The X+ 2Πg, A+ 2Πu, B+ 2Δu, and a[sup +][sup 4]Σ[sub u][sup −] electronic states of...

The X+2Πg, A+2Πu, B+2Δu, and a+4Σu− electronic states of Cl 2+ studiedby high-resolution photoelectron spectroscopySandro Mollet and Frédéric Merkt Citation: J. Chem. Phys. 139, 034302 (2013); doi: 10.1063/1.4812376 View online: http://dx.doi.org/10.1063/1.4812376 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v139/i3 Published by the AIP Publishing LLC. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS 139, 034302 (2013)

The X+ 2�g, A+ 2�u, B+ 2�u, and a+ 4�−u electronic states of Cl+2 studied

by high-resolution photoelectron spectroscopySandro Mollet and Frédéric MerktLaboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland

(Received 21 May 2013; accepted 12 June 2013; published online 15 July 2013)

Partially rotationally resolved pulsed-field-ionization zero-kinetic-energy photoelectron spectra ofthe three isotopomers (35Cl2, 35Cl37Cl, and 37Cl2) of Cl2 have been recorded in the wavenum-ber ranges 92 500–96 500 cm−1, corresponding to transitions to the low vibrational levels of theX+ 2�g (� = 3/2, 1/2) ground state of Cl+2 , and 106 750–115 500 cm−1, where the a+ 4�−

u← X 1�+

g , A+ 2�u ← X 1�+g , and B+ 2�u ← X 1�+

g band systems overlap with transitions to highvibrational levels (v+ > 25) of the X+ state. The observation of Franck-Condon-forbidden transi-tions to vibrational levels of the X+ state of the cation with v+ ≥ 25 is rationalized by a mechanisminvolving vertical excitation of predissociative Rydberg states of mixed singlet-triplet character withan A+ ion core which are coupled to Rydberg states converging to high-v+ levels of the X+ state. Thesame mechanism is proposed to also be responsible for the observation of Cl+ − Cl− ion pairs andquartet states in the photoionization of Cl2. The potential energy function of the X+ state of Cl+2 wasdetermined in a direct fit to the experimental data. Transitions to vibrational levels of the A+ 2�u, 3/2

and B+ 2�u, 3/2 states of Cl+2 could be identified using the results of a recent analysis of the strongperturbation between the A+ 2�u, 3/2 and B+ 2�u, 3/2 states of Cl+2 observed in the A+ − X+ bandsystem [Gharaibeh et al., J. Chem. Phys. 137, 194317 (2012)], and transitions to several vibrationallevels of the upper spin-orbit component (2�u, 1/2) of the A+ state were detected in the photoelectronspectrum of Cl+2 . The a+ 4�−

u ← X 1�+g photoelectron band system, which is nominally forbidden

by single-photon ionization from the ground state was also observed for the first time and its vibra-tional and spin-orbit structures were analyzed. The 4�−

u state is split into two spin-orbit componentswith � = 1/2 and � = 3/2, separated by 37.5 cm−1. The vibrational energy level structure of bothcomponents is regular, which indicates that the splitting results from the interaction with one or moredistant ungerade � = 1/2 or � = 3/2 electronic states. © 2013 Author(s). All article content, exceptwhere otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4812376]

I. INTRODUCTION

The open-shell nature of the Cl+2 cation, with three va-cancies in the valence shell, implies the existence of manyelectronic states at low energies and a complex spectrum re-sulting from interactions between neighboring states and spin-orbit coupling. Ab initio calculations of the potential energycurves of the low-lying doublet and quartet states of Cl+2 havebeen performed1–3 and the potential energy functions depictedin Fig. 4 of Ref. 2 and Fig. 6 of Ref. 3 give an excellentoverview of the electronic structure of Cl+2 at low energies.Table I lists the configurations that need to be considered inthe region up to 3 eV of internal energy, which is at the focusof the present article, and the corresponding electronic states.Experimental information on the rovibrational and spin-orbitenergy level structure of several of these low-lying states hasbeen obtained by photoelectron spectroscopy4–9 and by opti-cal spectroscopy.2, 3, 10–16

At low resolution, the He I photoelectron spectrum re-veals a very simple structure with three main bands centeredat ≈11.8, 14.3, and 16 eV, which correspond to three S = 1/2cationic states that are formed from the (σg)2(πu)4(π∗

g )4

X 1�+g ground state of Cl2 by (π∗

g )−1, (πu)−1, and (σ g)−1

single-photon ionization.5 The spin-orbit and vibrationalstructure of the bands is observable at higher resolution andthe similarity of the vibrational and spin-orbit intervals inthe X+ and A+ states leads to a clustering of the photoelec-tron bands. The A+ ← X photoelectron band further revealsa pronounced perturbation below 14.35 eV.6 The intensitydistribution of the threshold photoelectron spectrum of Cl2differs strongly from that observed in He I and Ne I photo-electron spectra8 and enabled the observation of long vibra-tional progressions in the Franck-Condon gaps between theX+ ← X and A+ ← X band systems. In their study, Yenchaet al.8 noted the resemblance of the overall contour ofthe threshold photoelectron spectrum and both the electronenergy-loss spectrum of Cl2 reported by Stubbs et al.17 andthe photoionization and ion-pair production spectra reportedby Berkowitz et al.18 They also suggested that the structuresobserved in all three spectra result from the excitation of thesame autoionizing Rydberg states of Cl2, namely, those be-longing to the J and K series which are thought to be nsσ g

series converging on the A+ 2�u state of Cl+2 with an on-set at n = 5 and an energy of 12.244 eV (see discussion inRefs. 8, 17, and 18). These studies indicated that a broad rangeof vibrational levels of the X+ and A+ states could be studied

0021-9606/2013/139(3)/034302/19 © Author(s) 2013139, 034302-1


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034302-2 S. Mollet and F. Merkt J. Chem. Phys. 139, 034302 (2013)

TABLE I. Relevant reference electron configurations of Cl2 and Cl+2 . Onlythe molecular orbitals resulting from 3p atomic orbitals are given.

Reference configuration Electronic state(s)

Cl2 (σg)2(πu)4(π∗g )4 X 1�+

g

Cl+2 (σg)2(πu)4(π∗g )3 X+ 2�g

(σg)2(πu)3(π∗g )4 A+ 2�u

(σg)1(πu)4(π∗g )4 2�+

g

(σg)2(πu)4(π∗g )2(σ ∗

u )1 4�−u , 2�u,

2�−u , 2�+

u

at high resolution by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy and that in-formation on the mechanisms leading to ion-pair formation inthe photoionization of Cl2 might be obtained from such stud-ies. PFI-ZEKE photoelectron spectra of the low vibrationallevels (v+ ≤ 6) of the X+ state with partial rotational resolu-tion were reported by Li et al.9 who also determined precisevalues of the first adiabatic ionization energy of Cl2 and ofthe threshold for Cl+ (1D2) + Cl− (1S0) ion-pair formation. Arecent high-resolution measurement of the threshold ion-pair-formation spectrum of Cl219 near the Cl+ (3PJ, J = 0 − 2)+ Cl− (1S0) thresholds led to the observation of ion-pair statesof very high principal quantum numbers (≥1800) and to theobservation of interactions between series of ion-pair statesconverging to different ion-pair dissociation thresholds.

The most detailed information on the electronic statesof Cl+2 has been derived from high-resolution spectroscopyof the A+ → X+ emission of Cl+2 in discharges.2, 3, 10–16 Thestrongly perturbed nature of the A+ state was recognized byHuberman11 and Tuckett and Peyerimhoff2 who attributedthem to interactions with the neighboring 2�u, 3/2 and 2�u, 1/2

states. However, it is only very recently that a full under-standing of the A+ 2�u, 3/2 → X+ 2�g, 3/2 band system, in-cluding a complete treatment of the interaction between theA+ 2�u, 3/2 and the B+ 2�u, 3/2 states, could be reached, basedon a new high-resolution measurement of the laser-induced-fluorescence spectrum of Cl+2 and ab initio calculations.3

The low temperature of the Cl+2 sample used in this study,however, prevented the observation of transitions involv-ing the A+ 2�u, 1/2 state, the assignment of which remainsincomplete.

The goals of our investigation of the PFI-ZEKE photo-electron spectrum of Cl2 were (i) to obtain precise informationon the high vibrational levels of the X+ state of Cl+2 observedin the threshold photoelectron spectrum of Yencha et al.,8 (ii)to complete the analysis of the A+ ← X band system in theregion below 14.35 eV, where it is affected by perturbations,by observing and assigning the vibrational structure of theA+ 2�u, 1/2 spin-orbit component, (iii) to study the mecha-nisms that lead to the observation of high vibrational levelsof the X+ state and of Cl+ + Cl− ion pairs in the photoion-ization of Cl2, and (iv) to try and observe quartet states of Cl+2for the first time.

II. EXPERIMENTAL

The experiments were carried out using a pulsed, tun-able vacuum-ultraviolet (VUV) laser system described in

Ref. 20. Coherent, tunable VUV radiation with a bandwidthof ≈0.5 cm−1 and a pulse length of ≈3 ns was generated byresonance-enhanced sum-frequency mixing νVUV = 2ν1 + ν2

in Xe using the (5p)56p [1/2]0 ← (5p)6 1S0 two-photon reso-nance at 2ν1 = 80 118.984 cm−1.

For this purpose, two dye lasers were pumped at a repe-tition rate of 25 Hz by the frequency-tripled (355 nm, for thefirst dye laser) or -doubled (532 nm, for the second dye laser)output of a Nd:YAG laser. The laser radiation of wavenum-ber ν1 was obtained by frequency doubling the output of thefirst dye laser using a BBO crystal. To record photoelec-tron and photoionization spectra in the region of the adia-batic ionization energy (X+ 2�g ← X 1�+

g ) of Cl2 (92 500− 96 500 cm−1), the unconverted output of the second dyelaser was used in the sum-frequency mixing process. Spec-tra of the high-v+ levels of the X+ 2�g state, of the a+ 4�−

ustate and the low-v+ levels of the A+ 2�u and B+ 2�u

states (106 750 − 115 500 cm−1) were recorded using thefrequency-doubled output of this laser.

Photoelectron and photoionization spectra were acquiredby monitoring the yields of threshold photoelectrons and ofCl+2 ions, respectively, as a function of the VUV wave num-ber using a time-of-flight (TOF) mass spectrometer. The Cl2sample (35Cl2:57.5%, 35Cl37Cl:36.7%, 37Cl2:5.8%) was intro-duced into the spectrometer using a pulsed valve producing asupersonic expansion. A gas mixture of Ar and Cl2 with apressure ratio of 10:1 was used at a stagnation pressure of1.5 bars, resulting in rotational temperatures of about 5 K inthe photoexcitation region. The vibrational temperature of theCl2 sample turned out to be very sensitive to the experimentalconditions and showed large day-to-day fluctuations. The su-personic expansion was skimmed and crossed the VUV laserbeam at right angles in the middle of a cylindrical, 7.6 cm-long electrode stack used to extract the charged particles to-ward a microchannel plate (MCP) detector. Photoionizationspectra were obtained by extracting the Cl+2 ions with a volt-age pulse of 500 V, corresponding to an electric field of≈65.8 V/cm, applied 200 ns after the laser pulse.

