Constants of diatomic molecules

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Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A. All rights reserved.

Data compiled by: Klaus P. Huber and Gerhard H. Herzberg

Data collected through June, 1977

Symbols used in the table of constants
State electronic state and / or symmetry symbol
Te minimum electronic energy (cm-1)
ωe vibrational constant – first term (cm-1)
ωexe vibrational constant – second term (cm-1)
ωeye vibrational constant – third term (cm-1)
Be rotational constant in equilibrium position (cm-1)
αe rotational constant – first term (cm-1)
γe rotation-vibration interaction constant (cm-1)
De centrifugal distortion constant (cm-1)
βe rotational constant – first term, centrifugal force (cm-1)
re internuclear distance (Å)
Trans. observed transition(s) corresponding to electronic state
ν00 position of 0-0 band (units noted in table)
Diatomic constants for 23Na2
Diffuse bands of Na2 Van der Waals molecules close to the lines of principal series of Na.
Kuhn, 1932; Wurm, 1932
Several fragments of other UV emission and absorption band systems. 1
Kimura and Uchida, 1932; Yoshinaga, 1937; Sinha, 1947
E (1Πu) 35557.0 106.2 H 0.65        E ← X R 35530.6 H
Chang, 1950; Morales, 1963
D 1Πu 33486.8 111.3 2 H 0.48  3      D ↔ X R 33462.9 H
Sinha, 1947; Chang, 1950; Barrow, Travis, et al., 1960; Morales, 1963
1Σg+ (33000) 4           
Woerdman, 1976
C 1Πu 29382 119.33 5 H 0.53  3      C ↔ X R 29362 H
Pearse and Sinha, 1947; Sinha, 1949; Barrow, Travis, et al., 1960
B 1Πu 20320.02 124.090 Z 0.6999 6  0.125277 7 0.0007237 7  3.248E-7 8 4.75E-8 3.4228 B ↔ X 9 10 R 20302.49 11 Z
Loomis and Wood, 1928; Loomis and Nusbaum, 1932; Demtroder, McClintock, et al., 1969; Demtroder and Stock, 1975
A 1Σu+ 14680.58 117.323 Z 0.3576 12  0.110784 13 14 0.0005488 15  3.882E-7 16  3.6384 A ↔ X 17 R 14659.80 Z
Fredrickson, 1929; Fredrickson and Stannard, 1933; Kusch and Hessel, 1975; Kaminsky, Hawkins, et al., 1976; Kaminsky, 1977
a 3Π <14680 (145) 18   (0.140) 18       
X 1Σg+ 0 159.1245 Z 0.72547 19  0.154707 20 0.0008736 21  5.811E-7 22 3.59E-9 3.07887 23  


