Determination of the ionization and dissociation energies of H 2 and He 2
Jinjun Liu, Daniel Sprecher, Frédéric Merkt, Edcel J. Salumbides, and Wim Ubachs
Citation: AIP Conference Proceedings 1504, 495 (2012); doi: 10.1063/1.4771748
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Determination of the Ionization and Dissociation Energies of
H2 and He2
Jinjun Liu 1∗ , Daniel Sprecher∗ , Frédéric Merkt ∗ , Edcel J. Salumbides† and Wim
Ubachs†
∗
†
Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland
Laser Centre, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV
Amsterdam, The Netherlands
Keywords: dissociation energies, field ionization, helium, hydrogen neutral molecules, ionization potential, metastable states, photoelectron
spectra, photoexcitation, photoionization, potential energy functions, Rydberg states
PACS: 31.50.Df 33.15.Mt 33.15.Ry 33.60.+q 33.80.Eh 33.80.Gj 33.80.Rv
INTRODUCTION
Measuring the ionization and dissociation energies of molecules with high precision represents a challenge because
it is much more difficult to determine the onset of a continuum than the transition frequency between two bound
levels. Until recently the ionization and dissociation energies measured most accurately were those of H2 (with
uncertainties of ∼0.01 cm−1 or ∼5×10−8 Eh ). Calculated values of the same quantities have similar uncertainties.
In recent experiments, we have improved the precision with which these quantities can be determined by more than an
order of magnitude and hope to stimulate the interest of theoreticians in these new measurements. Improving current
calculations to reach the accuracy of our measurements (∼2×10−9 Eh ) represents a challenge.
H2
The hydrogen molecule (H2 ) is an important system for testing molecular quantum mechanics. Both the ionization energy (Ei ) and the dissociation energy (D0 ) of H2 are benchmark quantities for ab initio calculations and
have played a fundamental role in the validation of molecular quantum mechanics and quantum chemistry. The
precision of both quantities has been improved by more than an order of magnitude over the past three decades
(Refs. [1, 2] and references therein). The latest experimental values [Ei (H2 )exp =124417.476(12) cm−1 (Ref. [1]) and
D0 (H2 )exp =36118.062(10) cm−1 (Ref. [2])] are compatible with the latest theoretical ones [Ei (H2 )th =124417.491 cm−1
and D0 (H2 )th =36118.069 cm−1 (Ref. [3])].
A new experimental determination of the ionization energy of ortho-H2 has been carried out recently as a sum
1 +
of three energy intervals: the first between the X 1 Σ+
g (v = 0, N = 1) and the EF Σg (v = 0, N = 1) levels of orthoH2 [99109.73139(18) cm−1 (Ref. [4])], the second between the EF 1 Σ+
g (v = 0, N = 1) and the selected 54p11 (0)
+
+
+
Rydberg state [labelled using the notation nlNN (S)] belonging to series converging on the X + 2 Σ+
g (v = 0, N = 1)
+
−1
level of ortho-H2 [25209.99756(29) cm (Ref. [5])], and the third between the 54p11 (0) Rydberg state and the
+
+
−1 (Ref. [6])] . Combining the sum of
center of gravity of the X + 2 Σ+
g (v = 0, N = 1) ionic level [37.50902(2) cm
these three intervals with previous experimental and theoretical results for other energy level intervals, the ionization
and dissociation energies of the para-H2 could be determined with a precision of ∼10 MHz.
