JOURNAL OF CHEMICAL PHYSICS
VOLUME 120, NUMBER 2
8 JANUARY 2004
Superexcited state reconstruction of HCl using photoelectron
and photoion imaging
Constantin Romanescu, Sergei Manzhos, Dmitrii Boldovsky, Jennifer Clarke,
and Hans-Peter Loocka)
Department of Chemistry, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
共Received 9 July 2003; accepted 10 October 2003兲
The velocity-map imaging technique was used to record photoelectron and photofragment ion
images of HCl following two-photon excitation of the E ⌺ ⫹ (0 ⫹ ), V 1 ⌺ ⫹ (0 ⫹ ) 共␯⫽9,10,11兲 states
and subsequent ionization. The images allowed us to determine the branching ratios between
autoionization and dissociation channels for the different intermediate states. These branching ratios
can be explained on the basis of intermediate state electron configurations, since the configuration
largely prohibits direct ionization in a one-electron process, and competition between autoionization
and dissociation into H* (n⫽2)⫹Cl and H⫹Cl*共4s,4p,3d兲 is observed. From a fit to the
vibrationally resolved photoelectron spectrum of HCl⫹ it is apparent that a single superexcited state
acts as a gateway to autoionization and dissociation into H⫹Cl* (4s). Potential reconstruction of
the superexcited state to autoionization was undertaken and from a comparison of different
autoionization models it appears most likely that the gateway state is a purely repulsive and low-n
Rydberg state with a ( 4 ⌸) ion core. © 2004 American Institute of Physics.
关DOI: 10.1063/1.1630571兴
pair state arises from the 关¯兴 (5 ␴ ) 1 (2 ␲ ) 4 (6 ␴ * ) 1 configuration and it has its minimum at a much longer internuclear
distance.’’ Due to the noncrossing rule it forms an avoided
crossing with the E 1 ⌺ ⫹ (0 ⫹ ) state, thus producing a new set
of adiabatic states, the lower one of which is the B 1 ⌺ ⫹ (0 ⫹ )
state with a double minimum and a small barrier around 1.7
Å and about 83 780 cm⫺1.1 This is very close to the lowest
vibrational level of the inner well at 83 780 cm⫺1 and just
above the tenth vibrational level of the ion pair state. The
spectroscopy and mutual perturbations that arise from this
interaction have been described in theoretical and
experimental2,3 papers. Here, we focus on the ionization dynamics of the vibrational ground state of the E 1 ⌺ ⫹ (0 ⫹ )
state as well as three vibrational levels 共␯⬘⫽9,10,11兲 of the
V 1 ⌺ ⫹ (0 ⫹ ) ion pair state.
As expected, the electron configuration of the intermediate state has a profound influence on the ionization dynamics. The electron configuration of the X 2 ⌸ 3/2,1/2 state of
HCl⫹ is (5 ␴ ) 2 (2 ␲ ) 3 (6 ␴ * ) 0 , and if the intermediate state
can truly be described by the (5 ␴ ) 2 (2 ␲ ) 3 4 p ␲ configuration,
it is obtained by a one-electron excitation of the 4p ␲ electron into the ionization continuum. If, however, the intermediate electron configuration is different from any of the
simple 关 X 2 ⌸ 3/2,1/2兴 nl␭ configurations, direct ionization to
the ion’s ground state is not possible in a one-electron process.
For example, Spiglanin et al. found that upon absorption
of a third photon the E state dissociates into excited atoms in
accordance with contributions of the V 1 ⌺ ⫹ (0 ⫹ ) valence
character to the double minimum state.4 This is not expected
if its configuration were ( 2 ⌸)4p ␲ . In a photoelectron spectroscopic experiment, de Lange and co-workers have shown
that the main source of photoelectrons arising from excita-
I. INTRODUCTION
Resonance enhanced multiphoton ionization 共REMPI兲
has become an invaluable spectroscopic tool in the investigation of electronically excited states. The ionization step
frequently proceeds by direct ionization into the ground electronic state of the molecular ion and follows the ⌬␯⫽0 propensity rule. However, if the excited state is a Rydberg state
which is part of a series that converges to any other but the
ground state of the molecular ion, ionization into the molecular ion’s ground state can be understood as a two-electron
process and will therefore have to compete with other processes. Conversely, one can use the ionization dynamics to
probe the electron configuration of the excited state. The
ionization dynamics will depend on the nature of superexcited ‘‘gateway’’ states that can mediate autoionization but
may also dissociate into excited fragments. Thus a detailed
analysis of all competing channels can shed light onto both
the electronic structure of the intermediate excited state and
the superexcited state.
In this paper we report such experiments on excited
states of HCl in the 4p␲ Rydberg region and three vibrational levels of the HCl ion pair state. The X 1 ⌺ ⫹ (0 ⫹ )
ground-state configuration of HCl can be described as
(1 ␴ ) 2 (2 ␴ ) 2 (3 ␴ ) 2 (4 ␴ ) 2 (1 ␲ ) 4 (5 ␴ ) 2 (2 ␲ ) 4 (6 ␴ * ) 0 , and the
single-configuration Rydberg states are expressed by a product of the ion core wave function with the wave function of
the Rydberg electron, e.g., 关 ¯ 兴 (5 ␴ ) 2 (2 ␲ ) 3 nl␭. Here, the
quantum numbers n, l, and ␭ have their usual meaning. The
E 1 ⌺ ⫹ (0 ⫹ ) state that is used as an intermediate state in our
study is formally derived from the 关 ¯ 兴 (5 ␴ ) 2 (2 ␲ ) 3 4 p ␲
configuration, i.e., n⫽4, l⫽1, and ␭⫽1. The V 1 ⌺ ⫹ (0 ⫹ ) ion
a兲
Electronic mail: [email protected]
0021-9606/2004/120(2)/767/11/$22.00
767
© 2004 American Institute of Physics
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768
J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
tion of the ␯⫽9 level of the V 1 ⌺ ⫹ (0 ⫹ ) state is the photoionization of the excited hydrogen and chlorine atoms
formed following dissociation of a superexcited state.5 Similarly, Green and Wallace have observed a large contribution
of the photofragmentation channels upon excitation of the E
and V states.2 There exists therefore plenty of evidence that
the direct ionization of those Rydberg states which may mix
with the ion pair state will have to compete with photodissociation into excited state atoms, through a superexcited
‘‘gateway’’ state.5 Based on earlier work by Lefebvre-Brion
and Keller,6 it was suggested that this state is a 1 ⌺ ⫹ (0 ⫹ )
state derived from a (5 ␴ 1 2 ␲ 4 )4s ␴ configuration, i.e., the
lowest member of a Rydberg series converging to the first
excited state of the HCl⫹ ion. We believe that we have evidence against such an assignment and report in this paper on
photoelectron spectra that not only let us assign the superexcited state to a purely repulsive state but also provide us with
an analytical expression for such potential.
