check" } Table I\: integrated oscillator strength of the adopted constrained DOSD over \[E\_j, E\_j\+1\] \(the last to infinity\), rows j = 18\-48, abscissa E\_j \(eV, the lower edge; 21\.56 eV \- 100 keV\), 31 intervals\. Not a line\: an interval integral \(format need, source notes\)\. Constrained to refractivity data \(source notes\)\: a check\. kumar\_2010\_supplement/discrete\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "discrete_Ne", "material": "Ne", "file": "Ne/kumar_2010_supplement__discrete_Ne.csv", "table": "tbl_8fedf8f12d10", "quantity": "oscillator_strength", "abscissa": "label", "use": "check" } Table I row 'Discrete'\: 2\.800\(\-1\), the summed strength of the 17 discrete transitions of the adopted DOSD \(note e\), index abscissa\. A check\. kumar\_2010\_supplement/idos\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "idos_Ar", "material": "Ar", "file": "Ar/kumar_2010_supplement__idos_Ar.csv", "table": "tbl_8fedf8f12d10", "quantity": "interval_oscillator_strength", "abscissa_unit": "eV", "columns": { "x_upper": "eV" }, "use": "check" } Table I\: integrated oscillator strength of the adopted constrained DOSD over \[E\_j, E\_j\+1\] \(the last to infinity\), rows j = 21\-47, abscissa E\_j \(eV, the lower edge; 15\.76 eV \- 100 keV\), 27 intervals\. Not a line\: an interval integral \(format need, source notes\)\. Constrained to refractivity data \(source notes\)\: a check\. kumar\_2010\_supplement/discrete\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "discrete_Ar", "material": "Ar", "file": "Ar/kumar_2010_supplement__discrete_Ar.csv", "table": "tbl_8fedf8f12d10", "quantity": "oscillator_strength", "abscissa": "label", "use": "check" } Table I row 'Discrete'\: 7\.623\(\-1\), the summed strength of the 20 discrete transitions of the adopted DOSD \(note e\), index abscissa\. A check\. kumar\_2010\_supplement/idos\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "idos_Kr", "material": "Kr", "file": "Kr/kumar_2010_supplement__idos_Kr.csv", "table": "tbl_8fedf8f12d10", "quantity": "interval_oscillator_strength", "abscissa_unit": "eV", "columns": { "x_upper": "eV" }, "use": "check" } Table I\: integrated oscillator strength of the adopted constrained DOSD over \[E\_j, E\_j\+1\] \(the last to infinity\), rows j = 26\-54, abscissa E\_j \(eV, the lower edge; 14\.03 eV \- 100 keV\), 29 intervals\. Not a line\: an interval integral \(format need, source notes\)\. Constrained to refractivity data \(source notes\)\: a check\. kumar\_2010\_supplement/discrete\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "discrete_Kr", "material": "Kr", "file": "Kr/kumar_2010_supplement__discrete_Kr.csv", "table": "tbl_8fedf8f12d10", "quantity": "oscillator_strength", "abscissa": "label", "use": "check" } Table I row 'Discrete'\: 1\.092, the summed strength of the 25 discrete transitions of the adopted DOSD \(note e\), index abscissa\. A check\. kumar\_2010\_supplement/idos\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "idos_Xe", "material": "Xe", "file": "Xe/kumar_2010_supplement__idos_Xe.csv", "table": "tbl_8fedf8f12d10", "quantity": "interval_oscillator_strength", "abscissa_unit": "eV", "columns": { "x_upper": "eV" }, "use": "check" } Table I\: integrated oscillator strength of the adopted constrained DOSD over \[E\_j, E\_j\+1\] \(the last to infinity\), rows j = 29\-60, abscissa E\_j \(eV, the lower edge; 12\.17 eV \- 100 keV\), 32 intervals\. Not a line\: an interval integral \(format need, source notes\)\. Constrained to refractivity data \(source notes\)\: a check\. kumar\_2010\_supplement/discrete\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "discrete_Xe", "material": "Xe", "file": "Xe/kumar_2010_supplement__discrete_Xe.csv", "table": "tbl_8fedf8f12d10", "quantity": "oscillator_strength", "abscissa": "label", "use": "check" } Table I row 'Discrete'\: 1\.597, the summed strength of the 