bishop_1980#

D. M. Bishop and L. M. Cheung, J. Chem. Phys. 72, 5125 (1980)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Sum-over-states (Kramers-Heisenberg) calculation of the dynamic dipole polarizability of H2 (and HeH+) with rovibronic wave functions: explicitly correlated electronic basis (34 terms for the intermediate states of H2) times vibrational basis functions (M = 5), nuclear motion included in the states rather than by averaging alpha(omega; R) (Eq. 14); isotropic alpha = (alpha_par + 2 alpha_perp)/3 (Eq. 21), thermally averaged over J at 293 K with ortho:para 3:1 (Eq. 23).

Materials in structured entries: H2

Dataset quantities: polarizability

Contents: 8 datasets; 0 formulas.

Curation notes#

Units: polarizability in a0^3; wavelengths in A, converted from omega by lambda(A) = 455.64/omega(au) (p. 5127), hence vacuum wavelengths; the static limit is printed as infinity with footnote c. HeH+ is not a curated species; the anisotropies (Table VI, no vocabulary quantity) and the static parallel/perpendicular components of Table IX are not extracted (Table IX’s alpha_000(0) = 6.7693 and 4.7442 give the isotropic 5.4192, Table V’s J = 0 static 5.4193).

Accuracy: none stated for the calculation; against Victor & Dalgarno’s values ‘in nearly all cases an error of only ~0.1 %. In fact, the experimental error is probably of this order’ (p. 5131). The ‘Experimental’ column is Victor & Dalgarno (1969) (ref. 11): ‘values of alpha(omega) abstracted from refractive index data’ and, in parentheses, ‘semiempirical values ... derived from a model dipole spectrum which produced known experimental data’ (p. 5131). These are reproductions (and the experimental ones are themselves derived from refractivity measurements, e.g. Koch’s and Kirn’s older H2 data, which Peck & Huang 1977 found 0.25 % high); the semi-empirical ones are model values, not data.

Check: the thermal averages follow from the J = 0-4 columns with Eq. (23), the spin weights 1 (even J) and 3 (odd J) and the paper’s own rotational spacings (Table I: 118.4, 354.1, 705.0, 1168.0 cm^-1) at 293 K: 5.43388, 12.79797 and 6.36554 against 5.4339, 12.7980 and 6.3655 printed (static, 1215.7 and 2302.9 A; checked 2026-09-24). Eq. (23) is printed with ‘(2^J + 1)’ for the degeneracy; the check uses 2J + 1, which reproduces the table (a misprint in the equation). The ‘23 wavelengths’ expected are 22 in Table V (image checked).

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

Datasets#

bishop_1980/alpha_293K#

{
  "id": "alpha_293K",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_293K.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "primary",
  "parameters": {
    "temperature_k": 293,
    "average": "thermal (rotational Boltzmann with nuclear-spin weights, ortho:para 3:1)"
  }
}

Table V thermal rotational average at 293 K (normal H2, ortho:para 3:1).

bishop_1980/alpha_J0#

{
  "id": "alpha_J0",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_J0.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rotational_state_J": 0,
    "vibrational_state_v": 0
  }
}

Table V: isotropic alpha in the rotational state J = 0, v = 0 (the ingredient of alpha_293K).

bishop_1980/alpha_J1#

{
  "id": "alpha_J1",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_J1.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rotational_state_J": 1,
    "vibrational_state_v": 0
  }
}

Table V: isotropic alpha in the rotational state J = 1, v = 0 (the ingredient of alpha_293K).

bishop_1980/alpha_J2#

{
  "id": "alpha_J2",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_J2.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rotational_state_J": 2,
    "vibrational_state_v": 0
  }
}

Table V: isotropic alpha in the rotational state J = 2, v = 0 (the ingredient of alpha_293K).

bishop_1980/alpha_J3#

{
  "id": "alpha_J3",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_J3.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rotational_state_J": 3,
    "vibrational_state_v": 0
  }
}

Table V: isotropic alpha in the rotational state J = 3, v = 0 (the ingredient of alpha_293K).

bishop_1980/alpha_J4#

{
  "id": "alpha_J4",
  "material": "H2",
  "file": "H2/bishop_1980__alpha_J4.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "parameters": {
    "rotational_state_J": 4,
    "vibrational_state_v": 0
  }
}

Table V: isotropic alpha in the rotational state J = 4, v = 0 (the ingredient of alpha_293K).

bishop_1980/victor_dalgarno#

{
  "id": "victor_dalgarno",
  "material": "H2",
  "file": "H2/bishop_1980__victor_dalgarno.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "reproduced",
  "reproduced_from": [
    "G. A. Victor and A. Dalgarno, J. Chem. Phys. 50, 2535 (1969)"
  ]
}

Table V ‘Experimental’ values without parentheses: Victor & Dalgarno’s polarizabilities ‘abstracted from refractive index data’ (thermal, room temperature), to three or four figures (12.8 at 1215.7 A). Derived from older refractometry; prefer the original refractivity data where available.

bishop_1980/victor_dalgarno_semiempirical#

{
  "id": "victor_dalgarno_semiempirical",
  "material": "H2",
  "file": "H2/bishop_1980__victor_dalgarno_semiempirical.csv",
  "table": "tbl_7b56aafde20c",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "use": "check",
  "reproduced_from": [
    "G. A. Victor and A. Dalgarno, J. Chem. Phys. 50, 2535 (1969)"
  ]
}

Table V ‘Experimental’ values in parentheses (1300-1700 A): Victor & Dalgarno’s semi-empirical values from a model dipole spectrum, not measurements.

Formulas#

No formulas are recorded.

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.