lesiuk_2023
===========

M\. Lesiuk and B\. Jeziorski, Phys\. Rev\. A 107, 042805 \(2023\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/lesiuk_2023.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/physreva\.107\.042805 <https://doi.org/10.1103/physreva.107.042805>`__

**Source kind:** theory

**Recorded technique:** Ab initio composite calculation of the static dipole polarizability alpha\_0 and the dispersion \(Cauchy\) coefficients alpha\_2, alpha\_4 \(and alpha\_6\) of the argon atom \(40Ar, 39\.962 383 Da\), alpha\(omega\) = alpha\_0 \+ alpha\_2 omega^2 \+ alpha\_4 omega^4 \+ \.\.\. \(Eq\. \(6\)\)\. Nonrelativistic clamped\-nucleus part\: Hartree\-Fock in a 40s40p40d basis, then frozen\-core coupled\-cluster increments CCSD, CC3, CCSDT, CCSDTQ, CCSDTQP, CCSDTQPH \(orbital\-unrelaxed linear response\) in purpose\-built basis sets up to nonuple zeta \(X = 9, triply augmented\), extrapolated to the complete basis set with a Riemann\-zeta formula \(Eq\. \(8\)\); core\-core and core\-valence correlation \(all\-electron CC3, CCSDT, CCSDTQ\)\. Relativistic corrections\: one\-electron by DKH2 \(checked against Breit\-Pauli mass\-velocity \+ Darwin\), two\-electron Darwin and Breit \(Breit for alpha\_2, alpha\_4 at the Hartree\-Fock level, Appendix\), second\-order spin\-orbit estimated from four\-component Dirac\-Coulomb Hartree\-Fock \(alpha\_0 only\)\. QED\: leading\-order one\-electron term, Eq\. \(24\), with the Bethe logarithm ln k\_0 = 8\.7610, and the one\-loop 1/c^4 term, Eq\. \(27\)\. Finite nuclear size \(Eq\. \(29\), negligible\) and finite nuclear mass \(diagonal Born\-Oppenheimer correction, MP1, alpha\_0 only\)\. CODATA constants; c = 137\.035999084 a\.u\.

**Materials in structured entries:** Ar

**Dataset quantities:** cauchy\_moment, polarizability

**Contents:** 10 datasets; 2 formulas.

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

Atomic units throughout \(polarizability in e^2 a0^2/Eh = 4 pi eps0 a0^3, omega in hartree\)\. All corrections are included in alpha\_0 \(relativistic 1/c^2 incl\. Breit and two\-electron Darwin, spin\-orbit, QED incl\. one\-loop 1/c^4, finite nuclear size and mass for 40Ar\); alpha\_2 and alpha\_4 include the same except the two\-electron Darwin, spin\-orbit and finite\-mass terms, judged negligible \(pp\. 9\-11\)\. Uncertainties are the authors' estimates for each contribution \(typically twice the spread of the basis\-set extrapolations, 10\-50 % for small corrections\) combined in quadrature \('the standard error propagation formulas under the assumption that all contributions \.\.\. are independent', p\. 13\); no confidence level is stated\. alpha\_6 = 382\.5 \(Eq\. \(36\)\) is from Hartree\-Fock \+ valence CCSD \+ valence CC3 only, 'relative error no larger than 10%' \(p\. 13\)\.

The authors claim 'accuracy of around 10 ppm for wavelengths above roughly 450 nm' \(omega \<= 0\.1 a\.u\.\) when their dispersion coefficients are combined with Gaiser and Fellmuth's \(2018\) measured static polarizability \(abstract, pp\. 3\-4\); the first resonance is at omega about 0\.42 a\.u\. \(Minnhagen 1973, their Ref\. 36\)\. Their own alpha\_0 = 11\.0775\(19\) agrees with Gaiser and Fellmuth's 11\.077183\(27\)\.

alpha here is the electric dipole polarizability only\. For the refractive index the paper uses the Lorentz\-Lorenz form \(n^2\-1\)/\(n^2\+2\) = \(4 pi/3\)\(alpha \+ chi\_0\) rho \(Eq\. \(3\)\), with the static magnetic susceptibility chi\_0 = \-2\.30\(2\) x 10^\-4 a\.u\. \(Eq\. \(39\); \-2\.3004\(6\) x 10^\-4 from \<r^2\> = 25\.9193\(64\), Eq\. \(35\), nonrelativistic only, 1 % allowed for missing corrections\)\. The package's polarizability recovered from a refractivity is alpha \+ chi\_0\: the chi\_0 term \(\-21 ppm of alpha\_0\) must be added to these alpha values before they are compared with refractive\-index data\. The magnetic susceptibility itself is not a quantity of the package and is not extracted \(Table XIII, the chi\_0 comparison, likewise\)\.

Conversion used by the authors \(p\. 2\)\: 1 cm^3/mol = 11\.205 872 a0^3, i\.e\. their molar polarizability is N\_A alpha \(polarizability volume\), not the molar refractivity \(4 pi/3\) N\_A alpha\.

