High resolution spectroscopy and structure of molecular dications

Simon G. Cox,y Andrew D. J. Critchley,z Peter S. Kreynin, Iain R McNab,*

Ralph C. Shiellx and Fiona E Smith{

Physics, School of Natural Sciences, Herschel Building, University of Newcastle upon Tyne,Newcastle upon Tyne, UK NE1 7RU

Received 27th September 2002, Accepted 18th December 2002First published as an Advance Article on the web 8th January 2003

The structure and reactivity of molecular dications has been the subject of increasing attention fromtheoreticians and experimentalists. We consider vibrationally resolved spectra of molecular dications, withparticular emphasis on the interpretation of the observed spectral lines, before reviewing in detail all knownhigh resolution spectra of molecular dications. We give a progress report on the state of our own calculationsand ion beam measurements of the molecular dications DCl2+ and NO2+.

1. Introduction

Molecular dications have profoundly different physical andchemical properties from both singly charged ions and neutralmolecules. In solution dications are stabilised by interactionswith the solvent, but in the gas phase dications are often intrin-sically unstable. The simplest mechanisms by which gas phasemolecular dications can be produced are electron impact ioni-sation, or photo-double-ionisation, e.g.

NOþ e� ! NO2þ þ 3e�;

HBrþ hn ! HBr2þ þ 2e�:

Central to an understanding of the physics and chemistry ofmolecular dications is an understanding of their structure,both geometric (size and shape), and electronic (interactionsof electrons with one another and with atomic nuclei); andof the dynamics and manner of any dissociation processes(for thermodynamically unstable dications).Molecular dications have a role in plasma chemistry and

physics. Plasmas are of huge importance in nature (over 99%of the observable universe is plasma) and in commercial pro-cesses such as silicon chip manufacture. The constituents ofa plasma may contain many molecular ions, and under someconditions molecular dications are present in significant con-centrations (for example, the ratio of N2

2+ to N2+ can be as

high as 1 : 10 in a nitrogen plasma). In some regimes the ionisa-tion structure of plasmas can be dominated by collisions ofdoubly charged atomic ions with H, He and H2

1 and such colli-sions take place on the potential energy surface of the appro-priate doubly charged molecular ion.Molecular dications may also be important in the iono-

sphere2 and have been proposed as candidates for excimerlasers3 or even rocket propellants4 and many of the dica-tions and other ions of silicon compounds are of interest in

interstellar clouds and in hot material surrounding star form-ing regions.5 Despite the wide interest in molecular dications,there are only confirmed high resolution spectra of three spe-cies: N2

2+, NO2+ and DCl2+. However, these spectra can beused to benchmark theoretical calculations; comparisons of thehigh resolution spectra with calculations has shown that theo-retical calculations of the properties of molecular dications arefar more difficult than calculations for neutral molecules orsingly charged ions with equivalent numbers of electrons andsimilar nuclear masses. Accurate calculation of the propertiesof molecular dications typically requires full configurationinteraction calculations using very large basis sets.The best way of determining the structure and dynamics of

molecular dications is by high resolution spectroscopy, that isgas phase spectra with at least rotational resolution. Spectrawith rotational resolution have only been achieved for three(possibly four) molecular dications.Why are there so few high resolution spectra of molecular

dications? Typical densities of dications which can be formedin a laboratory are of order 102–106 cm�3 compared with1019 cm�3 for a gas at atmospheric pressure. Consequentlyspectroscopic detection sensitivities need to be far greater thanusual to obtain spectra of molecular dications. It is only possi-ble to form low concentrations of dications because they arehighly chemically reactive (ion–molecule reactions are amongstthe fastest processes known in chemistry), have intrinsic life-times that may be small, and are short lived in most environ-ments because they will either rapidly diffuse to the walls ofa container under the influence of small electric fields orrecombine with electrons.Pauling was the first person to show that an isolated gas

phase molecular dication (He22+) could theoretically be stable

(or quasi-stable),6 his potential curve is reproduced in Fig. 1.The first experimental detection of He2

