bishop_1982 =========== D\. M\. Bishop and L\. M\. Cheung, "Vibrational Contributions to Molecular Dipole Polarizabilities", J\. Phys\. Chem\. Ref\. Data 11, 119 \(1982\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.555658 `__ **Source kind:** compilation **Recorded technique:** Static vibrational polarizabilities of about a hundred molecules in the vibrational ground state, computed from experimental infrared band intensities\: alpha = \(2/3\) sum\_n g\_n mu\_n^2/\(h c omega\_n\) over the fundamentals \(Eq\. 1\), the transition moments from the absolute integrated intensities A\_n \(Eqs\. 2, 3\), and alpha = 3 eps0 P/N\_A = 0\.441 P x 10^\-40 C^2 m^2 J^\-1 with P in cm^3/mol \(Eq\. 4\)\. Harmonic approximation \(overtones and combination bands 'discarded as being inconsequentially small'\), closure over rotation, excited vibrational states unpopulated \(pp\. 119\-120\)\. Intensity survey to the end of 1980, 'a major source' Pugh and Narahari Rao \(1976\) \[9\]\. **Materials in structured entries:** CH4, CO, CO2, N2O, O3, SF6 **Dataset quantities:** None recorded. **Contents:** 0 datasets; 6 formulas. Curation notes -------------- First page checked \(pdf page 2; pdf page 1 is the publisher's cover\)\: J\. Phys\. Chem\. Ref\. Data 11, No\. 1, 1982; page numbers here are journal pages \(pdf page \+ 117\)\. This is the 'Bishop and Cheung' of zhao\_2026 \(Ref\. 44\) and sharipov\_2017 \(Table 2\)\. WHAT THE VALUES ARE\. The pure vibrational \(formerly 'atomic'\) static dipole polarizability alpha\_vib, the infrared response that a dielectric measurement sees and an optical one does not; not a total polarizability, and without the orientation term of polar molecules\. Units 10^\-40 C^2 m^2 J^\-1 \(1 au = 1\.64878e\-41 C^2 m^2 J^\-1 with the package's constants\)\. NO DATASETS\: the vocabulary has no quantity for a vibrational contribution to the polarizability \(the same format gap as sharipov\_2017; reported\)\. Storing these as 'polarizability' would make them total polarizabilities\. Instead each curated molecule's bands \(omega\_n, A\_n, P\_n\) and total alpha are recorded as a formula entry \(co, co2, n2o, o3, ch4, sf6\), the printed numbers as strings, each checked against Eqs\. \(1\)\-\(4\)\: every P\_n recomputes from A\_n and omega\_n as P\_n = 1e5 A\_n/\(3 pi^2 omega\_n^2\) \(cm^3/mol, A in km/mol, omega in cm^\-1; the degeneracy cancels\) to the printed digits, and every total as 0\.441 sum P\_n\. Table images checked \(Tables 1, 2, 4, 6; the library's Table 4 cells shift columns across the page break, and the totals of Tables 2, 4 and 6 sit on a separate line in the images\)\. THE DIRECT CHECK OF THE HITRAN INFRARED TERMS \(optmat\.gas\.infrared\.static\_infrared\_polarizability\_au, computed 2026\-09\-25\)\: Bishop and Cheung against HITRAN, au\: CO2 1\.759 / 2\.121 \(\-17 %\), N2O 1\.092 / 1\.186 \(\-8 %\), CH4 0\.2305 / 0\.2401 \(\-4 %\), SF6 15\.16 / 13\.94 \(\+8\.7 %\); CO 0\.1213 and O3 0\.788 have no HITRAN bands in data/external/hitran yet\. H2, D2, N2, O2 and the noble gases have no infrared\-active fundamentals and are not listed\. ACCURACY\. Error classes from the authors' stated intensity errors\: \(a\) \<= 5 %, \(b\) 5\-10 %, \(c\) \> 10 % \(p\. 120\) \- but the footnote letters are not the same in every table \(Tables 1, 2\: b 5 %, c 5\-10 %, d \> 10 %; Table 4\: d 5 %, e 5\-10 %, f \> 10 %; Table 6\: b 5 %, c 5\-10 %\)\. 'It is almost certainly true that the error limits on the intensities \.\.\. are unduly optimistic \.\.