To record pulsed-field-ionization zero-kinetic-energy(PFI-ZEKE) photoelectron spectra at a resolution limited bythe bandwidth of the VUV laser radiation, a sequence ofeleven electric-field pulses, depicted in Fig. 1(a), was usedto field-ionize high Rydberg states located just below thefield-free ionization thresholds. This sequence first consistedof a discrimination pulse of +132 mV/cm, immediately fol-lowed by ten successive detection pulses of −66 mV/cm,−92 mV/cm, −118 mV/cm, −145 mV/cm, −171 mV/cm,−197 mV/cm, −224 mV/cm, −250 mV/cm, −276 mV/cm,and −303 mV/cm.21 The first two detection pulses usuallydid not produce a significant field-ionization signal. The elec-tron signals generated by the eight remaining detection pulseswere monitored separately at the end of the TOF tube by in-tegrating the electron current over eight successive temporalgates centered around the corresponding times of flight. Con-sequently, each laser scan led to the obtaining of eight PFI-ZEKE photoelectron spectra, as illustrated in Fig. 1(b) withthe example of the central line of the photoelectron spec-trum of the X+ 2�g, 1/2 (v+ = 2) ← X 1�+

g (v = 0) tran-sition (35Cl+2 , J+ − J′′ = −1/2 band head). In Fig. 1(b),



93917 93917.5 93918

wave number / cm-1

35Cl

237Cl

2

35Cl

37Cl

0 1 2 3

time delay / μs

-0.3

-0.2

-0.1

0

0.1F

/ Vcm

-1

1 2 3 4 5 6 7 8 9 10

0

3

4

657

8910

93919 93919.5 93920

93890 93900 93910 93920 93930

wave number / cm-1

elec

tron

sig

nal /

arb

. uni

ts

(b)(a) (c)

(d)

FIG. 1. (Panel a) Electric-field sequence used to record the PFI-ZEKE photoelectron spectrum of Cl2. The dashed vertical line indicates the time of laserexcitation. (Panel b) Eight traces, shown in the wave number region below 93 920 cm−1 and corresponding to PFI-ZEKE photoelectron spectra of the �J= −1/2 branch of the X+ (v+ = 2) ← X (v = 0) transition of 35Cl2, obtained from the extraction pulses 3 to 10. (Panel c) Same spectra as in panel (b), butafter correcting for the field-induced shifts of the ionization thresholds. The bold line corresponds to the arithmetic mean of all spectra. (Panel d) PFI-ZEKEphotoelectron spectrum of the entire X+ (v+ = 2) ← X (v = 0) band as obtained from the fifth pulse of the sequence (upper trace) and from averaging theeight spectra recorded with pulses 3 to 10 (lower inverted trace).

each trace is labeled by the index (3 to 10) used to desig-nate the successive pulses of the field-ionization sequencein Fig. 1(a). These spectral lines gradually shift towardlower wave numbers with increasing pulse index because thesuccessive pulses of the sequence ionize Rydberg states ofprogressively lower principal quantum numbers. The highresolution that can be achieved in the PFI-ZEKE photoelec-tron spectra, which is the main advantage of this multi-pulsefield-ionization method, comes at the cost of a low signal-to-noise ratio because the total field-ionization signal is di-vided into several detection windows. This disadvantage wasovercome by adding spectra obtained with the different volt-age steps after correcting for the field-induced shifts of theionization thresholds, as explained in Refs. 21, 22. Fig. 1(c)presents the same spectra as Fig. 1(b), but after addition ofthe calculated field-induced shifts. The sum of all “corrected”spectra presented in Fig. 1(c) is depicted as a thick line inFig. 1(c). This spectrum simultaneously offers the advantagesof high resolution and good signal-to-noise ratio.

Figure 1(d) compares the PFI-ZEKE photoelectron spec-tra of the entire X+ 2�g, 1/2 (v+ = 2) ← X 1�+

g (v = 0) band,recorded with the fifth detection pulse (upper trace), to thesum of all eight spectra (lower, inverted trace). This improvedsignal-to-noise ratio turned out to be important in spectralregions where the photoelectron signal was weak, either be-cause of weak VUV laser intensity or because of intrinsicallylow partial photoionization cross sections.

In regions, where the PFI-ZEKE photoelectron spectrumwas very weak, a simple two-pulse sequence was used con-sisting of a discrimination pulse of +0.13 V/cm followed bya detection pulse of −1.3 V/cm. With this pulse sequence,the resolution of the PFI-ZEKE photoelectron spectrum(2.5 cm−1) was insufficient to resolve the rotational structure.

The efficiency of the sum-frequency mixing process inXe is subject to large fluctuations in the spectral region in

which the experiments were carried out. These fluctuations,which result from variations of the nonlinear susceptibilitytensor and phase-matching conditions caused by resonanceswith Rydberg states belonging to series converging to the2P3/2 (97 833.79 cm−1) and 2P1/2 (108 370.80 cm−1) ioniza-tion thresholds of Xe, greatly complicated the determinationof relative intensities in the photoionization and PFI-ZEKEphotoelectron spectra. The effect of the VUV laser intensityfluctuations could be reduced, but not fully suppressed, bydividing the electron or ion signals by the VUV laser inten-sity. In regions of very low VUV laser intensity, the divisionprocedure introduced a strong increase of the noise level. Inregions of very high VUV intensities, saturation of the VUVdetector could not be avoided, even after strongly reducingthe voltage applied to the solar-blind photomultiplier used tomonitor the VUV radiation. In these regions, the divided sig-nal was systematically overestimated. Despite our efforts toovercome these problems, the relative intensities of our spec-tra are estimated to only be accurate to approximately 50%.

III. RESULTS

A. Photoionization and photoelectron spectra in theregion of the Cl+2 X+ 2�g (v+ = 0 − 6) ← Cl2 X 1�+

g(v = 0, 1) ionization thresholds

1. Overall structure of the spectra

The photoionization and PFI-ZEKE photoelectron spec-tra of Cl2 in the vicinity of the first adiabatic ionization thresh-old are displayed in Fig. 2. The top trace in Fig. 2 representsthe VUV intensity, which undergoes strong fluctuations in thisregion and prevented the derivation of reliable intensities (seeSec. II). The three bottom traces show photoionization spec-tra of 35Cl2, 35Cl37Cl, and 37Cl2 that were acquired by set-ting appropriate detection windows in the TOF mass spec-tra. Above the photoionization spectra, an overview of the



93000 94000 95000 96000

wave number / cm-1

-2

-1

0

1

2

3

4el

ectr

on o

r C

l 2+ s

igna

l / a

rb. u

nits

2Π1/2

2Π3/2

ν1

1

ν0

n

0 1 2 3 4 5 6

0 1 2 3 4 5

ν1

5

35Cl

2

+

37Cl

2

+

35Cl

37Cl

+

FIG. 2. Overview of PFI-ZEKE and photoionization spectra in the region of the first adiabatic ionization threshold (X+ 2�g, � ← X 1�+g ) of Cl2. The three

bottom traces represent photoionization spectra of the three isotopomers. The relevant sections of the PFI-ZEKE photoelectron spectrum are displayed withvibronic assignments in the center part of the figure. The length of the vertical assignment bars encodes the isotopomer, the longest bars indicating 35Cl+2 andthe shortest bars indicating 37Cl+2 . Unlike the photoionization spectra, these spectra have not been divided by the VUV intensity (given as the top trace with thedotted line corresponding to zero VUV intensity).

PFI-ZEKE photoelectron spectrum is presented which con-sists of two vibrational progressions corresponding to tran-sitions to the first vibrational levels (v+ = 0 − 6) of the twospin-orbit components 2�g, � (� = 1/2, 3/2) of the X+ stateof the ion. To avoid an increase in noise level in regions oflow VUV intensities, the PFI-ZEKE photoelectron spectra inFig. 2, unlike the photoionization spectra, have not been di-vided by the VUV intensity. Each band reveals a substructureoriginating from the three naturally occurring isotopomers ofCl2. Because the vibrational constants of the Cl2 X and Cl+2X+ states are of similar magnitude, no isotopic shifts are vis-ible in the overview spectra of the v+ = 0 ← v = 0 transi-tions. The isotopic shifts, however, rapidly become noticeablewith increasing v+ value. The assignment of individual bandsto specific isotopomers was straightforward and is indicatedin Fig. 2 above the overview PFI-ZEKE photoelectron spec-trum. Several hot bands originating from the Cl2 X (v = 1)level are also observable in this spectrum, most notably thev+ = 1 ← v = 1 transition, marked ν1

1 in Fig. 2. The reasonfor the high intensity of this hot band is the coincidence witha strong resonance in the VUV intensity profile. The oppo-site effect is observable for the ν0

0 origin band, which appearsparticularly weak because of the low VUV intensity in thecorresponding spectral region.

The photoionization spectra of the three isotopomers sig-nificantly differ in intensity because of the different naturalabundances, but are otherwise qualitatively similar. Isotopiceffects can be recognized, but do not significantly alter theoverall appearance of the different spectra. The photoioniza-

tion spectra have been divided by the VUV-intensity, but asexplained in the Sec. II, the influence of the VUV-intensityon the Cl+2 -signal could not be entirely removed by this pro-cedure. The consequences are visible above 95 800 cm−1,where the intensity of the almost structureless photoionizationspectrum is correlated to the VUV-intensity distribution. Thedivision by the VUV-intensity was also responsible for addi-tional noise in regions where the VUV-intensity was particu-larly weak. An example of this effect can be seen in all threephotoionization spectra around 93 750 cm−1.

Above the adiabatic ionization energy at ≈92 600 cm−1,a rich structure is observed in the photoionization spectra.Particularly in the range 92 750–95 000 cm−1, the photoion-ization spectrum consists of sharp resonances caused by vi-brational and spin-orbit autoionization of Rydberg states con-verging to the Cl+2 X+ 2�g, � (v+ ≥ 1) levels, superimposedon the weak continuum associated with the open ionizationchannels. Above ≈95 000 cm−1, the photoionization spec-trum gradually loses its sharp structures because the transi-tions to autoionizing Rydberg states with v+ > 5 have verysmall Franck-Condon factors. The photoionization signal inthis region originates primarily from direct ionization to thecontinua associated with low vibrational levels of the X+

state.