1
Email: liu@xuv.phys.chem.ethz.ch
International Conference of Computational Methods in Sciences and Engineering 2009
AIP Conf. Proc. 1504, 495-498 (2012); doi: 10.1063/1.4771748
© 2012 American Institute of Physics 978-0-7354-1122-7/$30.00
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He2
The rare gas dimers in their electronic ground state form weakly bound van der Waals complexes, whereas their
excited states (and the cations) are strongly bound and often called excimers (“excited dimers”). In the case of the
helium dimer (He2 ), these excited states can be considered as Rydberg states and, hence, He2 can be described as
a Rydberg molecule — for many years it was the only known molecule fulfilling this definition [7]. With only four
+
(three) electrons, He2 (He+
2 ) represents, with H2 and H2 , one of the few molecular systems for which highly accurate
ab initio quantum chemical calculations are possible. Carrington et al. [8] determined the potential energy functions
+ 2 Σ+ states of He+ , from which the rovibrational energy levels of both states and the complete
of the X + 2 Σ+
u and A
g
2
+ 2 Σ+ electronic spectrum was predicted. The energy difference between the v+ = 0 and v+ = 1 levels of
A+ 2 Σ+
g −X
u
the ground state of 3 HeHe+ was determined accurately by IR spectroscopy. [9, 10]
3 +
The energy level structure of He+
2 and the photoionization dynamics of He2 (a Σu ) were previously studied in
our lab by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron and photoionization spectroscopy
[11]. In the present work, we focus on a precise determination of the ionization energy of the He2 a 3 Σ+
u state and
+
+
the lowest rotational energy levels of the X + 2 Σ+
u (v = 0) ground state of the He2 ion as a test for theoretical
calculations. Transitions from the metastable a 3 Σ+
u state of He2 , prepared in a discharge at the exit of a pulsed valve,
to high-np Rydberg states were recorded following single photon excitation and delayed pulsed field ionization using
the technique of Rydberg-state-resolved threshold-ionization (RSR-TI) spectroscopy [12]. The extrapolation of the
observed Rydberg series to their limits enabled the determination of the ionization energy of the a 3 Σ+
u state with a
precision of better than 20 MHz. The structure of the lowest rotational energy levels of the X + 2 Σ+
u ground state of
the He+
2 ion could also be determined by combining the present results with those of previous near-infrared emission
spectroscopy of He2 [13].
EXPERIMENTAL PROCEDURE
The experiments were carried out on samples of ground state H2 and metastable He2 molecules in pulsed supersonic
jet expansions. The molecules were excited to high-np Rydberg states which were field ionized and the ions or
electrons were extracted by applying a pulsed voltage and detected by a microchannel plate (MCP) detector. In the
+
H2 experiment, the H+
2 signal was detected, whereas both He2 ion and electron signals were detected in the He2
experiment.
H2
H2 was studied using a (2+1 ) two-step three-photon excitation sequence. In the first excitation step, H2 was excited
1 +
from the X 1 Σ+
g (v = 0, N = 1) level to the EF Σg (v = 0, N = 1) level in a nonresonant two-photon process using a
low-resolution UV laser (wavelength 202 nm, bandwidth ∼0.4 cm−1 ). In the second step, H2 was excited from the
+ 2 Σ+ (v+ = 0, N + = 1) ionic state
EF 1 Σ+
g (v = 0, N = 1) level to the 54p11 (0) Rydberg states located below the X
g
using a high-resolution UV laser (wavelength 397 nm, bandwidth ∼20 MHz). The UV radiation for the second step
was the second harmonic of the output of a pulsed titanium-doped sapphire (Ti:Sa) amplifier seeded by a cw Ti:Sa
ring laser [14, 15]. To measure the Doppler shift resulting from a possible nonorthogonality between the molecular
hydrogen beam and the 397 nm laser beam, the 397 nm laser beam was split into two components by a 50% beam
splitter and introduced into the interaction region in a counterpropagating configuration. The difference between the
transition wave numbers measured using each of these two components represents twice the Doppler shift, which can
be eliminated by taking the average value of the two measurements.
The wave number of the first transition has been determined to be 99109.73139(18) cm−1 in a two-photon Dopplerfree resonance-enhanced multiphoton ionization (REMPI) experiment carried out in Amsterdam [4]. The third interval,
+ 2 Σ+ (v+ = 0, N + = 1) ionization limit, had been determined to be
from the 54p11 (0) Rydberg state to the H+
g
2 X
−1
37.50902(2) cm in a prior measurement by millimeter wave spectroscopy carried out in Zürich [6]. To measure
the wave number of the second transition, the cw Ti:Sa ring laser was calibrated using the transmission signal of
a high-finesse Fabry-Pérot (FP) étalon and the Doppler-free saturation absorption spectrum of I2 in an experiment
carried out in Zürich [5]. The frequencies of the hyperfine components of the I2 transitions were determined with an
accuracy of better than 100 kHz by comparing with positions measured using a frequency comb [4]. Corrections and
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errors including residual Doppler shifts, frequency chirps and shifts in the pulsed Ti:Sa amplifier and the frequency
doubling, ac Stark shifts, dc Stark shifts, and pressure shifts were either measured or estimated to correct the second
transition frequency.
