Hydrogen

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Mass spectrum (electron ionization)

Go To: Top, Constants of diatomic molecules, References, Notes

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Data compiled by: NIST Mass Spectrometry Data Center, William E. Wallace, director

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Origin American Petroleum Institute Research Project 44
NIST MS number 245692

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Constants of diatomic molecules

Go To: Top, Mass spectrum (electron ionization), References, Notes

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 November, 1976

Symbols used in the table of constants
SymbolMeaning
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 H2
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
WAVELENGTH TABLES of the H2 spectrum from 2800 to 29000 Å with assignments of many of the lines Crosswhite, 1972. The TABLES OF ENERGY LEVELS Dieke, 1958 are also very useful as long as it is realized that the absolute values of the energy levels (n≥2) relative to the ground state need correction. Graphs and tables of POTENTIAL ENERGY CURVES for all known states of H2, H2+, and H2- Sharp, 1971.See note 1
Fragments of three other triplet systems. 2
u 3Πu 6pπ [123488.0] 3    [29.3]   [0.023]  [1.069] u → a 26232.3 4
Richardson, 1934; Dieke, 1958
t 3Σu+ 5fσ (121292) 5 (2661.4) (121.9)  6      t → a (25342)
Richardson, Yarrow, et al., 1934
q (3Σg+) 5dσ (121295) 5 [2172.6]   6      q → c (25325) 4
Richardson, Yarrow, et al., 1934, 2
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
n 3Πu 5pπ 120952.9 2321.4 62.86  29.95 1.24 7  [0.023]  1.057 n → a 24847.3 4
Richardson, 1934; Dieke, 1958
m 3Σu+ 4fσ (119317) 8 [2457.1]   6      m → a 23295.1 9
Richardson, Yarrow, et al., 1934
s 3Δg 4dδ 118875.2 2291.7 10 62.44 10  11      s → c 22949.3 12
Richardson, 1934; Foster and Richardson, 1953; Dieke, 1958
r 3Πg 4dπ 118613.7 2280.3 13 57.96 13  11      r → c 22683.2 13
Richardson, 1934; Foster and Richardson, 1953; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
p 3Σg+ 4dσ 118509.8 2303.1 76.90  6      p-k 14 
Miller and Freund, 1975
           p → c 22586.0 4
Richardson, 1934; Foster and Richardson, 1953; Dieke, 1958
v (3Πg) (118330) 15 2340 (57)  [(29.1)]     [(1.072)] v → c (22430)
Richardson, Yarrow, et al., 1934, 2
k 3Πu 4pπ 118366.2 16 2344.37 67.29 17 0.99 30.074 1.462 18  [0.0185]  1.0547 k → a 22271.0 4
Richardson, 1934; Cunningham and Dieke, 1950; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
f 3Σu+ 4pσ (116705) [2143.6] 19   [27.0] 19     [1.11] f → a 20526.0 19
Richardson, 1934; Dieke, 1958
o 3Σu+ (114234) 20 2399.1 91.0  [35]     [0.98] o → a (18160)
Richardson, Yarrow, et al., 1934
l 3Πu 113825 21 2596.8 106.0  [36]     [0.96] l → a 17846 4
Richardson, Yarrow, et al., 1934
j 3Δg 3dδ (113533) 2345.26 22 66.56 0.745 30.085 22 1.692  0.0190  1.0545 j ↔ c 23 R 17633.0 24
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
i 3Πg 3dπ (113132) 2253.55 22 67.05 25  29.221 22 1.506  0.0176  1.0700 i-d 26 
Freund and Miller, 1974
           i → e R 5384.81 27
Gloersen and Dieke, 1965
           i ↔ c 23 R 17185.8 24
Richardson, 1934; Dieke, 1958
h 3Σg+ 3sσ (112913) [2268.73] 28   [30.62] 28     1.045 1 h → c 16990.8 29
Richardson, Yarrow, et al., 1934, 3; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
g 3Σg+ 3dσ 112854.4 2290.86 105.43 30 2.403 31      g → e R 5116.6
Gloersen and Dieke, 1965
           g ↔ c 23 16917.6 29
Richardson, 1934; Richardson, Yarrow, et al., 1934, 3; Dieke, 1958
d 3Πu 3pπ 112700.3 32 2371.58 33 66.27 0.88 30.364 33 34 1.545  [1.91]  1.0496 d → a 35 R 16619.0 29
Dieke and Blue, 1935; Dieke, 1958
e 3Σu+ 3pσ 107774.7 2196.13 65.80 -0.433 27.30 1.515    1.107 e → a R 11605.6
Richardson, 1934; Dieke, 1935
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
a 3Σg+ 2sσ 95936.1 36 2664.83 71.65 37 0.92 34.216 1.671  [0.0216]  0.98879 a → b 38 39 
           (a-X) 95076.4 36
c 3Πu 3pπ 95838.5 40 2466.89 63.51 0.552 31.07 41 42 1.425  [0.0195]  1.0376 (c-X) 94881.0 43
b 3Σu+2Unstable; lower state of the continuous spectrum of H2 (a → b). Pot. function Kolos and Wolniewicz, 1965.
Several excited states above the ionization limit, established by electron impact studies and leading to two exited atoms or H + H+.
Continuous absorption above ~130000 cm-1. 44
v'=0 Rydberg series of rotational levels observed in low temperature absorption from X 1Σg+, v"=0, J"=0 and 1 and converging to:
RydbergN=2 of H2+: J=1 levels of npπ 1Πu+ (n=6,...,32, joining on to C, D, D', D")45; ν = 124591.5 46 - R/(n + 0.082)2. Similar series with v'=1,...,6 47. R(0) lines (para H2)
Herzberg, 1969; Takezawa, 1970; missing citation
N=1 of H2+: J=1 levels of npπ 1Πu- (n=6,...,43, joining on to C, D, D', D")48; ν = 124476.0 46 - R/(n + 0.082)2. Similar series with v'=1,...,5. Q(1) lines (ortho H2)
Herzberg, 1969; Takezawa, 1970; missing citation
