lesiuk_2023#

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

Source record · Catalogue · Review register

DOI: 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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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.

Corrections#

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.