The paper is organized as follows: The following section
describes the photofragment imaging apparatus and the procedure by which the resulting images are analyzed. Section
III describes the information obtained from the photofragment images. In the discussion of the images 共Sec. IV兲 we
focus on the oscillation of photoelectron intensities as a function of final vibrational state of the HCl⫹ ion. The photoelectron intensities are then used to obtain an analytical form of
the autionizing superexcited state potential.
II. EXPERIMENT AND ANALYSIS
In our experiments a 2⫹1 REMPI scheme was used to
select several states about 2.5 eV below the adiabatic ionization limit of HCl 共see Fig. 1兲. Time-of-flight mass spectrometry 共TOF-MS兲 was used, in conjunction with charged particle imaging, to analyze transitions stemming from the
resonant intermediate state.
Images and spectra were recorded by detection of the
H 35Cl⫹ , 35Cl⫹ , H⫹ photoions and of the photoelectrons.
They were used to determine the extent of photodissociation
as opposed to ionization into the ground state of the molecular ion. The proposed channels of ionization are shown in
Scheme 1.
In the velocity map imaging technique all photoions and
photoelectrons with the same initial velocity vector after
dissociation/ionization are mapped onto the same position on
the detector.7 Using energy and momentum conservation,
one can derive from these positions the quantum states of the
correlated recoil partner. The advantage of using photoelectron imaging to extract photoelectron kinetic energies form
the direct and indirect ionization processes is primarily in the
quantitative information that one can obtain about the
branching ratios of the competing channels.8 Since all electrons or photoions produced via a particular process are collected, there is no bias against channels with low electron
kinetic energy release or sensitivity towards anisotropic photoelectron angular distributions.
The TOF-MS apparatus 共Fig. 2兲 is based on the design
by Parker and Eppink.7 It consists of two stainless steel
vacuum chambers, the first one 共pumped to 10⫺7 Torr) housing a home-built molecular-beam valve with 500-␮m skim-
Romanescu et al.
FIG. 1. Potential-energy curves of the relevant electronic states of HCl
共solid lines兲 and HCl⫹ 共dashed lines兲. The potential curves of neutral HCl as
well as the X 2 ⌸ and A 2 ⌺ state of HCl⫹ were obtained using spectroscopic
data 共see text兲, whereas the repulsive curves of HCl⫹ were obtained from ab
initio calculations 共Ref. 28兲. Superexcited states 共short dashed curves兲 are
derived from a simple translation of the ionic states by the electron binding
energy.
mer, and the second one 共pumped to 10⫺8 Torr) housing the
TOF-MS electrodes, and a 75-mm chevron microchannel
plate 共MCP兲 imaging detector. The three 100-mm electrodes
共with 12-mm and 2⫻25-mm2 clear holes兲 and the 470-mm
drift zone of the TOF-MS were shielded from external fields
using a ␮-metal cylinder. For the observation of photofrag-
Scheme 1. Schematic energy-level diagram for photoionization and dissociation dynamics of HCl. The photons represented by the solid vertical
arrows have identical but tunable energy.
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J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
Superexcited state of HCl
769
FIG. 2. Sketch of the experimental setup. A pulsed tunable laser beam
intercepted a molecular beam traveling along the axis of a home-built timeof-flight mass spectrometer. A position sensitive microchannel plate detector
was coupled to a phosphorus screen, from which the photofragment image
was read with a CCD camera. Using a home-built Butterworth filter the
arrival times of the charged particles could be recorded simultaneously from
the current to the detectors rear plate.
ment ion images of the slow 35Cl⫹ fragments the drift tube
was extended to 810 mm. The ion and photoelectron images
were recorded by a 12-bit charge-coupled device 共CCD兲
camera 共1024⫻1024 pixels兲.
A Lambda Physik Excimer laser operating at 308 nm
pumped a Lambda Physik Scanmate dye laser using Coumarin 480. After frequency doubling in a BBO crystal 共250
␮J/pulse focused with a 30-cm lens, bandwidth less than 0.4
cm⫺1兲, the resulting wavelength was set to the REMPI lines
of the respective state. Since no ions were produced due to
resonant ionization of photofragments, scanning over the
Doppler resonance of photofragments was found to be unnecessary and the excitation wavelength was therefore kept
fixed to the maximum of the respective REMPI line. A pulse
width of 10–15 ns at a repetition rate of either 10 or 30 Hz
was obtained. The laser wavelength was calibrated with respect to the previously reported spectra of HCl.2 The energy
resolution of the excitation spectra 共Fig. 3兲 was given by the
laser bandwidth and was typically better than 1.0 cm⫺1 at the
two-photon level.
Spectra were recorded by measuring the total MCP current as a function of laser frequency. To this end, a homebuilt fast voltage divider based on a second-order Butterworth filter was inserted between the power supply and the
MCP. This device permitted the simultaneous recording of
TOF mass spectra and charged particle images.
A molecular beam of HCl was generated by expansion
of 10%–20 % HCl 共Matheson, 99.9%兲 in helium at a backing
pressure of 750 Torr through a pulsed valve and a skimmer
20 mm downstream of the valve. The molecular beam was
aligned along the time-of-flight axis and pointed at the center
of a position sensitive charged particle detector. The vertically polarized laser beam was perpendicular to the TOF axis
and crossed the molecular beam 70 mm downstream of the
valve in the region between the repeller and extractor electrodes. The potentials placed on the electrodes were typically
about 2000 and 1200 V for electrons, 1000/600 V for protons, and 500/300 V for Cl⫹ ions.
When recording images of photofragment ions the time
FIG. 3. Spectra of the E 1 ⌺ (0 ⫹ ) intermediate state obtained by gating the
detector either on the 共a兲 photoelectron signal or on the positive ion signals:
共b兲 H 35Cl⫹ , 共c兲 35Cl⫹ , and 共d兲 H⫹ . The spectra have been scaled to reflect
the branching ratios between the respective channels. Because of changed
expansion conditions the rotational temperature was higher when recording
the photoelectron spectrum. Spectra of the V 1 ⌺(0 ⫹ ) 共␯⬘⫽9,10,11兲 show
similar branching ratios 共see Table I兲.
resolution of about 100 ns is limited by our ability to pulse
the front MCP plate. For ungated operation the mass resolution of the TOF-MS is typically 1/100. The mass resolution
is high enough to resolve the isotopomers of HCl and to gate
on masses corresponding to H⫹ , 35Cl⫹ , H 35Cl⫹ , 37Cl⫹ , or
H 37Cl⫹ .
The raw images were averaged, first on the CCD chip
共typically 256 images in 12-bit resolution兲 and then on the
PC 共⬃8000 images, 16 bit兲. A background image, which was
recorded ‘‘off resonance,’’ was subtracted, and a threedimensional distribution of the ion cloud was reconstructed
from the averaged images using the onion-peeling
algorithm.9,10
Our onion-peeling program 共‘‘glass onion’’兲 is based on
the algorithm published by Helm9 but also allows for small
corrections in case the images are not exactly concentric,
thereby enhancing significantly the velocity resolution.
