stoicheff_1957

B. P. Stoicheff, “High resolution Raman spectroscopy of gases: IX. Spectra of H2, HD, and D2”, Can. J. Phys. 35, 730 (1957)

Source record · Catalogue · Review register

DOI: 10.1139/p57-079

Source kind: measurement

Recorded technique: Photographic spontaneous Raman spectroscopy of the gases at one to two atmospheres (p. 731): the N.R.C. 21-ft grating spectrograph in the second order, 1.2 A/mm, slit 0.02 mm, Kodak 103a-O plates, exposures of 10-36 hours, the apparatus of paper I (Stoicheff 1954). The pure rotational lines excited by Hg 4358 A (four Stokes and two anti-Stokes lines of H2; five and two of HD and D2), the Q branches of the 1-0 bands by Hg 4047 A (no S or O lines of the 1-0 bands were seen). Second- and third-order iron-arc standards; Edlen’s (1953) vacuum corrections applied, and the displacements taken from the Hg lines’ vacuum wavenumbers 24705.350 and 22938.134 cm-1 (pp. 731-732). Two plates per spectrum, averaged. Constants from the lines by least squares, Eqs. (1)-(6); H2’s v = 2 and 3 levels from Herzberg’s (1950) infrared quadrupole lines with this paper’s ground-state constants (p. 735).

Materials in structured entries: D2, H2

Dataset quantities: raman_shift, rotational_constant, vibrational_term_value

Contents: 23 datasets; 2 formulas.

Curation notes

Identity checked against the first page (title, author, journal, volume). PAGES: pdf page 1 is p. 730; pdf pages 2-3 are the unnumbered plate of Fig. 1; pdf page n (n >= 4) is p. 727 + n (Table I p. 732, Table II p. 734, Table III p. 736).

MATERIAL. H2 and D2 as supplied (the ortho:para ratio is not stated: normal hydrogen and deuterium assumed, as for any room-temperature sample); HD (Herzberg’s sample) is not a material: its values are in these notes only. Every value is the paper’s own except H2’s v = 2 and 3 constants, which it derives from Herzberg’s infrared measurements (G. Herzberg, Can. J. Research A 28, 144 (1950)).

CONVENTIONS (pp. 732-733). T(v, J) = G(v) + F_v(J), Eq. (1); F_v(J) = B_v J(J+1) - D_v J^2(J+1)^2 + H_v J^3(J+1)^3, Eq. (3); B_v = B_e - alpha_e (v+1/2) + gamma_e (v+1/2)^2, D_v = D_e + beta_e (v+1/2) + delta_e (v+1/2)^2, H_v ~ H_e ~ H_0 ~ H_1 (Eq. 4). The pure rotational lines, Eq. (6): S_0(J) = (4 B_0 - 6 D_0 + 27/4 H_e)(J + 3/2) - (8 D_0 - 34 H_e)(J + 3/2)^3 + 12 H_e (J + 3/2)^5; the Q lines, Q_v(J) = nu_{v-0} + (B_v - B_0) J(J+1) - (D_v - D_0) J^2(J+1)^2. The third rotational constant is H_e in Eq. (6) and the text, printed in Table II’s H_v row under v = 0; recorded here as H of v = 0. Wavenumber displacements in vacuum cm-1. The last digit of most Table II constants is printed as a subscript (a digit of lower weight); the files join it to the number.

UNCERTAINTIES. Lines (p. 731): ‘each line could be measured to +-0.02 cm-1 or better’ (pure rotational); ‘an accuracy of about +-0.05 cm-1 is estimated’ for the weak Q-branch lines. Constants (p. 738): ‘For all three molecules, it is estimated that the values of B_0 are reliable to 0.005 cm-1, the values of D_0 to 0.0003 cm-1, and the values of H_e to 0.5 x 10^-5 cm-1. The constants for the 1-0 bands cannot claim as high an accuracy’. B_e of H2 and HD ‘better than +-0.010 cm-1’ (pp. 735-737); D2’s B_e ‘estimated error of +-0.010 cm-1’ (p. 737). Levels not stated.