2. Vibrational structure of the spectra

To analyze the vibrational structure of the levels withv+ = 0 − 6, the centers νvv+ of all bands of the PFI-ZEKE



TABLE II. Experimentally determined positions of the X+ 2�g,3/2 (v+) ← X 1�+g (v = 0) photoionizing tran-

sitions of Cl2 compared with line positions calculated using fitted Dunham coefficients (Dun) or a fitted modelpotential (DVR).

v+ νobscm−1

νDunhamcm−1

�obs−Duncm−1

νDVRcm−1

�obs−DVRcm−1

35Cl+2 0 92 646.85(25) 92 646.80 0.05 92 647.44 − 0.591 93 285.81(25) 93 286.60 − 0.79 93 286.57 − 0.762 93 920.20(25) 93 920.27 − 0.07 93 920.08 0.123 94 547.90(25) 94 547.85 0.05 94 547.52 0.384 95 169.34(25) 95 169.39 − 0.05 95 169.25 0.095 95 785.05(25) 95 784.92 0.13 95 785.05 0.006 96 396.6(10) 96 394.46 2.14 96 394.94 1.66

7a 97 000.7(10) 96 997.86 2.84 96 999.07 1.6325 106 860.75(50) 106 859.81 0.94 106 861.42 − 0.6726 107 352.80(50) 107 351.80 1.00 107 352.84 − 0.0427 107 837.85(50) 107 837.78 0.07 107 838.23 − 0.3828 108 317.50(50) 108 317.72 − 0.22 108 317.66 − 0.1629 108 791.10(50) 108 791.58 − 0.48 108 791.12 − 0.0230 109 258.41(50) 109 259.32 − 0.91 109 258.54 − 0.1331 109 720.40(50) 109 720.90 − 0.50 109 719.93 0.4732 110 175.87(50) 110 176.28 − 0.41 110 175.33 0.5433 110 625.27(50) 110 625.39 − 0.12 110 624.73 0.5434 111 069.4(10) 111 068.20 1.15 111 068.06 1.3435 111 503.95(50) 111 504.64 − 0.69 111 505.34 − 1.3936 111 936.65(50) 111 934.66 1.99 111 936.60 0.0537 112 361.3(10) 112 358.19 3.06 112 361.83 − 0.5338 112 776.4(10) 112 775.17 1.23 112 780.97 − 4.5739 113 184.6(20) 113 185.54 − 0.94 113 194.03 − 9.4340 113 586.7(10) 113 589.22 − 2.57 113 601.03 − 14.3341 113 976.0(20) 113 986.14 10.14 114 001.96 − 25.96

35Cl37Cl+ 26 107 179.65(50) 107 178.98 0.67 107 180.21 − 0.5627 107 660.80(50) 107 660.53 0.27 107 661.17 − 0.3728 108 136.0(20) 108 136.22 − 0.22 108 136.34 − 0.3429 108 605.65(50) 108 606.01 − 0.36 108 605.70 − 0.0530 109 069.27(50) 109 069.86 − 0.59 109 069.17 0.1031 109 527.08(50) 109 527.73 − 0.65 109 526.78 0.3032 109 979.05(50) 109 979.58 − 0.53 109 978.59 0.4633 110 425.12(50) 110 425.37 − 0.25 110 424.54 0.5834 110 865.29(50) 110 865.04 0.25 110 864.59 0.70

35a 111 299.1(20) 111 298.58 0.52 111 298.76 0.3436 111 726.40(50) 111 725.82 0.58 111 727.08 − 0.6837 112 149.2(10) 112 146.82 2.38 112 149.53 − 0.3338 112 564.40(50) 112 561.48 2.92 112 566.05 − 1.6540 113 370.7(10) 113 371.52 − 0.87 113 381.39 − 10.6941 113 771.0(80) 113 766.77 4.23 113 780.23 − 9.23

37Cl+2 30 108 876.22(50) 108 876.66 − 0.44 108 876.09 0.1331 109 329.91(50) 109 330.70 − 0.79 109 329.81 0.1039 112 748.4(40) 112 748.95 − 0.55 112 754.47 − 6.0740 113 147.9(15) 113 148.69 − 0.79 113 156.81 − 8.91

aObserved as hot band.

photoelectron spectra were determined from their rotationalstructure, as explained in Subsection III A 3. The bandcenters and the corresponding assignments are presented inthe upper part of Table II for the lower (� = 3/2) spin-orbit component and in the upper part of Table III for thehigher (� = 1/2) spin-orbit component. Using the experi-mentally observed positions of the band origins and knowndata on neutral Cl2,23 the molecular constants T +

e , ω+e , and

ωex+e were determined in a least-squares fit based on the

standard expression24

νvv+ = νX→X+ − νvib + ν+vib

= T +e − (ρωe(v + 1/2) − ρ2ωexe(v + 1/2)2)

+ ρω+e (v+ + 1/2) − ρ2ωex

+e (v+ + 1/2)2

+ ρ3ωey+e (v+ + 1/2)3 − ρ4ωez

+e (v+ + 1/2)4, (1)



TABLE III. Experimentally determined positions of the X+ 2�g,1/2 (v+) ← X 1�+g (v = 0) photoionizing

transitions of Cl2 compared with line positions calculated using fitted Dunham coefficients (Dun) or a fittedmodel potential (DVR).

v+ νobscm−1

νDunhamcm−1

�obs−Duncm−1

νDVRcm−1

�obs−DVRcm−1

35Cl+2 0 93 363.82(25) 93 363.99 − 0.17 93 364.65 − 0.831 94 003.19(25) 94 003.07 0.12 94 003.11 0.082 94 635.96(25) 94 636.03 − 0.07 94 635.92 0.043 95 262.76(25) 95 262.89 − 0.13 95 262.63 0.134 95 883.69(25) 95 883.70 − 0.01 95 883.61 0.085 96 499.8(10) 96 498.48 1.32 96 498.63 1.17

24 107 055.69(50) 107 055.21 0.48 107 056.22 − 0.5325 107 551.80(50) 107 551.54 0.26 107 552.11 − 0.3126 108 041.75(50) 108 041.80 − 0.05 108 041.95 − 0.2027 108 525.65(50) 108 525.97 − 0.32 108 525.70 − 0.0528 109 003.60(50) 109 004.00 − 0.40 109 003.45 0.1529 109 475.05(50) 109 475.85 − 0.80 109 475.18 − 0.1330 109 941.15(50) 109 941.47 − 0.32 109 940.81 0.3431 110 400.73(50) 110 400.83 − 0.10 110 400.35 0.3832 110 854.28(50) 110 853.85 0.43 110 853.86 0.4234 111 741.40(50) 111 740.71 0.69 111 742.62 − 1.2235 112 176.4(15) 112 174.42 1.93 112 177.83 − 1.4336 112 602.4(10) 112 601.57 0.78 112 606.95 − 4.5537 113 018.9(10) 113 022.09 − 3.19 113 029.98 − 11.0838 113 435.9(10) 113 435.90 − 0.00 113 446.87 − 10.9739 113 838.5(50) 113 842.95 − 4.45 113 857.60 − 19.10

35Cl37Cl+ 24 106 893.00(50) 106 892.30 0.70 106 893.46 − 0.4625 107 384.60(50) 107 383.90 0.70 107 384.63 − 0.0327 108 349.20(50) 108 349.41 − 0.21 108 349.26 − 0.0628 108 822.88(50) 108 823.25 − 0.37 108 822.79 0.0929 109 290.27(50) 109 291.09 − 0.82 109 290.46 − 0.1930 109 752.55(50) 109 752.90 − 0.35 109 752.19 0.3631 110 208.52(50) 110 208.62 − 0.10 110 208.01 0.5132 110 658.28(50) 110 658.21 0.07 110 657.96 0.3233 111 103.0(15) 111 101.61 1.36 111 102.01 0.9934 111 540.1(15) 111 538.78 1.32 111 540.10 0.0035 111 971.0(15) 111 969.65 1.35 111 972.25 − 1.2536 112 399.0(50) 112 394.17 4.83 112 398.49 0.5137 112 814.5(15) 112 812.27 2.23 112 818.81 − 4.3138 113 222.7(25) 113 223.88 − 1.18 113 233.14 − 10.4439 113 626.0(20) 113 628.94 − 2.94 113 641.50 − 15.5040 114 027.0(20) 114 027.38 − 0.38 114 043.90 − 16.90

37Cl+2 25 107 214.0(50) 107 213.18 0.82 107 214.06 − 0.0628 108 638.73(50) 108 639.04 − 0.31 108 638.67 0.0629 109 102.3(10) 109 102.74 − 0.47 109 102.15 0.1531 110 011.5(10) 110 012.55 − 1.02 110 011.83 − 0.3332 110 458.62(50) 110 458.56 0.06 110 458.10 0.5233 110 898.8(15) 110 898.59 0.21 110 898.63 0.1739 113 408.7(20) 113 409.94 − 1.24 113 420.56 − 11.86

where ρ is the square root of the ratio of the reduced masses ofthe different isotopomers (see Eq. (5) below). In the analysisof the vibrational level structure up to v+ = 6, the last twoterms on the right-hand side of Eq. (1) can be neglected. T +

e

can then be converted into the adiabatic ionization energy E(0)I

(see also Eq. (13) below) using

E(0)I

hc∼= T +

e +(

ω+e

2− ωex

+e

4

)−

(ωe

2− ωexe

4

). (2)

The molecular constants of the main isotopomer 35Cl2 ob-tained by the fit are listed in Table IV and can be scaled us-ing the appropriate ratios of the reduced masses μi to yieldthe corresponding values of the minor isotopomers using therelations24

ω(i)e = ρij · ω(j)

e , (3)

ωex(i)e = ρ2

ij · ωex(j)e , with (4)

ρij =√

μj

μi

. (5)



TABLE IV. Molecular constants of 35Cl2 X 1�+g and 35Cl+2 X+ 2�g. All data are given in units of cm−1.

This work/cm−1 This work/cm−1

(v+ ≤ 6 levels) (all levels) Previous work/cm−1 Reference

Cl2 ωe . . . . . . 559.711(2) 23ωexe . . . . . . 2.70133(5) 23B0 . . . . . . 0.24321(2) 23

Cl+2 (� = 3/2) T +e 92 603.8(3) 92 603.8(3) . . .

ω+e 645.6(3) 645.97(6) 645.61 11

646 8ωex

+e 2.98(4) 3.10(1) 3.015 11

2.92 8ωey

+e . . . 0.0078(6) 0.007 11

0.00088 8ωez

+e . . . 0.000125(8) . . .

B+e 0.2707(11) . . . 0.2695 11

α+e 0.0012(4) . . . 0.00164 11

Cl+2 (� = 1/2) T +e 93 321.3(4) 93 321.3(4) . . .

