Hydrogen cation

Formula: H₂⁺
Molecular weight: 2.01533
IUPAC Standard InChI: InChI=1S/H2/h1H/q+1
IUPAC Standard InChIKey: ZZIJOQHRUPVPQC-UHFFFAOYSA-N
CAS Registry Number: 12184-90-6
Chemical structure:
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Constants of diatomic molecules

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

Data collected through November, 1976

Symbols used in the table of constants
Symbol	Meaning
State	electronic state and / or symmetry symbol
T_e	minimum electronic energy (cm^-1)
ω_e	vibrational constant – first term (cm^-1)
ω_ex_e	vibrational constant – second term (cm^-1)
ω_ey_e	vibrational constant – third term (cm^-1)
B_e	rotational constant in equilibrium position (cm^-1)
α_e	rotational constant – first term (cm^-1)
γ_e	rotation-vibration interaction constant (cm^-1)
D_e	centrifugal distortion constant (cm^-1)
β_e	rotational constant – first term, centrifugal force (cm^-1)
r_e	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⁺
State	T_e	ω_e	ω_ex_e	ω_ey_e	B_e	α_e	γ_e	D_e	β_e	r_e	Trans.	ν₀₀
Several other excited states, mostly repulsive. 1
C ²Π_u 2pπ	(102696.₇) 2	(266.0₁)	(6.45₄)		(1.899)	(0.075₈)		(0.00039)		(4.19₈)	(C-B)	(8806.3) 2
C ²Π_u 2pπ	↳Bishop, Shih, et al., 1975
B ²Σ_g⁺ 3dσ	(93804.₅) 2	(437.1₅)	(5.24₇)		(1.530)	(0.031₂)		(0.000075)		(4.67₇)	(B-X)	(92877.₄)
B ²Σ_g⁺ 3dσ	↳Bishop, Shih, et al., 1975
A ²Σ_u⁺ 2pσ 3											A ← X
A ²Σ_u⁺ 2pσ 3	↳Richardson, Jefferts, et al., 1968
State	T_e	ω_e	ω_ex_e	ω_ey_e	B_e	α_e	γ_e	D_e	β_e	r_e	Trans.	ν₀₀
X ²Σ_g⁺ 1sσ	0	2321.₇ 4	66.2 4	0.6	30.2₁ 4 5 6	1.68₅ 4	0.6	4		1.052 7 8
X ²Σ_g⁺ 1sσ	↳Jefferts, 1969

Notes

Electronic wavefunctions and energies are given by Bates, Ledsham, et al., 1953 where references to earlier literature may be found.

Data for these two states are entirely theoretical [adiabatic approximation Bishop, Shih, et al., 1975; see also Kroll, 1970]. ν₀₀(C-B) refers to N=1 of C ²Π_u and N=0 of B ²Σ_g⁺; see Table VI of Bishop, Shih, et al., 1975. Beckel (lecture at Columbus l976) gives +8803.9₀.

Repulsive state. 10

From Rydberg series limits of H₂ Herzberg and Jungen, 1972; ΔG(1/2) = 2191.2. Similar constants (and D_e = 0.018) were obtained Cunningham and Dieke, 1950 by extrapolation from low members of the series np³Π (n=2-5). Higher vibrational levels and their B_v values have been derived from photoelectron spectra Siegbahn, Nordling, et al., 1967, Asbrink, 1970. See also 11.

For 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.

Franck-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.

The most recent theoretical value Schaad and Hicks, 1970 is r_e= 1.0569 Å Schaad and Hicks, 1970.

Spin reorientation sp. 11

Experimental 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.

Observed 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 ¹Σ_g⁺ 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.

Observed for N=1 and N=2 of v=4...8. For v=4, N=2 the spin splitting is σs= 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.

References

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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 2pπ_u and 3dσ_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 2pπ_u-3dσ_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 ²Σ_g⁺ and ²Σ_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-Σx¹Σ) 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: ²Σ_u⁺(2pσ_u) state of H₂⁺, J. Chem. Phys., 1969, 50, 4595. [all data]

Notes

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Data from NIST Standard Reference Database 69: NIST Chemistry WebBook
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