From the inverted images velocity profiles and spatial
anisotropy parameters were obtained. Within our experimental resolution there exists a linear relationship between the
diameter of each ring and the velocity of the fragments.
Branching ratios were obtained by dividing the area of these
Gaussian functions by the total fitted area.
The values for the spatial anisotropy parameters,11 especially for photoelectrons, are not straightforward to understand in a resonance enhanced 2⫹1 photon excitation process, when the excited atomic fragment is also possibly
aligned. We are in the process of applying the theoretical
framework to these processes and intend to focus on the
angular distributions in a future publication.
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770
J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
Romanescu et al.
FIG. 4. Photoelectron image from 共2⫹1兲 REMPI of the E 1 ⌺ ⫹ (0 ⫹ ) state
via the 关␯⫽0, Q(1)] line. The left half of the image represent the raw image,
while the right half shows the inverted image obtained using the onionpeeling algorithm and the velocity profile with the charged particle intensity
integrated over a 360° angle. The laser polarization is set vertical.
III. RESULTS
Photoelectron and photoion spectra of molecular-beamcooled HCl were recorded in the range of 82 750– 84 250
cm⫺1, thus probing the E 1 ⌺ ⫹ state 共␯⬘⫽0兲, g 3 ⌺ ⫺ state
共␯⬘⫽0兲, and F 1 ⌬(2) state of HCl as well as the V 1 ⌺ ⫹ state
共␯⬘⫽9,10,11兲. The spectroscopy and ionization dynamics of
the g and F state confirmed previous reports and contained
no surprises.5,12–15 Spectra and images of those states were
therefore only used to aid laser wavelength calibration and to
assign the fragmentation channels in the images. The E 1 ⌺ ⫹
state yields HCl⫹ parent ions as well as dissociation products
共Fig. 3兲. Formation of Cl⫺ through the ion pair dissociation
channel H⫹ ⫹Cl⫺ is only significant for vibrational states
␯⫽11,12,13 of the V 1 ⌺ ⫹ state. When exciting via the E 1 ⌺ ⫹
state the ion pair dissociation contributes less than 3% to the
entire H⫹ image 关Fig. 5共a兲兴. Ions from the dissociation of
HCl clusters were not found in this wavelength range.
Photoelectron images and images of H⫹ and 35Cl⫹ ions
were recorded at numerous fixed excitation wavelengths corresponding to excitation of H 35Cl to the E state via the
Q(0 – 3) lines, V 1 ⌺ ⫹ state ( ␯ ⬘ ⫽9) Q(1), V 1 ⌺ ⫹ state ( ␯ ⬘
⫽10) Q(1), V 1 ⌺ ⫹ state 共␯⬘⫽11兲 Q共1兲. In Figs. 4 and 5, we
display the velocity map images of the photoelectrons and of
the H⫹ and 35Cl⫹ ions obtained from excitation of the E 1 ⌺ ⫹
state via the Q(1) transition.
To demonstrate the kinetic energy resolution of the velocity map imaging apparatus, the expected and calculated
energies for the photoelectron image are listed in Table I.
Velocity profiles for Q(1) transitions are shown in Fig. 6 and
Table I lists branching ratios associated with each of these
channels.
For all intermediate states probed a number of competing dissociation and ionization channels were seen. The sce-
FIG. 5. 共a兲 H⫹ and 共b兲 Cl⫹ images from 共2⫹1兲 REMPI of the E 1 ⌺ ⫹ (0 ⫹ )
state via the 关 ␯ ⫽0,Q(1) 兴 line. The laser polarization is set vertical.
narios are summarized in Scheme 1. After excitation from
the intermediate state we will have to consider direct ionization or excitation of a superexcited state. This superexcited
state can autoionize into a large number of vibrational levels
of HCl⫹ in both spin-orbit states. The superexcited state may
also dissociate to give excited H* or Cl* atoms. Curve crossings will then have to be considered. Finally, in the proton
images it is seen that vibrationally excited HCl⫹ dissociates
on the four photon level to give H⫹ ⫹Cl ( 2 P) as indicated by
the six largest diameter rings 关Fig. 5共a兲兴. Dissociation to
form H⫹Cl⫹ ( 3 P) is also possible, but since the Cl image is
dominated by the much more intense signal arising from the
ionization of excited Cl* atoms, we were not able to confirm
that process.
Previously reported ionization potentials and atomic
spectra of H atoms16 and Cl atoms17 and the reported spectroscopic constants of the 2 ⌸ 3/2,1/2 states of HCl⫹ 共Ref. 18兲
were used to assign the photofragment images.
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J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
Superexcited state of HCl
771
TABLE I. Photoelectron kinetic energies 共KE兲 共in cm⫺1兲 and branching ratios 共BR兲 of all channels obtained
from the photoelectron image in Fig. 4. The Cl* (4p) states are overlapped in our photoelectron spectrum and
their assignment is therefore taken from Ref. 5. The error associated with the rings corresponds to typically a
subpixel uncertainty in the fit to the ring radius. Details on the inversion routine may be obtained from Ref. 10.
The branching ratios are given as a percentage of all lines in the photoelectron velocity profile that could be
fitted to, i.e., overlapped lines were assumed to have no contribution.