2+ was not until1985.7 The potential for He2

2+ shows features common to allquasistable molecular dications: at long range the potential issimply due to Coulomb repulsion, while at short range chemi-cal bonding forces overcome the repulsion leading to theformation of a molecule. The first detailed theoreticalcalculations on molecular dications were performed in 1961by Hurley8 and since then the depths and shapes of theirpotential energy curves have been the subject of much debate(for a review of the nature of the bonding interactions, seeref. 9). Potential curves such as that for He2

2+ are occasionally

y Permanent address: Department of Physics, University of Durham,Rochester Building, Science Laboratories, South Road, Durham, UKDH1 3LE.z Permanent address: Department of Physics and Astronomy, Univer-sity of Birmingham, Edgbaston, UK B15 2TT.x Permanent address: SCOAP, CPES, University of Sussex, Falmer,Brighton, UK BN1 9QH.{ Permanent address: Medical Physics Department, University ofNewcastle upon Tyne, Newcastle upon Tyne, UK NE1 7RU.

DOI: 10.1039/b209398g Phys. Chem. Chem. Phys., 2003, 5, 663–676 663

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called ‘volcanic ’, and vibration–rotation levels supported bysuch curves lie above the dissociation asymptote. All vibra-tion–rotation states above the dissociation asymptote arequasibound with a finite lifetime to decay into their ionicfragments. The lifetimes of the quasibound levels of a molecu-lar dication depends upon the masses of the nuclei and on thepotential energy surfaces. For isolated potentials the lifetime isdetermined by tunnelling through the barrier, but for poten-tials that are crossed by states of different symmetries, couplingbetween potentials may determine the lifetime. Such states ofmolecular dications may be described as kinetically stable.Molecular dications may be kinetically stable, or thermody-

namically stable. Whether a particular ground state dicationpotential energy curve is kinetically or thermodynamicallystable depends upon the ionisation potentials of the constitu-ent atoms. For a generic dication, AB2+, in which atom Ahas a lower ionization potential than atom B, the dissociationproducts are determined by the relative magnitudes of theatomic ionisation potentials (IP); provided that IP(A)+IP(A+) > IP(A)+ IP(B), the molecule will dissociate to givetwo charged atoms (A++B+) and will either be completelyunbound or kinetically stable (such potentials are shown inFig. 1(B). Such a molecular dication decays on a unimoleculartimescale with a release of kinetic energy in the form of aCoulomb explosion, for example:

DCl2þðL;v;J;tÞ ! Dþ þ Clþ with release of energy;

where the quantum numbers L, v and J signify the electronic,vibrational and rotational state of the molecule, and t is theintrinsic lifetime of this particular quantum state.Alternatively, if IP(A)+ IP(A+)< IP(A)+ IP(B), the ground

state will dissociate to one neutral atom (B) and one doubly-positively charged atom (A2+), leading to a thermodynami-cally stable potential such as that shown in Fig. 1(C). AsIP(A) appears on both sides of these expressions, it is usual10

to define a stability parameter D ¼ IP(A+)� IP(B). Negativevalues of D lead to the potential energy curve for A2++B lyingbelow that for A++B+, and ensure that the molecular dica-tion is thermodynamically stable. Such stable molecular dica-tions have been observed in experiments11–14 and have beenthe subject of numerous calculations15 and a recent featurearticle,16 but no high resolution spectra of these species haveyet been obtained and we do not consider them further.The determination of dissociation dynamics of kinetically

stable molecular dications (that is the measurement of thequantum resolved lifetimes (t) defined above) is also best

achieved by high resolution spectroscopy. Predissociation line-widths of spectral lines enable rotationally resolved lifetimes tobe determined directly and with a high precision. All the mole-cular dications that have been studied using high resolutionspectroscopy have energy levels that are above the lowest dis-sociation limits, and are therefore quasibound. Quasiboundlevels decay on a timescale determined by the potential energycurves and interactions between them. Lifetimes within a singleelectronic state of a diatomic dication may vary from years inthe lowest vibrational level to femtoseconds in the uppermostvibrational levels. The lifetimes of molecular dications dependupon many different factors, and have proved particularlychallenging to calculate accurately.The first experimental observation of molecular dications

was made by J. J. Thomson in 1921.17 The fact that a molecu-lar dication could be observed in a mass spectrometer showedthat the kinetic stability of some states was at least as great as amicrosecond. Recent measurements in an ion storage ring18

confirmed that a kinetically stable molecular dication (CO2+)had states with lifetimes greater than 3.8 s. Despite the earlydetection of molecular dications, the first rotationally resolvedspectrum of a molecular dication (N2