28 discrete transitions of the adopted DOSD \(note e\), index abscissa\. A check\. Formulas -------- kumar\_2010\_supplement/pseudospectrum\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pseudospectrum_Ne", "form": "oscillator", "energy_unit": "hartree", "terms": { "f": [ "1.72761e-1", "7.05592e-2", "2.39565e-1", "5.90543e-1", "1.10197", "1.80237", "2.34931", "1.71152", "1.90122", "6.01847e-2" ], "E": [ "6.18514e-1", "7.25160e-1", "8.27158e-1", "1.02722", "1.39273", "2.10855", "3.68085", "8.11069", "4.74204e+1", "5.96639e+2" ] }, "range_nm": [ 81.0, "inf" ], "material": "Ne", "equation": "Ten-term pseudospectrum, page 3, tbl_ef48d8ee5ced", "printed": "columns headed f, E: 6.18514e-1 1.72761e-1; 7.25160e-1 7.05592e-2; 8.27158e-1 2.39565e-1; 1.02722 5.90543e-1; 1.39273 1.10197; 2.10855 1.80237; 3.68085 2.34931; 8.11069 1.71152; 4.74204e+1 1.90122; 5.96639e+2 6.01847e-2", "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units", "state": "none (per atom)", "density": "none", "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.618514 hartree (73.67 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.", "check": "S(k) = sum f_i E_i^k reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3e-4 (the table's rounding), S(0) = 10.0000; S(-2) = 2.66934 against 2.669. Half-integer k are not constrained: S(-0.5) is 3e-4 off (checked 2026-09-25)." } COLUMNS SWAPPED IN THE ORIGINAL\: the column headed f holds the excitation energies \(hartree\) and the column headed E the oscillator strengths\. Evidence\: the E column sums to the electron number \(the TRK sum rule S\(0\) = N\), the f column's smallest entry is at the first resonance, and only this reading reproduces kumar\_2010's S\(k\) \(check\)\. terms\.f is therefore the printed E column and terms\.E the printed f column \(a structural relabelling, like a wrong caption; each coefficient is as printed\)\. Not independent of the refractivity data used as constraints \(source notes\)\: a check against those data, not a fit to them\. kumar\_2010\_supplement/pseudospectrum\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pseudospectrum_Ar", "form": "oscillator", "energy_unit": "hartree", "terms": { "f": [ "3.18677e-1", "5.02810e-2", "5.84382e-1", "1.45663", "2.30431", "1.46024", "8.33644e-1", "5.68760", "4.96822", "3.36019e-1" ], "E": [ "4.32014e-1", "4.61341e-1", "5.48086e-1", "6.79814e-1", "8.90090e-1", "1.22282", "2.92264", "1.04118e+1", "4.39529e+1", "9.13390e+2" ] }, "range_nm": [ 116.0, "inf" ], "material": "Ar", "equation": "Ten-term pseudospectrum, page 3, tbl_bdf9d0b1140e", "printed": "columns headed f, E: 4.32014e-1 3.18677e-1; 4.61341e-1 5.02810e-2; 5.48086e-1 5.84382e-1; 6.79814e-1 1.45663; 8.90090e-1 2.30431; 1.22282 1.46024; 2.92264 8.33644e-1; 1.04118e+1 5.68760; 4.39529e+1 4.96822; 9.13390e+2 3.36019e-1", "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units", "state": "none (per atom)", "density": "none", "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.432014 hartree (105.47 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.", "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3e-4, S(0) = 18.0000, S(-2) = 11.0787 against 11.08; S(-0.5) is 1.5e-3 off (half-integer k not constrained) (checked 2026-09-25)." } COLUMNS SWAPPED IN THE ORIGINAL\: the column headed f holds the excitation energies \(hartree\) and the column headed E the oscillator strengths\. Evidence\: the E column sums to the electron number \(the TRK sum rule S\(0\) = N\), the f column's smallest entry is at the first resonance, and only this reading reproduces kumar\_2010's S\(k\) \(check\)\. terms\.f is therefore the printed E column and terms\.E the printed f column \(a structural relabelling, like a wrong caption; each coefficient is as printed\)\. Not independent of the refractivity data used as constraints \(source notes\)\: a check against those data, not a