raj_2018
========

A\. Raj, H\. Hamaguchi, and H\. A\. Witek, J\. Chem\. Phys\. 148, 104308 \(2018\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/raj_2018.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.5011433 <https://doi.org/10.1063/1.5011433>`__

**Source kind:** theory

**Recorded technique:** CCSD linear\-response dynamic polarizabilities alpha\_par\(omega; r\), alpha\_perp\(omega; r\) of H2 \(DALTON; aug\-mcc\-pV6Z plus five sets of bond functions 8s6p\) on 176 internuclear distances 0\.2\-12\.0 a0 and 44 frequencies 0\.25\-0\.0345 hartree \(182\.25\-1320\.6 nm\) plus the static limit; rovibrational wave functions of H2, HD and D2 \(v = 0\-4, J = 0\-15\) from the radial equation with Wolniewicz's potential \(adiabatic, relativistic and radiative corrections\), accurate to about 1 cm^\-1; matrix elements \<v,J\|Omega\|v',J'\> = integral psi psi Omega r^2 dr over 0\.2\-4\.48 a0 \(Eq\. \(2\)\) with Omega = \(2 alpha\_perp \+ alpha\_par\)/3 for the mean polarizability, cubic splines in r and in wavelength \(pp\. 3\-5, PDF pp\. 3\-5\)\.

**Materials in structured entries:** D2, H2

**Dataset quantities:** polarizability

**Contents:** 33 datasets; 0 formulas.

Curation notes
--------------

Units\: atomic units \(a0^3\); wavelengths in nm are the program's vacuum wavelengths lambda = 1e7/\(omega 219474\.6313702\) for omega in hartree \(rovibME\.py\), so the printed laser wavelengths are vacuum wavelengths; the static limit is printed 'Static' and stored as inf\. HD is not a curated species\. The anisotropy gamma \(Tables T7\-T15, Table II\), the Raman transition elements \(off\-diagonal columns of T1\-T6\), the static alpha\(r\) of Table T17 and the depolarization ratios of Table I are not refractive\-index quantities here and are not extracted\.

Accuracy\: 'The computed matrix elements are accurate to about 10^\-3, and for that reason we tabulate them \.\.\. only up to four digits after the decimal point' \(PDF p\. 10\); 'correct to about 10^\-3 due to inaccuracies in the computed values of alpha\_par and alpha\_perp' \(PDF p\. 5\)\. The package README says 'the net numerical uncertainty in the computed matrix element is \+/\- 1e\-4' \(integration about 1e\-6\)\. The datasets carry 1e\-3 a\.u\. \(absolute, level not stated\)\. Against Bishop & Cheung \(1980\) the authors find up to 0\.25 % for the diagonal alpha elements and against Rychlewski \(1983\) 0\.15 % \(PDF pp\. 6\-7\); they cannot say which is more accurate\.

THE PROGRAM\. The per\-state values and the thermal averages are COMPUTED here, not printed in the paper\: tools/extract/raj\_2018\.py \-\-program runs the authors' own Python module rovibME\.py \(their GitHub package H2\-PolarizabilityMatrixElements, Ref\. 39, 'master' snapshot whose files are dated 24 Jan 2018, kept outside the repository \(found at $RAJ\_2018\_PROGRAM by tools/extract/raj\_2018\.py\); python\-module/rovibME\.py SHA\-256 75823f2ee89d6d649d980e84deaf82480a7424e8ae2b228ead70a78c68197570, checked at every run\) unmodified, through tools/extract/\_raj\_2018\_program\.py, in a pinned environment \(Python 3\.11\.16, NumPy 1\.24\.4, SciPy 1\.10\.1; uv inline script metadata\), because the module fails under NumPy 2 \(\(n,1\) arrays converted to scalars\) and calls scipy\.integrate\.quadrature, removed in SciPy 1\.15\. Run 2026\-09\-25\. The package carries no licence for its own code \(the only LICENSE\.txt is SciPy's, in the FORTRAN directory\); nothing of it is copied into this repository\. The module prints each value rounded to seven decimals; that printed number is the stored value\. The same results came from an independent environment \(Python 3\.9, NumPy 1\.21\.6, SciPy 1\.7\.3\) for the five states checked\. Check\: every \<0,0\|alpha\|0,0\> computed at T1's and T5's 52 wavelengths and the static limit rounds to the printed four decimals \(asserted by the extraction script, 106 values\)\.