STRUCTURAL FIXES (the script’s docstring). Table I: the library merged H2’s |Delta nu| column into the designation cell and shifted the others left; the script restores the layout of the image. Table II: two subscript digits misread, H2 D_2 ‘0.0427;’ (image 0.0427 subscript 7: 0.04277) and D2 D_1 ‘0.01073’ (image 0.0107 subscript 5: 0.01075; the text’s D_0 - D_1 = 0.00059 cm-1, p. 737, and the Q-branch O - C_1 column, which 0.01075 reproduces to 0.001 cm-1 and 0.01073 misses by 0.008 at Q_1(4), both require 5). No erratum: both are mis-extractions.

CHECKS (scratch, 2026-09-27). Table II’s constants reproduce Table I’s O - C_1 column: H2 S_0 and Q_1 to +-0.001 cm-1 (the Q lines with the unbracketed v = 1 constants: the bracketed ones leave O - C of 0.014, -0.003, -0.024, 0.013); D2 Q_1 to +-0.001; a least-squares fit of Eq. (6) to the lines returns the printed B_0, D_0, H_e of H2 (59.3392, 0.04600, 5.21e-5), HD (44.6678, 0.02592, 2.25e-5) and D2 (29.9105, 0.01133, 0.356e-5). FINDING: D2’s printed O - C_1 of the pure rotational lines (-0.001, +0.003, -0.006, +0.003, -0.002) are the NEGATIVES of that fit’s residuals (0.000, -0.004, +0.006, -0.003, +0.001): the column is C - O, or its signs are misprinted; the fit itself is not affected. HD’s S_0 O - C_1 need H_e = 2.24e-5 (the rounded 2.2e-5 misses S_0(4) by 0.027).

HD (not a material; Tables I-III): S_0(0)-S_0(4) 267.086, 443.081, 616.089, 784.993, 948.818; Q_1(0)-Q_1(3) 3632.055, 3628.197, 3620.511, 3608.992 cm-1. B_0 44.6678, D_0 0.02592, H_e 2.2e-5, B_1 42.7414, D_1 0.02553, nu_1-0 3632.053, I_0 0.62660e-40 g cm2, r_0 0.74973 A; B_e 45.638, I_e 0.61329, r_e 0.74173; B_e* 45.678, I_e* 0.61274, r_e* 0.74140. Equilibrium constants (p. 737, ‘tentative only’): G(v) = 3811.92_4 (v+1/2) - 90.711_3 (v+1/2)^2 + 0.4775_9 (v+1/2)^3; B_v = 45.637_8 - 1.9500_4 (v+1/2) + 0.0140_2 (v+1/2)^2; D_v = 0.02634_1 - 0.00085_7 (v+1/2) + 0.000033 (v+1/2)^2; H_e = 2.2_4e-5 cm-1. Dunham a_0-a_4: 79598, -1.595, 1.854, -2.047, 2.250. Theory (Dunham): D_e 0.02617, beta_e -0.000780, H_e 2.12e-5.

OTHER TEXT VALUES (notes only). The constants from the line spacings (p. 738): H2 B_0 59.343, D_0 0.04604 (H_e fixed at 5.21e-5); HD 44.668, 0.02591, 2.23e-5; D2 29.912, 0.01137, H_e 4.04e-6 cm-1. S_2(0) of H2’s 2-0 band (Herzberg) lies 0.065 cm-1 below its calculated position and was left out (p. 735). Effective I_0 (1e-40 g cm2) and r_0 (A) of v = 0 (Table II): H2 0.47168, 0.75105; D2 0.93576, 0.74820. Table III’s I_e, r_e (experimental) H2 0.46004, 0.74173 (r_e +-0.00006, p. 736); D2 0.91943, 0.74165; the corrected I_e*, r_e*: H2 0.45951, 0.74130 +- 0.00006; D2 0.91890, 0.74143 +- 0.00012. H2’s Dunham a_0-a_4 (p. 739): 79566, -1.598, 1.868, -2.072, 2.261 (formula dunham_potential_H2). Dunham’s theoretical D_e 0.04652, beta_e -0.00168, H_e 5.02e-5 cm-1 (p. 739); the rotation-vibration corrected omega_e^a 4401.063, B_e^a 60.856, D_e^a 0.04679 cm-1 and B_e* 60.910, omega_e* 4404.18 cm-1 (p. 740). D2 (p. 737): B_0 - B_1 = 1.0623 ~ alpha_e, D_0 - D_1 = 0.00059 ~ beta_e (in magnitude: D_v falls with v), D_e = 0.01164 cm-1 by linear extrapolation.

