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 `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.