THE AVERAGE\. normal\_\* datasets\: normal H2 and normal D2, the nuclear\-spin species in their high\-temperature proportions and each Boltzmann\-distributed over its own rotational levels\: alpha\(T\) = sum\_s f\_s sum\_{J in s} \(2J\+1\) exp\(\-E\_J/kT\) alpha\_J / sum\_{J in s} \(2J\+1\) exp\(\-E\_J/kT\), f\_s = g\_s/\(g\_even \+ g\_odd\), v = 0, J = 0\-10, kT from CODATA \(optmat\.constants\)\. Inputs and their sources\: \(1\) alpha\_J\: the program\_J\* datasets\. \(2\) E\_J\: the authors' own S0\(J\) = E\(0,J\+2\) \- E\(0,J\) transition energies, J = 0\-8, Tables T26 \(H2\) and T29 \(D2\) 'Our' columns \(supplement PDF pp\. 31\-32; images checked\), computed with the same wave functions as the matrix elements; they give the even levels relative to J = 0 and the odd levels relative to J = 1, up to J = 10; each S0 agrees with S1\(J\) \- Q1\(J\+2\) and Q1\(J\) \- O1\(J\+2\) of the same tables to 7e\-4 cm^\-1 \(asserted to 1e\-3\)\. They lie 0\.17\-0\.71 cm^\-1 below experiment \(the tables' Delta columns\); HITRAN's H2 lower\-state energies \(HITRAN API, 2026\-09\-25, isotopologue 103, 4591 lines; not committed\) differ from them by 0\.17\-2\.6 cm^\-1 up to J = 10 and would change the H2 average by at most 1\.3e\-5 a\.u\. \(3\) Spin weights\: H2 1 \(even J\) and 3 \(odd J\), Bishop & Cheung \(1980\), text after Eq\. \(23\) \('normal H2 ortho\:para ratio of 3\:1'\), and HITRAN's H2 g'' = 1 x \(2J\+1\) for even and 3 x \(2J\+1\) for odd J; D2 6 \(even\) and 3 \(odd\)\: 'The spin of the D nucleus is I\_N = 1, so that for the D2 molecule, even j states are twice as populated as odd j' \(Unverified\_09b870d2f279, observed title 'Single\-shot, space\- and time\-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O', file name Chen et al\. 2007, PDF p\. 15; the same page misstates H2 as even 3 times odd\), and for two spin\-1 nuclei 'the multiplicity \.\.\. equals 6 for even j and 3 for odd j' \(Borysow et al\., Mol\. Phys\. 118, e1663287 \(2019\), for 14N2, PDF p\. 8\)\. No library paper or HITRAN \(which has no D2\) states the D2 weights directly as numbers; the 6\:3 weights also reproduce Rychlewski's D2 Table V from his Table II \(rychlewski\_1983 notes\)\. DIRECT SOURCE \(TC\-105, TC\-173\)\: Murphy & Johnston \(murphy\_1934\) measure g\_s/g\_a = 1\.97 \+\- 0\.03 from the D2 band intensity alternation, 'agrees best with the theoretical ratio of 2', nuclear spin 1, even J symmetric and more intense, Bose\-Einstein statistics \(pp\. 95\-98, Eq\. \(2\)\); the ratio 2 \: 1 is all the thermal average uses, and 6 \: 3 is that ratio\. Teal & MacWood \(teal\_1935\) confirm the even\-J\-stronger alternation in the Raman spectrum\. \(4\) Temperatures 273\.15, 293\.15 and 296\.15 K\. \(5\) Omitted\: v = 1 \(Q1\(0\) = 4160\.9359 and 2993\.5309 cm^\-1, T26/T29\: population below 5e\-7 at 296\.15 K\) and J \> 10 \(the last levels kept, J = 9 and 10, hold 1\.7e\-5 and 1\.3e\-6 of their D2 species at 296\.15 K, 3e\-10 and 2e\-12 for H2\)\. Normal rather than equilibrium\: at 293\.15 K the equilibrium ortho fraction of H2 \(0\.7491 with HITRAN's E\(J=1\) = 118\.4869 cm^\-1\) changes the average by 1\.4e\-5 a\.u\. at most\.

