komasa_2011#
J. Komasa, K. Piszczatowski, G. Lach, M. Przybytek, B. Jeziorski and K. Pachucki, “Quantum electrodynamics effects in rovibrational spectra of molecular hydrogen”, J. Chem. Theory Comput. 7, 3105 (2011)
Source record · Catalogue · Review register
DOI: 10.1021/ct200438t
Source kind: theory
Recorded technique: Ab initio rovibrational levels of the X 1Sigma_g+ state of H2 and D2 (pp. 3105-3109): the Born-Oppenheimer potential from James-Coolidge (R < 12 bohr) and generalized Heitler-London (12-20 bohr) explicitly correlated bases, accurate to about 1e-9 cm-1 (fitted to 1e-5 cm-1); adiabatic and nonadiabatic corrections by nonadiabatic perturbation theory (NAPT: R-dependent reduced masses and a nonadiabatic potential, Eqs. 6-9); relativistic (Breit-Pauli, Eq. 11), leading QED (alpha^3, Eq. 12, with the R-dependent Bethe logarithm and the Araki-Sucher term), the one-loop alpha^4 estimate (Eq. 14) and the finite nuclear size (Eq. 15) as corrections to the potential, from 1200-term ECG bases; the radial equation (Eq. 6) solved for every bound level. Uncertainties from the missing recoil terms, the higher-order NAPT terms and 50 % of the one-loop alpha^4 term, in quadrature (pp. 3110-3111).
Materials in structured entries: D2, H2
Dataset quantities: raman_shift, vibrational_term_value
Contents: 12 datasets; 0 formulas.
Curation notes#
Identity checked against the first page. PAGES: pdf page n is journal p. 3104 + n (Table 1 p. 3108; Table 2 pp. 3109-3110; Tables 3-4 p. 3111; Tables 5-6 p. 3112; Tables 7-8 p. 3113). Materials: H2 and D2 (HD is not treated here: ref 28). Theory for the pure isotopologues; no ortho:para question.
WHAT IS TABULATED. Tables 1 and 2: ‘Theoretically Predicted Dissociation Energies (in cm-1) of All 302 Bound States of H2’ and ‘of All 598 Bound States of D2’: D_vJ, the energy needed to dissociate the molecule from level (v, J) into two ground-state atoms, i.e. the level’s depth below the dissociation limit (the atomic hyperfine structure is subtracted from experimental D_0, p. 3107), as totals (nonrelativistic nonadiabatic + relativistic + QED + finite size). E(v, J) - E(0, 0) = D_00 - D_vJ. The zero of each table is therefore the dissociation limit, D_00 = 36118.0696 (H2) and 36748.3634 (D2) cm-1. The per-level contributions (adiabatic, nonadiabatic, relativistic with the finite size, QED) and uncertainties are in the Supporting Information, which is not in the library (missing). Precision ‘about 0.001 cm-1 for D2 and from 0.001 to 0.005 cm-1 for H2’ (p. 3110). Levels marked b are ‘entirely due to nonadiabatic effects’ (H2 (3, 27) at 19.79 and (14, 4) at 0.03 cm-1; D2 (21, 1) at 0.05 cm-1) and may be ‘substantially less accurate’.