He2
A supersonic beam of metastable He∗2 a 3 Σ+
u molecules was generated using a pulsed discharge at the exit of a
pulsed valve prior to the gas expansion into vacuum [11]. Overview scans of photoionization spectra to high-np
Rydberg states using a low-resolution UV laser (wavelength 290 nm, bandwidth ∼0.3 cm−1 ) were recorded first [11].
In the high-resolution RSR-TI experiment that followed, the third harmonic of the same Ti:Sa amplifier as used in the
H2 experiment was employed to excite He2 to high-np Rydberg states. High-resolution RSR-TI spectra of Rydberg
series with n up to 150 and with resolved fine structure of the initial He∗2 a 3 Σ+
u state [13] were recorded. The frequency
was calibrated with the high-finesse FP étalon and the Doppler-broadened absorption spectrum of I2 .
RESULTS AND DISCUSSION
H2
The wave number of the 54p11 (0) ← EF 1 Σ+
g (v = 0, N = 1) transition was determined to be 25209.99756
±(0.00022)statistical ±(0.00007)systematic cm−1 [5]. The experimental precision is limited mainly by the statistical uncertainty in the determination of the centers of the H+
2 lines and the systematic uncertainty in the frequency shift arising
in the Ti:Sa amplifier. By adding the statistical and systematic errors, the result can be given as 25209.99756(29) cm−1 .
1 +
This result, when combined with the other two transition frequencies [EF 1 Σ+
g (v = 0, N = 1) ← X Σg (v = 0, N = 1)
+
+
and X + 2 Σ+
g (v = 0, N = 1) ← 54p11 (0)], enables us to derive a more precise value of the ionization energy of
ortho-H2 . The ionization energy Ei (H2 ) of para-H2 can also be derived from this new measurement by including
previous results on the rotational energy level intervals for the lowest vibronic states of the neutral molecule and the
cation [16, 17]. The ionization energies of ortho-H2 and para-H2 have been determined to be 124357.23797(36) cm−1
and 124417.49113(37) cm−1 , respectively [5]. The dissociation energy of H2 was derived from the relations:
D0 (H2 ) = E i (H2 ) + D0 (H+
2 ) − E i (H)
+
= E i (H2 ) + E i (H2 ) − 2E i (H)
(1)
(2)
−1
using the calculated values for Ei (H)[109678.7717426(10) cm−1 (Ref. [18])] and Ei (H+
2 )[131058.121975(49) cm
(Ref. [17])] based on the newest values of fundamental physical constants, and the experimental value of Ei (H2 )
determined in the present work. The dissociation energy of H2 was determined to be 36118.06962(37) cm−1 [5], the
final uncertainty being entirely limited by the experimental uncertainty of Ei (H2 ).
He2
The photoionization spectra of He2 (a 3 Σ+
u ) reveal a dense structure of very sharp features that can be attributed to
+
transitions to Rydberg states converging on the first (N + = 1 − 7) rotational levels of the X + 2 Σ+
u (v = 0) ground state
+
of He2 . Many of these Rydberg states associated with rotationally excited levels of the ion core (rotational quantum
number N + ) are embedded in the continua of the N + − 2 and N + − 4 ionization channels. The rotational autoionization
dynamics is complex and is strongly influenced by the application of weak electric fields. Several series are immune
to ionization and the corresponding states are metastable. The energy level structure and the rotational autoionization
dynamics can be analyzed by multichannel quantum defect theory (MQDT).
The assignment of the Rydberg states observed in the high-resolution RSR-TI experiment is based on the photoionization spectra and the MQDT calculations. The extrapolation of the observed Rydberg series in the Q(1)-type
+ + 2 +
+
+
transition (from v = 0, N = 1 level of the He2 a 3 Σ+
Σu state)
u state to the v = 0, N = 1 threshold of the He2 X
using the Rydberg formula:
RHe2
ν̃ (n) = Ei −
(3)
(n − δl )2
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where δl is the quantum defect, enabled the determination of the ionization energy of the a 3 Σ+
u state to the value:
34301.21009 ±(0.00062)statistical ±(0.006)systematic cm−1 . The wave numbers of Q(3)- and Q(5)-type transitions have
also been determined. Because the rotational structure of the He2 a 3 Σ+
u (v = 0) state had been derived previously from
the near-infrared emission spectrum of He2 [13], the structure of the lowest rotational energy levels (N + = 1, 3, 5) of
+ 2 Σ+ (v+ = 0) state could be determined to a precision of ∼ 200 MHz.
the He+
u
2 X
CONCLUSIONS AND OUTLOOK
Compared to previous experimental values of the ionization and dissociation energies of H2 , the present values (124417.49113(37) cm−1 and 36118.06962(37) cm−1 , respectively) are more precise by a factor of ∼30.
