kumar_1985b
===========

A\. Kumar, G\. R\. G\. Fairley and W\. J\. Meath, "Dipole properties, dispersion energy coefficients, and integrated oscillator strengths for SF6", J\. Chem\. Phys\. 83, 70 \(1985\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/kumar_1985b.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.449794 <https://doi.org/10.1063/1.449794>`__

**Source kind:** compilation

**Recorded technique:** Constrained dipole oscillator strength distribution \(DOSD\)\: measured SF6 photoabsorption and electron\-energy\-loss oscillator strengths \(Hitchcock and Van der Wiel 5\.0\-63\.0 eV; Simpson et al\. 10\.1\-32\.0; Blechschmidt et al\. 10\.1\-49\.0 and 150\-250; Hitchcock et al\. 13\.66\-226\.0; Sasanuma et al\. 15\.1\-39\.0; Lee et al\. 16\.76\-68\.88; Zimkina and Fomichev 164\.1\-300\.0 eV\), the mixture rule sigma\(SF6\) = sigma\(S\) \+ 6 sigma\(F\) with Veigele's atomic cross sections from 250 eV to 100 keV \(Eq\. \(1\)\), and the non\-relativistic Stobbe formula above 100 keV; each region's df/dE scaled by \(1 \+ a\_i\) \(Eq\. \(2\), N = 50 regions\) so that the DOSD satisfies the TRK sum rule \(Z = 70\) and Watson and Ramaswamy's molar refractivity at 6440 A; the adopted DOSD has the smallest spread \(STD about 3\) of some 13 000 constructed\. The total DOSD adds Pack's infrared oscillator strengths \(from Fox and Person's and Person and Overend's IR data\) and is constrained also to S\_0\(total\) = 70\.018 \(with the nuclear\-motion correction\) and S\_\-2\(total\) = 44\.21 \(Tipton et al\.'s microwave polarizability, via Pack\) \(pp\. 70\-72\)\.

**Materials in structured entries:** SF6

**Dataset quantities:** cauchy\_moment, interval\_oscillator\_strength, molar\_refractivity, oscillator\_strength

**Contents:** 12 datasets; 2 formulas.

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

PDF page 1 is a download cover sheet; PDF pages 2\-9 = journal pages 70\-77\. Values per molecule, rotationally averaged \(isotropic\)\. Sums S\_k = integral of \(E/2R\)^k df/dE \(Eq\. \(3\)\), atomic units; S\_\-2 is the static polarizability in a0^3 \(UV\: electronic; total\: with the infrared part\)\. Powers of ten are printed in parentheses, 7\.437\(\-2\); stored in e\-notation, digits unchanged\.

Constraint \(p\. 72\)\: Watson and Ramaswamy's R\(6440 A\) = 11\.4057 and R\(4360 A\) = 11\.5212 cm^3/mol could not both be imposed \(their difference is of the order of the refractivity error\); the adopted DOSD uses 6440 A only\. It gives R\(4359\.6 A\) = 11\.6474 cm^3/mol, 1 % above experiment, and a DOSD constrained at 4359\.6 A instead gives R\(6440 A\) = 11\.2843, 1 % below \(p\. 75\)\: 'an uncertainty of about 1% in the experimental refractivity results'\. With that alternative DOSD the UV S\_k are lower by about 0\.3, 0\.5, 0\.8, 1, 1\.3, 1\.5, 1\.9 and 2\.2 % for \-k = 0\.5, 1, 1\.5, 2, 2\.5, 3, 4, 6, the I\_k higher by \<= 0\.5 %, C6\(SF6\-SF6\) lower by 1\.5 %; 'most of the dipole properties \.\.\. are probably slightly high' \(pp\. 75\-76\)\. Uncertainties \(p\. 75\), assuming reliable refractivities\: UV S\_k about 2 % for k = 1, \<= 1 % for \-4 \<= k \< 1, \<= 3 % for k \> 0 \(dominated by the high\-energy data\), increasing substantially below k = \-5; the infrared part matters only for k \<= \-3/2 and the total S\_k for k \< \-2 are less reliable\. So the sums are not independent of Watson and Ramaswamy's refractivity\: checks\.