E 1 ⌺(0 ⫹ )
Autoionization channels
Expected
KE
HCl⫹ ( ␯ ⫽11,2 ⌸ 3/2)⫹e ⫺
HCl⫹ ( ␯ ⫽10,2 ⌸ 1/2)⫹e ⫺
990
HCl⫹ ( ␯ ⫽10,2 ⌸ 3/2)⫹e ⫺
1 638
HCl⫹ ( ␯ ⫽9,2 ⌸ 1/2)⫹e ⫺
2 680
HCl⫹ ( ␯ ⫽9,2 ⌸ 3/2)⫹e ⫺
3 328
HCl⫹ ( ␯ ⫽8,2 ⌸ 1/2)⫹e ⫺
4 463
5 111
HCl⫹ ( ␯ ⫽8,2 ⌸ 3/2)⫹e ⫺
HCl⫹ ( ␯ ⫽7,2 ⌸ 1/2)⫹e ⫺
6 339
HCl⫹ ( ␯ ⫽7,2 ⌸ 3/2)⫹e ⫺
6 987
HCl⫹ ( ␯ ⫽6,2 ⌸ 1/2)⫹e ⫺
8 310
HCl⫹ ( ␯ ⫽6,2 ⌸ 3/2)⫹e ⫺
8 958
HCl⫹ ( ␯ ⫽5,2 ⌸ 1/2)⫹e ⫺
10 378
HCl⫹ ( ␯ ⫽5,2 ⌸ 3/2)⫹e ⫺
11 026
HCl⫹ ( ␯ ⫽4,2 ⌸ 1/2)⫹e ⫺
12 543
HCl⫹ ( ␯ ⫽4,2 ⌸ 3/2)⫹e ⫺
13 191
HCl⫹ ( ␯ ⫽3,2 ⌸ 1/2)⫹e ⫺
14 807
HCl⫹ ( ␯ ⫽3,2 ⌸ 3/2)⫹e ⫺
15 455
HCl⫹ ( ␯ ⫽2,2 ⌸ 1/2)⫹e ⫺
17 172
HCl⫹ ( ␯ ⫽2,2 ⌸ 3/2)⫹e ⫺
17 820
HCl⫹ ( ␯ ⫽1,2 ⌸ 1/2)⫹e ⫺
19 638
HCl⫹ ( ␯ ⫽1,2 ⌸ 3/2)⫹e ⫺
20 286
HCl⫹ ( ␯ ⫽0,2 ⌸ 1/2)⫹e ⫺
22 207
HCl⫹ ( ␯ ⫽0,2 ⌸ 3/2)⫹e ⫺
22 855
HCl** →H⫹Cl* (4s) 2 P
11 121
→H⫹Cl⫹ ( 3 P 2 )⫹e ⫺
HCl** →H⫹Cl* (4p) 2 D 2 P 2 S ⬃22 000
→H⫹Cl⫹ ( 3 P 2,1,0 )⫹e ⫺
**
HCl →H⫹Cl* (3d) 4 D
24 874
→H⫹Cl⫹ ( 3 P 2,1,0 )⫹e ⫺
HCl** →H⫹Cl* (3d) 4 F
→H⫹Cli⫹ ( 3 P 2,1,0 )⫹e ⫺
HCl**→H*⫹Cl
14 484
→H⫹ ⫹Cl⫹e ⫺
Observed
KE
978
1 619
2 669
3 395
4 461
5 146
6 301
7 031
8 251
9 030
10 299
12 459
13 173
15 531
16 925
17 727
19 438
20 435
23 115
11 294
V 1 ⌺(0 ⫹ )
Energy error
BR
␯⬘⫽0
Not accessible
12
1.53
19
1.49
11
0.49
⫺67
0.48
2
2.16
⫺35
2.53
38
1.39
⫺44
1.85
59
1.54
⫺72
2.15
79
2.29
Overlapped
84
2.17
18
2.76
Overlapped
⫺76
6.38
247
1.81
93
3.49
200
2.48
⫺149
6.36
Overlapped
⫺260
ol
⫺173
13.55
BR
␯⬘⫽9
BR
␯⬘⫽10
BR
␯⬘⫽11
1.50
0.93
0.74
0.66
0.76
2.04
2.14
1.69
2.88
3.18
5.45
ol
6.07
3.65
ol
2.12
2.19
1.90
3.51
4.96
9.16
20.20
3.32
5.94
6.23
6.48
4.49
3.93
4.38
2.90
3.31
3.67
3.01
2.48
1.91
3.65
ol
ol
0.85
1.43
ol
6.30
ol
ol
20.38
3.89
2.19
2.37
1.76
1.96
2.53
2.85
1.22
1.35
1.16
1.16
ol
ol
2.98
2.47
ol
2.09
1.54
2.96
1.72
4.96
ol
ol
11.17
22 067
⬃⫺70
24.43
5.32
3.40
23.54
24 897
⫺23
2.98
5.26
weak
3.16
Not accessible
14 527
From the photoelectron images one can identify the vibrational progression of HCl⫹ through determination of the
photoelectron kinetic energies. This progression was assigned using the reported constants for the ionization potential 共IP兲 共HCl兲⫽102 802.8共2.0兲 cm⫺1,19 the spin–orbit constant 共648 cm⫺1兲,20 as well as ␻ e ⫽2673.69 cm⫺1 and ␻ e␹ e
⫽52.537 cm⫺1 . 21 We found excellent agreement of the observed photoelectron energies with the energies expected
from ionization of excited H and Cl atoms in their respective
ⴰ
) states as
H* (n⫽2) and Cl* (4s 2 P 3/2) and Cl* (4 p 2 S 1/2
well as for the low members of the vibrational progression.
For vibrational states with ␯ ⫹ ⬎5, we observe a deviation
form the expected values due to higher-order anharmonicity
terms. Keeping the values for ␻ e ⫽2673.69 cm⫺1 and ␻ e ␹ e
⫽52.537 cm⫺1 fixed in a fit to the progression associated
with the 2 ⌸ 3/2 state of HCl⫹ , we obtained ␻ ey e⫽0.35
⫾0.1 cm⫺1 in agreement with the value of 0.42共2兲 obtained
in Ref. 18. The dissociation energy of HCl⫹ was given by
Michel et al. as D0 (HCl⫹ )⫽37 536.7⫾0.5 cm⫺1 , 22 in excel-
⫺43
11.23
15.69
13.71
11.93
9.73
FIG. 6. Photoelectron intensity distributions for the transitions via the Q(1)
lines of four of the intermediate states under study. The empty triangles
represent the expected photoelectron energy associated with autoionization,
whereas the solid symbols refer to expected energies of electrons arising
from ionization of excited hydrogen 共triangles兲 or chlorine atoms 共circles兲.
The intensity distributions are not scaled with respect to each other.
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772
Romanescu et al.
J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
lent agreement with an earlier value derived using a Born
cycle argument:
⫹
D 0 共 HCl 兲 ⫽D 0 共 HCl兲 ⫹IP共Cl兲-IP共HCl)
⫽37 536.4 共 2.8兲 cm⫺1 ,
where D 0 (HCl)⫽35 748.2 (0.8) cm⫺1 , 23 IP共Cl兲⫽104 591
cm⫺1,17 and IP共HCl兲⫽102 802.8 共2.0兲 cm⫺1.19
Protons may be formed when superexcited HCl dissociates into H* (n⫽2) and Cl( 2 P) atoms, and the excited hydrogen atoms ionize through absorption of a fourth photon,
as is evident from the two strong innermost rings in Fig. 5共a兲.
There exist not one but two rings, because the departing
electron transfers momentum to the proton, thus adding a
velocity component to the protons due to recoil.24 The rings
are split along the vertical direction since this is the main
component of the electrons velocity ( ␤ 2 ⬃0.8, see Fig. 4兲.
As expected from the energy balance, no protons from
ionization of states with n⬎2 were observed, but several
other rings appear on the H⫹ image and can be attributed to
dissociation of HCl⫹ into H⫹ ⫹Cl( 2 P). Two possibilities exist which account for the apparent splitting of the large rings.