N=1 of H2+: J=0 levels of npσ 1Σu+ (n=5,...,19, joining on to B, B', B")48; ν = 124476.0 46 - R/(n + 0.203)2. Similar series with v'=1,2,3. P(1) lines (ortho H2)
Takezawa, 1970; missing citation
N=0 of H2+: J=1 levels of npσ 1Σu+ (n=5,...,40, joining on to B, B', B")45; ν = 124417.0 46 - R/(n + 0.203)2. Similar series with v'=1,...,6. 5 R(0) lines (para H2)
Herzberg, 1969; Takezawa, 1970; missing citation
B bar 1Σu+State causing ion-pair formation after excitation of higher Rydberg states; also responsible for perturbations in B' 1Σu+. Correlates at small r with B" 1Σu+, forming a double-minimum state.
Dabrowski and Herzberg, 1974; Chupka, Dehmer, et al., 1975; Kolos, 1976
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
D" 1Πu 5pπ 121211.0 49 2319.92 49 63.041  30.76 50 51 1.45 50  (0.03)  1.043 D" ← X R 120176.0 49
Monfils, 1965; Monfils, 1968
D' 1Πu 4pπ 118865.3 49 2329.97 49 63.140  29.89 52 51 1.11 52 -0.53 [0.025] 52  [(1.058)] D' ← X R 117835.2 49
Namioka, 1964; Monfils, 1965; Monfils, 1968
S 1Δg 4dδ [119893] 53 3    [(28.8)] 54     [(1.078)] S → B V 27510
Richardson, 1934; Dieke, 1958
O 1Σ+ 4sσ [(119870)] 55 3    [(32)]     [(1.02)] O → B V (27487) 56
Richardson, 1934
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
R 1Πg 4dπ (118688) 57 [2142] 58   [(30)] 54     [(1.06)] (R → C) (18488)
Richardson, 1934; Dieke, 1958
           R → B V 27376 45
Richardson, 1934; Dieke, 1958
P 1Σg+ 4dσ [119531] 59 3    [(30)] 54     [(1.06)] (P → C) 18260 49
Richardson, 1934; Dieke, 1958
           P → B V 27148 60
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
T 1Σ+ [119512.6] 61 3    [(25.4)]     [(1.148)] T → B V 27130.1
Richardson, 1934; Dieke, 1958
B" 1Σu+ 4pσ 117984.5 2197.5 68.136  26.68 62 63 1.19 62  [0.034]  [(1.1198)] B" ← X R 116886.9 64
missing citation; Monfils, 1965; Monfils, 1968; missing citation
N 1Σg+ (116287) 65 [1983.3]   [(18.4)]     [(1.35)] N → B R 24896.4
Richardson, 1934; Dieke, 1958
U (1Σg+) [116707.7] 65 66    [(18.8)]     [(1.33)] U → B 67 R 24325.1
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
M 1Σg+ (114485) 65 [2176.0]   [(13)]     [(1.60)] M → B R 23190.0 68
Richardson, 1934; Dieke, 1958
L 1Σg+ (114520) 65 [(1835)]   [(9.7)]     [(1.86)] L → B R 23054.8
Richardson, 1934; Dieke, 1958
H 1Σg+ 3sσ 113899 69 2538 124  [(29.5)]     [(1.065)] H → C R 13866.6
Richardson, 1934; Dieke, 1958
           H → B V 22754.1 70
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
D 1Πu 3pπ 113888.7 2359.91 68.816 71  30.296 72 73 63 1.42 72  0.0201 74  1.0508 D → E R 13709.7
Richardson, 1937; Dieke, 1958
           D ↔ X 75 R 112872.3 76
missing citation; Monfils, 1965; Monfils, 1968; missing citation
J 1Δg 3dδ (113550) 2341.15 77 63.23 77  30.081 77 1.718 77  0.0189 77  1.0546 J → C 78 R 13435.6 79
Richardson, 1934; Dieke, 1958
           J → B 78 V 22322.5 79
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
I 1Πg 3dπ (113142) 80 2259.15 77 78.41 77 80  29.259 77 81 1.584 77  0.0180 77  1.0693 I → C 81 R 12982.5 82
Richardson, 1934; Dieke and Lewis, 1937; Dieke, 1958
           I → B V 21869.5 82
Richardson, 1934; Dieke and Lewis, 1937; Dieke, 1958
G 1Σg+ 3dσ 112834 83 2343.9 55.9 84  [(28.4)] 85     [(1.085)] G → C 86 85 R 12722.2 87
Richardson, 1934; Dieke, 1958
           G → B 86 V 21609.2 87
Richardson, 1934; Dieke, 1958
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
K (1Σg+) (112669) 88 [2232.59] 30  [10.8]     [1.76] K → C R 12538.6
Richardson, 1934; Dieke, 1958
           K → B R 21425.4
Richardson, 1934; Dieke, 1958
Q (1Πg) (113163) 89 [742]   [(16.3)]     1.43 Q → B R 21151.1
Richardson, Yarrow, et al., 1934; Dieke, 1958
B' 1Σu+ 3pσ 111642.8 90 2039.52 83.406 91  26.705 92 2.781 93  [0.012] 94  1.1192 B' → E,F 95 11311.5 96
Porto and Jannuzzi, 1963
           B' ← X 97 R 110478.2
Namioka, 1964; Namioka, 1965; Monfils, 1965
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
F 1Σg+ 2pσ2 100911 98 99 [1199] 98  100   101    F → B 102 R 103 
Dieke, 1949; Porto and Jannuzzi, 1963
E 1Σg+ 2sσ 100082.3 98 104 2588.9 104 130.5 104  32.68 104 1.818 104  [0.0228] 104  1.0118 E → B 102 V 8961.23
Dieke, 1936; Porto and Dieke, 1955; Dieke, 1958; Porto and Jannuzzi, 1963
C 1Πu 2pπ 100089.8 95 2443.77 69.524 105 106  31.3629 106 1.6647 107  0.0223 -0.00074 1.03279 C ↔ X 108 109 R 99120.17 95
Dieke, 1938; Namioka, 1964, 2; Namioka, 1965; Dabrowski and Herzberg, 1974
B 1Σu+ 2pσ 91700.0 110 1358.09 20.888 111  20.0154 112 1.1845 113  0.01625 114  1.29282 B ↔ X 115 116 117 R 90203.35
Herzberg and Howe, 1959; Wilkinson, 1968; Dabrowski and Herzberg, 1974
StateTeωeωexeωeyeBeαeγeDeβereTrans.ν00
X 1Σg 1sσ2 0 4401.213 121.336 118  60.8530 119 3.0622 120  0.0471 121  0.74144 122  
Herzberg, 1950; Fink, Wiggins, et al., 1965; Terhune and Peters, 1959; Foltz, Rank, et al., 1966; Brannon, Church, et al., 1968
Raman sp. 123
Stoicheff, 1957; Foltz, Rank, et al., 1966
Rotational 124 and nuclear rf magn. Reson.
Harrick and Ramsey, 1952; Barnes, Bray, et al., 1954; Kolsky, Phipps, et al., 1952; Harrick, Barnes, et al., 1953

