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Hydrogen cation

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 November, 1976

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 H2+
Several other excited states, mostly repulsive. 1
C 2Piu 2ppi (102696.7) 2 (266.01) (6.454)  (1.899) (0.0758)  (0.00039)  (4.198) (C-B) (8806.3) 2
Bishop, Shih, et al., 1975
B 2Sigmag+ 3dsigma (93804.5) 2 (437.15) (5.247)  (1.530) (0.0312)  (0.000075)  (4.677) (B-X) (92877.4)
Bishop, Shih, et al., 1975
A 2Sigmau+ 2psigma 3           A larrow X 
Richardson, Jefferts, et al., 1968
X 2Sigmag+ 1ssigma 0 2321.7 4 66.2 4 0.6 30.21 4 5 6 1.685 4 0.6 4  1.052 7 8  
Jefferts, 1969


1Electronic wavefunctions and energies are given by Bates, Ledsham, et al., 1953 where references to earlier literature may be found.
2Data for these two states are entirely theoretical [adiabatic approximation Bishop, Shih, et al., 1975; see also Kroll, 1970]. nu00(C-B) refers to N=1 of C 2Piu and N=0 of B 2Sigmag+; see Table VI of Bishop, Shih, et al., 1975. Beckel (lecture at Columbus l976) gives +8803.90.
3Repulsive state. 10
4From Rydberg series limits of H2 Herzberg and Jungen, 1972; DeltaG(1/2) = 2191.2. Similar constants (and De = 0.018) were obtained Cunningham and Dieke, 1950 by extrapolation from low members of the series np3Pi (n=2-5). Higher vibrational levels and their Bv values have been derived from photoelectron spectra Siegbahn, Nordling, et al., 1967, Asbrink, 1970. See also 11.
5For two recent ab initio calculations of the potential functions. Peek, 1965, Hunter, Yau, et al., 1974; relativistic corrections Luke, Hunter, et al., 1969, Lamb shift corrections Gersten, 1969, Jeziorski and Kolos, 1969, non-adiabatic corrections Bishop, 1974. Rotational and vibrational levels up to v=18 from ab initio calculations in Wind, 1965, Hunter and Pritchard, 1967, Beckel, Hansen, et al., 1970, Hunter, Yau, et al., 1974, include quasi-bound levels.
6Franck-Condon factors for photoionization of H2 Halmann and Laulicht, 1965, Dunn, 1966, Nicholls, 1968. Effect of r-dependence of the transition moment Itikawa, 1973. Experimental cross sections Spohr and Puttkamer, 1967, Berkowitz and Spohr, 1973.
7The most recent theoretical value Schaad and Hicks, 1970 is re= 1.0569 Å Schaad and Hicks, 1970.
8Spin reorientation sp. 11
9Experimental value derived from D00(H2) and I.P.(H2) Herzberg and Jungen, 1972.The latest theoretical value [non-adiabatic calculation Bishop, 1974, and including relativistic and Lamb shift corrections] is 2.65073 eV; see also Hunter and Pritchard, 1967, Jeziorski and Kolos, 1969.
10Observed in the photodissociation of H2+ Richardson, Jefferts, et al., 1968, Jefferts, 1969 and in the photoelectron spectrum of H2 Samson, 1972; the direct transition from the X 1Sigmag+ ground state causes a shoulder in the absorption spectrum of H2 near 380 Å. Of recent ab initio calculations of the potential function the most detailed seems to be that of Peek, 1965. This state has a small van der Waals minimum (D0 = 3.4 cm-1) at 6.64 Å Peek, 1969.
11Observed for N=1 and N=2 of v=4...8. For v=4, N=2 the spin splitting is sigmas= 0.0027059 cm-1; for odd N the hyperfine structure due to the proton spins is superposed which gives a much larger splitting. The strongest of the observed five transitions for v=4, N=1 occurs at 0.0423810 cm-1; the extrapolated wavenumber for v=0,N=l is 0.046842.


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

Bishop, Shih, et al., 1975
Bishop, D.M.; Shih, S.-K.; Beckel, C.L.; Wu, F.-M.; Peek, J.M., Theoretical study of H2+ spectroscopic properties. IV. Adiabatic effects for the 2p«pi»u and 3d«sigma»g electronic states, J. Chem. Phys., 1975, 63, 4836. [all data]

Richardson, Jefferts, et al., 1968
Richardson, C.B.; Jefferts, K.B.; Dehmelt, H.G., Alignment of the H2+ molecular ion by selective photodissociation. II. Experiments on the radio-frequency spectrum, Phys. Rev., 1968, 165, 80. [all data]

Jefferts, 1969
Jefferts, K.B., Hyperfine structure in the molecular ion H2+, Phys. Rev. Lett., 1969, 23, 1476. [all data]

Bates, Ledsham, et al., 1953
Bates, D.R.; Ledsham, K.; Stewart, A.L., Wave functions of the hydrogen molecular ion, Philos. Trans. R. Soc. London A, 1953, 246, 215. [all data]