Not extracted\: Tables I\-X \(individual contributions by basis set and their CBS limits\), Table XI's contribution rows \(components of the Total row\), Table XIII \(chi\_0\)\. The budget rows of Table XI sum to its totals \(11\.0775, 27\.9755, 95\.0182; quadrature 0\.00194, 0\.0154, 0\.106; checked 2026\-09\-24\)\.

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

Datasets
--------

lesiuk\_2023/cauchy\_Ar
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cauchy_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__cauchy_Ar.csv",
     "table": "tbl_cb5cfdf665dc",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table XI 'Total'\: alpha\_0, alpha\_2, alpha\_4 = S\(\-2\), S\(\-4\), S\(\-6\), rows by moment order k\. Electric polarizability only \(add chi\_0 = \-2\.30e\-4 a\.u\. for refractive\-index comparisons; source notes\)\. Also Table XII 'This work' and the abstract\. The sum of the budget rows reproduces the totals \(checked 2026\-09\-24\)\.

lesiuk\_2023/cauchy\_alpha6\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cauchy_alpha6_Ar",
     "material": "Ar",
     "table": "text",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "primary",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     }
   }

1 inline points in the source record.

Eq\. \(36\), p\. 13\: alpha\_6 = S\(\-8\) = 382\.5 from the Hartree\-Fock \(297\.775\(6\), Eq\. \(7\)\), valence CCSD \(67\.906\(26\), Eq\. \(10\)\) and valence CC3 \(16\.85\(30\), Eq\. \(12\)\) contributions only \(sum 382\.53\); 'relative error no larger than 10%' \(read as a bound\)\.

lesiuk\_2023/egan\_2019\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "egan_2019_Ar",
     "material": "Ar",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "egan_2019"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

Eq\. \(37\), p\. 14\: Egan et al\.'s molar polarizability of argon from laser refractometry at lambda\_E = 632\.9908\(2\) nm \(omega\_E = 0\.071981 a\.u\., red He\-Ne laser; a vacuum wavelength\), converted by Lesiuk and Jeziorski to atomic units\: 11\.22431\(17\)\. From refractometry, so it is alpha\(omega\_E\) \+ chi\_0 \(p\. 14\), which is what the package's refractivity\-derived polarizability means\. The conversion from cm^3/mol is the authors' \(1 cm^3/mol = 11\.205872 a0^3\)\. The original is now curated \(egan\_2019\), which the fits use instead\.

lesiuk\_2023/theory\_egan\_wavelength\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_egan_wavelength_Ar",
     "material": "Ar",
     "table": "text",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

Eq\. \(38\), p\. 14\: alpha\_theory\(omega\_E\) = 11\.22445\(11\), Gaiser and Fellmuth's static alpha\_0 plus chi\_0 \(Eq\. \(35\)\) plus alpha\_2 omega^2 \+ alpha\_4 omega^4 from Table XI \(formula recommended\)\. Reproduced\: 11\.077183 \- 0\.00023004 \+ 27\.976 omega^2 \+ 95\.02 omega^4 at omega = 45\.56335/632\.9908 = 0\.0719811 gives 11\.224455 \(checked 2026\-09\-24\)\. Includes chi\_0, so comparable with refractive data\.

lesiuk\_2023/kumar\_2010\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kumar_2010_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__kumar_2010_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "kumar_2010"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table XII, 'Kumar and Thakkar \[93\]' \(experimental or semiempirical\: the constrained DOSD\), S\(\-2\), S\(\-4\), S\(\-6\) rounded, with 1 % uncertainties; see kumar\_2010 for the originals\.

lesiuk\_2023/orcutt\_1967\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "orcutt_1967_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__orcutt_1967_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "R. Orcutt and R. Cole, J. Chem. Phys. 46, 697 (1967)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table XII, 'Orcutt and Cole \[94\]'\: static polarizability from dielectric\-constant measurements, 11\.0753\(54\), converted to atomic units by Lesiuk and Jeziorski\. The original is in the library \(Orcutt\_1967\_DielectricConstantsImperfect\) but has no source record yet; switch reproduced\_from to its id when it gets one\.

lesiuk\_2023/buckley\_2000\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "buckley_2000_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__buckley_2000_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "T. J. Buckley, J. Hamelin, and M. R. Moldover, Rev. Sci. Instrum. 71, 2914 (2000)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table XII, 'Buckley at al\. \[95\]' \(sic\)\: static polarizability 11\.0774\(10\) \(dielectric\-constant measurement, converted to atomic units by Lesiuk and Jeziorski\)\. The original is not in the library\.

lesiuk\_2023/gaiser\_2018\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "gaiser_2018_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__gaiser_2018_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "gaiser_2018"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table XII, 'Gaiser and Fellmuth \[21\]'\: static polarizability 11\.077183\(27\) from dielectric\-constant gas thermometry, 'accurate to about 2 parts per million' \(p\. 2\); the most accurate argon value, which the authors combine with their dispersion coefficients \(Eq\. \(38\)\)\. The original is now curated \(gaiser\_2018\), which the fits use instead\.