CHECKS OF THE AVERAGE\. \(a\) The authors' own 293 K average of H2 \(Table II, 'Our', averaging up to v = 0, J = 7\) is reproduced at all 15 wavelengths to 4e\-5 a\.u\. \(0\.001 %\)\. \(b\) Against Bishop & Cheung's 293 K Table V \(bishop\_1980/alpha\_293K\) at their 16 wavelengths in the program's range\: \-0\.015 % static, rising to \+0\.146 % at 185\.46 nm \(mean \+0\.043 %\), the trend the authors describe \(up to 0\.2 %\)\. \(c\) Against Rychlewski's 293 K H2 Table VI \(rychlewski\_1983/alpha\_293K\_H2\), 14 wavelengths\: \+0\.007 to \+0\.057 % \(mean \+0\.030 %\)\. \(d\) Against Rychlewski's D2 Table V \(rychlewski\_1983/alpha\_293K\)\: \+0\.015 to \+0\.055 % \(mean \+0\.031 %\)\. Printed by raj\_2018\.py \-\-compare \(T = 293\.0 K for these\), 2026\-09\-25\. Bishop and Rychlewski's wavelengths below 182\.25 nm are outside the program's range\. \(e\) The D2/H2 ESHG phase\-match density ratio \[alpha\_H2\(2w\) \- alpha\_H2\(w\)\] / \[alpha\_D2\(2w\) \- alpha\_D2\(w\)\] from these normal\-gas averages \(295\.15 K, the program run at the fundamentals and harmonics\) is 1\.0317 at 694\.5 nm rising to 1\.0345 at 476\.6 nm, 0\.0009\-0\.0026 above Shelton & Mizrahi's measured shelton\_1986/ratio\_D2\_H2 \(1\.0301\-1\.0319, errors 0\.0002\-0\.0007\) and close to their evaluation of Rychlewski \(1\.0310\-1\.0347\)\: like Rychlewski's, this theory overestimates the H2\-D2 difference in dispersion at high frequency \(computed in a one\-off run, 2026\-09\-25, not stored\)\.

Table II also reproduces Bishop & Cheung's 293 K values \(Ref\. 75; identical to bishop\_1980/alpha\_293K at the 15 shared wavelengths\) and Victor & Dalgarno's \(Ref\. 82, curated as the reproduction bishop\_1980/victor\_dalgarno\); neither is extracted again\. The Bridge & Buckingham \(Ref\. 79\) 632\.8 nm values of \<0,0\|alpha\|0,0\> \(5\.527\(27\) for H2\) are not extracted\: reproduced, derived with a refractive index, and the D2 rows of alpha and gamma are printed swapped \(alpha '2\.0254', gamma '5\.4514'; T5 gives alpha = 5\.4515 at 632\.80 nm; image checked\)\. Table T29 prints D2 O1\(8\) Delta^a = 0\.893 against a smooth 0\.025\-0\.109 for J = 4\-7, probably 0\.137 or similar; not used\.

Use\: normal\_293K is marked primary for both gases, normal\_273K and normal\_296K check \(the same theory at other temperatures; fit one\)\. For H2 this is a third ab initio set beside rychlewski\_1983 and bishop\_1980 \(the three agree to 0\.15 %\); which to fit is a decision recorded in the register \(TC\-95\)\.

**Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

raj\_2018/alpha\_v0\_J0\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_v0_J0_H2",
     "material": "H2",
     "file": "H2/raj_2018__alpha_v0_J0.csv",
     "table": "tbl_b0cae9bc8235",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 0
     }
   }

Supplement Table T1 column \<alpha\>\_{00,00}\: H2 in v = 0, J = 0 \(para\-H2 ground state\) at 52 laser wavelengths and 'Static', four decimals \(image checked\)\. Reproduced by the program to the printed digits\.

raj\_2018/alpha\_v1\_J0\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_v1_J0_H2",
     "material": "H2",
     "file": "H2/raj_2018__alpha_v1_J0.csv",
     "table": "tbl_b0cae9bc8235",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 1
     }
   }

Supplement Table T1 column \<alpha\>\_{10,10}\: H2 in v = 1, J = 0 \(image checked\)\. Not populated in a gas at room temperature\.

raj\_2018/alpha\_v0\_J0\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_v0_J0_D2",
     "material": "D2",
     "file": "D2/raj_2018__alpha_v0_J0.csv",
     "table": "tbl_3f331311ba2d",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 0
     }
   }

Supplement Table T5 column \<alpha\>\_{00,00}\: D2 in v = 0, J = 0 at 52 laser wavelengths and 'Static', four decimals \(image checked\)\. Reproduced by the program to the printed digits\.

raj\_2018/alpha\_v1\_J0\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_v1_J0_D2",
     "material": "D2",
     "file": "D2/raj_2018__alpha_v1_J0.csv",
     "table": "tbl_3f331311ba2d",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 1
     }
   }

Supplement Table T5 column \<alpha\>\_{10,10}\: D2 in v = 1, J = 0 \(image checked\)\. Not populated in a gas at room temperature\.

raj\_2018/thermal\_293K\_table\_ii
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "thermal_293K_table_ii",
     "material": "H2",
     "file": "H2/raj_2018__thermal_293K_table_ii.csv",
     "table": "tbl_aa58a97e916a",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 293,
       "average": "thermal rotational average (normal H2 assumed), v = 0, J <= 7"
     }
   }

Table II '\<alpha\> av' column 'Our' \(footnote c\: 'Averaging up to v = 0, J = 7 at 293 K'; f\: 'Thermal rotational average'\), 15 wavelengths, image checked\. The spin weights and energies used are not stated\. Reproduced to 4e\-5 a\.u\. by normal\_293K's procedure \(source notes\); normal\_293K supersedes it\.

raj\_2018/normal\_273K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_273K_H2",
     "material": "H2",
     "file": "H2/raj_2018__normal_273K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 273.15,
       "average": "normal H2: spin species 1:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal H2 \(para\:ortho 1\:3\) at 273\.15 K, v = 0, J = 0\-10, at T1's 52 wavelengths and the static limit, seven decimals \(far below the 1e\-3 accuracy\)\.

raj\_2018/normal\_293K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_293K_H2",
     "material": "H2",
     "file": "H2/raj_2018__normal_293K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 293.15,
       "average": "normal H2: spin species 1:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal H2 \(para\:ortho 1\:3\) at 293\.15 K, v = 0, J = 0\-10, at T1's 52 wavelengths and the static limit, seven decimals\. Reproduces the paper's own Table II average to 4e\-5 a\.u\.; \+0\.03 % from Rychlewski \(1983\) and \-0\.015 to \+0\.15 % from Bishop & Cheung \(1980\)\.

raj\_2018/normal\_296K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_296K_H2",
     "material": "H2",
     "file": "H2/raj_2018__normal_296K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 296.15,
       "average": "normal H2: spin species 1:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal H2 \(para\:ortho 1\:3\) at 296\.15 K \(HITRAN's reference temperature\), v = 0, J = 0\-10, at T1's 52 wavelengths and the static limit, seven decimals\.

raj\_2018/normal\_273K\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_273K_D2",
     "material": "D2",
     "file": "D2/raj_2018__normal_273K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 273.15,
       "average": "normal D2: spin species 6:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal D2 \(ortho\:para 2\:1, spin weights 6 even J, 3 odd J\) at 273\.15 K, v = 0, J = 0\-10, at T5's 52 wavelengths and the static limit, seven decimals\.

