kolos_1967#

W. Kolos and L. Wolniewicz, J. Chem. Phys. 46, 1426 (1967)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Variation-perturbation calculation of the static clamped-nucleus polarizabilities alpha_par(R) and alpha_perp(R) of H2 (54-term James-Coolidge-type ground state in elliptic coordinates with r12, 34-term first-order functions of Sigma_u and Pi_u symmetry) for R = 0.4-4.0 a0 (Table II), averaged over the rovibrational wave functions of the adiabatic potential (diagonal corrections for nuclear motion included) for H2, HD and D2 (Eq. (14), Table III).

Materials in structured entries: D2, H2

Dataset quantities: polarizability

Contents: 3 datasets; 1 formula.

Curation notes#

Static only: the paper has no frequency-dependent values. Units: atomic units (a0^3) in Table III; cubic angstroms in Table VI. HD is not a curated species; the anisotropies gamma, the clamped-nucleus alpha(R) of Table II, the off-diagonal elements of Table IV and the relative isotope effects of Table V (H2 - D2: 1.27 % calculated, 1.26 % measured by Hermans et al. 1965) have no vocabulary quantity and are not extracted.

Table III’s per-state values are stored one dataset per gas with each row a rovibrational state (row id v<v>J<J>, all at wavelength inf): the format has no state axis, so these check datasets must not be read as a wavelength series. ‘The polarizabilities computed in the Born-Oppenheimer approximation ... differed by less than 0.1 % from the values given in Table III’ (p. 1429). No other accuracy is stated.

Table VI (p. 1430): alpha_00 ‘This calculation’ 0.8023 A^3 (J = 0; Table III’s 5.4139 a.u.) and 0.8045 A^3 (footnote d, ‘Rotational average for 293 K’, ‘assuming normal H2 and T = 293 K’, p. 1430). Check: the normal-H2 average of Table III’s v = 0, J = 0-10 values at 293 K with the spin weights 1 and 3 and Raj et al.’s (2018) rotational energies gives 5.42905 a.u. = 0.80450 A^3 (checked 2026-09-25). The same procedure gives 5.36081 a.u. for normal D2 (with the J = 14 erratum; J = 14 does not enter).

‘Experimental’ alpha_00 = 0.8056 A^3 (footnote c, Reference 19): the static limit of Schueler and Wolf’s (1925) dispersion formula (Eq. (17), recorded below) with n - 1 = 1.3600e-4 and Eq. (16), n - 1 = 2 pi N0 alpha, N0 = 2.6867e19 cm^-3; a reproduction of an extrapolated formula, not extracted as a dataset. (The library’s JSON marks it ‘^{e}’; the image prints c, and footnote c is ‘Reference 19’.) The Ishiguro et al. (1952) column and the anisotropy and Raman values are not extracted.

Table III is superseded for refraction by the dynamic, more accurate calculations (bishop_1980, rychlewski_1983, raj_2018); kept as checks.

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

Datasets#

kolos_1967/static_states_H2#

{
  "id": "static_states_H2",
  "material": "H2",
  "file": "H2/kolos_1967__static_states.csv",
  "table": "tbl_008b76c50f4e",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rows": "rovibrational states v<v>J<J>, all static"
  }
}

Table III alpha_{vJ,vJ} of H2, static, for v = 0, J = 0-31 and J = 0, v = 1-8 (40 states; row id v<v>J<J>, every row at wavelength inf; image checked). Not a wavelength series: each row is a different rovibrational state.

kolos_1967/static_states_D2#

{
  "id": "static_states_D2",
  "material": "D2",
  "file": "D2/kolos_1967__static_states.csv",
  "table": "tbl_008b76c50f4e",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rows": "rovibrational states v<v>J<J>, all static"
  }
}

Table III alpha_{vJ,vJ} of D2, static, for v = 0, J = 0-31 and J = 0, v = 1-8 (40 states; row id v<v>J<J>, every row at wavelength inf; image checked). Row v0J14 is corrected by an erratum. Not a wavelength series.

kolos_1967/normal_293K_H2#

{
  "id": "normal_293K_H2",
  "material": "H2",
  "file": "H2/kolos_1967__normal_293K.csv",
  "table": "tbl_3187f42a4fee",
  "quantity": "polarizability",
  "unit": "angstrom3",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "temperature_k": 293,
    "average": "rotational average, normal H2 (p. 1430)"
  }
}

Table VI alpha_00 ‘This calculation’, second value of the merged cell, footnote d ‘Rotational average for 293 K’ (normal H2): 0.8045 A^3, static. Reproduced from Table III (source notes).

Formulas#

kolos_1967/schuler_wolf#

{
  "id": "schuler_wolf",
  "material": "H2",
  "equation": "Eq. (17), p. 1430",
  "printed": "n - 1 = 0.91997 x 10^27 / (1.01305 x 10^31 - nu^2) + 0.75379 x 10^27 / (1.66813 x 10^31 - nu^2)",
  "variable": "nu: frequency of the light in s^-1 (cycles per second: the poles lie at c/nu = 94.2 and 73.4 nm)",
  "state": "1atm_0C",
  "density": "ideal",
  "range": "not stated (Schueler and Wolf's data; used by Kolos for the static limit only)",
  "coefficients": {
    "B1": "0.91997e27",
    "C1": "1.01305e31",
    "B2": "0.75379e27",
    "C2": "1.66813e31"
  },
  "check": "Static limit n - 1 = 1.35999963e-4 against the printed 1.3600e-4, and alpha = (n - 1)/(2 pi N0) = 0.80564 A^3 with N0 = 2.6867e19 cm^-3 against the printed 0.8056 (checked 2026-09-25)."
}

Reproduced: H. Schueler and K. L. Wolf, Z. Physik 34, 343 (1925) (Ref. 19), as used by Karplus (1964) (Ref. 20); not in the library. The state is inferred from Kolos’s use of the Loschmidt number N0 = 2.6867e19 cm^-3 (0 degrees C, 1 atm, ideal gas) with it; Schueler and Wolf’s own reference state and wavelength range are not given. No form is assigned: in wavenumbers (cm^-1) it is dn_wavenumber2 with B_i/c^2 and C_i/c^2 (c in cm/s), i.e. converted coefficients.

Corrections#

[
  {
    "dataset": "static_states_D2",
    "row": "v0J14",
    "column": "value",
    "printed": "9.8344",
    "corrected": "5.8344",
    "reason": "Misprinted leading digit: D2's alpha_{0 14, 0 14} lies between J = 13 (5.7703) and J = 15 (5.9027).",
    "evidence": "Table image checked: the cell prints 9.8344. With 5.8344 the column's first differences run 0.0598, 0.0641, 0.0683, 0.0725 (J = 12-16), second differences 0.0043, 0.0042, 0.0042 as along the whole column (0.0039-0.0048); 9.8344 gives 4.0043 and -7.9958."
  }
]

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.