WHO REPRINTS IT. weber_1979’s Table 3.2 H2 and D2 constants (B_0, D_0, and note a’s H_0) are this paper’s Table II v = 0 values (re-pointed, 2026-09-27); bischel_1986b’s zero-density Q(1) position cites it among four papers.

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

Datasets

stoicheff_1957/table1_S0_H2

{
  "id": "table1_S0_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table1_S0_H2.csv",
  "table": "tbl_8dcc7741bb44",
  "quantity": "raman_shift",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.02,
    "level": "not stated"
  },
  "parameters": {
    "transition": "S0(J), v = 0, J -> J + 2, per row"
  }
}

Table I (p. 732): the pure rotational S0(0)-S0(3) lines of H2 (v = 0, J -> J + 2), observed wavenumber displacements |Delta nu| in vacuum cm-1, the mean of two plates, excited by Hg 4358 A at 1-2 atm (pressure shift not removed). ‘Each line could be measured to +-0.02 cm-1 or better’ (p. 731). O - C_1 (Table II’s constants) and O - C_2 (the equilibrium constants) stay in printed.

stoicheff_1957/table1_Q1_H2

{
  "id": "table1_Q1_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table1_Q1_H2.csv",
  "table": "tbl_8dcc7741bb44",
  "quantity": "raman_shift",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.05,
    "level": "not stated"
  },
  "parameters": {
    "transition": "Q1(J), v = 0 -> 1, per row"
  }
}

Table I (p. 732): the Q1(0)-Q1(3) lines of the H2 1-0 band, vacuum cm-1, excited by Hg 4047 A at 1-2 atm (pressure shift not removed). ‘An accuracy of about +-0.05 cm-1 is estimated for these lines’ (p. 731).

stoicheff_1957/table1_S0_D2

{
  "id": "table1_S0_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table1_S0_D2.csv",
  "table": "tbl_8dcc7741bb44",
  "quantity": "raman_shift",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.02,
    "level": "not stated"
  },
  "parameters": {
    "transition": "S0(J), v = 0, J -> J + 2, per row"
  }
}

Table I (p. 732): the pure rotational S0(0)-S0(4) lines of D2, vacuum cm-1, Hg 4358 A, 1-2 atm. +-0.02 cm-1 or better (p. 731). The printed O - C_1 column has the opposite sign to the least-squares residuals of Eq. (6) (source notes).

stoicheff_1957/table1_Q1_D2

{
  "id": "table1_Q1_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table1_Q1_D2.csv",
  "table": "tbl_8dcc7741bb44",
  "quantity": "raman_shift",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.05,
    "level": "not stated"
  },
  "parameters": {
    "transition": "Q1(J), v = 0 -> 1, per row"
  }
}

Table I (p. 732): the Q1(0)-Q1(4) lines of the D2 1-0 band, vacuum cm-1, Hg 4047 A, 1-2 atm. About +-0.05 cm-1 (p. 731).

stoicheff_1957/table2_B0_H2

{
  "id": "table2_B0_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_B0_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.005,
    "level": "not stated"
  },
  "parameters": {
    "constant": "B"
  }
}

Table II (p. 734): B_0 of H2 (row v = 0), fitted with D_0 and H_e to the four pure rotational lines (Eq. 6). ‘Reliable to 0.005 cm-1’ (p. 738).

stoicheff_1957/table2_Bv_H2

{
  "id": "table2_Bv_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_Bv_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "constant": "B"
  }
}

Table II (p. 734): B_v of H2, v = 1-3 (the row). v = 1 from the four Q lines with the v = 0 constants (the value printed first; the refit in parentheses is table2_B1_refit_H2); v = 2 and 3 from Herzberg’s infrared 2-0 and 3-0 quadrupole lines with this paper’s v = 0 constants (p. 735). No accuracy stated (‘cannot claim as high an accuracy’ as B_0, p. 738).

stoicheff_1957/table2_B1_refit_H2

{
  "id": "table2_B1_refit_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_B1_refit_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "constant": "B"
  }
}

Table II (p. 734), H2 v = 1 in parentheses: B_1 refitted to the Q lines with D_1 fixed at the value calculated from D_e, beta_e, delta_e (D_1 of the fit deviated 2 % from the smooth curve through D_0, D_2, D_3; p. 735). ‘They differ from the constants determined initially from the 1-0 band alone by approximately the estimated errors’ (p. 735). A second determination of the same B_1: check, beside table2_Bv_H2.