Either both 2 ⌸ ⍀ spin–orbit states of HCl dissociate to form
H⫹ ⫹ 2 PJ , where J is only one of the 1/2 or 3/2 states, or
only one of the ⍀⫽1/2 or 3/2 spin–orbit states dissociates to
form both atomic J states. Unfortunately, since the spin–
orbit constants of HCl⫹ (A SO⫽648 cm⫺1 ) and Cl 2 P (A SO
⫽881 cm⫺1 ) are similar, these two scenarios cannot be distinguished in our experiment.
Energetically, the formation of excited chlorine atoms in
their ( 3 P)4s, ( 1 D)4s and some ( 3 P)4 p and ( 3 P)3d states
is also possible. In a photoelectron spectroscopic study, de
Lange and co-workers found contributions from only a small
number of atomic states to the photoelectron signal.5
They
observed
atoms
in
their
( 3 P)4s 2 P 3/2 ,
3
2 ⴰ
3
2 ⴰ
( P)4p D 5/2-3/2 , and ( P)4 p S 1/2 states. An unassigned
feature in their photoelectron spectrum also indicates the formation of the ( 3 P)3d 4 D 7/2-3/2 . Each of the photoelectron
peaks is split according to ionization into different spin–orbit
states of the Cl⫹ ion. Similarly, we find contributions of
these channels also in the photoelectron images presented
here, albeit with worse energy resolution. Since our apparatus cannot resolve the ( 3 P)4 p states, we adopt in Table I the
assignment of de Lange’s group.
The intensities of the photoelectrons and protons following ionization of H* (n⫽2) can be used to scale the intensity
of the proton image to the photoelectron image. Scaling of
the Cl-atom images to the photoelectron images is complicated by the weak and broad Cl⫹ rings obtained from ionization of excited chlorine atoms. Nevertheless, the relative
intensities of the Cl* (4s), Cl* (4 p), and Cl* (3d) channel in
the Cl-atom image scale 19:60:21 whereas they are 33:60:7
in the photoelectron image. Given the very low kinetic energy release in the Cl-photofragment images, we consider
this agreement acceptable.
IV. DISCUSSION
A. Qualitative characterization
of the superexcited state
The B 1 ⌺ ⫹ state arises from the avoided crossing of
the ion pair state V 1 ⌺ ⫹ with the E 1 ⌺ ⫹ state. It has two
minima, the one at shorter internuclear distance possessing
some Rydberg character and the one at longer distance exhibiting valence character.25 At energies around 10.35 eV one
can excite the double-minimum 1 ⌺ ⫹ (0 ⫹ ) either in the
Rydberg E 1 ⌺ ⫹ well or into the valence V 1 ⌺ ⫹ well. Direct
ionization of HCl via excitation of the Rydberg well was
expected to contribute to the ion signal, whereas indirect
ionization, as well as photodissociation and subsequent ionization of the excited atomic photofragments, occurs via the
valence well of the B 1 ⌺ ⫹ state.2,4,5 While we do observe
ionization and dissociation products 共Fig. 4兲, the extent of
direct versus autoionization remains to be quantified.
The photoelectrons arising from the X 2 ⌸ 3/2,1/2⫹e ⫺
←E 1 ⌺ ⫹ transition show a broad vibrational distribution
over all energetically accessible vibrational levels 共Fig. 4兲.
Furthermore, each vibrational line is split about equally into
2
⌸ 3/2 and 2 ⌸ 1/2 spin–orbit states. Rotational structure in the
photoelectron spectrum was not observed, and considering
that the E state is prepared in a single rotational level, we
expect selection rules to permit only a very small number of
rotational states of the HCl⫹ ion.26 Most intriguingly, we see
a marked oscillation in intensities between vibrational levels,
which is especially pronounced for the high vibrational states
of HCl⫹ .
The weak ionization signal, the observed distribution
over a large number of vibrational states, and especially the
oscillation in ionization probabilities between vibrational
levels suggest that the E 1 ⌺ ⫹ state does not ionize into the
X 2 ⌸ 3/2,1/2 state of HCl⫹ by a direct process. Rather it is
likely that electronic autoionization of a superexcited ‘‘gateway state’’ is responsible for almost the entire photoelectron
signal. Given that the photoelectron intensity pattern—
including the oscillation—is similar for images obtained via
excitation of the ␯⬘⫽9, 10, and 11 of the V 1 ⌺ ⫹ ion pair
state, we can further propose that the same or similar gateway states are involved in the photoionization of the ion pair
state as well. In the next section, the intensities of the photoelectron signal will be used to find an analytical expression
for the potential of the superexcited gateway state.
The intermediate states probed in these experiments possess some Rydberg character at small internuclear distance,
and hence excitation of high-n Rydberg states of higher vibrational levels is feasible. Since the highest vibrational levels of HCl⫹ energetically accessible through direct ionization
are ␯ ⫹ ⫽10 共for ␯⬙⫽9 or 10 of the V state兲 or v⫹ ⫽11 共for E
state and ␯⬙⫽11 of V state兲, it may be suspected that that
those vibrational levels may also be populated through vibrational autoionization. For example, with the E 1 ⌺ ⫹ state as
an intermediate state, according to the vibrational autoionization propensity rule 共⌬␯⫽⫺1兲, the ␯ ⫹ ⫽10 of HCl⫹ is expected to show some contribution from vibrational autoionization. Indeed, we observed a positive value for the
anisotropy parameter, ␤ 2 , of the photoelectrons resulting
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J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
from 共auto兲ionization into ␯ ⫹ ⫽10 of HCl⫹ , whereas ␤ 2 parameters for all other photoelectron rings were small negative numbers.
It is remarkable that the spatial anisotropy of the photofragments is high for the H*-atom channel 关 ␤ 2 ⫽0.9 for the
H* ⫹Cl( 2 P 1/2) dissociation channel, and ␤ 2 ⫽⫺0.2 for H*
⫹Cl( 2 P 3/2)] and for the Cl* (4s) channel ( ␤ 2 ⫽1.4), indicating that the dissociation is direct and fast on the rotational
time scale. It appears therefore reasonable to assume that the
superexcited states responsible for dissociation are either
purely repulsive states or bound states which are excited
above their dissociation threshold. These superexcited states
will be low-lying members of Rydberg series converging to
the bound A 2 ⌺ ⫹ state or the repulsive 4 ⌸ and 4 ⌺ states of
HCl⫹ . Just as the A 2 ⌺ ⫹ state correlates to the H⫹ ⫹Cl fragment limit, its corresponding superexcited state will yield
electronically excited H* atoms. Conversely, it is expected
that superexcited states based on the repulsive 4 ⌸ and 4 ⌺
cores produce electronically excited chlorine atoms.
In principle, one must also consider that excitation of a
single state can lead to many different dissociation products.