Table I \(p\. 71\)\: the adopted UV DOSD integrated over 27 regions \(dataset dosd\_SF6; sums to 69\.996, checked 2026\-09\-27\)\. The caption gives the infrared oscillator strengths \(E in units of 2R\)\: Pack's initial \(0\.0027999, 1\.327\(\-5\)\) and \(0\.0043190, 2\.264\(\-4\)\), adjusted to f1 = 1\.331\(\-5\) and f2 = 2\.317\(\-4\) \(inline datasets\); and the absorption edges '\-164\.1' \(sic\: 164\.1, S L2,3\), 228\.5 \(S L1\), 2472 \(S K\) and 648\.7 eV \(F K; Table I's region edge is 684\.7\)\. The initial\-data columns are not extracted; the text \(p\. 73\) notes that Blechschmidt et al\.'s and Sasanuma et al\.'s data over 13\.6\-39\.0 and 15\.1\-39\.0 eV are about 33 % and 30 % above the adopted strengths \(about 16\)\.

Table II \(p\. 72\)\: the adopted S\_k, k = 2, 1, \-1/2, \-1, \-3/2, \-2, \-5/2, \-3, \-4, UV and total \(datasets\)\. The text \(p\. 73\) adds S\_\-6 = 982\.1 \(UV\) and quotes Pack's Cauchy\-fit S\_\-2 = 3\.038\(1\) \+\- \.02, S\_\-4 = 3\.26\(1\) \+\- 4\.9 and S\_\-6 = 680 \+\- 310 \(from Watson and Ramaswamy's refractivities\), Tipton et al\.'s total S\_\-2 44\.21 \+\- 0\.05 \(via Pack\), Hosticka and Bose's 44\.27 \+\- 0\.07, and Lazzeretti et al\.'s coupled Hartree\-Fock S\_\-2 = 22\.76 \(inline datasets\)\. The mean excitation energies I\_k \(Table II, eV\: UV I\_2 = 4\.553\(4\), I\_1 = 1\.674\(3\), I\_0 = 1\.284\(2\), I\_\-1 = 3\.679\(1\), I\_\-2 = 2\.302\(1\); total 4\.553\(4\), 1\.674\(3\), 1\.283\(2\), 3\.637\(1\), 4\.196\(0\)\) have no quantity\: not extracted\.

Table III \(p\. 74\)\: ten\-term UV and twelve\-term total \(two IR \+ ten UV\) pseudo\-DOSDs, E in units of 2R \(hartree\) \(formulas\)\. They reproduce Table II's integer\-k sums; at k = \-1/2 they give 40\.43 \(UV\) and 40\.46 \(total\) against Table II's 40\.34 and 40\.37 \(the half\-integer sums are not constrained in the fit, Eq\. \(6\)\)\.

Table IV \(p\. 74\)\: C6\(SF6\-B\) for 19 partners, UV and total, with Pack's Pade values and uncertainties \(C6\(SF6\-SF6\) = 578\.2 UV, 585\.8 total\); C9\(SF6,SF6,SF6\) = 1\.202\(5\) \(UV\), 1\.237\(5\) \(total\) \(p\. 75\)\: no quantity, not extracted\.

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

Datasets
--------

kumar\_1985b/dosd\_SF6
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_SF6",
     "material": "SF6",
     "file": "SF6/kumar_1985b__dosd_SF6.csv",
     "table": "tbl_e5a10522c2c9",
     "quantity": "interval_oscillator_strength",
     "abscissa_unit": "eV",
     "columns": {
       "x_upper": "eV"
     },
     "use": "check"
   }

Table I 'Adopted values, UV, and higher energy spectrum'\: the constrained SF6 DOSD integrated over 27 energy regions, 5\.0 eV to infinity \(row = the region, x and x\_upper its edges; the data reference of each region in the printed cell, \[M\] the mixture rule\)\. Sums to 69\.996 \(S\_0 = Z = 70\)\. Constrained to Watson and Ramaswamy's refractivity\: a check\.

kumar\_1985b/infrared\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "infrared_SF6",
     "material": "SF6",
     "table": "text",
     "quantity": "oscillator_strength",
     "abscissa_unit": "hartree",
     "use": "check"
   }

2 inline points in the source record.

