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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/komasa_2011.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1021/ct200438t <https://doi.org/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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.