1Molecular absorption cross sections 27000-62500 cm-1 Hudson, 1965.
2Vibrational constants from Chang, 1950.
3 Barrow, Travis, et al., 1960 report the following rotational constants for D: Be = 0.1185, αe = 0.001; C: Be = 0.128l5, αe = 0.00084. Considerably different constants, however, are quoted by Richards in Rosen, 1970. D: Be = 0.1152, αe = 0.00110; C: Be = 0.1185, αe = 0.00096.
4Fragment observed in two-photon excited Na2 fluorescence.
5Vibrational constants from Sinha, 1949 (except Te which has been recalculated). Barrow, Travis, et al., 1960, without details, give Te = 29393, ωe = 117.3, ωexe = 0.55, while Richards Rosen, 1970 quotes 29384.8, 119.53, and 0.782, respectively.
6-0.000495(v+1/2)3 - 0.000153(v+1/2)4 + 7.01E-6(v+1/2)5 - 1.804E-7(v+1/2)6; from the laser-induced fluorescence spectrum, including levels with v'≤ 29 Demtroder and Stock, 1975. This state has a potential hump of ~ 550 cm-1 (0.069 eV); see Demtroder and Stock, 1975, also Callender, Gersten, et al., 1974. The non-appearance of levels with v'>26 in the magnetic rotation spectrum may be due to weak predissociation; see King and Van Vleck, 1939.
7-3.159E-5(v+1/2)2 + 1.040E-6(v+1/2)3 - 2.920E-8(v+1/2)4. The constants are for P and R lines, B(R,P) - B(Q) = +0.0000128 Demtroder and Stock, 1975.
8He = -2.145E-11and higher order constants Demtroder and Stock, 1975.
9Radiative lifetimes of 24 different levels (v',J') have been measured with an accuracy of ~ 1% by means of a delayed coincidence single-photon counting technique Demtroder, Stetzenbach, et al., 1976; the observed lifetimes [see also McClintock, Demtroder, et al., 1969, Baumgartner, Demtroder, et al., 1970] vary from 7.0 to 7.5 ns and have been used to determine the electronic transition moment and its variation with r. The results are in good agreement with Hessel, Smith, et al., 1974 and with the ab initio calculations of Stevens, Hessel, et al., 1977. See, however, Callender, Gersten, et al., 1974, Williams and Rousseau, 1974.
10Franck-Condon factors, dependence on rotation Demtroder, Stetzenbach, et al., 1976.
11The band origin given here does not include -BΛ2.
12+5.167E-6(v+1/2)3 + 9.277E-6(v+1/2)4 - 1.456E-7(v+1/2)5; from Kaminsky, 1977, see also Kusch and Hessel, 1975. The observations extend to v' = 44 Kaminsky, Hawkins, et al., 1976, Kaminsky, 1977.
13Rotational perturbations in v=0 and 1 are caused by levels belonging to the three components of the lower lying a 3Π state Kusch and Hessel, 1975. Similar perturbations affect the higher vibrational levels and are responsible for theappearance of an A-X magnetic rotation spectrum Fredrickson and Stannard, 1933, Carroll, 1937.
14RKR potential function Kaminsky, 1977.
15+1.625E-8(v+1/2)2 + 3.165E-8(v+1/2)3 - 9.205E-10(v+1/2)4; from Kaminsky, 1977, see also Kusch and Hessel, 1975.
16He = +1.129E-12 Kaminsky, 1977, see also Kusch and Hessel, 1975.
17Radiative lifetimes Ducas, Littman, et al., 1976 are nearly constant for 1≤v≤25, τ = 12.5 ± 0.5 ns Ducas, Littman, et al., 1976, in very good agreement with theory Stevens, Hessel, et al., 1977.
18Constants estimated from the perturbations in A 1Σu+ Carroll, 1937, see 13. Bardsley, Junker, et al., 1976 predict Te = 13500 Bardsley, Junker, et al., 1976, ωe = 160, Be = 0.154.
19-0.00l095(v+1/2)3 - 4.72E-5(v+1/2)4 + 3.21E-7(v+1/2)5 - 7.53E-9(v+1/2)6; the analysis of the B→X system includes levels with v"≤46 Demtroder and Stock, 1975.
20RKR potential functions Demtroder and Stock, 1975.
21-3.146E-6(v+1/2)2 - 2.400E-7(v+1/2)3 + 4.84E-9(v+1/2)4 - 8.73E-11(v + 1/2)5, from Demtroder and Stock, 1975.
22He = +1.92E-12, also higher order constants Demtroder and Stock, 1975.
23Mol. beam magn. Reson. 26
24From De0 = 5890 ± 70 cm-1 based on the RKR potential curve for the ground state Demtroder, McClintock, et al., 1969, Demtroder and Stock, 1975. The thermochemical value of Lewis, 1931, obtained by a molecular beam technique, is 0.732 eV.
25From photoionization Hudson, 1965, Foster, Leckenby, et al., 1969. A similar value is obtained by extrapolation of the Rydberg series B, C, D, E Barrow, Travis, et al., 1960, Morales, 1963, Velasco, 1973.
26gJ = (+)0.03892 μN Brooks, Anderson, et al., 1963. From the nuclear resonance spectrum Logan, Cote, et al., 1952 determined eqQ, but much improved hyperfine coupling constants eqQ and c [spin rotational constant, see also Konig and Weber, 1976] in the v=0, J=28 level have recently been obtained by Rosner, Holt, et al., 1975 using a laser-fluorescence molecular-beam-resonance technique.


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Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A. All rights reserved.