stoicheff_1957/table2_D0_H2

{
  "id": "table2_D0_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_D0_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.0003,
    "level": "not stated"
  },
  "parameters": {
    "constant": "D"
  }
}

Table II (p. 734): D_0 of H2 (row v = 0), sign convention -D_v J^2(J+1)^2 (Eq. 3). ‘Reliable to 0.0003 cm-1’ (p. 738).

stoicheff_1957/table2_Dv_H2

{
  "id": "table2_Dv_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_Dv_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "constant": "D"
  }
}

Table II (p. 734): D_v of H2, v = 1-3 (the row); v = 2 and 3 from Herzberg’s infrared lines. Row 2 is 0.04277 (the image; the library cell reads ‘0.0427;’: a structural fix in the script). The paper judged its own v = 1 value (0.04323) 2 % off the smooth curve through D_0, D_2, D_3 and left it out of the equilibrium fit (p. 735); the value calculated from that fit is table2_D1_refit_H2.

stoicheff_1957/table2_D1_refit_H2

{
  "id": "table2_D1_refit_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_D1_refit_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "constant": "D"
  }
}

Table II (p. 734), H2 v = 1 in parentheses: D_1 CALCULATED from D_e, beta_e and delta_e (fitted to D_0, D_2, D_3; p. 735), not measured; the equilibrium formula gives 0.04435.

stoicheff_1957/table2_H0_H2

{
  "id": "table2_H0_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_H0_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "scale": 1e-05,
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.5,
    "level": "not stated"
  },
  "parameters": {
    "constant": "H"
  }
}

Table II (p. 734): the H_v row, printed under v = 0 (5.2 x 10^-5); in Eq. (6) and the text it is H_e, taken as common to the low levels (H_v ~ H_e ~ H_0 ~ H_1, Eq. 4), and fitted with B_0 and D_0 to the pure rotational lines. ‘H_e to 0.5 x 10^-5 cm-1’ (p. 738). The equilibrium fit gives 5.2_1 x 10^-5 (p. 735).

stoicheff_1957/table2_nu_H2

{
  "id": "table2_nu_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_nu_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "vibrational_term_value",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "reference": "v0",
    "electronic_state": "X 1Sigma_g+"
  }
}

Table II (p. 734): nu_{v-0}, the band origin of the v - 0 band = G(v) - G(0), v = 1-3 (the row); v = 1 from the Raman Q lines (the value printed first; the refit in parentheses is table2_nu1_refit_H2), v = 2 and 3 from Herzberg’s infrared quadrupole lines (p. 735). No accuracy stated.

stoicheff_1957/table2_nu1_refit_H2

{
  "id": "table2_nu1_refit_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table2_nu1_refit_H2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "vibrational_term_value",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "reference": "v0",
    "electronic_state": "X 1Sigma_g+"
  }
}

Table II (p. 734), H2 nu_{1-0} in parentheses: refitted with the calculated D_1 (see table2_B1_refit_H2). The equilibrium formula gives 4161.114.

stoicheff_1957/table2_B0_D2

{
  "id": "table2_B0_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_B0_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.005,
    "level": "not stated"
  },
  "parameters": {
    "constant": "B"
  }
}

Table II (p. 734): B_0 of D2 (row v = 0), fitted with D_0 and H_e to the five pure rotational lines. ‘Reliable to 0.005 cm-1’ (p. 738).

stoicheff_1957/table2_Bv_D2

{
  "id": "table2_Bv_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_Bv_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "constant": "B"
  }
}

Table II (p. 734): B_1 of D2 (row v = 1), from the five Q lines with the v = 0 constants. No accuracy stated.

stoicheff_1957/table2_D0_D2

{
  "id": "table2_D0_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_D0_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.0003,
    "level": "not stated"
  },
  "parameters": {
    "constant": "D"
  }
}

Table II (p. 734): D_0 of D2 (row v = 0). ‘Reliable to 0.0003 cm-1’ (p. 738).

stoicheff_1957/table2_Dv_D2

{
  "id": "table2_Dv_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_Dv_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "constant": "D"
  }
}

Table II (p. 734): D_1 of D2 (row v = 1), 0.01075: the image prints 0.0107 with a subscript 5, which the library read as 3 (structural fix in the script); the text’s D_0 - D_1 = 0.00059 (p. 737) and Table I’s O - C_1 confirm it. No accuracy stated.