For example, the bound superexcited state based on the
A 2 ⌺ ⫹ core correlates diabatically to the H*⫹Cl photofragment limit, but can also produce Cl(4s) fragments via
avoided crossings with repulsive states. Such nonadiabatic
interactions between superexcited states in the photodissociation dynamics of HI above the ionization threshold were
observed before.27 In the case of HCl—just as the A 2 ⌺ excited state of HCl⫹ is crossed by the a 4 ⌸ state with configuration 5 ␴ 1 2 ␲ 3 6 ␴ 1 —its Rydberg analog is crossed by
the Rydberg analog of the 4 ⌸ state, i.e., a 3 ⌸ state with a
configuration described by 5 ␴ 1 2 ␲ 3 6 ␴ * 4s ␴ . This dissociation process will lead to formation of H⫹Cl* (4s) through a
diabatic dissociation process, whereas adiabatic dissociation
will lead to formation of excited hydrogen atoms, i.e.,
H* (n⫽2)⫹Cl. However, in the case of HCl, nonadiabatic
dissociation dynamics may be ruled out by a simple Landau–
Zener calculation. The surface ‘‘hopping’’ probability can be
estimated from the slopes of the corresponding ionic
potentials28 and spin–orbit interaction terms between the
A 2 ⌺ ⫹ ionic state and the repulsive 4 ⌸ and 4 ⌺ states from
theory or predissociation measurements (H12⫽260 cm⫺1 and
H12⬇50 cm⫺1 , respectively兲.29 The model predicts a hopping probability close to unity for any reasonable slopes and
spin–orbit coupling values, thus only diabatic potentials
were used in the calculation described below. Clearly, one
has to invoke contributions from excitation of four superexcited states to invoke the formation of the four fragment
states.
B. Calculation of the potential parameters
of the superexcited gateway state
1. Model and computational approach
From the considerations above, the following picture begins to emerge: First, a single superexcited ‘‘gateway’’ state,
which—following excitation via the E 1 ⌺ state or the V 1 ⌺
state—electronically autoionizes, is responsible for the photoelectron signals leading to a large number of vibrational
Superexcited state of HCl
773
and spin–orbit levels of the X 2 ⌸ 3/2,1/2 states. Second, four
repulsive states produce H* (n⫽2) and Cl* (4s,4p,3d) in a
direct photodissociation process. Given this information,
four mechanistic possibilities exist: 共i兲 One of the four repulsive states leading to dissociation is also the gateway state
for autoionization. 共ii兲 While there are four states which dissociates superexcited HCl into excited atoms, there is also a
fifth state that independently mediates the autoionization process. This state may be 共ii a兲 a bound, low-lying member of
the (A 2 ⌺ ⫹ )nl␭ Rydberg series excited either above the dissociation threshold, 共ii b兲 below the dissociation threshold
near a vibrational resonance, or 共ii c兲 it may be another
purely repulsive state.
The mechanism of formation of HCl⫹ ground-state ions
upon absorption of three photons is different from that in a
one-photon process,30,31 since the transition intensities depend on the intermediate state wave function. It should be
noted that vibrational progressions which cannot be described by direct ionization alone have been observed in experiments on the copper dimer,32 N2 O, 33 NO,34,35 and many
other diatomic molecules.36 For example, for Cu2 , part of
the photoelectron intensity distribution could be understood
from overlap integrals derived from ab initio curves. For the
remainder of the photoelectron signal, attempts have been
made at reconstruction of autoionized potentials to reproduce
those photoelectron spectra.32 Those calculations did not succeed, which may possibly be due to the limited computational capabilities available to researchers in the late 1980s.
Part of the difficulties also arose from attempting to simulate
the autoionization branching ratios using simple exponential
functions only. The problem is more involved than first apparent because of an extreme sensitivity of the intensities of
the photoelectron spectrum to the potential form and because
of multiple local minima that may trap a fitting algorithm. It
was found that different potential shapes and scans over a
large region of parameter space may be needed.
In the next paragraphs we illustrate how the relative intensities of the vibrational states of HCl⫹ in the photoionization process can be modeled using 共i兲 direct ionization, 共ii兲
autoionization via a repulsive potential, and 共iii兲 via a bound
gateway state. First, we calculate the expected branching ratios from the overlap of the known E state 关␯⬘⫽0兴 wave
function with the vibrational wave functions of HCl⫹ in an
attempt to quantify the contributions of direct ionization. We
then use three different types of potentials to calculate wave
functions above their respective dissociation energies in order to identify possible unbound superexcited states as candidates for the ‘‘gateway state.’’ These potentials are expected to be similar in shape to either the bound A 2 ⌺ ⫹ state
of HCl⫹ or the unbound 4 ⌸ or 4 ⌺ states. Finally, we consider autoionization from resonant low-␯⬘ vibrational levels
of higher-lying members of the A 2 ⌺ ⫹ nl␭ Rydberg series
with n⫽4 and 5.
The observation that the branching between autoionization and dissociation of the gateway state is similar for the E
state and for all three vibrational states of the V state probed
共Fig. 6, Table I兲—together with the fact that the same kind of
an extended HCl⫹ oscillating vibrational progression is observed for these different intermediate states—indicates that
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774
Romanescu et al.
J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
wave function of the gateway state共s兲 changes only slightly
with a small change in photon energy. This suggests that the
corresponding state共s兲 is unbound as will be shown below. At
the same time the branching ratio between dissociation into
excited chlorine and hydrogen atoms changes dramatically,
reflecting the altered overlap of the intermediate state nuclear
wave functions with those of the repulsive states responsible
for formation of dissociation products.
In what follows, we argue that, with the E 1 ⌺ state and
the V 1 ⌺ state as intermediates, autoionization of a single
purely repulsive superexcited state is responsible for the observed HCl⫹ ␯ distribution in the photoelectron spectrum
and that its potential curve can be reconstructed from the
experimental ␯ envelope.
The computational approach included a number of approximations, which may be justified by the errors in the
measurements of the ionization ratios. They include 共i兲 the
assumption that both direct and autoionization are governed
only by the Franck–Condon principle for vibronic wave
functions, i.e., the distance dependence of the transition dipole was ignored, and 共ii兲 use of simple Morse potentials for
bound states and single exponential or inverse-power curves
for unbound states.
Morse potential parameters for the ground state of HCl⫹
ion were calculated from the spectroscopic parameters of
Ref. 18. The corresponding wave functions were calculated
using the Numerov method,37 with eigenvalue corrections
calculated according to Cooley38 for the bound X 2 ⌸ state
and bound Rydberg states. The wave function for the intermediate state was calculated from the ab initio potential by
Peyerimhoff.25 The H⫹Cl* and H*⫹Cl channel asymptotes
were calculated by adding the corresponding atomic energies
to the HCl dissociation limit.39 Least-square fitting was performed of the potential parameters to the experimental vibrational distribution. A gradient-descent40 algorithm was used
to minimize the dimensionless standard error,41
¯␴ ⫽
冑
1
N⫺M
N⫺1
兺
␯ ⫽0
冉
I ␯calc⫺I obs
␯
⌬I ␯
冊
FIG. 7. HCl⫹ ␯ distributions: experimental 共black兲 and the best fit assuming
a single unbound autoionized state 共light gray: exponential decay; dark gray:
inverse-power function兲. Fits using direct ionization 共hatched兲 and autoionization of bound Rydberg states 共for ␯⫽4; crosshatched兲 did not converge.