lesiuk\_2023/pawlowski\_2005\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "pawlowski_2005_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__pawlowski_2005_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "F. Pawłowski, P. Jørgensen, and C. Hättig, in Advances in Quantum Chemistry, edited by J. R. Sabin, Vol. 48 (Academic Press, 2005), pp. 9-21"
     ]
   }

Table XII, 'Pawłowski et al\.'\: CC3, sextuple\-zeta basis \(note a\), nonrelativistic; S\(\-2\), S\(\-4\), S\(\-6\); no uncertainty given\.

lesiuk\_2023/lupinetti\_2005\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "lupinetti_2005_Ar",
     "material": "Ar",
     "file": "Ar/lesiuk_2023__lupinetti_2005_Ar.csv",
     "table": "tbl_787fa31e3c55",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "C. Lupinetti and A. J. Thakkar, J. Chem. Phys. 122, 044301 (2005)"
     ]
   }

Table XII, 'Lupinetti et al\.'\: finite\-field CCSD\(T\) static polarizability 11\.07 \(note b\); no uncertainty given\.

Formulas
--------

lesiuk\_2023/cauchy\_theory
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cauchy_theory",
     "form": "alpha_series",
     "terms": {
       "c": [
         "11.0775",
         "27.976",
         "95.02",
         "382.5"
       ]
     },
     "range_nm": [
       450.0,
       "inf"
     ],
     "material": "Ar",
     "equation": "Eq. (6), p. 3, with Table XI (Total) and Eq. (36)",
     "printed": "alpha(omega) = alpha_0 + alpha_2 omega^2 + alpha_4 omega^4 + ...; alpha_0 = 11.0775(19), alpha_2 = 27.976(15), alpha_4 = 95.02(11), alpha_6 = 382.5",
     "variable": "omega: photon energy (angular frequency) in atomic units (hartree); alpha in atomic units",
     "state": "none (per atom)",
     "density": "none",
     "range": "wavelengths above roughly 450 nm (omega <= 0.1 a.u.; first resonance at about 0.42 a.u.)",
     "coefficients": {
       "alpha_0": "11.0775",
       "alpha_2": "27.976",
       "alpha_4": "95.02",
       "alpha_6": "382.5"
     },
     "check": "The Table XI contributions sum to the totals (checked 2026-09-24). At omega_E = 0.0719811 a.u. (632.9908 nm) it gives alpha = 11.225055 with alpha_6 (11.225002 without); with chi_0 = -2.3004e-4 added and alpha_6 omitted, 11.224772: 0.00032 above Eq. (38) (the difference of the two alpha_0 values, 11.0775 against 11.077183) and 0.00046 (41 ppm) above Egan et al.'s 11.22431(17), within the theory's 0.0019 uncertainty. Checked 2026-09-24."
   }

The paper's own ab initio series \(all corrections included, source notes\)\. ELECTRIC polarizability\: it omits the magnetic susceptibility chi\_0 = \-2\.30\(2\)e\-4 a\.u\. that the Lorentz\-Lorenz relation for the refractive index needs \(Eq\. \(3\)\); a refractivity computed from this model is low by 21 ppm unless chi\_0 is added\. alpha\_6 has a 10 % uncertainty and contributes 4e\-4 a\.u\. \(37 ppm\) at 450 nm\.

lesiuk\_2023/recommended
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "recommended",
     "form": "alpha_series",
     "terms": {
       "c": [
         "11.077183",
         "27.976",
         "95.02"
       ]
     },
     "range_nm": [
       450.0,
       "inf"
     ],
     "material": "Ar",
     "equation": "Eq. (6) with Table XI and Gaiser and Fellmuth's alpha_0, as used for Eq. (38), p. 14",
     "printed": "alpha(omega) = alpha_0 + alpha_2 omega^2 + alpha_4 omega^4, alpha_0 = 11.077183(27) (Gaiser and Fellmuth), alpha_2 = 27.976(15), alpha_4 = 95.02(11); plus chi_0 = -2.3004(6) x 10^-4 for refraction",
     "variable": "omega: photon energy (angular frequency) in atomic units (hartree); alpha in atomic units",
     "state": "none (per atom)",
     "density": "none",
     "range": "wavelengths above roughly 450 nm, 'accuracy of around 10 ppm' (abstract)",
     "coefficients": {
       "alpha_0": "11.077183",
       "alpha_2": "27.976",
       "alpha_4": "95.02",
       "chi_0": "-2.3004e-4"
     },
     "check": "With chi_0 added: 11.224455 at 632.9908 nm, Eq. (38)'s 11.22445(11); Egan et al.'s measured 11.22431(17) lies 1.4e-4 (12 ppm) below, 'within their combined uncertainty' (p. 14). Checked 2026-09-24."
   }

The combination the paper recommends \(Sec\. IX\)\: the measured static polarizability with the calculated dispersion coefficients\. As structured \(terms c\) it is the electric polarizability; chi\_0 \(Eq\. \(35\), \-2\.3004\(6\)e\-4 a\.u\.\) is NOT in the terms and must be added for the refractive index \(n from Lorentz\-Lorenz with alpha \+ chi\_0\)\. alpha\_6 is omitted as in Eq\. \(38\) \(it adds 5e\-5 a\.u\. at 633 nm\)\.

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.