ω+e 645.1(3) 645.26(6) 644.77 11

635 8ωex

+e 3.03(6) 3.10(1) 2.988 11

2.31 8ωey

+e . . . 0.0075(5) 0.011 8

ωez+e . . . 0.000130(7) . . .

B+e 0.2699(5)a . . . 0.2697 11

α+e 0.0015(1)a . . . 0.00167 11

aIn the derivation of these parameters, data from emission spectra for v+ = 715 and v+ = 816 was included in the fit.

To obtain the relative intensities of the transitions to dif-ferent v+-levels, VUV-intensity fluctuations must be takeninto account, as explained in Sec. II. The relative intensitiesof the transitions to the v+ = 0 − 6 ionic levels derived fromthe PFI-ZEKE photoelectron spectrum are compared in Fig. 3

with those obtained by He I photoelectron spectroscopy.5, 6

When recording He I photoelectron spectra, the moleculesare ionized in a structureless part of the ionization contin-uum and, therefore, the relative vibrational intensity distri-bution is expected to be well described by Franck-Condon

FIG. 3. (a) PFI-ZEKE photoelectron spectra of the X+ 2�g, � (v+ = 0 − 6) ← X 1�+g (v = 0) photoionizing transitions of Cl2, obtained after division by the

VUV intensity. The intensities in the v+ = 4 − 6 region cannot be related to the intensities in the v+ = 0 − 3 region for experimental reasons. (b) CalculatedFranck-Condon factors of the X+ 2�g, � (v+) ← X 1�+

g (v = 0) transitions. The Franck-Condon factors are given as sticks for both spin-orbit components.

In (a) and (b), the broad envelope is obtained by convoluting the spectrum with a Gaussian line profile with full-width at half-maximum of 300 cm−1. (c) HeI photoelectron spectrum, as reported in Ref. 6. The peak around 92 100 cm−1, marked with an asterisk, corresponds to the v+ = 0 ← v = 1 hot band. (d) HeI photoelectron overview spectrum, as reported in Ref. 5. The lowest-lying band (labeled “1”) corresponds to the vibrational levels depicted in the left panels(v+ = 0 − 6). The bands labeled “2” and “3” correspond to (πu)−1 and (σ g)−1 ionization processes.



92640 92645 92650

wave number / cm-1

0

0.2

0.4

0.6

0.8

elec

tron

sig

nal /

arb

. uni

ts

ΔJ = 1/2ΔJ = -1/2

ΔJ = 3/2ΔJ = -3/2

ΔJ = 5/2ΔJ = -5/2

ΔJ = 7/2ΔJ = -7/2

1 3 5 7 9 J’

FIG. 4. PFI-ZEKE photoelectron spectrum of the X+ 2�g, 3/2 (v+ = 0) ← X 1�+g (v = 0) photoionizing transition, used to determine the adiabatic ionization

energy of Cl2. The dashed line represents a calculated spectrum assuming a rotational temperature Trot = 5 K and a Gaussian lineshape function with a full-widthat half-maximum of 0.55 cm−1. For clarity the rotational branches are only given for the main isotopomer 35Cl2.

factors. In PFI-ZEKE photoelectron spectroscopy, channel in-teractions also influence the relative intensity distributions25

and the differences in the intensity distributions observed byHe I and PFI-ZEKE photoelectron spectroscopy in the rangev+ = 0 − 6 can be attributed to the channel interactions thatgive rise to sharp structures in the photoionization spectrum.The influence of channel interactions on the appearance ofthe PFI-ZEKE photoelectron spectra and the mechanism bywhich transitions to levels with v ≥ 20 become observabledespite vanishing Franck-Condon factors will be discussed inmore detail in Subsection III D.

3. Rotational structure of the spectra

Figure 4 shows a high-resolution PFI-ZEKE photoelec-tron spectrum of the origin band of the X+ 2�g, 3/2 ← X 1�+

gtransition. The spectra of the three isotopomers overlap be-

cause the isotopic shifts of the v+ = 0 ← v = 0 transitionare small (<1.0 cm−1). The resulting spectral congestion andthe weakness of the VUV intensity in this region (see Fig. 2)prevented the recording of a well-resolved spectrum. The iso-topic shifts are well-resolved in the � = 1/2 v+ = 2 ← v = 0band, as depicted in Fig. 5. In this region, the VUV intensityis strong, so that the rotational structure of the bands can beobserved.

The partially resolved rotational structure of the spec-tra depicted in Figs. 4 and 5 enabled the determination ofthe ionization energy of Cl2 and of molecular constants ofthe cationic states. For this purpose, the line positions weremodeled using the rigid-rotor approximation for both theground neutral and ground cationic states. Centrifugal dis-tortion terms were not included in the analysis because theyare negligible, at our resolution, for the low rotational levels(J′ ≤ 10) populated in the supersonic expansion (estimated

94600 94610 94620 94630 94640 94650

wave number / cm-1

-1.5

-1

-0.5

0

0.5

1

1.5

elec

tron

sig

nal /

arb

. uni

ts

37Cl

2

+

35Cl

37Cl

+

35Cl

2

+

FIG. 5. PFI-ZEKE photoelectron spectrum of the X+ 2�g, 1/2 (v+ = 2) ← X 1�+g (v = 0) photoionizing transition (upper trace). Stick spectrum and calculated

spectrum (lower, inverted trace) assuming a rotational temperature Trot = 5 K and a Gaussian lineshape function with a full-width at half-maximum of 0.55 cm−1.



rotational temperature of 5 K). The rovibronic transition wavenumbers were analyzed using26

νrve = νvv+ + ν+rot − νrot

= νvv+ +B+v (J+ − 1/2)(J+ + 3/2)−BvJ (J + 1). (6)

The expression used for ν+rot in Eq. (6) holds in the Hund’s

case (a) limit of a 2� state,26 for which the � = 3/2 and �

= 1/2 states can be treated independently of each other. Thisapproximation is excellent in the present case because of thesmall ratio of B+

v to A+v (see Table IV and Fig. 9). The gen-

eral rovibronic photoionization selection rules for diatomicmolecules27 are

g ↔ g, u ↔ u, g � u for � = odd, (7)

g ↔ u, g � g, u � u for � = even, (8)

and

�J = � + 3/2, . . . , −� − 3/2, (9)

where � is the orbital angular momentum quantum numberof the photoelectron partial wave. The X+ ← X transitionis a g↔g transition and therefore only odd-� photoelectronpartial waves are allowed. The single-center expansion of theπ∗

g molecular orbital from which an electron is removed uponphotoionization is dominated by a d contribution, which re-sults in p and f photoelectron partial waves. For �max = 3, thephotoionization selection rule (9) predicts the existence of 10rotational branches with

�J = ±1/2, ±3/2, ±5/2, ±7/2, ±9/2. (10)

The relative intensities of individual transitions were calcu-lated using the expression,

I = fB · fNSS · fna · f�J , (11)

where fB is the Boltzmann factor describing the initial statepopulations,

fB =(2J + 1) exp

(− BJ (J + 1) · hc

kT

)∑∞

J=0(2J + 1) exp(

− BJ (J + 1) · hckT

) , (12)

and fNSS (= 6 for even-J and 10 for odd-J levels) is a nuclear-spin statistical factor that has to be taken into account for35Cl2 (I(35Cl) = 3/2) and 37Cl2 (I(37Cl) = 3/2). fna repre-sents the product of the natural abundances of the Cl-isotopes(75.76(10)% for 35Cl and 24.24(10)% for 37Cl) that constitutean isotopomer and f�J is an empirically derived rotational-branch-specific intensity factor which incorporates the effectof rovibronic channel interactions. The stick spectra presentedin Figs. 4 and 5 were obtained by using f�J values of 0.5,1.5, 1.5, 2.0, 1.5, 1.6, 1.8, 0.9, 0.2, and 0.2 for the brancheswith �J = −9/2, − 7/2, ..., + 9/2, respectively. These inten-sity factors enable a satisfactory description of the intensitydistributions of most bands with v+ ≤ 6. The calculated spec-tra presented in Figs. 4 (dashed line) and 5 (inverted trace)were finally obtained by convoluting the stick spectra with aGaussian lineshape function of full-width at half-maximum = 0.55 cm−1.

The adiabatic ionization energy of 35Cl2 was determinedto be

νIP = ν(X+ (v+ = 0, J+ = 3/2) ← X (v = 0, J = 0)

)= 92 647.7 ± 0.5 cm−1, (13)

which is slightly more precise than the value of 92 645.9± 1.0 cm−1 reported in Ref. 9. The band centers ν0v+ de-rived from the analysis of the rotational structure are listed inTables II and III and formed the basis for the analysis ofthe vibrational structure presented in Subsection III A 2.The analysis also yielded the rotational constants B+

v = B+e

− α+e (v+ = 1/2) of the v+ = 0 − 4 levels of all three iso-

topomers, which are related by

B(i)e = ρ2

ij · B(j)e , (14)

α(i)e = ρ3

ij · α(j)e . (15)

The values of B+e and α+

e for 35Cl+2 are listed in Table IV.

B. Photoionization and PFI-ZEKE photoelectronspectra of the high v+ levels (v+ = 24 − 41)of the X+ state of Cl+2 and observation of theCl+ (1D2) + Cl− (1S0) ion-pair dissociation threshold

1. Overall structure of the spectra

To complement the data on the X+ 2�g (� = 1/2, 3/2)states of Cl+2 , PFI-ZEKE photoelectron spectra were alsorecorded in the region 106 800–115 500 cm−1, as dis-played in Figs. 6 (106 800–113 100 cm−1) and 7 (113 050–115 500 cm−1). The overview of the spectrum in this regioncontains transitions to vibrational levels of the X+ state of Cl+2with v+ = 24 − 41. The photoelectron bands in these spectraare assigned using a stick spectrum, where black (gray) stickscorrespond to bands belonging to the lower � = 3/2 (upper� = 1/2) spin-orbit component. The lengths of the sticks en-code the isotopomers, the longest, medium-sized and short-est sticks designating bands of 35Cl2, 35Cl37Cl, and 37Cl2, re-spectively. In the region beyond 112 900 cm−1, the X+ ← Xband system overlaps with the A+ ← X, B+ ← X, anda+ ← X band systems that will be discussed separately inSubsections III F and III G. The unambiguous identificationof all X+ (v+) levels in this spectral range was a prerequisitefor the identification of lines belonging to other band systems.