Table I caption\: the infrared oscillator strengths of the total DOSD, Pack's initial values adjusted by the constraint procedure to f1 = 1\.331\(\-5\) and f2 = 2\.317\(\-4\), at E1 = 0\.002 7999 and E2 = 0\.004 3190 \(units of 2R = hartree, i\.e\. 614\.5 and 947\.9 cm^\-1\)\. The total pseudo\-DOSD's IR terms \(Table III\) are the same to their digits\.

kumar\_1985b/infrared\_pack\_1982
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "infrared_pack_1982",
     "material": "SF6",
     "table": "text",
     "quantity": "oscillator_strength",
     "abscissa_unit": "hartree",
     "use": "reproduced",
     "reproduced_from": [
       "R. T Pack, J. Phys. Chem. 86, 2794 (1982)"
     ]
   }

2 inline points in the source record.

Table I caption\: Pack's infrared oscillator strengths \(E, f\) = \[0\.002 7999, 1\.327\(\-5\)\] and \[0\.004 3190, 2\.264\(\-4\)\], the initial values \(from Fox and Person's and Person and Overend's IR data as refined by Pack\)\.

kumar\_1985b/moments\_uv\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_uv_SF6",
     "material": "SF6",
     "file": "SF6/kumar_1985b__moments_uv_SF6.csv",
     "table": "tbl_bfe8065fdca1",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check",
     "uncertainty": {
       "relative": 0.01,
       "level": "not stated",
       "relative_rows": {
         "2": 0.03,
         "1": 0.02
       }
     }
   }

Table II, first line of each property, '\(UV \+ higher energy\)'\: the electronic DOSD's S\_k \(rows k; \-0\.5 for \-1/2 \.\.\.\); S\_\-2 = 30\.04 is the electronic static polarizability\. Uncertainty \(p\. 75\)\: about 2 % for k = 1, \<= 1 % for \-4 \<= k \< 1, \<= 3 % for k \> 1 \(stored so\), given reliable refractivities; the 1 % refractivity uncertainty would lower these by 0\.3\-1\.9 % \(source notes\)\. A check\.

kumar\_1985b/moments\_total\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_total_SF6",
     "material": "SF6",
     "file": "SF6/kumar_1985b__moments_total_SF6.csv",
     "table": "tbl_bfe8065fdca1",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check"
   }

Table II, second line of each property, '\(total including IR\)'\: the total DOSD's S\_k \(rows k\); S\_\-2 = 44\.21 is the constraint \(mark a, Tipton et al\. via Pack\), the total static polarizability\. The infrared dominates for k \<= \-3/2; S\_k for k \< \-2 'are less reliable' \(p\. 75\), no number given\. A check\.

kumar\_1985b/moment\_s6\_uv\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moment_s6_uv_SF6",
     "material": "SF6",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check"
   }

1 inline points in the source record.

p\. 73\: 'the result 982\.1 corresponding to our adopted DOSD' for S\_\-6 \(UV\)\. The uncertainty 'increase\[s\] substantially as k decreases below k = \-5' \(p\. 75\); the 4359\.6 A\-constrained DOSD gives about 2\.2 % less\. A check\.

kumar\_1985b/pack\_1982\_cauchy
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "pack_1982_cauchy",
     "material": "SF6",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "R. T Pack, J. Phys. Chem. 86, 2794 (1982)",
       "watson_1936"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

3 inline points in the source record.

p\. 73\: Pack's UV sums from a Cauchy\-type fit to Watson and Ramaswamy's refractivities, 'S\_\-2 = 3\.038\(1\) \+\- \.02, S\_\-4 = 3\.26\(1\) \+\- 4\.9, and S\_\-6 = 680 \+\- 310' \(sigma column\: the printed \+\- read as absolute au, as the S\_\-4 one must be \(4\.9 on 32\.6\); if the S\_\-2 '\.02' referred to the mantissa it would be 0\.2 au\)\. Pack notes his S\_\-4 and S\_\-6 uncertainties could be larger\. S\_\-4 disagrees substantially with the DOSD's 88\.59\.

kumar\_1985b/total\_polarizability\_tipton
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "total_polarizability_tipton",
     "material": "SF6",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "A. B. Tipton, A. P. Deam and J. E. Boggs, J. Chem. Phys. 40, 1144 (1964)",
       "R. T Pack, J. Phys. Chem. 86, 2794 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 72\: 'S\_\-2^total is the accurate value \(error \+\-0\.05\) of the total \(including IR contribution\) dipole sum S\_\-2 obtained from microwave polarizability data of Tipton et al\. by Pack', 44\.21 au, used as a constraint \(the total static polarizability\)\.