Notes

1The Te values for the upper states of the triplet transitions are based on Te" for the lower state (a or c) and have been calculated assuming Y'00 ~ Y"00.
23B→c, 3C→c, 7pπ→a Richardson, 1934, Richardson, Yarrow, et al., 1934, 2.
3Only v=0 observed.
4Referred to the (non-existent) N=0 level in 3Π states; the N=1 levels of c 3Π (+ and -) lie 60.7 cm-1 above N=0.
5t and q are designated 3F and 3G, respectively, in Richardson, Yarrow, et al., 1934, 2, Richardson, Yarrow, et al., 1934.
6The states g 3Σg+(3dσ), p 3Σg+(4dσ), q 3Σg+(5dσ), m 3Σu+(4fσ) and t 3Σu+(5fσ) are strongly affected by l-uncoupling. The N=1 levels lie below N=0 for v=0 and 1; meaningful B values cannot be given until the whole d and f complexes have been fully analyzed, see Ginter, 1967.
7Represents B0 and B1 of 3Π- only; B2 = 26.26 Richardson, Yarrow, et al., 1934, B3 = 24.54 Richardson, Yarrow, et al., 1934.
83E of Richardson, Yarrow, et al., 1934.
9Refers to N'=0 which lies above N'=4 because of strong l-uncoupling.
10Constants refer to N=2; from v= 0,1,2.
11Because of strong l-uncoupling no meaningful B values can be given; see 6.
12Refers to the N=2 level of s 3Δg- above the hypothetical level N=0 of c 3Πu; see 4.
13The constants refer to N=1 of r 3Πg-; ν00 is the energy above the hypothetical level N=0 of c(v=0), see 4.
14Anticrossings and microwave transitions. The energy difference between k 3Πu(v=1,N=3) and p 3Σg+(v=1,N=5) is +0.2785 cm-1. Fine structure parameters.
153A of Richardson, Yarrow, et al., 1934, 2; probably a doubly excited state. The possibility (1sσ)(4fπ) mentioned by Richardson, Yarrow, et al., 1934, 2 and quoted in MOLSPEC 1 can be ruled out since it does not give rise to an even state.
16A0(ortho)= -0.00937 Freund, Miller, et al., 1973, Miller, Freund, et al., 1974, Miller and Freund, 1975, A0(para)= -0.00710 cm-1 Freund, Miller, et al., 1973, Miller, Freund, et al., 1974, Miller and Freund, 1975; also hyperfine structure investigated by these authors.
17ωeye= +0.99 Cunningham and Dieke, 1950.
18From B0 and B1 of Π- only Richardson, 1934.
19Calculated from the data in Richardson, 1934 and Dieke, 1958. ΔG(1/2) and ν00 refer to actual N=0 level which is strongly perturbed.
203D of Richardson, Yarrow, et al., 1934. Probably a doubly excited state: (2pσ)(3dσ).
213Y of Richardson, Yarrow, et al., 1934. Probably a doubly excited state: (2pσ)(3dπ).
22These constants [from Ginter, 1967] refer to the 3Π- and 3Δ- components and are based on "Approximation 2" of Ginter, 1966 for the evaluation of the l-uncoupling. The observed levels are given by Dieke, 1958.
23Observed in absorption in flash discharges Herzberg, 1967.
24Lower component of N'=l (i 3Π) or 2 (J 3Δ) relative to the (non-existent) N"=0 level of c 3Π.
25Ab initio calculations Browne, 1965, Wright and Davidson, 1965 give a pronounced potential maximum near 2.5 Å for this state.
26Anticrossings and microwave transitions; i 3Πg(v=3,N=2) is 1.9244 cm-1 above d 3Πg(v=3,N=1).
27Refers to Π-(N=1). Π+(N=1) is at 5471.70 cm-1 above e 3Σu+(v=0,N=0). The rotational levels are very irregular, only partly on account of l-uncoupling.
28From Dieke, 1958. ωe = 2395.2 Richardson, Yarrow, et al., 1934, 3, ωexe = 64.2 Richardson, Yarrow, et al., 1934, 3, B0 = 30.0 Richardson, Yarrow, et al., 1934, 3. According to Dieke, 1958 the v=0 levels may be spurious. If so, only v=1 remains with B1 = 28.72.
29Referred to the (non-existent) N=0 level in 3Π states; the N=1 levels of c 3Π (+ and -) lie 60.7 cm-1 above N=0.
30Calculated from the N=0 levels of Dieke, 1958.
31The states g 3Σg+ (3dσ), p 3Σg+ (4dσ), q 3Σg+ (5dσ), m 3Σu+ (4fσ) and t 3Σu+ (5fσ) are strongly affected by l-uncoupling. The N=1 levels lie below N=0 for v=0 and 1; meaningful B values cannot be given until the whole d and f complexes have been fully analyzed, see Ginter, 1967.
32The fine structure in the N=1 levels of both ortho- and para-H2 has been observed in microwave-optical double resonance by Freund and Miller, 1973 who give Ae = 0.0281 Freund and Miller, 1973 as well as spin-spin coupling constants. For para-H2, v=0, N=1, the three component levels J=1,2, and 0 are at -0.01241, -0.00695, and +0.07197 cm-1, respectively. For ortho-H2 the hyperfine structure has also been studied.
33Constants refer to 3Π-. 3Π+ is strongly perturbed, i.e. the Λ - type doubling is fairly large and irregular Dieke, 1935, 2.
34Breaking-off of P and R branches (3Π+) above v'=3 on account of predissociation. Breaking-off of Q branches (3Π-) for v'=7,8 above N=1 on account of preionization Beutler and Junger, 1936.
35Lifetime τ=63 ns Cahill, 1969; see, however, Marechal, Jost, et al., 1972 who give τ= 31 ns Marechal, Jost, et al., 1972.
36The T000) value is derived from singlet-triplet anti-crossings in a magnetic field Miller and Freund, 1974, Jost and Lombardi, 1974 and corresponds to v=0, N=0. It agrees fairly well with 95073.2 obtained from the energy of a 3Σu+(v=0,N=0) below the ionization limit, 29344 ± 2 cm-1 Beutler and Junger, 1936, combined with the new value of I.P.(H2). Dieke, 1958 gives T0 = 95226 without explanation; the most recent theoretical value is T0= 95077.3 Kolos, 1975. The Te value in the table takes account of Y00 in both upper (Y'00= 4.92) and lower state.
37ωeye= +0.92. Precise ab initio potential function (including diagonal corrections) and predicted vibrational levels in Kolos and Wolniewicz, 1968. Except for a constant shift, the latter agree well with the observed levels Dieke, 1958.
38Lifetime τ(v=0,1) = 10.45 ns Smith and Chevalier, 1972, King, Read, et al., 1975.
39Reproduction in MOLSPEC 1, Fig.l2.