The observation of transitions to all vibrational levels inthe range v+ = 24–41 in the PFI-ZEKE photoelectron spec-trum is consistent with the threshold photoelectron spectrum8

but stands in sharp contrast to the He I photoelectron spectrum(see Fig. 3(d)), in which such transitions are entirely missing.The photoionization spectra of the three isotopomers do notreveal sharp structures in this spectral region and are thereforenot displayed, because they are consistent with the photoion-ization spectrum reported by Berkowitz et al.18 This spec-tral region corresponds to the Franck-Condon gap betweenthe X+ ← X and A+ ← X bands of the He I spectrum (seeFig. 3(d)), where structures originating from autoionizing Ry-dberg states belonging to series converging on the A+ stateof Cl+2 are observable.8, 17, 18 The diffuse appearance of the



107000 107500 108000 108500 109000 109500

elec

tron

sig

nal /

arb

. uni

ts

25 26 27 28 29 30 3124 25 26 27 28 29

° ° °

Cl+(1D

2) + Cl

-(1S

0)

110000 110500 111000 111500 112000 112500 113000

wave number / cm-1

30 31 32 33 34 35 36 3732 33 34 35 36 37 38

**

* *

*

** * * * * ** *

* *

*

* **

*

*

*° °

°° ° °

° ° ° °

FIG. 6. PFI-ZEKE photoelectron spectrum recorded in the region of the X+ 2�g (v+ = 24 − 39) ← X 1�+g (v = 0) photoionizing transitions. The vibrational

assignments are given below the inverted sticks, the lengths of which encode the isotopomers (long for 35Cl2, medium for 35Cl37Cl and short for 37Cl2). Thediagonal dotted lines connect the v+ = 26 levels of the three isotopomers of both spin-orbit components. The black and gray sticks designate transitions to theX+ 2�g, 3/2 and X+ 2�g, 1/2 components, respectively. The lines marked by asterisks correspond to transitions to the a+ 4�−

u state. The position marked by avertical dashed line corresponds to the position of the transition to the v+ = 0 level of the A+ 2�u, 3/2 state, estimated using the data of Ref. 3. The verticalarrow in the upper panel indicates the position of the Cl+ (1D2) + Cl− (1S0) ion-pair dissociation threshold. Bands marked with a circle are hot band transitionsX+ 2�g (v+) ← X 1�+

g (v = 1).

photoionization spectra and the observation of Franck-Condon forbidden transitions to high v+ levels of the X+ statesuggest that these Rydberg states are predissociative, as willbe discussed further in Subsection III D.

Several of the bands in Fig. 6 cannot be assigned to tran-sitions to vibrational levels of the X+ state. These bands aremarked by asterisks in Fig. 6. Because two of these bands canbe attributed to hot bands, one can be certain that they do not

°

B4A6 B3A5A4 B0 B1

A2 A3

°

°° ° ° °°

°°

°

° ° °

°

*

*

* **

* *

*

* *

38(1/2)38(1/2)

39(1/2)

39(1/2)39(1/2)

40(1/2)

40(1/2)

A5(1/2)A4(1/2)A3(1/2)

A2(1/2)A1 A1(1/2)A0(1/2)

FIG. 7. PFI-ZEKE photoelectron spectrum of Cl2 recorded in the region of the A+ 2�u, � (v+ = 0 − 6) ← X 1�+g (v = 0) photoionizing transitions with

assignments provided below the inverted sticks. The numbers indicate the vibrational quantum numbers. The labels A and B indicate transitions to vibrationallevels of the A+ 2�u, � and B+ 2�u, 3/2 states, respectively, and labels without capital letters indicate transitions to X+ 2�g, � (v+) levels. Labels with “(1/2)”designate transitions to the upper � = 1/2 spin-orbit component of the respective states. The length of the sticks encodes the isotopomer (long for 35Cl2,medium for 35Cl37Cl and short for 37Cl2). Dashed assignment sticks indicate tentative assignments. Bands marked with an asterisk are transitions to levels ofthe a+ 4�−

u state and bands marked with a circle are hot band transitions.



EIPD 0 2(Cl ( S ) + Cl ( D ))- 1 + 1

FIG. 8. Pulsed-field-dissociation (thick trace) and ion-pair formation (thin trace) spectrum of 35Cl+, recorded near the Cl+(1D2) + Cl−(1S0) ion-pair disso-ciation threshold. The vertical black line indicates the ion-pair dissociation threshold; the dashed line marks the wave number down to which ion-pair statesare field-dissociated by the DC offset field used to separate the prompt Cl+ ion signal from the Cl+ ion signal generated by the pulsed field. The dotted linecorresponds to the wave number down to which ion-pair states could in principle be field dissociated by the pulsed electric field.

originate from an impurity in the sample. They must belongto another electronic state of the Cl+2 cation than the X+ 2�g,A+ 2�u, and B+ 2�u states, which all have been observed inthe present study. This state can only be the a+ 4�−

u state, thestructure of which is discussed in Subsection III G.

2. Vibrational structure of the X+ ← X photoelectronband of Cl2 at high v+ values

Because of the lower photoelectron signal strength in thespectral region displayed in Fig. 6 compared to the region ofthe adiabatic ionization threshold, larger voltage steps had tobe used to record the PFI-ZEKE photoelectron spectra witha satisfactory signal-to-noise ratio (see Sec. II). The result-ing loss of resolution made the determination of rotationalconstants impossible. To analyze the vibrational structure ofthe v+ = 24–41 levels of Cl+2 , the rotational contours of thecorresponding bands in the PFI-ZEKE photoelectron spec-tra were calculated as described in Subsection III A 3 forthe vibrational levels v+ = 0–6 using rotational constants ex-trapolated from the results obtained for the lowest vibrationallevels. The band origins determined in this way are listed inTables II and III.

To assign vibrational quantum numbers, the molecularconstants derived for low vibrational levels, given in Table IV,were employed to obtain approximate band positions. Bandpositions determined from threshold photoelectron spectra7, 8

and LIF spectra3 were used to bridge the gap between thev+ = 0–6 and the v+ = 24–41 regions. Whereas the molecu-lar constants ω+

e and ωex+e are sufficient to describe the vibra-

tional structure of the X+ state at low v+ values, anharmonic

constants of higher order (ωey+e and ωez

+e , see Eq. (1)) had

to be included in the analysis of the higher v+ levels. Themolecular constants obtained in this way for 35Cl+2 are givenin the third column of Table IV. The differences from the val-ues of the molecular constants obtained in the analysis of thelowest levels (second column of Table IV) originate from thefact that the expansion series in (v+ + 1/2)n becomes inad-equate to describe the vibrational energy level structure be-yond v+ ∼= 38. In this region, the anharmonicity is such thatan additional anharmonicity constant would be required to de-scribe each additional experimental line position within theerror bars. Moreover, the density of lines rapidly increasesbeyond 113 000 cm−1, which prohibits unambiguous assign-ments of v+ levels beyond 40. Our attempts at assigning v+

levels beyond v+ = 40 from a direct potential fit are describedin Subsection III D.

3. The Cl+(1D2) + Cl−(1S0) ion-pair dissociationthreshold

The fourth ion-pair dissociation threshold of Cl2, lead-ing to Cl+ (1D2) + Cl− (1S0) products, is located in the vicin-ity of the v+ = 25 level of the X+ 2�g, 3/2 state (see ver-tical arrow in Fig. 6). To complement our earlier study ofthe Cl+ (3PJ) + Cl− (1S0) threshold ion-pair formation,19 wehave also recorded the ion-pair formation at the Cl+ (1D2)+ Cl− (1S0) threshold using the technique of threshold ion-pair production spectroscopy.28 The results are presented inFig. 8, where the delayed pulsed-field-dissociation spectrumof the long-lived ion-pair states of very high vibrational quan-tum number (n > 14 000), located just below threshold, is



displayed as a thick black trace. The thin black trace cor-responds to the spectrum obtained by monitoring the Cl+

(or Cl−) signal produced directly at the time of photoexci-tation. By correcting for the field-induced shift of the dissoci-ation threshold following the same procedure as described inRef. 19, the ion-pair dissociation threshold was determined tolie at 107 103.4 ± 1.0 cm−1 (see full vertical line in Fig. 8).The pulsed-field-dissociation spectrum was recorded using apulsed field of 100 V/cm and a DC discrimination field of1.8 V/cm. This DC field is expected to lower the thresh-old down to the position of the dashed line in Fig. 8.The dotted vertical line indicates the lowest wave number(107 063.4 cm−1) at which pulsed field dissociation couldhave been observed with the extraction pulse used in the ex-periment. The pulsed-field-dissociation signal has its onsetat higher wave number (≈107 086 cm−1), corresponding to aprincipal quantum number of n ≥ 14 200. We therefore con-clude that only ion-pair states with n ≥ 14 200 contributeto the pulsed-field-dissociation spectrum, either because allstates below n = 14 200 are too short lived to be observed, orbecause the excitation cross section to these states vanishes.

Unlike the pulsed-field-dissociation spectra observedjust below the Cl+(3P2) + Cl−(1S0) ion-pair dissociationthreshold,19 the pulsed-field-dissociation spectrum observedat the Cl+ (1D2) + Cl− (1S0) threshold (see Fig. 8) has asmooth intensity distribution. The only still closed ion-pairdissociation channel which could in principle couple to theCl+ (1D2) + Cl− (1S0) channel, and thereby lead to sharpstructures by predissociation, is the one associated with theCl+(1S0) + Cl−(1S0) dissociation threshold. This thresholdlies 16 224.4 cm−1 above the Cl+ (1D2) + Cl− (1S0) disso-ciation threshold. The corresponding predissociative ion-pairstates would have principal quantum numbers of n* = 464.3and spacings of �n, n + 1 = 69.9 cm−1 in the region of theCl+ (1D2) + Cl− (1S0) dissociation threshold. Such an ion-pair state spacing is larger than the 15 cm−1 width of thepulsed-field-dissociation line of the Cl+ (1D2) + Cl− (1S0)dissociation threshold.

The Cl+ (1D2) + Cl− (1S0) ion-pair dissociation thresh-old is located in the Franck-Condon gap between theX+ ← X and A+ ← X photoelectron bands, where transitionsto Rydberg states with an A+ ion core are observable in thephotoionization spectrum.18 The mechanism for the forma-tion of the ion pairs in this region must therefore involve theexcitation of these Rydberg states, which must be predissocia-tive (see middle dashed-dotted line in Fig. 10 and discussionin Subsection III E).

C. Spin-orbit splitting between the X+ 2�3/2and X+ 2�1/2 states

The low-lying X+ 2� states of Cl+2 have an inverted spin-orbit structure with a negative spin-orbit coupling constant, sothat the � = 3/2 component lies below the � = 1/2 compo-nent. For simplicity, we list only the absolute values of thespin-orbit coupling constants in this article. The spin-orbitsplittings A+

v of the vibrational levels of the X+ state corre-spond to the wave-number differences between the two com-ponents (� = 3/2 and � = 1/2) of the X+ 2�g, � state of

0 10 20 30 40vibrational quantum number v

+

640

660

680

700

720

spin

-orb

it s

plit

ting

/ cm

-1

35Cl

2

+

35Cl

37Cl

+

37Cl

2

+

FIG. 9. Experimentally observed spin-orbit splittings between the 2�g, 1/2and 2�g, 3/2 components of the X+ state, plotted against the vibrationalquantum number. The dotted line represents values of A+

v calculatedwith Eq. (16) and the constants A+

e = 717.5 cm−1, A+1 = 0.3 cm−1, and

A+2 = −0.0283 cm−1.