Kuhn, 1932
Kuhn, H., Uber spektren von unecht gebundenen molekulen (polarisationsmolekulen) K2, Na2, Cs2 und verbreiterung von absorptionslinien, Z. Phys., 1932, 76, 782. [all data]

Wurm, 1932
Wurm, K., Uber eine die D-Linien des natriums begleitende diffuse bande, Z. Phys., 1932, 79, 736. [all data]

Kimura and Uchida, 1932
Kimura, M.; Uchida, Y., Ultra-violet absorption bands of sodium vapour, Sci. Pap. Inst. Phys. Chem. Res. Jpn., 1932, 18, 109. [all data]

Yoshinaga, 1937
Yoshinaga, H., New ultraviolet absorption bands of sodium and potassium molecules, Proc. Phys. Math. Soc. Jpn., 1937, 19, 847. [all data]

Sinha, 1947
Sinha, S.P., Ultra-violet bands of Na2, Proc. Phys. Soc. London, 1947, 59, 610. [all data]

Chang, 1950
Chang, C.S., Sodium bands in the ultra-violet λλ3100-2750, Chin. J. Phys., 1950, 7, 377. [all data]

Morales, 1963
Morales, V., Espectro ultravioleta de la molecula Na2, An. R. Soc. Esp. Fis. Quim. Ser. A, 1963, 59, 3. [all data]

Barrow, Travis, et al., 1960
Barrow, R.F.; Travis, N.; Wright, C.V., Excited electronic states of lithium and sodium molecules, Nature, 1960, 187, 141. [all data]

Woerdman, 1976
Woerdman, J.P., Doppler-free two-photon transitions of the sodium molecule, Chem. Phys. Lett., 1976, 43, 279. [all data]

Pearse and Sinha, 1947
Pearse, R.W.B.; Sinha, S.P., Absorption bands of Li2, Na2, K2 and NaK, Nature (London), 1947, 160, 159. [all data]

Sinha, 1949
Sinha, S.P., Ultra-violet bands of Na2, Proc. Phys. Soc. London Sect. A, 1949, 62, 124. [all data]

Loomis and Wood, 1928
Loomis, F.W.; Wood, R.W., The rotational structure of the blue-green bands of Na2, Phys. Rev., 1928, 32, 223. [all data]

Loomis and Nusbaum, 1932
Loomis, F.W.; Nusbaum, R.E., Magnetic rotation spectrum and heat of dissociation of the sodium molecule, Phys. Rev., 1932, 40, 380. [all data]

Demtroder, McClintock, et al., 1969
Demtroder, W.; McClintock, M.; Zare, R.N., Spectroscopy of Na2 using laser-induced fluorescence, J. Chem. Phys., 1969, 51, 5495. [all data]

Demtroder and Stock, 1975
Demtroder, W.; Stock, M., Molecular constants and potential curves of Na2 from laser-induced fluorescence, J. Mol. Spectrosc., 1975, 55, 476. [all data]

Fredrickson, 1929
Fredrickson, W.R., Rotational structure of the red bands of sodium, Phys. Rev., 1929, 34, 207. [all data]

Fredrickson and Stannard, 1933
Fredrickson, W.R.; Stannard, C.R., Magnetic rotation spectrum of the red bands of sodium, Phys. Rev., 1933, 44, 632. [all data]

Kusch and Hessel, 1975
Kusch, P.; Hessel, M.M., Perturbations in the A1Σu+ state of Na2, J. Chem. Phys., 1975, 63, 4087. [all data]

Kaminsky, Hawkins, et al., 1976
Kaminsky, M.E.; Hawkins, R.T.; Kowalski, F.V.; Schawlow, A.L., Identification of absorption lines by modulated lower-level population: spectrum of Na2, Phys. Rev. Lett., 1976, 36, 671. [all data]

Kaminsky, 1977
Kaminsky, M.E., New spectroscopic constants and RKR potential for the A1Σu+ state of Na2, J. Chem. Phys., 1977, 66, 4951-4953. [all data]

Hudson, 1965
Hudson, R.D., Measurements of the molecular absorption cross section and the photoionization of sodium vapor between 1600 and 3700, J. Chem. Phys., 1965, 43, 1790. [all data]

Rosen, 1970
Rosen, B., International tables of selected constants. 17. Spectroscopic data relative to diatomic molecules, Pub. Pergamon Press, Oxford, 1970, 0. [all data]