NOT TAKEN AS DATA (no quantity in the vocabulary; reported for review). Tables 1-2 (the D_vJ of every level), Table 3 (the ground-state dissociation energies D_0) and Table 5 (the H2 v = 0 rotational term values Delta E(J) = E(0, J) - E(0, 0), J = 1-16) are level energies or term values that are neither a vibrational term value G(v) nor a transition: a quantity for rovibrational level energies (with v, J and the zero: dissociation limit or (0, 0)) would hold them. The library tables: Table 1 tbl_5530737a2ef0 (CSV; the v = 13 and 14 rows of J = 0-4 and the v = 2 and 3 rows of J = 24-27 are each merged into one row, ‘v = 1314’ and ‘23’, whose cells hold two numbers run together: 18 levels need a structural fix), Table 2 tbl_a1d28e56f1ea, tbl_c41b072bc8fa, tbl_8d57e031e429 and the continuation tbl_975a70612c6c (CSV; merged rows ‘v = 2021’ and ‘910111213’ of the same kind: 33 levels). CHECK (scratch, 2026-09-27): every theoretical value of Tables 4-8 taken here is a difference of the Table 1-2 D_vJ to +-0.0001 cm-1 (e.g. H2 Q1(1) = D(0,1) - D(1,1) = 35999.5827 - 31844.3290 = 4155.2537, printed 4155.2538; D2 Q1(2) = 36569.2963 - 33582.0029 = 2987.2934, printed 2987.2934; H2 G(1) = 36118.0696 - 31956.9034 = 4161.1662, printed 4161.1661): the transition and excitation datasets are the level tables’ content. Table 3 (p. 3111), D_0: H2 theory 36118.0696(11) against experiment 36118.06(4) (Eyler and Melikechi 1993), 36118.062(10) (Zhang et al. 2004) and 36118.06962(37) (Liu et al. 2009, ref 1: liu_2009); D2 theory 36748.3634(9) against 36748.32(7), 36748.343(10) and 36748.36286(68) (Liu et al. 2010, ref 2: liu_2010); differences 0.0000(12) and 0.0005(11). Table 5 (p. 3112), H2 v = 0, Delta E(J) theory (J = 1-16): 118.486812(9), 354.37313(3), 705.51883(5), 1168.79743(9), 1740.1895(1), 2414.8970(2), 3187.4705(2), 4051.9430(3), 5001.9628(4), 6030.9202(5), 7132.0634(6), 8298.6014(6), 9523.7916(7), 10801.0121(9), 12123.819(1), 13485.990(1) cm-1; against Salumbides et al. 2011 (ref 29) within their errors except J = 4 (4 sigma: 1168.7982(2)).
QED BREAKDOWN (notes only). The relativistic and QED corrections to the ground level are 0.5318(5) and 0.1964(8) cm-1 (Figs. 1-2); the QED part of the H2 rotational excitation energies, Table 5’s last columns, -0.001030(4) (J = 1) to -0.1030(4) cm-1 (J = 16), agrees with the experimental QED part ‘extracted from the experimental data by subtracting our relativistic energies’ except J = 4: ‘the first observation of QED effects in a molecular spectrum’ (p. 3114). D2’s v = 0 -> 1 QED correction -0.0155 cm-1 (p. 3113). QED lowers the rotational constant by about 8e-6 (relative) (p. 3114).
THE J = 0 -> 1 ENERGIES (Table 4, notes: not a Raman transition): H2 theory 118.486812(9), experiment 118.48684(10) (ref 68, Jennings, Bragg and Brault 1984); D2 theory 59.780615(3), experiment 59.78130(95) (ref 2).
UNCERTAINTIES. The theoretical ones are estimates (quadratic sum of four error components, pp. 3110-3111; level not stated); the experimental ones as printed by this paper for each reference (Table 4’s d: ‘not measured directly but ... extracted from a set of experimental literature lines fitted to the Dunham expansion’, p. 3112, ‘one standard deviation of this fit’, p. 3113). Parenthesised uncertainties are on the last digits; the files give them in cm-1.
DISAGREEMENTS THE PAPER REPORTS (p. 3114). H2 S0(2)-S0(5) of Jennings and Brault (ref 53) differ from theory by 5-15 of their sigma (pressure shift? higher-order nonadiabatic terms?); Q1 and S1 (ref 54) exceed the experimental error but fit within theory + experiment; Q2(1) and S2(1) differ by almost twice the combined uncertainty; Campargue suggests a calibration problem in ref 54. D2 agrees with refs 55, 56; Maddaloni et al.’s S1(0), S1(1) (3166.3620(2), 3278.5220(2)) disagree. D2 v = 0 -> 1: theory 2993.6171(2) against 2993.6130(19), 2 sigma.
COMPARISON WITH OTHER CURATED VALUES (2026-09-27). stoicheff_1957: H2 S0(0)-S0(3) 354.381, 587.055, 814.406, 1034.651 against 354.37313, 587.03202, 814.42430, 1034.67068 (+0.008, +0.023, -0.018, -0.020: within Stoicheff’s +-0.02); H2 Q1(1) 4155.201 against 4155.2538 (-0.053, his +-0.05 at 1-2 atm); H2 nu_1-0 4161.137 against G(1) 4161.1661; D2 S0(0)-S0(4) within 0.013; D2 nu_1-0 2993.561 against 2993.6171 (-0.056). bischel_1986b’s zero-density H2 Q(1) 4155.25 +- 0.01 agrees (theory 4155.2538, ref 54 4155.25469(8)). piszczatowski_2015 and puchalski_2016 (the comparison first requested) are the same group’s HELIUM polarizability papers: nothing to compare (no H2 level 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#
komasa_2011/table4_theory_H2#
{
"id": "table4_theory_H2",
"material": "H2",
"file": "H2/komasa_2011__table4_theory_H2.csv",
"table": "tbl_e9a74a8c3fc7",
"quantity": "vibrational_term_value",
"unit": "cm-1",
"abscissa": "label",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference": "v0",
"electronic_state": "X 1Sigma_g+"
}
}
Table 4 (p. 3111), H2 ‘theory’, v = 0 -> 1: E(1, 0) - E(0, 0), the row v = 1. The same number as table6_theory_H2’s row 1 (a duplicate: check). Theoretical uncertainty estimate.