kumar\_1985b/total\_polarizability\_hosticka
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "total_polarizability_hosticka",
     "material": "SF6",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "hosticka_1974"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 72\: the total S\_\-2 'in good agreement with the value 44\.27 \+\- 0\.07 obtained by Hostika and Bose' \(sic\: Hosticka\), from dielectric measurements\. Hosticka and Bose 1974 is curated in another extraction as hosticka\_1974\: the re\-point is left to review\.

kumar\_1985b/lazzeretti\_1983
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "lazzeretti_1983",
     "material": "SF6",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "P. Lazzeretti, U. Pincelli, E. Rossi and R. Zanasi, J. Chem. Phys. 79, 4085 (1983)"
     ]
   }

1 inline points in the source record.

p\. 73\: 'The coupled Hartree\-Fock result of Lazzeretti et al\. for the dipole polarizability of SF6 corresponds to S\_\-2 = 22\.76', about 24 % below the adopted electronic 30\.04\.

kumar\_1985b/constraint\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "constraint_SF6",
     "material": "SF6",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "watson_1936"
     ]
   }

2 inline points in the source record.

p\. 72\: Watson and Ramaswamy's molar refractivities 'R\(lambda = 6440 A\) = 11\.4057 and R\(lambda = 4360 A\) = 11\.5212 cm^3 mol^\-1' \(the first the adopted DOSD's constraint; both together could not be imposed\)\. Vacuum wavelengths as watson\_1936's 6440\.24 and 4359\.56 A; the density convention \(virial or ideal\) is not stated here\.

kumar\_1985b/dosd\_refractivity
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_refractivity",
     "material": "SF6",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

2 inline points in the source record.

p\. 75\: the adopted DOSD \(constrained at 6440 A\) 'yields R\(lambda = 4359\.6 A\) = 11\.6474 cm^3 mol^\-1 which is 1% higher than the experimental value'; a DOSD constrained at 4359\.6 A instead 'yields R\(lambda = 6440 A\) = 11\.2843 cm^3 mol^\-1 which is 1% lower' \(row alternative\_6440\: a different DOSD\)\. Model values\: checks\.

Formulas
--------

kumar\_1985b/pseudospectrum\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "pseudospectrum_SF6",
     "form": "oscillator",
     "energy_unit": "hartree",
     "terms": {
       "f": [
         "6.02730e-3",
         "3.57892e-2",
         "4.56141e-2",
         "1.48164e-1",
         "1.58865e0",
         "8.29346e0",
         "1.61049e1",
         "2.09223e1",
         "2.16830e1",
         "1.17211e0"
       ],
       "E": [
         "1.89971e-1",
         "2.08697e-1",
         "2.36507e-1",
         "3.68745e-1",
         "5.31116e-1",
         "8.12799e-1",
         "1.47230e0",
         "3.74198e0",
         "2.34722e1",
         "4.79384e2"
       ]
     },
     "range_nm": [
       263.9,
       "inf"
     ],
     "material": "SF6",
     "equation": "Table III, p. 74, with Eq. (6); alpha(omega) = sum_i f_i / (E_i^2 - omega^2)",
     "printed": "(E_i, f_i), UV and higher energy, E_i in units of 2R: (1.899 71( - 1), 6.027 30( - 3)); (2.086 97( - 1), 3.578 92( - 2)); (2.365 07( - 1), 4.561 41( - 2)); (3.687 45( - 1), 1.481 64( - 1)); (5.311 16( - 1), 1.588 65(0)); (8.127 99( - 1), 8.293 46(0)); (1.472 30(0), 1.610 49(1)); (3.741 98(0), 2.092 23(1)); (2.347 22(1), 2.168 30(1)); (4.793 84(2), 1.172 11(0))",
     "variable": "omega: photon energy (angular frequency) in hartree; alpha in atomic units",
     "state": "none (per molecule)",
     "density": "none",
     "range": "The pseudo-DOSD represents the UV DOSD's sums; its lowest pole is at 0.189971 hartree (239.9 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (as kumar_2010_supplement, TC-119), not the paper's.",
     "check": "S(k) = sum f_i E_i^k reproduces Table II's UV sums: S_2 = 2.816e5 (2.816(5)), S_1 = 1180 (1.181(3)), S_0 = 70.00, S_-1 = 31.45, S_-3/2 = 29.02 (2.903(1)), S_-2 = 30.04, S_-5/2 = 34.21, S_-3 = 42.72, S_-4 = 88.59, S_-6 = 982.1 (text); S_-1/2 = 40.43 against 40.34 (half-integer k not constrained) (computed 2026-09-27). Terms equal Table III (asserted by tools/extract/kumar_1985b.py). Against the package's fitted SF6 model: alpha(632.8 nm) = 30.53 au, 0.8 % higher; 5.7 % higher at 300 nm (the adopted DOSD is 1 % above Watson and Ramaswamy at 435.96 nm by the paper's own account, and its 5.0-10.1 eV strength, 0.117, puts poles at 5.2-6.4 eV) (computed 2026-09-27)."
   }