40A = -0.1249 cm-1 Jette, 1974, Jette and Miller, 1974. Te takes account of Y00 in both upper (Y'00= 4.18) and lower state.
41The Λ-type doubling is quite small (~ 0.5 cm-1 for N=6); the constants refer to the average. The triplet splitting in N=2 of para-H2 has been fully resolved in molecular beam experiments of Lichten, 1960 yielding Δν(J=2-1) = 0.16438 Lichten, 1960, Δν(J=2-3) = 0.19674 cm-1 Lichten, 1960 with J=2 at the top. The hyperfine structure in N=1,J=2 of ortho-H2 is Δν(F=3-2) = 0.0236 Frey and Mizushima, 1962, Δν(F=2-1) = 0.0154 cm-1 Frey and Mizushima, 1962 as quoted by Frey and Mizushima, 1962. Foster and Richardson, 1953 give spin splittings for N = 1,2,3,4,5 without resolving J=N+l from J=N-1.
42The levels of c 3Πu+ are strongly predissociated by the b 3Σu+ state Herzberg, 1967; the levels of c 3Πu- are either very weakly affected by a forbidden predissociation to b 3Σu+ Lichten, 1962, Chiu, 1964 or decay radiatively (by magnetic dipole radiation) to the b 3Σu+ state as suggested by the lifetime measurements of Johnson, 1972, τ(v=0)= 1.02 ms Johnson, 1972 independent of spin component and isotope. Johnson, 1974 observed quenching of c 3Πu- in an electric field. The Stark effect is large (~ E+4 times greater than for the ground state) and has been studied experimentally by Kagann and English, 1976 and compared with the theoretical values of English and Albritton, 1975.
43This number, obtained from ν00(a-X) + ν00(e-a) + ν00(g-e) - ν00(g-c), is 87 cm-1 higher than given in MOLSPEC 1, a change made necessary by the work of Gloersen and Dieke, 1965. See also 36.
44Theoretical and experimental values for the ionization probability into the various vibrational levels of H2+ are given by Dunn, 1966, Villarejo, 1968, Nicholls, 1968, Ford, Docken, et al., 1975 and Villarejo, 1968, 2, Turner, 1968, respectively. The ionization cross section near the ionization limit has been studied at high resolution by Chupka and Berkowitz, 1968, Comes and Wellern, 1968. See also Backx, Wight, et al., 1976.
45For high n there is strong l-uncoupling and the two series of 1Σu+ and 1Πu+ levels of para-H2 should be called np0 and np2, respectively, corresponding to the fact that the first converges to N=0, the second to N=2 of H2+ There are strong systematic perturbations between the J=1 levels of these two series (because of l- uncoupling) so that the formulae as given do not represent the series very well. An accurate representation can be obtained by Fano's quantum defect theory; see Herzberg and Jungen, 1972. Levels of npπ, 1Πu+ above N=0 of H2+ are preionized resulting in asymmetrically broadened absorption lines with apparent emission wings.
46Limits of Rydberg series above v"=0, J"=0.
47 Chupka, Dehmer, et al., 1975 have observed Rydberg levels with v = 9,10,11 in the study of ion-pair formation.
48These two series of ortho levels are essentially unperturbed.
49Average of Π+ and Π-. ν00 referred to (N'=0).
50Refers to Π-; Π+ is perturbed; B0+) = 30.178, B1+) = 31.370.
51RKR potential function in Monfils, 1968, 2.
52Refers to Π-; γe = -0.53. Π+ is perturbed, B0+) = 31.095, B1+) = 29.165.
534F of Dieke, 1958, 41χ of Richardson, 1934.
54The states P,R,S form a d complex with strong uncoupling. As a result the constants given have only limited meaning.
5541O of Richardson, 1934, not given by Dieke, 1958.
56From R(0) and P(1) according to the data of Richardson, 1934.
5741B of Richardson, 1934, 4E of Dieke, 1958.
58Refers to 1Π-.
5941C of Richardson, 1934, 4D of Dieke, 1958.
60The J=1 level is observed at 27207.62 cm-1 above J=0, v=0 of B 1Σu+. The value given for J=0 is extrapolated and, because of the uncoupling, is rather uncertain.
6141K of Richardson, 1934, doubly excited state.
62Representing only B0 and B1. The Bv curve has a positive curvature for low v and a strong negative curvature for high v. Bv = 27.13 - 2.35(v+1/2) + 0.665(v+1/2)2 - 0.0729(v+1/2)3 Monfils, 1965.
63RKR potential function Monfils, 1968, 2. Ab initio potential function Kolos, 1976.
64Deperturbed value from Namioka, 1964. The observed value for J=0 [perturbed by B'(v=4)] is 116885.6 according to Namioka, 1964 and 116885.3 according to Monfils, 1965, while in the more recent paper Monfils, 1968 gives 116882.00.
65All these states are considered as doubly excited states by Dieke, 1958. They may well form one or two double-minimum states (similar to E, F) together with H 1Σg+.
66Only v=0.
67This is the λ4142.8 progression of Richardson, 1934 as revised by Dieke, 1958.
68These values agree with Dieke, 1958; Richardson, 1934 gives 23057.22 and 23191.66 for L and M, respectively.
69310 of Richardson, 1934.
70From R(0) of the 0-0 band and F(1)-F(0) as given by Richardson, 1934. The basis for 22751.6 in Richardson, 1934 is not clear.
71ωexe= +1.0274(v+1/2)3 - 0.04202(v+1/2)4; the vibrational constants Monfils, 1968 refer to the average of Π+ and Π-. See also 73.
72The rotational constants Namioka, 1964 represent only the levels v= 0, 1, 2 of Π-. The Π+ levels are strongly perturbed by the B' state which also causes the predissociation of 1Π+ for v'≥ 3; see 73. Monfils, 1965 gives for the deperturbed values: Bv+)= 32.51- 2.00(v+1/2) + 0.071(v+1/2)2 - 0.0040(v+1/2)3 ; Bv-)= 30.81 - 1.96(v+1/2) + 0.102(v+1/2)2 - 0.0053(v+1/2)3 .