raj\_2018/normal\_293K\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_293K_D2",
     "material": "D2",
     "file": "D2/raj_2018__normal_293K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 293.15,
       "average": "normal D2: spin species 6:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal D2 \(ortho\:para 2\:1, spin weights 6 even J, 3 odd J\) at 293\.15 K, v = 0, J = 0\-10, at T5's 52 wavelengths and the static limit, seven decimals\. \+0\.015 to \+0\.055 % from Rychlewski's \(1983\) D2 average\.

raj\_2018/normal\_296K\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "normal_296K_D2",
     "material": "D2",
     "file": "D2/raj_2018__normal_296K.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 296.15,
       "average": "normal D2: spin species 6:3 (even:odd J), each Boltzmann over its own levels; v = 0, J = 0-10",
       "computed_with": "rovibME.py (sha256 75823f2e...) per-state values, raj_2018.py extract(); energies from Tables T26/T29; run 2026-09-25"
     }
   }

COMPUTED here from the authors' program \(source notes\: THE PROGRAM, THE AVERAGE\)\: normal D2 \(ortho\:para 2\:1, spin weights 6 even J, 3 odd J\) at 296\.15 K, v = 0, J = 0\-10, at T5's 52 wavelengths and the static limit, seven decimals\.

raj\_2018/program\_J0\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J0_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J0.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=0\|alpha\|v=0,J=0\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J1\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J1_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J1.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 1,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=1\|alpha\|v=0,J=1\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J2\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J2_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J2.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 2,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=2\|alpha\|v=0,J=2\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J3\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J3_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J3.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 3,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=3\|alpha\|v=0,J=3\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J4\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J4_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J4.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 4,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=4\|alpha\|v=0,J=4\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J5\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J5_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J5.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 5,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=5\|alpha\|v=0,J=5\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J6\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J6_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J6.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 6,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=6\|alpha\|v=0,J=6\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J7\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J7_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J7.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 7,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=7\|alpha\|v=0,J=7\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J8\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J8_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J8.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 8,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=8\|alpha\|v=0,J=8\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J9\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J9_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J9.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 9,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=9\|alpha\|v=0,J=9\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J10\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J10_H2",
     "material": "H2",
     "file": "H2/raj_2018__program_J10.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 10,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=10\|alpha\|v=0,J=10\> of H2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J0\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J0_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J0.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 0,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=0\|alpha\|v=0,J=0\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J1\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J1_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J1.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 1,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=1\|alpha\|v=0,J=1\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J2\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J2_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J2.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 2,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=2\|alpha\|v=0,J=2\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J3\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J3_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J3.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 3,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=3\|alpha\|v=0,J=3\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J4\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J4_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J4.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 4,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=4\|alpha\|v=0,J=4\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J5\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J5_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J5.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 5,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=5\|alpha\|v=0,J=5\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J6\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J6_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J6.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 6,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=6\|alpha\|v=0,J=6\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J7\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J7_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J7.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 7,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=7\|alpha\|v=0,J=7\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J8\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J8_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J8.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 8,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=8\|alpha\|v=0,J=8\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J9\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J9_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J9.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 9,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=9\|alpha\|v=0,J=9\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

raj\_2018/program\_J10\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "program_J10_D2",
     "material": "D2",
     "file": "D2/raj_2018__program_J10.csv",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "absolute": 0.001,
       "level": "not stated"
     },
     "parameters": {
       "rotational_state_J": 10,
       "vibrational_state_v": 0,
       "computed_with": "rovibME.py (sha256 75823f2e...), Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1; run 2026-09-25"
     }
   }

Computed \(not printed in the paper\)\: \<v=0,J=10\|alpha\|v=0,J=10\> of D2 from the authors' program rovibME at T1's wavelengths and the static limit \(source notes\: version, environment, inputs\); the value is the program's printed number \(seven decimals\), its output line kept in the file's printed column\. An ingredient of the normal\_\* averages\.

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.