They are consistent with, but more precise than, the result of the latest ab initio calculations of Wolniewicz [3]
[Ei (H2 )th =124417.491 cm−1 and D0 (H2 )th = 36118.069 cm−1 ]. Our new result thus represents a test for future calculation of Ei (H2 ) and D0 (H2 ).
Most recently, Pachucki and coworkers recalculated the dissociation energy of H2 and D2 with improved precision
by including complete α 2 and α 3 as well as the major (one-loop) α 4 terms of the relativistic and QED corrections
[19]. The dissociation energy of H2 was calculated as 36118.0693(10) cm−1 , which is in excellent agreement with
our result. It would be important to see whether these calculations can be further extended to reach the experimental
accuracy. Experiments to determine the ionization energies of D2 as well as HD with the same accuracy as in H2 are
in progress.
+ 2 Σ+ (v+ = 0) state can be derived from the ab initio
For the helium dimer, the rotational structure of the He+
u
2 X
calculations of Carrington et al. [8]. The agreement between the calculated result and the experimental result based
on our RSR-TI spectra and the near-infrared spectra [13] is better than 0.04 cm−1 . Accurate ab initio values of the
ionization energy of He2 (a 3 Σ+
u ) are needed for comparison with our result.
ACKNOWLEDGMENTS
This work was financially supported by the European Research Council (ERC grant Nr. 228286), the Swiss National
Science Foundation under project No. 200020-116245, the Netherlands Foundation for Fundamental Research of
Matter (FOM) and Laserlab-Europe (RII3-CT-2003-506350).
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
A. de Lange, E. Reinhold, and W. Ubachs, Phys. Rev. A 65, 064501 (2002).
Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, 203003 (2004).
L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).
S. Hannemann, E. J. Salumbides, S. Witte, R. T. Zinkstok, E.-J. van Duijn, K. S. E. Eikema, and W. Ubachs, Phys. Rev. A 74,
062514 (2006).
J. Liu, E. J. Salumbides, U. Hollenstein, J. C. J. Koelemeij, K. S. E. Eikema, W. Ubachs, and F. Merkt, J. Chem. Phys. 130,
174306 (2009).
A. Osterwalder, A. Wüest, F. Merkt, and Ch. Jungen, J. Chem. Phys. 121, 11810 (2004).
G. Herzberg, Ann. Rev. Phys. Chem. 38, 27 (1987).
A. Carrington, C. H. Pyne, and P. J. Knowles, J. Chem. Phys. 102, 5979 (1995).
N. Yu, and W. H. Wing, Phys. Rev. Lett. 59, 2055 (1987), see erratum in Phys. Rev. Lett. 60, 2445 (1988).
N. Yu, W. H. Wing, and L. Adamowicz, Phys. Rev. Lett. 62, 253 (1989).
M. Raunhardt, M. Schäfer, N. Vanhaecke, and F. Merkt, J. Chem. Phys. 128, 164310 (2008).
R. Seiler, U. Hollenstein, G. M. Greetham, and F. Merkt, Chem. Phys. Lett. 346, 201 (2001).
C. Focsa, P. F. Bernath, and R. Colin, J. Mol. Spectrosc. 191, 209 (1998).
R. Seiler, Th. Paul, M. Andrist, and F. Merkt, Rev. Sci. Instr. 76, 103103 (2005).
Th. A. Paul, and F. Merkt, J. Phys. B: At. Mol. Opt. Phys. 38, 4145 (2005).
D. E. Jennings, S. L. Bragg, and J. W. Brault, Astrophys. J. 282, L85 (1984).
V. I. Korobov, Phys. Rev. A 73, 024502 (2006); V. I. Korobov, ibid. 74, 052506 (2006); V. I. Korobov, ibid. 77, 022509 (2008).
F. Biraben, Eur. Phys. J. Special Topics 172, 109 (2009).
K. Piszczatowski, G. Łach, B. Jeziorski, M. Przybytek, J. Komasa, and K. Pachucki (private communication).
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