73Strong predissociation for v'≥3; no bands with v'≥3 have ever been observed in emission. In absorption strongly broadened lines with apparent emission wings (Beutler- Fano shapes) in D 1Πu- ← X 1Σg- Herzberg, 1971; line widths of 4 and 11.5 cm-1 for J=1 and 2, respectively, have been observed Comes and Schumpe, 1971 and accounted for by interaction with the continuum of B' 1Σu- Fiquet-Fayard and Gallais, 1971, Julienne, 1971, Fiquet-Fayard and Gallais, 1972. Widths for D 1Πu- ← X 1Σg- (Q) lines are much smaller. Lyα fluorescence as a result of predissociation Comes and Wellern, 1968, Comes and Wenning, 1969, Mentall and Gentieu, 1970. Electric field induced component of predissociation Comes and Wenning, 1970.
74From Namioka, 1964; Monfils, 1965 gives Dv+) = 0.033+0.0010(v+1/2) Monfils, 1965, Dv-) =0.0283 - 0.0012(v+1/2) Monfils, 1965.
75RKR Franck-Condon factors Spindler, 1969. Absorption coefficients of D←X bands Cook and Metzger, 1964. 0scillator strengths f00 = 0.00614 Lewis, 1974, f20 = 0.0109 Lewis, 1974.
76Average of Π+ and Π- extrapolated to J=0. The Λ-type doubling for v=0, J=1 is 4.2 cm-1 with Π+ above Π-.
77These constants Ginter, 1967 refer to Π- and Δ- and take into account the effects of l- uncoupling in the d-complex according to the formulae of Ginter, 1966. They cannot be used to derive energy levels without the use of these formulae. The observed levels are given in Dieke, 1958.
78The forbidden 1Δg1Σu- transition occurs because of strong uncoupling in the upper state. Only Q branches are observed in these bands.
79Refers to J=2 of Δ- at 10.8 cm-1 below J=2 of Δ+.
8031B of Richardson, 1934, 3E of Dieke, 1958. Mulliken, 1964 and Browne, 1965 predict a fairly high (0.4 eV) maximum in the potential function of this state.
81Zeeman effect studies Dieke, Cunningham, et al., 1953 yield g(v=0,J=1) = 0.498 Dieke, Cunningham, et al., 1953, g(v=0,J=2) = 0.412 Dieke, Cunningham, et al., 1953, etc.; lifetime τ(v=0,J=2) = 38 ns van der Linde and Dalby, 1972, see 85.
82Referred to J'=1 of I 1Π-; J=1 of I 1Π+ is 62.32 cm-1 higher.
8331C of Richardson, 1934, 3D of Dieke, 1958.
84No levels higher than v=3 have been observed which suggests that the dissociation limit is 12S + 22S,2P at 118377.6 cm-1. The constants represent only v=0,1,2.
85This value Richardson, 1934 does not represent the low rotational levels because of l-uncoupling, e.g. the J=1 level is below J=0. The actual levels are given in Dieke, 1958. Hyperfine structure for v=1,J=1; A = 1.0 ± 0.17 MHz Melieres-Marechal and Lombardi, 1974. Large Zeeman splittings corresponding to the strong l-uncoupling Dieke, Cunningham, et al., 1953, g(v=0,J=1) = 0.901 Dieke, Cunningham, et al., 1953, g(v=0,J=2) = 0.571 Dieke, Cunningham, et al., 1953, etc.; see also Freund and Miller, 1972. Lifetimes from Hanle effect observations van der Linde and Dalby, 1972; τ(v=0,J=1) = 27 ns van der Linde and Dalby, 1972, τ(v=0,J=2,3) = 39 ns van der Linde and Dalby, 1972.
86The G→B system gives rise to the strongest lines in the visible region.
87Referred to J'=0 which, because of l-uncoupling, has an anomalous position.
8831K of Richardson, 1934, probably due to (2sσ)2.
89Fragmentary, possibly (2pσ)(2pπ).
90Takes account of Y00 in both upper and lower state. Y'00 = 15.3 cm-1 is rather uncertain and depends strongly on the number of levels included. See 93.
91ωexe= +3.533(v+1/2)3 - 0.93750(v+1/2)4; these are the constants of Namioka, 1964 [except Te which is taken from Dabrowski and Herzberg, 1974], they apply only to v=0,...,4. Monfils, 1968 gives a very different set of constants based on seven levels v=0,...,6. The ΔG curve (in H2, HD, and D2) has a characteristic tail which makes representation of the higher vibrational levels by a conventional formula meaningless Namioka, 1964, Dabrowski and Herzberg, 1974.
92RKR potential functions Namioka, 1965, Monfils, 1968, 2. A very slight maximum of the potential function at 2.9 Angstroms has been predicted by Ford, Browne, et al., 1975 but not confirmed in the calculations of Kolos, 1976; see also Wolniewicz, 1975. The experimental data, while suggesting an anomalous form of the potential function, do not indicate a maximum Dabrowski and Herzberg, 1974.
93av= +0.540(v+1/2)2 - 0.0917(v+1/2)3; these constants Namioka, 1964 represent only the first five (deperturbed) Bv values. If only three levels are used Bv= 26.371- 1.9000(v+1/2)-0.0050(v+1/2)2 leading to a very different Y00 value (3.6) from the one used here (see 90).
94The higher Dv values are quite irregular.
95The Te values for B and C include the effects of Y00 on the zero point energies in both upper and lower states; Y'00(B) = 8.7, Y'00(C) = 5.0 cm-1. On the other hand, the Te value of C 1Πu and ν00(C-X) exclude the term - BΛ2 in the energy formula, a term that is usually included to form part of the effective potential energy. With this inclusion and disregarding Y00 Namioka, 1965 gives Te = 100063.42 and ν00 = 99090.35 on the basis of older data for v=0...4 and his own precise data for v=5....13.
96From the 0-1 band of Porto and Jannuzzi, 1963; from T0(B')-T0(E) one obtains 11313.62.
97RKR Franck-Condon factors Spindler, 1969. Oscillator strengths f10 = 0.0028 Lewis, 1974, f30 = 0.0048 Lewis, 1974.
98Because of strong interaction the two states E [21X of Richardson, 1934, 2A of Dieke, 1958] and F, in zero approximation lsσ2sσ and (2pσ)2, form a single state with two minima as first recognized by Davidson, 1961. The most detailed calculation of the potential function and the energy levels is that of Kolos and Wolniewicz, 1969 whose numbering and ΔG(1/2) value for the F 1Σg- component has been adopted in the table. According to Kolos and Wolniewicz, 1969 ν00(F-B) would be at 9146.8 cm-1 but v=0,1,2,3 of F have not been observed. The observed v=4 level lies just below the potential maximum.