Therefore the branching ratios were calculated from the ab initio curves.
The large errors for the photoelectron intensities 共␯⫽0–3兲 bias against contributions from direct ionization. When reducing the error bars by restricting
the number of fitting parameters to the velocity profile, direct ionization
contributes up to 50% to the photoelectron signal mainly to the low-␯ levels,
while not affecting the superexcited state potential parameters.
of the two spin–orbit components did not differ within the
experimental and fit accuracy and were averaged. Consequently, only the ⍀⫽ 23 potentials were used for fitting. Experimental errors were used to weight the intensity distribution. However, these errors were obtained from the multiGaussian fit to the experimental velocity profile and for ␯⬎6
likely underestimate the true measurement error.
To obtain information about the relative contributions of
direct ionization versus autoionization, we normalized the
distributions for direct and autoionization independently and
then used their relative contribution as another fitting parameter,
2
,
where N is the number of vibrational levels of the ion used,
M the number of degrees of freedom, I obs
␯ and ⌬I ␯ are the
experimental intensity of the ␯th vibrational photoelectron
line and its uncertainty, respectively. Finally, I ␯calc is the
Franck–Condon integral of the ␯th level wave function and
the wave function of the ionized state under consideration,
i.e., I ␯calc⬀ 具 ␺ ␯ 兩 ␺ s 典 2 . The degrees of freedom in the fitting
procedure are restricted by the known asymptotes of the superexcited states, i.e., H* (n⫽2)⫹Cl( 2 P) the 1 ⌺ ⫹ an A 2 ⌺
core and H⫹Cl* (4s,4p,3d) for the respective repulsive
( 4 ⌸)nl␭ or ( 4 ⌺)nl␭ states. The calculated distribution was
normalized with respect to the measured intensities to minimize ¯␴ .
Only in the E 1 ⌺ state and V 1 ⌺ state 共␯⫽11兲 photoelectron images the rings corresponding to ionization were intense enough to quantify their relative contribution. The vibrational population in the X 2 ⌸ state was obtained from a
multi-Gaussian fit of the velocity profile shown in Figs. 4
and 6 and is given in Table I and in Fig. 7. The distributions
C DI/AI⫽
兺 ␯ I DI
␯
兺 ␯ I AI
␯
.
2. Fit results
An extensive exploration of the possible ionization
mechanisms was undertaken only for the photoelectron intensity distribution arising from E 1 ⌺ state ionization. The
photoelectron spectrum from the ionization of the V 1 ⌺ state
共␯⫽11兲, was only used to confirm that both states ionize
through the same process.
In the model of a dissociative superexcited gateway
state, we fitted three unbound states using either a simple
exponential function of the form V⫽Ae ⫺B(r⫺r 0 ) ⫹C or an
inverse-power function V⫽A/r B ⫹C. These states converged to the Cl* (4s,4p,3d) asymptotes and C was therefore
kept fixed in the fit. Another fit involved the bound 1 ⌺(0 ⫹ )
superexcited gateway state excited above the dissociation
threshold. Here a Morse potential of the form V⫽A(1
⫺e ⫺B(r⫺r 0 ) ) 2 ⫹C was used with the asymptote A⫹C
⫽118 007 cm⫺1 at the energy of the H* (n⫽2) channel. The
fitting algorithm was permitted to converge for many sets of
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J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
Superexcited state of HCl
775
fit was not realistic and nowhere near the ab initio curve of
the A 2 ⌺ state 共see Fig. 8兲.
共ii兲 A purely repulsive state converging to Cl* (4s) can
be modeled with both inverse-power and exponential functions. Both fit the experimental data reasonably well. The
error bars are only exceeded for a couple of the highest vibrational levels, for which errors were likely underestimated
共see below and Fig. 7兲.
共iii兲 Inclusion of the unbound states converging to the
Cl* 4 p or 3d limit did not noticeably influence the fit quality
because of the small overlap of their wave functions with
those of the vibrational states of the HCl⫹ ion.
共iv兲 Autoionization is clearly responsible for the oscillation in photoelectron intensities for ␯ ⫹ ⫽4 – 10. Since the
fully correlated intensity errors bias against the low HCl⫹
vibrational levels, their dependence on the contribution of
direct ionization is small. When reducing the intensity errors
by fitting the velocity profile to Gaussian functions with
fixed width and position 共not shown兲, direct ionization contributes up to 50% of the total intensity—populating levels
v ⫹ ⫽1 – 3, while not changing the fit quality and the superexcited state potential parameters. Both, the adiabatic E-state
wave function and a diabatic Gaussian wave function based
on a harmonic approximation of the E state well were used in
the calculation of direct ionization and give similar branching ratios between direct ionization and autoionization while
not changing the superexcited state potential parameters.
共v兲 Both repulsive state models 共exponential and
inverse-power兲 appear to favor fitting parameters close to
those of the 4 ⌸ state 共Fig. 8, Table II兲.28 Although the agreement may be somewhat coincidental, there is independent
evidence for a repulsive 3 ⌸ (0) gateway state to autoionization.
共vi兲 While we did not explore all of the above five
points for the V 1 ⌺ state 共␯⫽11兲, it was confirmed that the
photoelectron intensities can also be used in a fit to an unbound exponential potential. In particular, the superexcited
state potential parameters 共Table II兲 are similar to those ob-
FIG. 8. The superexcited state potentials based on the 4 ⌸ and 4 ⌺ ion core—
shown as thin solid and dashed lines, respectively—were obtained by simple
translation of the ab initio potentials 共Ref. 28兲 by the electron binding energy of the respective nl atomic Rydberg electron. The superexcited state
potential responsible for autoionization was obtained from a fit to the photoelectron intensities displayed in Figs. 4 and 6 共dotted line兲. It is very
similar to the approximate 关 ( 4 ⌸)4s ␴ 兴 3 ⌸(0 ⫹ ) state potential. The expected
1 ⫹
⌺ (0) state potential curve is obtained by translation of the A 2 ⌺ curve
共solid line兲, while the result of the fit yields an unrealistic bound potential
共dotted line兲.
initial parameters and the global minimum was obtained by
comparison of the numerous local minima. These scans over
parameter space also included initial parameters corresponding to the exponential/inverse-power and Morse potentials
fitted to numerical ab initio curves28 for the HCl⫹ 4 ⌺, the 4 ⌸
state and A 2 ⌺ state, respectively. Finally, different combinations of such potentials were used, thereby considerably increasing the parameter space.