Kroll, 1970
Kroll, M., A prediction of the discrete electronic transition 2p«pi»u-3d«sigma»g of H2+, J. Mol. Spectrosc., 1970, 35, 436. [all data]

Herzberg and Jungen, 1972
Herzberg, G.; Jungen, Ch., Rydberg series and ionization potential of the H2 molecule, J. Mol. Spectrosc., 1972, 41, 425. [all data]

Cunningham and Dieke, 1950
Cunningham; Dieke, Johns Hopkins University, Department of Physics, Rpt. NYO-692, 1950, 1. [all data]

Siegbahn, Nordling, et al., 1967
Siegbahn, K.; Nordling, C.; Fahlman, A.; Nordberg, R.; Hamrin, K.; Hedman, J.; Johansson, G.; Bergmark, T.; Karlsson, S.-E.; Lindgren, I.; Lindberg, B., ESCA. Atomic, molecular and solid state structure studied by means of electron spectroscopy, Nova Acta Regiae Soc. Sci. Ups., 1967, 20, 208-282. [all data]

Asbrink, 1970
Asbrink, L., The photoelectron spectrum of H2, Chem. Phys. Lett., 1970, 7, 549. [all data]

Peek, 1965
Peek, J.M., On the 2«SIGMA»g+ and 2«SIGMA»u+ states of the hydrogen molecule ion, Sandia Laboratory, Albuquerque, NM, 1965, 49. [all data]

Hunter, Yau, et al., 1974
Hunter, G.; Yau, A.W.; Pritchard, H.O., Rotation-vibration level energies of the hydrogen and deuterium molecule-ions, At. Data Nucl. Data Tables, 1974, 14, 11. [all data]

Luke, Hunter, et al., 1969
Luke, S.K.; Hunter, G.; McEachran, R.P.; Cohen, M., Relativistic theory of H2+, J. Chem. Phys., 1969, 50, 1644. [all data]

Gersten, 1969
Gersten, J.I., Evaluation of the lamb shift for the hydrogen molecule-ion, J. Chem. Phys., 1969, 51, 3181. [all data]

Jeziorski and Kolos, 1969
Jeziorski, B.; Kolos, W., On the ionization potential of H2, Chem. Phys. Lett., 1969, 3, 677. [all data]

Bishop, 1974
Bishop, D.M., Non-adiabatic calculations for H2+, HD+ and D2+, Mol. Phys., 1974, 28, 1397. [all data]

Wind, 1965
Wind, H., Vibrational States of the hydrogen molecular ion, J. Chem. Phys., 1965, 43, 2956. [all data]

Hunter and Pritchard, 1967
Hunter, G.; Pritchard, H.O., Born-Oppenheimer separation for three-particle systems. III. Applications, J. Chem. Phys., 1967, 46, 2153. [all data]

Beckel, Hansen, et al., 1970
Beckel, C.L.; Hansen, B.D., III; Peek, J.M., Theoretical study of H2+ ground electronic state spectroscopic properties, J. Chem. Phys., 1970, 53, 3681. [all data]

Halmann and Laulicht, 1965
Halmann, M.; Laulicht, I., Isotope effects on vibrational transition probabilities. III. Ionization of isotopic H2, N2,,O2, NO, CO, and HCl molecules, J. Chem. Phys., 1965, 43, 1503. [all data]

Dunn, 1966
Dunn, G.H., Franck-Condon factors for the ionization of H2 and D2, J. Chem. Phys., 1966, 44, 2592. [all data]

Nicholls, 1968
Nicholls, R.W., Franck-Condon factors for ionizing transitions of O2, CO, NO and H2 and for the NO+(A1-«SIGMA»x1«SIGMA») band system, J. Phys. B:, 1968, 1, 1192. [all data]

Itikawa, 1973
Itikawa, Y., Calculation of the cross sections for the photoionization of H2 and D2 into different vibrational states of the ion, J. Electron Spectrosc. Relat. Phenom., 1973, 2, 125. [all data]

Spohr and Puttkamer, 1967
Spohr, R.; Puttkamer, E.v., Energiemessung von Photoelektronen und Franck-Condon-Faktoren der Schwingungsubergange einiger Molekulionen, Z. Naturforsch., 1967, 22a, 705. [all data]

Berkowitz and Spohr, 1973
Berkowitz, J.; Spohr, R., Comparison of photoelectron intensities and Franck-Condon factors in the photoionization of H2, HD and D2, J. Electron Spectrosc. Relat. Phenom., 1973, 2, 143. [all data]

Schaad and Hicks, 1970
Schaad, L.J.; Hicks, W.V., Equilibrium bond length in H2+, J. Chem. Phys., 1970, 53, 851. [all data]

Samson, 1972
Samson, J.A.R., Observation of double electron excitation in H2 by photoelectron spectroscopy, Chem. Phys. Lett., 1972, 12, 625. [all data]

Peek, 1969
Peek, J.M., Discrete vibrational states due only to long-range forces: 2«SIGMA»u+(2p«sigma»u) state of H2+, J. Chem. Phys., 1969, 50, 4595. [all data]


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