99From the observed ν40 and the energy of v=4 above the (outer) minimum as calculated by Kolos and Wolniewicz, 1969.
100B4 = 6.24 129
101R4=2.315 129
102Franck-Condon factors Lin, 1974. Electronic transition moment Wolniewicz, 1969.
103ν40 =13635.1
104These numbers represent only the lower vibrational levels near the inner minimum. Owing to the interaction of E and F (see 98) higher ΔG(v+1/2), Bv, Dv values are irregular.
105ωexe= +0.73l2(v+1/2)3 - 0.04l5(v+1/2)4. These constants refer to the (unperturbed) Π- component and are based on an 8-level fit to the data of Dabrowski and Herzberg, 1974 [v=0-4] and Namioka, 1964, 2 [v=5-7]. Somewhat different constants are given by Namioka, 1965. Note, that the Te values in Dieke, 1958 are too low by 8.4 cm-1 Namioka, 1965. The constants of Monfils, 1968 are affected by not recognizing this error.
106Theoretical work King and Van Vleck, 1939, Mulliken, 1960, Kolos and Wolniewicz, 1965, Rothenberg and Davidson, 1966, Kolos, 1967 has predicted, and the analysis of the spectrum Namioka, 1964, Dabrowski and Herzberg, 1974 has confirmed, that the potential curve of C 1Πu has a van der Waals maximum of ~ 105 cm-1 above the asymptote near r=4.8 Angstroms. ab initio potential function (without diagonal corrections) and predicted vibrational levels Kolos and Wolniewicz, 1968. RKR potential functions Namioka, 1965 Monfils, 1968, 2; see, however, Julienne, 1973.
107αv= +0.0296(v+1/2)2 - 0.00296(v+1/2)3. These constants refer to the Π- component (Π+ is strongly perturbed by B 1Σu-) and are from an 8-level least- squares fit of the data of Dabrowski and Herzberg, 1974 [v = 0-4] and Namioka, 1964, 2 [v=5-7]. Somewhat discordant Bv values for both Π- and Π+ (the latter after deperturbation) are given by Namioka, 1964, 2, Monfils, 1965, Dabrowski and Herzberg, 1974. The Λ-type doubling for v=0, J-l is 1.17 cm-1; for other v, J as well as theoretical values see Julienne, 1973, Ford, 1974.
108Lifetime τ(v=0,1,2,3) = 0.6 ns Hesser, 1968.
109RKR Franck-Condon factors calculated by missing citation,89 and "measured" by Geiger and Schmoranzer, 1969, Schmoranzer and Geiger, 1973, Fabian and Lewis, 1974 who have also determined the dependence of the transition moment on r. Ab initio calculation of the latter by Wolniewicz, 1969. Theoretical transition probabilities and f values Wolniewicz, 1969, Allison and Dalgarno, 1970, Allison and Dalgarno, 1970, 2, Dalgarno and Stephens, 1970, experimental values Hesser, 1968, Fabian and Lewis, 1974, Lewis, 1974: f10 = 0.059, f20 = 0.060, f30 = 0.044,... Calculated transitions to the continuum of X 1Σg- Stephens and Dalgarno, 1972. Selective enhancements of v=0 and 2 of C 1Πu in Ar-H2 mixtures have been studied by Takezawa, Innes, et al., 1966; similar enhancements have also been observed in Kr-H2 mixtures. For stimulated emission in the Q(1) and P(3) lines of the 1-4, 2-5, 2-6, 3-7 Werner bands see Hodson and Dreyfus, 1972, Waynant, 1972.
110The Te values for B and C include the effects of Y00 on the zero point energies in both upper and lower states; Y'00(B) = 8.7, Y'00(C) = 5.0 cm-1. On the other hand, the Te value of C 1Πu and ν00(C-X) exclude the term - BΛ2 in the energy formula, a term that is usually included to form part of the effective potential energy. With this inclusion and disregarding Y00 Namioka, 1965 gives Te = 100063.42 and ν00 = 99090.35 on the basis of older data for v=0...4 and his own precise data for v=5....13.
111ωexe= +0.7196(v+1/2)3 - 0.0598(v+1/2)4 +0.002l6(v+1/2)5, Y00 = 8.7; from a least squares fit Dabrowski and Herzberg, 1974 to the first eight levels as given by Herzberg and Howe, 1959. Wilkinson, 1968 gives slightly different constants based on the first five levels only. Monfils, 1968 and Namioka, 1964, 2 have observed levels up to v= 35 and 37, respectively, very close to the dissociation limit at 118377.6 cm-1 Herzberg, 1970. The dissociation energy of the B 1Σu- state is 28174.2 cm-1.
112RKR potential functions Tobias and Vanderslice, 1961, Namioka, 1965,$ 72, Spindler, 1969; see also Stwalley, 1973. Precise ab initio potential function (including diagonal corrections) and predicted vibrational levels Kolos and Wolniewicz, 1968, Kolos and Wolniewicz, 1975.
113αv= +0.1214(v+1/2)2 - 0.0117(v+1/2)3 + 0.00046(v+1/2)4, from a least squares fit Dabrowski and Herzberg, 1974 to the first eight levels. Wilkinson, 1968 gives slightly different constants based on the first five levels only. For v≥8 there are strong rotational perturbations caused by interaction with C 1Πu. Only after deperturbation can meaningful Bv values for these levels be obtained [see Dabrowski and Herzberg, 1974]. For a theoretical discussion of the intensities in the perturbed region see Ford, 1974.
114Dv= -2.165E-3(v+1/2) + 2.289E-4(v+1/2)2 - 1.185E-5(v+1/2)3. For individual Bv and Dv values see Herzberg and Howe, 1959, Namioka, 1964, 2, Dabrowski and Herzberg, 1974.
115Lifetime τ(v=3...7) = 0.8 ns Hesser, 1968; τ(v=8...11) = 1.0 ns Smith and Chevalier, 1972.
116Franck-Condon factors from RKR potentials Halmann and Laulicht, 1966, Spindler, 1969; from ab initio potential functions Dalgarno and Allison, 1968, Allison and Dalgarno, 1970, Allison and Dalgarno, 1970, 2, including theoretical oscillator strengths; see also Lin, 1975. J dependence of Franck-Condon factors and transition probabilities Villarejo, Stockbauer, et al., 1969, Wolniewicz, 1969, Becker and Fink, 1971. Experimental Franck-Condon factors and oscillator strengths Geiger and Topschowsky, 1966, Haddad, Lokan, et al., 1968, Hesser, Brooks, et al., 1968, Geiger and Schmoranzer, 1969, Fabian and Lewis, 1974, Lewis, 1974, Schmoranzer, 1975; Σfv'0 = 0.29. Variation of transition moment with r Hesser, Brooks, et al., 1968, Geiger and Schmoranzer, 1969, Schmoranzer, 1975 and, ab initio, Dalgarno and Allison, 1968, Wolniewicz, 1969. Selective enhancements of v=3 and 10 of B 1Σu- in an Ar-H2 mixture, first observed by Lyman, have recently been studied by Takezawa, Innes, et al., 1966; similar enhancements were also observed in Kr-H2 mixtures. Stimulated emission in the P branches of the 3-10, 4-11, 5-12, 6-13, 7-13 Lyman bands Hodgson, 1970, Waynant, Shipman, et al., 1970.