Cl+2 and can be derived from the positions listed in Tables IIand III. They are displayed as a function of v+ in Fig. 9. Thespin-orbit splittings decrease with increasing value of v+, orequivalently with increasing average internuclear separation,and can be accurately modeled by the quadratic function

A+v = A+

e − A+1 (v+ + 1/2) + A+

2 (v+ + 1/2)2. (16)

A+e represents the difference T +

e (� = 1/2) − T +e (� = 3/2)

between the electronic term values (A+e = 717.5(5) cm−1,

see Table IV). The values A+1 = 0.30(4) cm−1 and A+

2= −0.0283(12) cm−1 were determined from the experimentaldata in a least-squares fit.

At high v+ value, the spin-orbit coupling constant dropssignificantly below the spin-orbit splitting of the 2PJ Cl frag-ments (882.4 cm−1 29) and below the splitting between the 3P2

and 3P1 levels of Cl+. This indicates that, on their way to dis-sociation, the 2�g, 3/2 and 2�g, 1/2 states are likely to undergoavoided crossings with the molecular states arising from thesix possible low-energy dissociation asymptotes (listed inTable V). These avoided crossings in the potential energyfunctions at long range are, in turn, expected to lead to per-turbations of the energy level structure and complicate the as-signments at high v+ values.

TABLE V. Lowest-lying dissociation energies De, � of Cl+2 . In the last col-umn, the dissociation energies are given relative to the lowest dissociationthreshold. Atomic term values were taken from Ref. 29.

Dissociation limit De, 3/2/cm−1 De, 1/2/cm−1 De, rel/cm−1

Cl(2P3/2) + Cl+(3P2) 32 262.8(11) 31 545.3(11) 0.0Cl(2P3/2) + Cl+(3P1) 32 958.8(11) 32 241.3(11) 696.00Cl(2P1/2) + Cl+(3P2) 33 145.1(11) 32 427.6(11) 882.35Cl(2P3/2) + Cl+(3P0) 33 259.2(11) 32 541.7(11) 996.47Cl(2P1/2) + Cl+(3P1) 33 841.1(11) 33 123.6(11) 1 578.35Cl(2P1/2) + Cl+(3P0) 34 141.6(11) 33 424.1(11) 1 878.82



D. Potential energy function of the Cl+2 X+ 2�gground state

To confirm the assignment of the vibrational levels pre-sented in Subsection III B 2 and to be able to calculate theFranck-Condon factors of the X+ ←X transitions, model po-tentials for the X+ 2�g, � (� = 3/2, 1/2) electronic stateswere determined in a direct fit based on the solution of theSchrödinger equation using a discrete variable representa-tion (DVR).30, 31 The model potential we used (see Ref. 32)consists of three contributions: a repulsive short-range con-tribution V short(R) that also contains the effect of chemicalbonding, an attractive long-range contribution V attr(R), and aconstant Ediss that defines the origin of the energy scale:

V (R) = V short(R) + V attr(R) + Ediss. (17)

The short-range contribution consists of two terms

V short(R) = Ae−bR − Be−bR/β, (18)

where b and β are adjustable parameters. The values of Aand B were not adjusted in the fit because A and B can beparametrized in terms of b, β, the equilibrium internucleardistance Re and the equilibrium dissociation energy De usingthe conditions

dV (R)

dR

∣∣∣∣R=Re

= 0 (19)

and

V (Re) = Ediss − De (20)

(see Eqs. (A4) and (A5) of Ref. 32). V attr(R) describes thelong-range interaction series originating from the multipolemoments of the neutral or ionic atomic constituents

V attr(R) = −∞∑

n=2

f2n(R, b)C2n

R2n, (21)

where the Tang-Toennies damping functions f2n(R, b)33

f2n(R, b) = 1 − e−bR

2n∑k=0

(bR)k

k!(22)

prevent contributions of the long-range interactions at shortinternuclear distance. The C2n-coefficients are long-range in-teraction coefficients. In the current study, only the lead-ing n = 2 term of the long-range interaction series was re-tained, which describes the charge-induced dipole interactionin terms of the atomic polarizability of Cl. The value of C4

was taken from the literature34–36 and was left unchanged.The inclusion of an adjustable C6-coefficient in the poten-tial model (neither measured nor ab initio values for C6 areknown to us) did not lead to any improvement of the fit. Weattribute the fit insensitivity to the n = 3 term of the attractivepart of the potential to the lack of experimental data close tothe dissociation threshold. Indeed, only vibrational levels upto approximately two thirds of the dissociation energy wereobserved.

The DVR-calculations were carried out on an equidis-tant grid of 1001 points from 0.1 to 10.1 a0. The equilib-rium internuclear distance was assumed to be Re = 1.89Å,as determined from the value of B+

e (see Table IV and

Ref. 37). The fit of the potential parameters to the experimen-tal data with v+ ≤ 38 yielded the potential parameters b3/2

= 3.180(23) Å−1, β3/2 = 1.562(27), De, 3/2 = 34 473(60) cm−1

and a normalized (unitless) RMS-value of 1.06 for the� = 3/2 state and b1/2 = 3.129(32) Å−1, β1/2 = 1.493(36),De, 1/2 = 34 050(76) cm−1 and a RMS-value of 0.96 for the� = 1/2 state.

To further ascertain the correctness of the model poten-tial, the rotational constants that result from the derived vibra-tional eigenstates were calculated in the v+ = 0 − 6 region,where they could be compared to the experimentally observedvalues. From the vibrational eigenfunction ψ+

v , the rotationalconstants of the states |v+〉 were calculated according to

B+v = h

8π2cμ

∫dR ψ∗

v+ (R)1

R2ψv+ (R). (23)

For both spin-orbit components � = 3/2, 1/2, the B+v -

values that were obtained can be accurately described usingB+

e = 0.2694 cm−1 and α+e = 1.53 × 10−3 cm−1, which is

in good agreement with the values determined experimentallyand listed in Table IV.

Another possibility to validate the model potential is bycomparison with the measured X+ 2�g, 3/2 (v+ = 7–15) en-ergy levels reported in Table III of Ref. 3. The positions ofthese levels, which were not observed in the present study,could be reproduced within 1 cm−1 with the potential energyfunction derived from the PFI-ZEKE photoelectron spectrum.

Although the RMS-values of the direct potential fits arearound 1, the results of these fits are unsatisfactory in two re-gards: First, the deviations between calculated and observedtransition wave numbers rapidly increase in the region beyondv+ = 38, even after inclusion of the n = 2 long-range inter-action term. The level energies beyond v+ = 38 are system-atically overestimated by the calculations. Second (and con-sistent with the former observation), the dissociation energiesDe, � of the fitted potential are larger than the dissociation en-ergies one can calculate using the known values of D0(Cl+2 ),the spin-orbit and vibrational zero-point energies of theX+ 2�g electronic state of the Cl+2 -cation, and the positions ofthe low-lying atomic energy levels of the Cl atom and the Cl+

cation (see Table IV). The rapid increase of the deviations be-tween calculated and observed vibrational term values beyondv+ = 38 may be an indication of the onset of an interactionwith gerade states correlating to different dissociation limitsat large R+ values.

Despite these deficiencies, the two potential energy func-tions provide an accurate description of the experimental ob-servations below v+ = 38 for both spin-orbit components ofthe 2�g state (see Tables II and III). The Franck-Condonfactors |〈v+|v = 0〉|2 calculated with the vibrational eigen-functions ψ+

v (R) of the ionic states and ψ0(R) of the groundneutral state are plotted as a stick spectrum in Fig. 3(b) andlead to an intensity distribution of the photoelectron spec-trum that is in excellent agreement with that of the He Iphotoelectron spectrum (Fig. 3(c)). Only transitions to ioniclevels with v+ ≤ 6 have significant Franck-Condon factors(∑6

v+=0 |〈v+|0〉|2 > 0.9999). In the region beyond v+ = 25depicted in Fig. 6, the Franck-Condon factors are less than10−10. One can therefore conclude that only the lowest



FIG. 10. Schematic illustration of the proposed mechanism of bond length-ening and intensity transfer to ion-pairs and to Franck-Condon-forbidden vi-brational levels of the X+ state of Cl+2 (see text for details). The gray areacorresponds to the internuclear distances accessible according to the Franck-Condon principle. The potential energy functions of Rydberg states with X+and A+ ion cores are drawn as dashed lines below the potential energy func-tions of the corresponding states of Cl+2 . The bond lengthening is facilitatedby the interaction, at short range, with repulsive valence or Rydberg states(dashed-dotted lines) which also intersect the ion-pair potential energy func-tions at longer range. For clarity, only the ion-pair potential energy func-tion associated with the lowest ion-pair dissociation threshold (Cl+ (3P2) +Cl− (1S0)) is represented.

vibrational levels of the X+ 2�g state are directly accessiblefrom the ground neutral state and that photoionization transi-tions to the high-v+ levels observed experimentally draw theirintensity from another mechanism.

E. Qualitative interpretation of the observationof Franck-Condon forbidden transitions to highvibrational levels of the X+ state

The observation of excited vibrational levels beyondv+ = 24 in the PFI-ZEKE photoelectron spectrum and in ear-lier threshold photoelectron spectra7, 8 implies a substantiallengthening of the internuclear separation. A plausible mech-anism providing an explanation for this lengthening is illus-trated schematically in Fig. 10 and involves the excitation, atshort range, to predissociative Rydberg states having an A+

ion core which is adiabatically converted, at long-range, intoa high Rydberg state with an X+ ion core. The same short-range interactions also provide an explanation for the forma-tion of Cl+ (3PJ) + Cl− (1S0) ion pairs beyond 100 000 cm−1

observed by Berkowitz et al.18 The triplet nature of the Cl+

fragment suggests that repulsive triplet levels play a role inthe predissociation of the X+- and A+-core Rydberg states(see also discussion in Ref. 18). According to Yencha et al.,8

the transitions to A+-core Rydberg states have their onset

at ≈98 700 cm−1, which is located beyond the lowest ion-pair formation thresholds. The ion-pair states of very highprincipal quantum numbers located just below the Cl+ (3P2)+ Cl− (1S0) threshold19 therefore cannot be explained by thismechanism, but must involve predissociative Rydberg stateswith an X+ (v+ > 5) ion core, rather than with an A+ ioncore.