A ten\-term pseudo\-DOSD fitted to S\_k, k = 2 \.\.\. \-17, of the adopted UV DOSD; electronic only\. Not independent of Watson and Ramaswamy's refractivity \(source notes\)\: a check against those data, not a fit to them\. Adopted DOSD 'probably slightly high' \(the 1 % refractivity uncertainty, source notes\)\.

kumar\_1985b/pseudospectrum\_SF6\_total
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "pseudospectrum_SF6_total",
     "material": "SF6",
     "equation": "Table III, p. 74, with Eq. (6)",
     "printed": "(E_i, f_i), IR + UV and higher energy, E_i in units of 2R: (2.799 91( - 3), 1.331 27( - 5)); (4.319 00( - 3), 2.316 96( - 4)); (1.899 71( - 1), 6.029 95( - 3)); (2.086 97( - 1), 3.580 49( - 2)); (2.365 07( - 1), 4.563 09( - 2)); (3.687 84( - 1), 1.484 80( - 1)); (5.311 46( - 1), 1.591 73(0)); (8.127 47( - 1), 8.312 16(0)); (1.471 99(0), 1.611 03(1)); (3.741 44(0), 2.091 49(1)); (2.347 22(1), 2.168 06(1)); (4.793 88(2), 1.172 09(0))",
     "variable": "E: excitation energy in units of 2R (hartree); f: oscillator strength; alpha(omega) = sum f / (E^2 - omega^2) in atomic units. E1, E2 are the infrared bands, E3-E12 the effective UV terms",
     "state": "none (per molecule)",
     "density": "none",
     "range": "the static and long-wavelength total dipole properties; not near or between the infrared bands",
     "coefficients": {
       "E1": "2.79991e-3",
       "f1": "1.33127e-5",
       "E2": "4.31900e-3",
       "f2": "2.31696e-4",
       "E3": "1.89971e-1",
       "f3": "6.02995e-3",
       "E4": "2.08697e-1",
       "f4": "3.58049e-2",
       "E5": "2.36507e-1",
       "f5": "4.56309e-2",
       "E6": "3.68784e-1",
       "f6": "1.48480e-1",
       "E7": "5.31146e-1",
       "f7": "1.59173e0",
       "E8": "8.12747e-1",
       "f8": "8.31216e0",
       "E9": "1.47199e0",
       "f9": "1.61103e1",
       "E10": "3.74144e0",
       "f10": "2.09149e1",
       "E11": "2.34722e1",
       "f11": "2.16806e1",
       "E12": "4.79388e2",
       "f12": "1.17209e0"
     },
     "check": "S(k) reproduces Table II's total sums: S_0 = 70.02 (70.018 constraint), S_-1 = 31.54, S_-3/2 = 29.97 (2.998(1)), S_-2 = 44.21, S_-5/2 = 255.4, S_-3 = 3525, S_-4 = 8.826e5; S_-1/2 = 40.46 against 40.37 (computed 2026-09-27). Terms equal Table III (asserted by the extraction script)."
   }

The total pseudo\-DOSD\: the adopted infrared strengths \(the Table I caption's f1, f2 at E1, E2\) plus ten UV terms fitted to S\_k\(total\) \- S\_k\(IR\)\. No form\: the infrared poles make it unsuitable as an optical dispersion model beyond the static limit\.

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.