117A continuous spectrum corresponding to transitions to the continuum of X 1Σg- has been observed Dalgarno, Herzberg, et al., 1970 and the intensity distribution found to be in agreement with calculations. Dalgarno and Stephens, 1970, Stephens and Dalgarno, 1972 have calculated transition probabilities and the fractions that go to the continuum for v' = 0.... 36. Allison and Dalgarno, 1969 calculated the continuous spectrum corresponding to absorption from the ground state to the continuum of B 1σu-.
118ωexe= +0.8129(v+1/2)3; these constants Foltz, Rank, et al., 1966 represent only the levels v=0,1,2,3. Herzberg and Howe, 1959 has less accurate constants representing higher G(v) values. "True" ωe= 4403.2 Fink, Wiggins, et al., 1965 (including Dunham corrections) Fink, Wiggins, et al., 1965. The zero-point energy (Y00 = 8.93 included) is 2179.27 cm-1. Herzberg and Monfils, 1960.
119RKR potential functions Tobias and Vanderslice, 1961, Weissman, Vanderslice, et al., 1963, Ginter and Battino, 1965, see also Zhirnov and Vasilevskii, 1970; ab initio potential functions Kolos and Wolniewicz, 1974, Kolos and Wolniewicz, 1975, 2. Rotational and vibrational levels calculated from the latter are given in Kolos and Wolniewicz, 1975, 2; see also Waech and Bernstein, 1967, Kolos and Wolniewicz, 1968, 2. Waech and Bernstein, 1967 include some of the quasi-bound levels above the dissociation limit [see also Allison, 1969]; for their experimental observation see Herzberg and Howe, 1959, Herzberg and Mckenzie, 1979. Recent comparisons between ab initio calculated and observed energy levels Bunker, 1972, Orlikowski and Wolniewicz, 1974, Dabrowski and Herzberg, 1976, Bishop and Shih, 1976.
120αv= +0.0577(v+1/2)2 - 0.0051(v+1/2)3; these constants Foltz, Rank, et al., 1966 represent only B0...3 which are the best known Bv values. Brannon, Church, et al., 1968 from the field-induced spectrum give a very slightly different B0 (59.3343 versus 59.3362); see also Buijs and Gush, 1971. The formula Bv= 60.8635 - 3.07638(v+1/2) + 0.06017(v+1/2)2 - 0.0048l(v+1/2)3 (v≤8) of Herzberg and Howe, 1959 holds up to v=8. Higher Bv values Herzberg and Howe, 1959 require higher and higher terms in the formula. All the constants given are Y01,...Y31 values; Fink, Wiggins, et al., 1965 have introduced Dunham corrections and give the "true" Be = 60.8679 Fink, Wiggins, et al., 1965. According to Ramsey, 1952 the hyperfine levels F=1 and 2 for J=1,v=0 are 1.823E-5 and 2.005E-5 cm-1 below the F=0 component.
121Dv= -0.00274(v+1/2) + 0.00040(v+1/2)2; Hv = [4.9-0.5(v+1/2)]E-5 Fink, Wiggins, et al., 1965; see also Foltz, Rank, et al., 1966.
122Quadrupole 130 and field-induced sp..131
123Raman cross sections Harney, Randolph, et al., 1975.
124Rotational g factor gJ = 0.88291.
125This is an upper limit (36118.3 ± 0.5 cm-1), the lower limit being 4.4779 eV. According to Herzberg, 1970 the true value is probably close to the upper limit; see also Stwalley, 1970 who gives D00 = 36118.6 cm-1 Stwalley, 1970 on the basis of a reassignment of the last vibrational levels of the B state. The most recent theoretical value of Kolos and Wolniewicz, 1968, 2 - including a small non-adiabatic correction of Bunker, 1979 - is D00= 36117.9 cm-1 Kolos and Wolniewicz, 1968, 2, Bunker, 1979. An earlier independent calculation Hunter, 1966 (not including the non-adiabatic correction) gave D00= 36118.1 cm-1 Hunter, 1966.
126From the limit of the npσ, 1Σu+ Rydberg series (124417.2 cm-1) taking account of perturbations and pressure shift of high n lines Herzberg and Jungen, 1972. The earlier value of Takezawa, 1970 was higher by 1.2 cm-1 because it was not corrected for pressure shift. The latest theoretical (ab initio) value Jeziorski and Kolos, 1969 including relativistic, Lamb shift, and non-adiabatic corrections is 15.42590 eV; see Herzberg and Jungen, 1972.
127The two J=2 levels are observed at 27631.3 and 27732.9 cm-1 above J=0, v=0 of B 1Σu+ Dieke, 1958. The ν00 value given is an extrapolated average for J=0 and, because of the uncoupling, is rather uncertain.
128The two J=1 levels are observed at 27385.8 and 27487.1 cm-1 above J=0, v=0 of B 1Σu+ Dieke, 1958. The ν00 value given is an extrapolated average for J=0 and, because of the uncoupling, is rather uncertain.
129Vibrational numbering of Kolos and Wolniewicz, 1969. See 98.
130 Fink, Wiggins, et al., 1965 give absolute intensity measurements of the quadrupole rotation-vibration spectrum (1-0, 2-0, 3-0) as well as corrections for pressure shifts; see also Margolis, 1973, McKellar, 1974, Chackerian and Giver, 1975. Dependence of quadrupole moment on r Kolos and Wolniewicz, 1965. Predicted intensities in the rotation-vibration spectrum James, 1969, in the rotation spectrum Dalgarno and Wright, 1972. Predicted lifetimes of rotation-vibration levels Black and Dalgarno, 1976, e.g. τ(v=1,J=1)= 1.17E+6 s Black and Dalgarno, 1976.
131The rotation and rotation-vibration spectrum has been observed in pressure- induced absorption, see the review by Welsh, 1972.