komasa_2011/table4_expt_H2#
{
"id": "table4_expt_H2",
"material": "H2",
"file": "H2/komasa_2011__table4_expt_H2.csv",
"table": "tbl_e9a74a8c3fc7",
"quantity": "vibrational_term_value",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"M. Stanke, D. Kedziera, S. Bubin, M. Molski and L. Adamowicz, J. Chem. Phys. 128, 114313 (2008)"
],
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"reference": "v0",
"electronic_state": "X 1Sigma_g+"
}
}
Table 4 (p. 3111), H2 ‘experiment’, note b (Ref. 46): G(1) - G(0) ‘not measured directly but ... extracted from a set of experimental literature lines fitted to the Dunham expansion’ (p. 3112), the error ‘one standard deviation of this fit’ (p. 3113). Theory - experiment 0.0001(9).
komasa_2011/table4_theory_D2#
{
"id": "table4_theory_D2",
"material": "D2",
"file": "D2/komasa_2011__table4_theory_D2.csv",
"table": "tbl_e9a74a8c3fc7",
"quantity": "vibrational_term_value",
"unit": "cm-1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference": "v0",
"electronic_state": "X 1Sigma_g+"
}
}
Table 4 (p. 3111), D2 ‘theory’, v = 0 -> 1: E(1, 0) - E(0, 0) (row v = 1), with the QED correction (-0.0155 cm-1; without it 2993.6326(2), matching Bubin et al.’s 2993.6326(10), p. 3113). Theoretical uncertainty estimate. The only D2 vibrational excitation the paper tabulates.
komasa_2011/table4_expt_D2#
{
"id": "table4_expt_D2",
"material": "D2",
"file": "D2/komasa_2011__table4_expt_D2.csv",
"table": "tbl_e9a74a8c3fc7",
"quantity": "vibrational_term_value",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"S. Bubin, M. Stanke, M. Molski and L. Adamowicz, Chem. Phys. Lett. 494, 21 (2010)"
],
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"reference": "v0",
"electronic_state": "X 1Sigma_g+"
}
}
Table 4 (p. 3111), D2 ‘experiment’, note d (Ref. 45): from a Dunham fit to literature lines, one standard deviation (pp. 3112-3113). Theory - experiment 0.0041(19), 2 sigma.
komasa_2011/table6_theory_H2#
{
"id": "table6_theory_H2",
"material": "H2",
"file": "H2/komasa_2011__table6_theory_H2.csv",
"table": "tbl_9ca11361dde2",
"quantity": "vibrational_term_value",
"unit": "cm-1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference": "v0",
"electronic_state": "X 1Sigma_g+"
}
}
Table 6 (p. 3112), ‘theory’: the H2 vibrational excitation energies E(v, J = 0) - E(v = 0, J = 0), v = 1-14 (the row), with theoretical uncertainty estimates. The differences from Dabrowski’s experiment (+-0.1 cm-1) and from Wolniewicz 1995 stay in printed.
komasa_2011/table7_theory_H2#
{
"id": "table7_theory_H2",
"material": "H2",
"file": "H2/komasa_2011__table7_theory_H2.csv",
"table": "tbl_e291b29bef99",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "as the row: S0(J), Q1(J), S1(J), Q2(J), S2(J) (v = 0 -> 0, 1, 2)"
}
}
Table 7 (p. 3113), ‘theory’: H2 transition energies of the S0(0)-S0(5), Q1(1)-Q1(4), S1(0)-S1(3), Q2(1)-Q2(3) and S2(0)-S2(2) lines (the row labels: branch, lower v as subscript, lower J), in vacuum cm-1: the quadrupole lines, the same level differences as the Raman lines. Theoretical uncertainty estimates (level not stated). The S0 rows come from a collapsed library row (structural fix in the script).