\. it is not unusual for the results from two different laboratories to differ by 100%'; realistic classes are \(a\) \<= 10 %, \(b\) 10\-50 %, \(c\) \> 50 % \(p\. 120\), and 'these estimates should be at least doubled' \(p\. 120\)\. Curated\: CO 5 %, CO2 5\-10 %, N2O 5 %, O3 none given, CH4 5 %, SF6 5 % \(as stated; double them\)\. Not recorded\: the non\-curated molecules \(about a hundred\), the isotopologues \(CD4, CH3D, \.\.\.; not curated species\), the anisotropic contributions \(derivable from the per\-band P\_n\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- No datasets are recorded. Formulas -------- bishop\_1982/co ~~~~~~~~~~~~~~~ .. code-block:: text { "id": "co", "material": "CO", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 1, p. 121", "printed": "CO: omega 2143 [9], A 61.2 [12] km/mol, P 0.045 cm^3/mol, alpha 0.020^b x 10^-40 C^2 m^2 J^-1", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega": "2143", "A": "61.2", "P": "0.045", "alpha": "0.020" }, "check": "P = 1e5 A/(3 pi^2 omega^2) (Eqs. 1-4, A in km/mol, omega in cm^-1) gives 0.04501 (printed 0.045); alpha = 0.441 P = 0.0198 (printed 0.020). Checked 2026-09-25." } Error class b \(Table 1\)\: 'The estimated error is 5%' \(the authors' own class; 'these estimates should be at least doubled', p\. 120\)\. Intensity from Varanasi and Sarangi, JQSRT 15, 473 \(1975\) \[12\]; frequency from Pugh and Narahari Rao \[9\]\. 0\.020e\-40 = 0\.1213 au \(1 au = 1\.64878e\-41 C^2 m^2 J^\-1\)\: the value zhao\_2026 quotes as '20\(1\) x 10^\-43'; christiansen\_1998's CCSD\(T\) pure vibrational mean is 0\.1246 au \(\+3 %\)\. HITRAN's CO bands are not yet in data/external/hitran\. bishop\_1982/co2 ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "co2", "material": "CO2", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 2, p. 122", "printed": "CO2: nu_2(pi_u) omega 667 [9], A 47.8 [22], P 0.36; nu_3(sigma_u+) 2349, 498.7 [23], 0.31; alpha 0.29^c", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega_2": "667", "A_2": "47.8", "P_2": "0.36", "omega_3": "2349", "A_3": "498.7", "P_3": "0.31", "alpha": "0.29" }, "check": "P_n from A_n: 0.36287, 0.30525 (printed 0.36, 0.31); alpha = 0.441 x 0.6681 = 0.2946 (printed 0.29). Checked 2026-09-25." } Error class c \(Table 2\)\: 'between 5 and 10%'\. Intensities\: Madden 1961 \[22\] \(nu\_2\), Tubbs and Williams 1972 \[23\] \(nu\_3\)\. 0\.29e\-40 = 1\.759 au, 17 % below the HITRAN\-derived static infrared polarizability of optmat\.gas\.infrared \(2\.121 au; HITRAN sums every band, including hot bands and isotopologues, which Eq\. \(1\) omits\)\. sharipov\_2017 quotes it as 0\.26 A^3\. bishop\_1982/n2o ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2o", "material": "N2O", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 2, p. 122", "printed": "N2O: nu_1(sigma+) 1285 [9], 59.1 [30], 0.12; nu_2(pi) 589, 8.20 [31], 0.080; nu_3(sigma+) 2224, 289. [32], 0.20; alpha 0.18^b", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega_1": "1285", "A_1": "59.1", "P_1": "0.12", "omega_2": "589", "A_2": "8.20", "P_2": "0.080", "omega_3": "2224", "A_3": "289.", "P_3": "0.20", "alpha": "0.18" }, "check": "P_n: 0.12088, 0.07983, 0.19734 (printed 0.12, 0.080, 0.20); alpha = 0.441 x 0.3980 = 0.1755 (printed 0.18). Checked 2026-09-25." } Error class b\: 5 %\. Intensities\: Goody and Wormell 1951 \[30\], Yamada and Person 1966 \[31\], Boissy et al\. 1975 \[32\]\. 