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 · Catalogue · 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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.