kolos_1967 ========== W\. Kolos and L\. Wolniewicz, J\. Chem\. Phys\. 46, 1426 \(1967\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.1840870 `__ **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 \(row id v\J\, all at wavelength inf\)\: 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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 vJ, all static" } } Table III alpha\_{vJ,vJ} of H2, static, for v = 0, J = 0\-31 and J = 0, v = 1\-8 \(40 states; row id v\J\, every row at wavelength inf; image checked\)\. Not a wavelength series\: each row is a different rovibrational state\. kolos\_1967/static\_states\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 vJ, all static" } } Table III alpha\_{vJ,vJ} of D2, static, for v = 0, J = 0\-31 and J = 0, v = 1\-8 \(40 states; row id v\J\, every row at wavelength inf; image checked\)\. Row v0J14 is corrected by an erratum\. Not a wavelength series\. kolos\_1967/normal\_293K\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ----------- .. code-block:: text [ { "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 :doc:`review register ` for the checks and decisions.