References

Go To: Top, Mass spectrum (electron ionization), Constants of diatomic molecules, Notes

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

Crosswhite, 1972
Crosswhite, H.M., The hydrogen molecule wavelength tables of Gerhard Heinrich Dieke, Wiley-Interscience, Division of John Wiley & Sons, Inc., New York, 1972, 616. [all data]

Dieke, 1958
Dieke, G.H., The molecular spectrum of hydrogen and its isotopes, J. Mol. Spectrosc., 1958, 2, 494. [all data]

Sharp, 1971
Sharp, T.E., Potential-energy curves for molecular hydrogen and its ions, At. Data, 1971, 2, 119. [all data]

Richardson, 1934
Richardson, O.W., Molecular Hydrogen and Its Spectrum, Yale University Press, New Haven, 1934, 343. [all data]

Richardson, Yarrow, et al., 1934
Richardson, O.W.; Yarrow, F.R.S.; Rymer, T.B., The spectrum of H2. Part III. New bands and band systems ending on 2s 3Σ and an extension of the singlet system 1Q → 2p 1Σ, Proc. R. Soc. London A, 1934, 147, 272. [all data]

Richardson, Yarrow, et al., 1934, 2
Richardson, O.W.; Yarrow, F.R.S.; Rymer, T.B., The spectrum of H2. Part II - The band systems due to transitions from four new triplet states to 2p 3Π, Proc. R. Soc. London A, 1934, 147, 251. [all data]

Foster and Richardson, 1953
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Miller and Freund, 1975
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Cunningham and Dieke, 1950
Cunningham; Dieke, Johns Hopkins University, Department of Physics, Rpt. NYO-692, 1950, 1. [all data]

Freund and Miller, 1974
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Gloersen and Dieke, 1965
Gloersen, P.; Dieke, G.H., Molecular spectra of hydrogen and helium in the infrared, J. Mol. Spectrosc., 1965, 16, 191. [all data]

Richardson, Yarrow, et al., 1934, 3
Richardson, O.W.; Yarrow, F.R.S.; Rymer, T.B., The spectrum of H2 (the ordinary hydrogen molecule). Part I - The 3, 4d 3Σ, Π, Δ → 2p 3Π and 3s 3Σ → 2p 3Π systems, Proc. R. Soc. London A, 1934, 147, 24. [all data]

Dieke and Blue, 1935
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Dieke, 1935
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Kolos and Wolniewicz, 1965
Kolos, W.; Wolniewicz, L., Potential-energy curves for the X1Σg+, b3Σu+, and C1Πu states of the hydrogen molecule, J. Chem. Phys., 1965, 43, 2429. [all data]

Herzberg, 1969
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Takezawa, 1970
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Dabrowski and Herzberg, 1974
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Chupka, Dehmer, et al., 1975
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Kolos, 1976
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Monfils, 1965
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Monfils, 1968
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Namioka, 1964
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Richardson, 1937
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Dieke and Lewis, 1937
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Porto and Jannuzzi, 1963
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Namioka, 1965
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Dieke, 1936
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Porto and Dieke, 1955
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Dieke, 1938
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Namioka, 1964, 2
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Herzberg and Howe, 1959
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Wilkinson, 1968
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Fink, Wiggins, et al., 1965
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Terhune and Peters, 1959
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Notes

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