fit to them\. kumar\_2010\_supplement/pseudospectrum\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pseudospectrum_Kr", "form": "oscillator", "energy_unit": "hartree", "terms": { "f": [ "2.30481e-1", "2.04092e-1", "7.97974e-1", "1.66947", "2.45289", "1.93397", "1.05176", "1.20500e+1", "1.48626e+1", "7.46743e-1" ], "E": [ "3.69130e-1", "3.95530e-1", "4.80849e-1", "5.95979e-1", "7.93650e-1", "1.15661", "2.76628", "8.56933", "5.46172e+1", "2.53759e+3" ] }, "range_nm": [ 136.0, "inf" ], "material": "Kr", "equation": "Ten-term pseudospectrum, page 3 (text: the Kr list is not a library table; checked against the pdf page image)", "printed": "columns headed f, E: 3.69130e-1 2.30481e-1; 3.95530e-1 2.04092e-1; 4.80849e-1 7.97974e-1; 5.95979e-1 1.66947; 7.93650e-1 2.45289; 1.15661 1.93397; 2.76628 1.05176; 8.56933 1.20500e+1; 5.46172e+1 1.48626e+1; 2.53759e+3 7.46743e-1", "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units", "state": "none (per atom)", "density": "none", "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.36913 hartree (123.43 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.", "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 2.5e-4, S(0) = 36.0000, S(-2) = 16.7939 against 16.79; S(-0.5) is 4.8e-3 off (half-integer k not constrained) (checked 2026-09-25)." } COLUMNS SWAPPED IN THE ORIGINAL\: the column headed f holds the excitation energies \(hartree\) and the column headed E the oscillator strengths\. Evidence\: the E column sums to the electron number \(the TRK sum rule S\(0\) = N\), the f column's smallest entry is at the first resonance, and only this reading reproduces kumar\_2010's S\(k\) \(check\)\. terms\.f is therefore the printed E column and terms\.E the printed f column \(a structural relabelling, like a wrong caption; each coefficient is as printed\)\. Not independent of the refractivity data used as constraints \(source notes\)\: a check against those data, not a fit to them\. kumar\_2010\_supplement/pseudospectrum\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pseudospectrum_Xe", "form": "oscillator", "energy_unit": "hartree", "terms": { "f": [ "2.76315e-1", "3.60490e-1", "1.01180", "1.97196", "2.43455", "1.59870", "6.57194", "8.39325", "3.03664e+1", "1.01457" ], "E": [ "3.10093e-1", "3.58976e-1", "4.13159e-1", "5.08407e-1", "6.74362e-1", "9.90276e-1", "3.02203", "6.13092", "5.62237e+1", "4.90145e+3" ] }, "range_nm": [ 162.0, "inf" ], "material": "Xe", "equation": "Ten-term pseudospectrum, page 3, tbl_38b4d6bcc5ce", "printed": "columns headed f, E: 3.10093e-1 2.76315e-1; 3.58976e-1 3.60490e-1; 4.13159e-1 1.01180; 5.08407e-1 1.97196; 6.74362e-1 2.43455; 9.90276e-1 1.59870; 3.02203 6.57194; 6.13092 8.39325; 5.62237e+1 3.03664e+1; 4.90145e+3 1.01457", "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units", "state": "none (per atom)", "density": "none", "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.310093 hartree (146.93 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.", "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3.8e-4, S(0) = 54.0000, S(-2) = 27.1637 against 27.16; S(-0.5) is 7.3e-3 off (half-integer k not constrained) (checked 2026-09-25)." } COLUMNS SWAPPED IN THE ORIGINAL\: the column headed f holds the excitation energies \(hartree\) and the column headed E the oscillator strengths\. Evidence\: the E column sums to the electron number \(the TRK sum rule S\(0\) = N\), the f column's smallest entry is at the first resonance, and only this reading reproduces kumar\_2010's S\(k\) \(check\)\. terms\.f is therefore the printed E column and terms\.E the printed f column \(a structural relabelling, like a wrong caption; each coefficient is as printed\)\. Not independent of the refractivity data used as constraints \(source notes\)\: 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 :doc:`review register ` for the checks and decisions.