komasa_2011/table7_jennings_brault_H2#
{
"id": "table7_jennings_brault_H2",
"material": "H2",
"file": "H2/komasa_2011__table7_jennings_brault_H2.csv",
"table": "tbl_e291b29bef99",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"D. E. Jennings and J. W. Brault, J. Mol. Spectrosc. 102, 265 (1983)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "S0(J), v = 0, per row"
}
}
Table 7 (p. 3113), S0(J) ‘experiment’ (Ref. 53), J = 0-5, as this paper prints them (recovered from two merged library cells: the script). S0(2)-S0(5) differ from theory by 5-15 of their sigma (p. 3114).
komasa_2011/table7_salumbides_H2#
{
"id": "table7_salumbides_H2",
"material": "H2",
"file": "H2/komasa_2011__table7_salumbides_H2.csv",
"table": "tbl_e291b29bef99",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"E. J. Salumbides, G. D. Dickenson, T. I. Ivanov and W. Ubachs, Phys. Rev. Lett. 107, 043005 (2011)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "S0(J), v = 0, per row"
}
}
Table 7 (p. 3113), S0(J) ‘experiment’ (Ref. 29), J = 0-5: the S0 line energies ‘that can be obtained from’ Salumbides et al.’s level energies (p. 3114; Table 5’s Delta E(J + 2) - Delta E(J)), not lines measured as such.
komasa_2011/table7_bragg_H2#
{
"id": "table7_bragg_H2",
"material": "H2",
"file": "H2/komasa_2011__table7_bragg_H2.csv",
"table": "tbl_e291b29bef99",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"S. L. Bragg, W. H. Smith and J. W. Brault, Astrophys. J. 263, 999 (1982)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "as the row: Q1(J), S1(J), Q2(J), S2(J)"
}
}
Table 7 (p. 3113), ‘experiment’ (Ref. 54) for the Q1(1)-Q1(4), S1(0)-S1(3), Q2(1)-Q2(3) and S2(0)-S2(2) quadrupole lines of H2, as this paper prints them. Q1(1) = 4155.25469(8): bischel_1986b’s zero-density 4155.25 +- 0.01 cites this among four.
komasa_2011/table8_theory_D2#
{
"id": "table8_theory_D2",
"material": "D2",
"file": "D2/komasa_2011__table8_theory_D2.csv",
"table": "tbl_7ba5682f91e7",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "as the row: S0(J), S1(J), O1(J), Q1(J)"
}
}
Table 8 (p. 3113), ‘theory’: D2 transition energies of the S0(0)-S0(6), S1(0)-S1(3), O1(2)-O1(4) and Q1(1)-Q1(4) lines, vacuum cm-1, with theoretical uncertainty estimates (level not stated). The Q1(J) are the D2 Raman Q branch: Q1(2) = 2987.2934.
komasa_2011/table8_jennings_D2#
{
"id": "table8_jennings_D2",
"material": "D2",
"file": "D2/komasa_2011__table8_jennings_D2.csv",
"table": "tbl_7ba5682f91e7",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"D. E. Jennings, A. Weber and J. W. Brault, Appl. Opt. 25, 284 (1986)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "S0(J), v = 0, per row"
}
}
Table 8 (p. 3113), S0(J) ‘experiment’ (Ref. 55), J = 0-6, as printed. Ref. 55 is the paper bischel_1986b cites (its Ref. 31) as ‘Raman spectroscopy of gases with a Fourier transform spectrometer: the spectrum of D2’.
komasa_2011/table8_mckellar_oka_D2#
{
"id": "table8_mckellar_oka_D2",
"material": "D2",
"file": "D2/komasa_2011__table8_mckellar_oka_D2.csv",
"table": "tbl_7ba5682f91e7",
"quantity": "raman_shift",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"A. R. W. McKellar and T. Oka, Can. J. Phys. 56, 1315 (1978)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "as the row: S1(J), O1(J), Q1(J)"
}
}
Table 8 (p. 3113), ‘experiment’ (Ref. 56) for S1(0)-S1(3), O1(2)-O1(4) and Q1(1)-Q1(4) of D2, as printed; ‘general agreement’ with theory (p. 3114).
Formulas#
No formulas are recorded.
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.