stoicheff_1957/table2_H0_D2

{
  "id": "table2_H0_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_H0_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "scale": 1e-05,
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.5,
    "level": "not stated"
  },
  "parameters": {
    "constant": "H"
  }
}

Table II (p. 734): D2’s H_v row under v = 0, 0.36 x 10^-5 (H_e of Eq. 6, as for H2). ‘H_e to 0.5 x 10^-5 cm-1’ (p. 738), larger than the value; the line spacings give 4.04 x 10^-6 (p. 738).

stoicheff_1957/table2_nu_D2

{
  "id": "table2_nu_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table2_nu_D2.csv",
  "table": "tbl_6bd75ebe07be",
  "quantity": "vibrational_term_value",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "parameters": {
    "reference": "v0",
    "electronic_state": "X 1Sigma_g+"
  }
}

Table II (p. 734): nu_{1-0} of D2 = G(1) - G(0) (row v = 1), the band origin fitted to the Q lines. No accuracy stated.

stoicheff_1957/table3_Be_H2

{
  "id": "table3_Be_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table3_Be_H2.csv",
  "table": "tbl_f87804e5f4e4",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.01,
    "level": "bound"
  },
  "parameters": {
    "constant": "B_e"
  }
}

Table III (p. 736), ‘Experimental value’: B_e of H2 from the equilibrium fit (formula equilibrium_H2, 60.840_7), ‘an accuracy better than +-0.010 cm-1’ (pp. 735-736). An effective value: the ‘true’ B_e* (corrected for Dunham’s and Van Vleck’s effects) is table3_Be_corrected_H2.

stoicheff_1957/table3_Be_corrected_H2

{
  "id": "table3_Be_corrected_H2",
  "material": "H2",
  "file": "H2/stoicheff_1957__table3_Be_corrected_H2.csv",
  "table": "tbl_f87804e5f4e4",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "constant": "B_e* (corrected: the mechanical equilibrium value)"
  }
}

Table III (p. 736), ‘Corrected value’: B_e* = B_e / (1 + gamma_a + gamma_b + gamma_c + gamma_d), the experimental B_e with Dunham’s rotation-vibration correction and Van Vleck’s theoretical corrections for electronic-nuclear interaction, L-uncoupling and state interaction (pp. 739-740). Theory-corrected, not a level constant: check.

stoicheff_1957/table3_Be_D2

{
  "id": "table3_Be_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table3_Be_D2.csv",
  "table": "tbl_f87804e5f4e4",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "primary",
  "uncertainty": {
    "absolute": 0.01,
    "level": "not stated"
  },
  "parameters": {
    "constant": "B_e"
  }
}

Table III (p. 736), ‘Experimental value’: B_e of D2 by linear extrapolation from v = 0 and 1, B_e = B_0 + (B_0 - B_1)/2 with B_0 - B_1 = 1.0623 ~ alpha_e (p. 737; reproduced: 30.44165), ‘with an estimated error of +-0.010 cm-1’. No overtone data exist for D2 (p. 737).

stoicheff_1957/table3_Be_corrected_D2

{
  "id": "table3_Be_corrected_D2",
  "material": "D2",
  "file": "D2/stoicheff_1957__table3_Be_corrected_D2.csv",
  "table": "tbl_f87804e5f4e4",
  "quantity": "rotational_constant",
  "unit": "cm-1",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "constant": "B_e* (corrected: the mechanical equilibrium value)"
  }
}

Table III (p. 736), ‘Corrected value’, dagger: ‘B_e* for D2 is an approximate value; gamma_a = -0.00014 was obtained from provisional equilibrium constants calculated from the values of H2 and HD using the simple isotopic rules, and gamma_b + gamma_c + gamma_d = -0.00044 according to Van Vleck (1936)’. Check.