The mechanism responsible for the observation of high-v+ levels of the X+ state in the PFI-ZEKE photoelectronspectrum of Cl2 is similar to the mechanism of “resonant au-toionization” proposed by Guyon and co-workers to explainthe observation, by threshold photoelectron spectroscopy, oftransitions to high vibrational levels of N2O+ and CO+

2 in theFranck-Condon gap between the X+ and A+ states.38, 39 Therole played by triplet states is also manifested by the observa-tion of quartet states of Cl+2 in the PFI-ZEKE photoelectronspectrum (see Subsection III G).

F. The PFI-ZEKE photoelectron spectrum of the A+,B+ ← X band systems

The PFI-ZEKE photoelectron spectrum in the region ofthe onset of the A+ ← X band system is depicted in Fig. 7.This region of the photoelectron spectrum is very congestedand irregular and consists of transitions to high vibrationallevels of the X+ state with v+ > 38, transitions to low vi-brational levels of the A+ and B+ states and several addi-tional lines. The spectral assignments were carried out inthree steps: (i) First, the transitions to X+ levels were iden-tified by progressively extending the analysis to higher v+

levels as described in Subsections III B–III D; (ii) then, vi-brational intervals were searched for that would match vi-brational intervals observed in the optical spectrum of theA+ − X+ band system.2, 3, 11 In the case of transitions to theA+ 2�u, 3/2 and B+ 2�u, 3/2 states, this search was greatly facil-itated once the results of the analysis of the LIF spectrum be-came available.3, 40 (iii) Finally, transitions to the A+ 2�u, 1/2

state were identified from the positions of the A+ 2�u, 3/2 lev-els by using the data reported in Refs. 2 and 11.

The vibrational quantum number of the A+ 2�u, 1/2 pro-gression could be unambiguously assigned from the iso-topic shifts of the bands located at ≈114 660 cm−1 and≈115 020 cm−1 and labeled A3(1/2) and A4(1/2) in Fig. 7,respectively. In the analysis, we used the deperturbed vi-brational constants of the A+ 2�u, 3/2 state, as reported byGharaibeh et al.,3 as initial estimates of the vibrational con-stants of the A+ 2�u, 1/2 state. The isotopic shifts calcu-lated from these values immediately gave close agreementwith the observed isotopic shifts assuming that the bandsat ≈114 660 cm−1 and ≈115 020 cm−1 correspond to thev+ = 3 and v+ = 4 levels of the A+ 2�u, 1/2 state. No otherassignments were compatible with the observations.

The interval between successive members of theA+ 2�u, 1/2 vibrational progression decreases up to v+ = 5and then increases again between v+ = 5 and v+ = 6. Thisobservation suggests that the A+ 2�u, 1/2 state is perturbed bya 2�+

u state (see discussion in Refs. 2, 3, and 11) and thatthe lowest vibrational level of the perturbing 2�+

u state might



TABLE VI. Positions of the A+ 2�u,3/2 (v+), B+ 2�u,3/2 (v+), and A+ 2�u,1/2 (v+) ← X 1�+g (v = 0, 1)

photoionizing transitions of Cl2. For each band, the position of maximum intensity is given in the table. The label“hb” indicates that the observed band is a hot band originating from the X 1�+

g (v = 1) vibrational level.

35Cl+235Cl37Cl+ 37Cl+2

v+ νobscm−1 v+ νobs

cm−1 v+ νobscm−1

A+ 2�u, 3/2 1 113 306(4)2 113 676.3(10) 2 113 669.2(10)

hb 2 113 119.2(20)3 114 028.1(10) 3 114 015.9(10) 3 114 003.3(10)

hb 3 113 474.2(10) hb 3 113 469.3(10)4 114 327.5(10) 4 114 316.3(10)5 114 846.1(10) 5 114 826.0(10) 5 114 805.7(10)6 115 141.9(10) 6 115 119.7(10) 6 115 096.2(10)

hb 6 114 587.3(15) hb 6 114 572.2(15)hb 7 115 035.6(10)

B+ 2�u, 3/2 0 114 520.1(10) 0 114 511.1(10) 0 114 502.6(10)hb 0 113 963.5(20)

1 114 619.1(10) 1 114 611.8(10)3 115 267.0(10) 3 115 252.5(10)4 115 433.5(10) 4 115 414.1(10) 4 115 393.3(10)

A+ 2�u, 1/2 0a 113 533(10)1a 113 914.2(15) 2a 113 910.1(15)2a 114 290.8(20) 2a 114 280.8(20)3 114 660.0(10) 3 114 645.8(10) 3 114 631.9(10)

hb 3 114 105.0(15) hb 3 114 098.7(10)4 115 020.4(10) 4 115 002.8(10)

hb 4 114 465.7(15) hb 4 114 454.9(15)5 115 345.8(10) 5 115 328.9(10)

hb 5 114 791.4(10) hb 5 114 782.0(15)hb 6 115 231.6(15)

aTentative assignment as discussed in the text.

be located between the v+ = 5 and 6 levels of the A+ 2�u, 1/2

state. In this region, we observe two so far unassigned transi-tions (at 115 499.4(10) cm−1 and 115 507.8(10) cm−1) whichmight correspond to the origin of the 2�+

u perturbing state.These positions are compatible with the potential curve ofthe lowest 2�+

u state calculated by Gharaibeh et al.3 Unfor-tunately, our data are too scarce to model this interaction.

To identify transitions to A+ 2�u, 1/2 (v+ ≤ 2) levels, weassumed that the A+ 2�u, 1/2 levels most perturbed by the2�+

u state are those located in its immediate vicinity and notthe v+ ≤ 2 levels. The effect of the 2�+

u state is to shift thev+ ≤ 5 levels of the A+ 2�u, 1/2 state toward lower wave num-bers and thus to reduce the spin-orbit splitting. We calcu-lated a fictive spin-orbit interval for the A+ 2�u (v+ = 3 − 5)levels by taking the difference between the positions of theA+ 2�u, 1/2 levels determined from our spectrum and thedeperturbed positions of the A+ 2�u, 3/2 (v+ = 3 − 5) lev-els from Ref. 3 and obtained Av+=3 = 567(2) cm−1, Av+=4

= 557(2) cm−1, and Av+=5 = 516(2) cm−1, which is in agree-ment with the expected reduction of Av+ with increasing v+

value. Extrapolating these values to the lower vibrational lev-els, we estimated A2, A1, and A0 to be in the range 570 cm−1

− 575 cm−1. With these values and the deperturbed positionsof the A+ 2�u, 3/2 state from Ref. 3 we could locate transitionsthat are likely to correspond to the A+ 2�u, 1/2 v+ = 1 and 2levels. This tentative assignment is supported by the obser-

vation of isotopic shifts of 4.1 cm−1 and 10.0 cm−1 for thev+ = 1 and 2 levels of the A+ 2�u, 1/2 state, respectively.Moreover, a weak band can even be discerned at the posi-tion expected for the transition to the v+ = 0 level of theA+ 2�u, 1/2 state (≈113 530 cm−1). Because the v+ = 0 − 2levels are the levels least perturbed by the 2�+

u state, weused these positions in combination with the deperturbedA+ 2�u, 3/2 (v+ = 0–2) positions to determine a value of575(15) cm−1 for the “deperturbed” spin-orbit coupling con-stant of the A+ 2�u state. This value lies very close to thevalue of 588.2 cm−1 one obtains from the spin-orbit split-ting ACl = 882.35 cm−1 of the Cl atom29 by calculatingA (A+ 2�u) = 2

3ACl.The spectral assignments are summarized in Table VI

which lists the transitions of the A+ 2�u, 3/2 ← X, B+ 2�u, 3/2

← X, and A+ 2�u, 1/2 ← X systems of 35Cl+2 , 35Cl37Cl+, and37Cl+2 observed in the photoelectron spectrum. These transi-tions are also assigned in Fig. 7 using the notation Av+, Bv+,and Av+(1/2), respectively. If the positions of the A+ 2�u, 3/2

and X+ 2�g, 3/2 states determined in the present study are usedto predict bands of the A+ → X+ band system, we obtain val-ues that differ by ≈1 cm−1 from those reported by Gharaibehet al.3 This difference results from the fact that the rotationalstructures of the A+ ← X bands are not resolved in our spec-tra and the positions we determine represent the intensitymaxima of the bands rather than their origins.



110000 110500 111000 111500

elec

tron

sig

nal /

arb

. uni

ts

112000 112500 113000 113500 114000

wave number / cm-1

v+ = 0 3 6

8 1 11 4

Ω = 3/2

Ω = 1/2

1 2 4 5 7

10 12 13 159

FIG. 11. Overview PFI-ZEKE photoelectron spectrum of the a+ 4�−u,� ← X 1�+

g photoionizing transition of Cl2 in the region of the v+ = 0 − 15 vibrationallevels of the a+ state. The lower and upper assignment bars correspond to the energetically lower � = 1/2 and upper � = 3/2 spin-orbit components of thea+ state, respectively. The differing lengths of the assignment bars designate the three naturally occurring isotopomers of Cl2 (long: 35Cl2, medium: 35Cl37Cl,short: 37Cl2).

G. First observation of the a+ 4�−u state of Cl+2

A large number of lines in the PFI-ZEKE photoelectronspectrum in the range from 109 600 cm−1 to 114 100 cm−1 aredesignated by asterisks in Figs. 6 and 7. These lines havevery irregular intensities and group in clusters separated byabout 325 cm−1. In the range between 109 600 cm−1 and111 700 cm−1, the a+ 4�−

u state is the only possible stateto which these transitions can be assigned.3 Our attempts atassigning them to transitions to the a+ 4�−

u state, assum-ing that this state is an almost pure (≈99.5% according toGharaibeh et al.3) quartet spin state with a negligible second-order spin-orbit interaction, remained unsuccessful. In con-trast to the spectral intensities, the spectral positions are regu-lar and can be grouped into two vibrational progressions withalmost identical spacings, but separated by about 40 cm−1.The two progressions, with contributions from all three iso-topomers, are indicated above the PFI-ZEKE photoelectronspectrum in Fig. 11. The vibrational assignments could be de-rived from the observed isotopic shifts in a straightforwardmanner and are summarized in Table VII. The line positionscan be accurately described by Eq. (1) and the molecularconstants obtained from a least-squares fit are presented inTable VIII.