0\.18e\-40 = 1\.092 au, 8 % below optmat\.gas\.infrared's HITRAN value \(1\.186 au\)\. A static value without the orientation term of N2O's small dipole moment\. bishop\_1982/o3 ~~~~~~~~~~~~~~~ .. code-block:: text { "id": "o3", "material": "O3", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 2, p. 122", "printed": "O3: nu_1(a_1) 1103 [9], 2.38 [33], 0.0066; nu_2(a_1) 701, 4.4 [34], 0.030; nu_3(b_1) 1042, 85.7 [34], 0.27; alpha 0.13", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega_1": "1103", "A_1": "2.38", "P_1": "0.0066", "omega_2": "701", "A_2": "4.4", "P_2": "0.030", "omega_3": "1042", "A_3": "85.7", "P_3": "0.27", "alpha": "0.13" }, "check": "P_n: 0.00661, 0.03024, 0.26658 (printed 0.0066, 0.030, 0.27); alpha = 0.441 x 0.3034 = 0.1338 (printed 0.13). Checked 2026-09-25." } No error class printed for O3\. Intensities\: Clough and Kneizys 1966 \[33\], McCaa and Shaw 1968 \[34\]\. 0\.13e\-40 = 0\.788 au \(0\.117 A^3\); sharipov\_2017's computed pure vibrational value is 0\.208 or 0\.312 A^3 and Naves et al\.'s 0\.209 A^3 \(as sharipov\_2017 quotes them\)\: Bishop and Cheung's is 40\-60 % lower\. For the ozone plan's static polarizability\. bishop\_1982/ch4 ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ch4", "material": "CH4", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 4, p. 125", "printed": "CH4: nu_3(t_2) 3019 [57], 65.5 [58], 0.024; nu_4(t_2) 1311, 31.8, 0.062; alpha 0.038^d", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega_3": "3019", "A_3": "65.5", "P_3": "0.024", "omega_4": "1311", "A_4": "31.8", "P_4": "0.062", "alpha": "0.038" }, "check": "P_n: 0.02427, 0.06249 (printed 0.024, 0.062); alpha = 0.441 x 0.0868 = 0.0383 (printed 0.038). Checked 2026-09-25." } Footnote d of Table 4 is 'The estimated error is 5%' \(Table 4's own lettering, page image of p\. 128 checked; in Tables 1 and 2 d means more than 10 %\)\. Frequencies Gray and Robiette 1979 \[57\], intensities Bode and Smit 1980 \[58\]\. 0\.038e\-40 = 0\.2305 au, 4 % below optmat\.gas\.infrared's HITRAN value \(0\.2401 au\); sharipov\_2017 computes 0\.236 au\. bishop\_1982/sf6 ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sf6", "material": "SF6", "equation": "Eqs. (1)-(4), pp. 119-120, with Table 6, p. 130", "printed": "SF6: nu_3(t_1u) 948 [83], 1361 [83], 5.1; nu_4(t_1u) 615, 74, 0.66; alpha 2.5^b", "variable": "omega_n: harmonic band frequency in cm^-1 (as printed, the observed fundamentals); A_n: absolute integrated band intensity in km/mol; P_n: molar vibrational polarization in cm^3/mol; alpha: static isotropic vibrational polarizability in 10^-40 C^2 m^2 J^-1. Only static values are printed; a dispersion model (not in the paper) would take one harmonic oscillator per band, alpha_vib(omega) = sum_n (3 eps0 / N_A) P_n omega_n^2 / (omega_n^2 - omega^2)", "state": "none (per molecule, vibrational ground state)", "density": "none", "range": "static (the paper treats static fields only, p. 119); the oscillator form extends it below the electronic resonances", "coefficients": { "omega_3": "948", "A_3": "1361", "P_3": "5.1", "omega_4": "615", "A_4": "74", "P_4": "0.66", "alpha": "2.5" }, "check": "P_n: 5.1147, 0.66079 (printed 5.1, 0.66); alpha = 0.441 x 5.7755 = 2.547 (printed 2.5). Checked 2026-09-25." } Footnote b of Table 6 is 'The estimated error is 5%' \(Table 6's lettering\: a estimated value, b 5 %, c 5\-10 %, d overlap average\)\. Kim, McDowell and King 1980 \[83\]\. 2\.5e\-40 = 15\.16 au, 8\.7 % above optmat\.gas\.infrared's HITRAN value \(13\.94 au, from measured cross sections\); sharipov\_2017 computes 12\.77 au and quotes Hohm 2013's 2\.035 A^3 \(13\.73 au\)\. 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 ` for the checks and decisions.