Callender, Gersten, et al., 1974
Callender, R.H.; Gersten, J.I.; Leigh, R.W.; Yang, J.L., Dependence of transition moment on internuclear separation in Na2, Phys. Rev. Lett., 1974, 32, 917. [all data]

King and Van Vleck, 1939
King, G.W.; Van Vleck, J.H., Dipole-dipole resonance forces, Phys. Rev., 1939, 55, 1165. [all data]

Demtroder, Stetzenbach, et al., 1976
Demtroder, W.; Stetzenbach, W.; Stock, M.; Witt, J., Lifetimes and Franck-Condon factors for the B1Πu → X1Σg+ system of Na2, J. Mol. Spectrosc., 1976, 61, 382. [all data]

McClintock, Demtroder, et al., 1969
McClintock, M.; Demtroder, W.; Zare, R.N., Level-crossing studies of Na2 using laser-induced fluorescence, J. Chem. Phys., 1969, 51, 5509. [all data]

Baumgartner, Demtroder, et al., 1970
Baumgartner, G.; Demtroder, W.; Stock, M., Lifetime-measurements of alkali-molecules excited by different laserlines, Z. Phys., 1970, 232, 462. [all data]

Hessel, Smith, et al., 1974
Hessel, M.M.; Smith, E.W.; Drullinger, R.E., Transition dipole moment of Na2 and its variation with internuclear distance, Phys. Rev. Lett., 1974, 33, 1251. [all data]

Stevens, Hessel, et al., 1977
Stevens, W.J.; Hessel, M.M.; Bertoncini, P.J.; Wahl, A.C., Theoretical transition dipole moments and lifetimes for the A1Σu+Σu → X1Σg+ system of Na2, J. Chem. Phys., 1977, 66, 1477. [all data]

Williams and Rousseau, 1974
Williams, P.F.; Rousseau, D.L., Dependence of the electronic transition moment on internuclear separation in Na2: a quantum mechanical treatment, Phys. Rev. Lett., 1974, 33, 1516. [all data]

Carroll, 1937
Carroll, T., Magnetic rotation spectra of diatomic molecules, Phys. Rev., 1937, 52, 822. [all data]

Ducas, Littman, et al., 1976
Ducas, T.W.; Littman, M.G.; Zimmerman, M.L.; Kleppner, D., Radiative lifetimes of selected vibrational levels in the A1Σu state of Na2, J. Chem. Phys., 1976, 65, 842. [all data]

Bardsley, Junker, et al., 1976
Bardsley, J.N.; Junker, B.R.; Norcross, D.W., Pseudopotential calculations for Na2+, Na and Na2-, Chem. Phys. Lett., 1976, 37, 502. [all data]

Lewis, 1931
Lewis, L.C., Die bestimmung des gleichgewichts zwischen den atomen und den molekulen eines alkalidampfes mit einer molekularstrahlmethode, Z. Phys., 1931, 69, 786. [all data]

Foster, Leckenby, et al., 1969
Foster, P.J.; Leckenby, R.E.; Robbins, E.J., The ionization potentials of clustered alkali metal atoms, J. Phys. B:, 1969, 2, 478. [all data]

Velasco, 1973
Velasco, R., Productos de disociacion de las series 1Π de Li2 Y Na2, Opt. Pura Apl., 1973, 6, 16. [all data]

Brooks, Anderson, et al., 1963
Brooks, R.A.; Anderson, C.H.; Ramsey, N.F., Rotational magnetic moments of diatomic alkalis, Phys. Rev. Lett., 1963, 10, 441. [all data]

Logan, Cote, et al., 1952
Logan, R.A.; Cote, R.E.; Kusch, P., The sign of the quadrupole interaction energy in diatomic molecules, Phys. Rev., 1952, 86, 280. [all data]

Konig and Weber, 1976
Konig, F.; Weber, H.G., NMR in Na2 and NaK by optical pumping, Chem. Phys. Lett., 1976, 44, 293. [all data]

Rosner, Holt, et al., 1975
Rosner, S.D.; Holt, R.A.; Gaily, T.D., Measurement of the zero-field hyperfine structure of a single vibration-rotation level of Na2 by a laser-fluorescence molecular-beam-resonance technique, Phys. Rev. Lett., 1975, 35, 785. [all data]


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