Formulas

stoicheff_1957/equilibrium_H2

{
  "id": "equilibrium_H2",
  "material": "H2",
  "equation": "p. 735, from Eqs. (2) and (4)",
  "printed": "G(v) = 4400.39_0 (v + 1/2) - 120.814_8 (v + 1/2)^2 + 0.7241_9 (v + 1/2)^3 cm-1; B_v = 60.840_7 - 3.0177_4 (v + 1/2) + 0.0285_5 (v + 1/2)^2 cm-1; D_v = 0.04684_1 - 0.00170_6 (v + 1/2) + 0.000030_8 (v + 1/2)^2 cm-1; H_v = 5.2_1 x 10^-5 cm-1",
  "variable": "v the vibrational quantum number of X 1Sigma_g+; the levels T(v, J) = G(v) + B_v J(J+1) - D_v J^2(J+1)^2 + H_v J^3(J+1)^3 (Eqs. 1, 3), in vacuum cm-1; a subscript digit (after _) is the last printed digit",
  "state": "H2, X 1Sigma_g+",
  "density": "unknown",
  "range": "v = 0-3 (the Raman v = 0 and 1 levels and Herzberg's infrared v = 2 and 3)",
  "coefficients": {
    "omega_e": "4400.390",
    "omega_e_x_e": "120.8148",
    "omega_e_y_e": "0.72419",
    "B_e": "60.8407",
    "alpha_e": "3.01774",
    "gamma_e": "0.02855",
    "D_e": "0.046841",
    "beta_e": "-0.001706",
    "delta_e": "0.0000308",
    "H_e": "5.21e-5"
  },
  "check": "Reproduces Table I's O - C_2 column (scratch, 2026-09-27) to within 0.01 cm-1 (S_0(0)-S_0(3): -0.008, +0.015, -0.003, +0.006 against printed +0.002, +0.015, -0.003, +0.005; Q_1(0)-Q_1(3): +0.020, +0.002, -0.022, +0.009 against +0.020, +0.002, -0.013, +0.008), and Table II: B_v 59.3390, 56.3783, 53.4748, 50.6283 (printed 59.3392, 56.3778 in parentheses, 53.4754, 50.6282), D_v 0.04600, 0.04435, 0.04277, 0.04125 (0.04599, 0.04435 in parentheses, 0.04277, 0.04125), nu_{v-0} 4161.114, 8087.116, 11782.352 (4161.120 in parentheses, 8087.112, 11782.352). The paper: deviations 'less than +-0.020 cm-1'."
}

The equilibrium constants ‘obtained from the present Raman data of the rotational spectrum and the 1-0 band, and from Herzberg’s infrared data of the 2-0 and 3-0 bands’ (p. 735); D_e, beta_e, delta_e from D_0, D_2, D_3 only. beta_e is printed as ‘- 0.00170_6 (v + 1/2)’: negative in D_v = D_e + beta_e (v + 1/2) (Eq. 4). B_e is effective (not corrected for the Dunham and Van Vleck effects; Table III). HD’s (tentative) set is in the source notes.

stoicheff_1957/dunham_potential_H2

{
  "id": "dunham_potential_H2",
  "material": "H2",
  "equation": "p. 739 (Dunham 1932)",
  "printed": "U = h c a_0 xi^2 (1 + a_1 xi + a_2 xi^2 + ...), xi = (r - r_e)/r_e; for H2, a_0 = 79566, a_1 = -1.598, a_2 = 1.868, a_3 = -2.072, a_4 = 2.261",
  "variable": "xi = (r - r_e)/r_e, r_e = 0.74173 A (the experimental value, Table III); a_0 in cm-1, a_1-a_4 dimensionless",
  "state": "H2, X 1Sigma_g+",
  "density": "unknown",
  "range": "the low vibrational levels (v = 0-3) the constants come from",
  "coefficients": {
    "a0": "79566",
    "a1": "-1.598",
    "a2": "1.868",
    "a3": "-2.072",
    "a4": "2.261"
  },
  "check": "a_0 = omega_e^2/(4 B_e) = 79566.1, a_1 = -alpha_e omega_e/(6 B_e^2) - 1 = -1.5979 and a_2 = 5 a_1^2/4 - 2 omega_e x_e/(3 B_e) = 1.8678 from formula equilibrium_H2's constants (scratch, 2026-09-27): all three to the printed digits. a_3 and a_4 (from omega_e y_e and gamma_e) not reproduced."
}

Derived from omega_e, omega_e x_e, omega_e y_e, B_e, alpha_e, gamma_e (p. 738). HD’s (79598, -1.595, 1.854, -2.047, 2.250) in the source notes. The paper contrasts a Morse function fitted at the bottom (a_2 = 1.489, a_3 = -1.020, a_4 = 0.561).

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.