The fits show that:
共i兲 The bound 1 ⌺ state 共correlating to H*, n⫽2) can be
excluded as a possible gateway state, as it does not provide
good fit quality on its own and is also ousted in combined fits
with unbound states. The potential curve resulting from the
TABLE II. The parameters obtained from the fit of the ab initio and superexcited state potentials. The numerical
ab initio potentials were taken from Ref. 28 and fitted to with exponential or inverse-power functions. The
superexcited state potential was obtained form a fit to the photoelectron intensities as described in the text. Both
types of repulsive potential functions converged to parameters that were close to the 4 ⌸ potential of HCl⫹ . All
values have been obtained with the E 1 ⌺ ⫹ (0) state as the intermediate state except when noted.
Exponential fit
Parameter
4
⫺1
Gateway
state
4
Inverse-power fit
⌺
4
⌸
Gateway
state
4
⌺
4
⌸
A, 10 cm
4.28共4兲
4.4共2.2兲a
2.68共4兲
4.46共7兲
48.9共1.5兲
54.4共1.3兲
48.3共2兲
B, Å⫺1 or ln⫺1 Å
2.46共4兲
2.38共28兲a
3.16共6兲
2.42共4兲
3.36共3兲
3.03共4兲
3.84共10兲
C, cm⫺1
109 974 fixed
1.315 共fixed兲
r0 , Å
RMS
a
2.0
0.9a
n/a
n/a
2.0
n/a
From the fit of the V 1 ⌺ ⫹ (0) ( ␯ ⫹ ⫽5,...,11) state photoelectron intensities.
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776
Romanescu et al.
J. Chem. Phys., Vol. 120, No. 2, 8 January 2004
tained from the fit of the E 1 ⌺ state 共␯⫽0兲, albeit with much
larger errors.
In the model of a vibrational level of a Rydberg state
acting as the gateway for autoionization, the ab initio potential for the A 2 ⌺ state28 as an initial approximation was used.
Further, any r dependence of the quantum defect42 was neglected. As before, we calculated the Franck–Condon autoionization intensities and performed a combined direct/
autoionization fit of superexcited state Morse potential
parameters similar to the one described above. The threephoton energy E ph⫽125 658 cm⫺1 is near the reported excitation energy to the resonant vibrational level of the
(A 2 ⌺) 5p ␲ 3 ⌸ Rydberg series (n⫽3.136, ␯⫽4兲 at 125 638
cm⫺1 with a strong neighboring ␯⫽1 peak of the
(A 2 ⌺,4d ␲ ) 1 ⌸ progression with n⫽3.795 at 125 067
cm⫺1.31 More recently, in Ref. 30, the ␯⫽3 and ␯⫽4 levels
of the 5p ␲ series were reassigned to n⫽3.31 at 125 564 and
126 806 cm⫺1.
Autoionization mediated by any of these levels was
found to not reproduce the experimental data. Since the fit
did not converge for any of the bound gateway states’ vibrational levels between ␯⫽0 and 5, the intensities in Fig. 7
were calculated for ␯⫽4 directly from the ab initio potential
curve. The combined direct/autoionization fits using bound
superexcited state wave functions favored direct ionization
over autoionization. However, as shown above, direct ionization does not account for the relative intensities of the high-␯
vibrational lines in the photoelectron image demonstrating
that this model is flawed.
Finally, vibrational autoionization mentioned above possibly contributes to the intensity of the ␯ ⫹ ⫽11 signal. When
omitting this value from the fitting routine, the potential parameters in Table II were confirmed within limits of their
fitting errors.
From these arguments, it becomes apparent that a single
repulsive state converging to Cl* 4s channel is responsible
for the observed HCl⫹ ␯ population. In Fig. 8 the best fit, a
single exponential repulsive state, is shown. The resulting
potential parameters are given in Table II. One notes the
similarity of the potential parameters to ab initio calculations
for the 4 ⌸ state 共Table II兲.28 Although the quality of the fit
alone does not support this assignment, we favor the hypothesis of a superexcited state with a 4 ⌸ core. Such a
( 4 ⌸)4s ␴ 3 ⌸(0 ⫹ ) state is excited from the intermediate state
via a one-electron process, as opposed to 3,5⌺ ⫺
0 states with
the 4 ⌺ ⫺ core requiring promotion of two electrons and violating the selection rule ⌺ ⫹ →⌺ ⫹ . As for the repulsive potentials converging to the Cl* 4p and Cl* 3d limits, the proximity of their asymptotes to the three-photon energy causes
an extreme sensitivity of the branching ratios to the potential
model and parameters. Therefore the higher-lying states were
not included in the fit.
We consider our calculations to be an indication that at
the three-photon level excitation and autoionization of unbound superexcited Rydberg states is favored. A more thorough study may be necessary with better knowledge about
the intermediate state potential curve to confirm that direct
ionization is only a minor channel. Although the fitted distribution is within error bars for almost all vibrational levels,
the convergence cannot be considered very good.
It should also be noted that the quantum defect’s dependence on r may significantly alter the (A 2 ⌺ ⫹ )nl␭ Rydberg
state potentials, as shown in Ref. 42 where ␮ (r) is modeled
with a Gaussian. For simplicity we neglected this effect.
Considering the restrictions imposed by the simple
model used here and the fact that only one model fitted the
experimental data, we believe that our calculations prove the
possibility of superexcited state potential reconstruction from
an autoionization spectrum thus allowing for direct comparison with ab initio curves.
V. SUMMARY AND CONCLUSIONS
Hydrogen chloride seeded in a molecular beam was
laser-excited in a two-photon process to different electronic
states. Resonance enhanced ionization and dissociation
yielded photoelectrons together with protons and Cl⫹ and
HCl⫹ ions. Velocity map images of photoelectrons and positive fragment ions were obtained and analyzed using the
‘‘onion-peeling’’ algorithm. The E 1 ⌺(0 ⫹ ) or V 1 ⌺(0 ⫹ )
关␯⫽9,10,11兴 states show comparable probabilities of dissociation and autoionization.
Since in the velocity-map imaging technique all photoelectrons arising from a specific process are collected, and
the photoelectron spectra are therefore quantitative, we were
able to use photoelectron peak intensities to draw conclusions about the nature of the superexcited states that mediate
the autoionization process. Different functional forms for superexcited gateway states were used in a fit to the photoelectron intensities. Here it was assumed that only vibrational
overlap integrals govern the relative intensities of the photoelectron peaks. The fit indicated that the gateway state is
purely repulsive and can likely be described by a single exponential function. The exponential fitting parameters were
close to those that describe the excited 4 ⌸ state of HCl⫹ ,
lending some support to the hypothesis that the gateway state
is a low-lying member of the Rydberg series converging to
the state, i.e., the ( 4 ⌸)4s ␴ 3 ⌸(0) state.
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