An isolated 4�−u state does not split into two components

but is expected to have a rotational structure characteristic ofHund’s angular momentum coupling case (b), each rotationalstate being split into a closely spaced quartet by the spin-rotation interaction. The splitting into two distinct progres-sions, separated by about 40 cm−1, is indicative of an interac-tion of the a+ 4�−

u state with � = 1/2 or � = 3/2 ungeradeelectronic states. We therefore assign the two vibrational pro-

gressions of the a+ 4�−u state to an � = 1/2 and an � = 3/2

state split by a second-order spin-orbit interaction.41 The reg-ular appearance of the progressions observed experimentallysuggests that perturbing states are located energetically out-side the spectral region depicted in Fig. 11. A 2�u state withits two (� = 1/2 and � = 3/2) spin-orbit components wouldpresumably shift the � = 1/2 and � = 3/2 components of thea+ 4�−

u state by an equal amount and not induce a significantsplitting. The interaction with a higher-lying 2�−

u or 2�u statewould specifically shift the � = 1/2 or � = 3/2 component ofthe a+ 4�−

u state to lower energies, respectively. The calcula-tions presented in Ref. 3 suggest that the � = 1/2 componentof the a+ 4�−

u state lies lower in energy than the � = 3/2component (see Fig. 7 of Ref. 3) and we have used this infor-mation to assign the lower-lying progression to the � = 1/2component. Because of the doublet-quartet mixing resultingfrom the spin-orbit interaction, the rotational structure of thea+ 4�−

u state is best analyzed in Hund’s angular momentumcoupling case (c).

In the spectral range corresponding to Fig. 11, the PFI-ZEKE photoelectron signal was too weak to record high-resolution spectra. The best signal-to-noise ratio was obtainedin the vicinity of the a+ 4�−

u,3/2 (v+ = 3) ← X 1�+g (v = 0)

band and for this band the rotational structure could be par-tially resolved. Fig. 12 compares the experimental spectrumof the transitions in 35Cl+2 and 35Cl37Cl (top panel) witha calculated spectrum (bottom panel) obtained by convolu-tion of a stick spectrum with a Gaussian lineshape functionof full-width at half-maximum of 0.7 cm−1. These calcula-tions enabled us to determine the rotational constant of thea+ 4�−

u,3/2 (v+ = 3) state to be 0.175(3) cm−1.



TABLE VII. Experimentally determined positions of the a+ 4�−u (v+) ← X 1�+

g (v = 0) photoionizing transitions of Cl2 compared with calculated linepositions obtained using the molecular constants given in Table VIII.

� = 1/2 � = 3/2

v+ νobscm−1

νcalccm−1

�obs−calccm−1 v+ νobs

cm−1νcalccm−1

�obs−calccm−1

35Cl+2 1 109 928.4(5) 109 928.38 0.02 1 109 967.0(5) 109 966.89 0.112 110 251.0(20) 110 250.47 0.53 2 110 289.9(20) 110 289.67 0.233 110 569.0(20) 110 569.08 − 0.08 3 110 608.6(10) 110 609.01 − 0.414 110 884.2(10) 110 884.20 0.00 4 110 925.6(30) 110 924.90 0.705 111 196.3(15) 111 195.83 0.47 5 111 237.6(10) 111 237.35 0.25

7 111 851.5(20) 111 851.91 − 0.418 112 110.0(10) 112 109.80 0.20 8 112 154.3(15) 112 154.02 0.289 112 407.6(25) 112 407.49 0.11 9 112 451.7(20) 112 452.69 − 0.99

10 112 701.0(50) 112 701.69 − 0.69 10 112 747.5(50) 112 747.91 − 0.4112 113 327.5(15) 113 328.02 − 0.52

13 113 562.4(20) 113 563.37 − 0.97 13 113 613.0(20) 113 612.91 0.0914 113 894.4(20) 113 894.35 0.05

35Cl37Cl+ 2 110 243.5(20) 110 243.37 0.13 2 110 282.4(20) 110 282.54 − 0.143 110 557.8(20) 110 557.78 0.02 3 110 597.3(10) 110 597.67 − 0.375 111 176.5(20) 111 176.43 0.076 111 480.5(20) 111 480.66 − 0.167 111 780.9(15) 111 781.51 − 0.61 7 111 825.2(10) 111 824.69 0.518 112 078.8(10) 112 078.96 − 0.16 8 112 122.9(15) 112 123.06 − 0.16

12 113 234.9(20) 113 243.84 0.06 12 113 282.9(30) 113 283.04 − 0.1413 113 515.6(10) 113 515.33 0.27 13 113 565.3(20) 113 564.65 0.65

37Cl+2 1 109 922.2(15) 109 922.70 − 0.50 1 109 960.9(15) 109 961.18 − 0.283 110 586.0(20) 110 586.18 − 0.18

Photoionizing transitions from the neutral ground stateto the 2�−

u and 2�u states, with which the a+ 4�−u state

can interact, are also forbidden. Consequently, the interac-tions that lead to the observed splitting between the � = 1/2and � = 3/2 components cannot be invoked to explain whythe a+ 4�−

u state is observed in the PFI-ZEKE photoelectronspectrum. The very irregular intensity distribution of the ob-served progression can only be interpreted by assuming anindirect mechanism, which we believe is the electronic au-toionization of triplet Rydberg states with an A+ ion corethat are populated as a result of singlet-triplet mixing inducedby the spin-orbit interaction. This mechanism is thus closelyrelated to the mechanisms invoked in Subsections III B andIII E to explain the observation of high vibrational levels ofthe X+ state and Cl+ + Cl− ion-pairs. Singlet-triplet mixing

TABLE VIII. Molecular constants of 35Cl2 X 1�+g and 35Cl+2 a+ 4�−

u . All

data are given in units of cm−1.

(cm−1) Reference

Cl2 ωe 559.711(2) 23ωexe 2.70133(5) 23

Cl+2 (� = 1/2) T +e 109 717.9±0.8 This work

ω+e 329.1±0.3 This work

ωex+e 1.743±0.021 This work

Cl+2 (� = 3/2) T +e 109 755.4±0.8 This work

ω+e 329.7±0.3 This work

ωex+e 1.722±0.021 This work

a+ 4Σ-

u,3/2 (v

+=3)

35Cl

235

Cl37

Cl

110590 110600 110610

wave number / cm-1

elec

tron

sig

nal /

arb

. uni

ts

FIG. 12. PFI-ZEKE photoelectron spectrum with partial rotational resolu-tion (upper panel) of the a+ 4�−

u, 3/2 (v+ = 3) ← X 1�+g transition of 35Cl2

and 35Cl37Cl and calculated spectrum (bottom panel) assuming a rotationaltemperature Trot = 5 K and a Gaussian lineshape function with a full-widthat half-maximum of 0.7 cm−1.



thus appears to be an essential feature of the photoionizationof Cl2 in the spectral region studied here.

IV. CONCLUSIONS

The photoionization of the three natural isotopomers ofCl2 (35Cl2, 35Cl37Cl, 37Cl2) has been studied in the regionof the X+ ← X and A+ ← X band systems followingsingle-photon excitation from the [...](σg)2(πu)4(π∗

g )4 X 1�+g

state. The spectroscopic data include: (i) high-resolution(0.5 cm−1) PFI-ZEKE photoelectron spectra of theX+ (v+ = 0 − 6) ← X bands with partially resolved rota-tional structure; (ii) medium-resolution (2 cm−1) PFI-ZEKEphotoelectron spectra of the X+ 2�g,�=1/2, 3/2 (v+ = 24–40),A+ 2�u,3/2 (v+ = 1–7), A+ 2�u,1/2 (v+ = 2–6),B+ 2�u,3/2 (v+ = 0, 1, 3, 4), and a+ 4�−

u (v+ = 1–15) ← Xbands; (iii) photoionization of Cl2 in the correspondingspectral regions; and (iv) threshold ion-pair formation spectranear the Cl+ (1D2) + Cl− (1S0) dissociation limit which ledto the observation of ion-pair states with principal quantumnumber beyond 14 000.

One of the most striking aspects of this study is theobservation of a large number of forbidden transitions.The transitions to X+ levels with v+ > 6 and the transi-tions to ion-pair states just below the dissociation thresh-olds have vanishing Franck-Condon factors, and transitionsto the B+ 2�u, 3/2 and a+ 4�−

u states, which both result fromthe [...](σg)2(πu)4(π∗

g )2(σ ∗u )1 configuration, are forbidden in a

single-electron-excitation approximation.The B+ ← X band system draws its intensity from the

A+ ← X band system as a result of the interaction betweenthe B+ 2�u, 3/2 and A+ 2�u, 3/2 states.3 To account for the ob-servation of the other forbidden transitions, we propose amechanism involving the excitation of Rydberg states with anA+ ion core which are subject to predissociation and singlet-triplet mixing induced by the spin-orbit interaction. The elec-tronic autoionization of the singlet-triplet mixed states pro-vides access to vibrational levels of the a+ 4�−

u state in thePFI-ZEKE photoelectron spectra. Their predissociative natureenables the increase of internuclear distance required to popu-late the high vibrational levels of the X+ state observed in thePFI-ZEKE photoelectron spectrum (see Figs. 6 and 7) and theion-pair states observed in threshold ion-pair formation spec-tra (see Fig. 8).

The analysis of the PFI-ZEKE photoelectron spectrumhas led to (i) the derivation of a potential energy functionfor the X+ state that accurately describes the spectroscopicobservations up to ≈60% of the dissociation energy; (ii) thefirst experimental characterization of the a+ 4�−

u state of Cl+2 ,which is split into an � = 1/2 and an � = 3/2 component,separated by 37.5 cm−1 by a second-order spin-orbit interac-tion; and (iii) the assignment of the vibrational structure ofthe A+ 2�u, 1/2 state, which complements the extensive dataset available on the A+ − X+ and B+ − X+ band systems ofCl+2 .2, 3, 11

Combined with data reported in previousinvestigations,29, 42 the ionization and ion-pair-dissociationthreshold determined from our spectra can be used to extractimproved values for the first adiabatic ionization energy

of Cl2 (E(0)I (35Cl2)/(hc) = 92 647.7 ± 0.5 cm−1), for the

dissociation energy of Cl2 (D0(35Cl2) = 19 997.4 ± 1.1 cm−1)and of Cl+2 (D0(35Cl+2 ) = 31 940.7 ± 1.1 cm−1), and for thedoublet-quartet interval in Cl+2 (16955.1 ± 2.0 cm−1).

Predissociation and singlet-triplet mixing of Rydbergstates with X+ and A+ ion cores induced by the spin-orbitinteraction appear to play an essential role in the photoioniza-tion of Cl2 and to be at the origin of the observation of longprogressions of Franck-Condon forbidden transitions in thethreshold photoelectron spectra of Cl2 and of ion-pair statesof very high principal quantum number.

ACKNOWLEDGMENTS

We thank Dr. Paul Marie Guyon (CNRS) for many dis-cussions on photoionization. It is a great pleasure to dedicatethis article to him on the occasion of his 75th birthday. Wealso thank Professor D. J. Clouthier (University of Kentucky)for useful discussions. This work is financially supported bythe Swiss National Science Foundation (NSF(CH)) (ProjectNo. 200020-146759).

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