2+) was not obtaineduntil 1958,19 that of the second species (NO2+) 29 years laterin 198720,21 and that of the third (DCl2+) in 1998.22 The timelapses between these measurements are a good indication oftheir difficulty.

2. Vibrational spectroscopy

We do not consider here the lowest resolution spectroscopictechniques that yield only the energy required to create parti-cular electronic states of the dication from a neutral molecule(the adiabatic double ionisation energy, or appearance poten-tial). The appearance potentials can be found from such tech-niques as electron impact ionisation studies,23 translationalenergy spectrometry24 and double charge transfer spectrome-try.25 Typically these low resolution techniques provide infor-mation about the energetic positions of various electronicstates but little, if any, information about the vibrationalenergy level structure within these states. Several recentreviews about these techniques and their applications to dica-tions may be found elsewhere.23–26 We begin our review with avery brief (and by no means exhaustive) description of somespectroscopic techniques that have been used to elucidatevibrational information for molecular dications.

Fig. 1 (A) The potential energy curve of He22+ calculated by Pauling in 1933 using the variational principle. Reprinted with permission from ref.

6. (B,C) Generic potential curves illustrating the types of potentials possible in molecular dications; (a) potential for a normal molecule or mole-cular ion, (b) quasibound potential for a kinetically stable molecular ion, (c) a purely repulsive electrostatic potential: by far the most common for amolecular dication, (d) a generic potential curve illustrating a thermodynamically stable molecular dication.

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2.1 Vibrationally resolved spectra of molecular dications

Most of the available vibrationally resolved spectra of molecu-lar dications have been obtained using Auger spectroscopy orcoincidence techniques. A kinetic energy spectrum of theAuger electron can display the electronic states of the dica-tion.27 The ultimate limit for the resolution is set by the life-time broadening of the initial core hole state, which istypically 0.1–0.2 eV, of a similar magnitude to fundamentalvibrational frequencies. Provided electronic states of the dica-tion are well separated, vibrational resolution can thereforeoften be observed for small molecules. We show, in Fig. 2,an N1s Auger spectrum of N2 , after absorption of light froman Al Ka source at 1487 eV, resulting in the formation of the X1Sþ

g electronic dicationic state.27

Coincidence techniques can be used to determine spectra ofmolecular dications. Consider a dication created by photon (orelectron) impact on the neutral molecule:

ABþ hn ! ðAB2þÞ� þ 2e� ! AB2þ þ hnf þ 2e�

or ABþ e� ! ðAB2þÞ� þ 3e� ! AB2þ þ hnf þ 3e�

where hnf is a fluorescence photon due to the creation of thedication in an excited state (AB2+)*. There is the possibilityof coincident detection of any combination of the parent dica-tion, a subsequent photon due to fluorescence and the resultingtwo (or three) electrons. Should the dication be formed in adissociative state then we have:

ABþ hn ! ðAB2þÞ� þ 2e� ! Aþ þ Bþ þ hnf þ 2e�

or ABþ e� ! ðAB2þÞ� þ 3e� ! Aþ þ Bþ þ hnf þ 3e�

and coincidence between the fragment ions and any of the two(or three) electrons can be observed (in this case whether fluor-escence can be observed depends upon the timescale of the dis-sociation). This ensures an increased selectivity and sensitivityto one particular formation or decay process and allows singleionisation events to be disregarded.Early coincidence studies were not vibrationally resolved.

Curtis and Eland28 observed the formation of dissociative dica-tionic states by coincident detection of the fragment ions fromseveral small molecules (e.g. HCl, NO, O2 , CF4) in a Photo-Ion–PhotoIon COincidence (PIPICO) technique. Averagekinetic energy releases were reported for these species, whichin most cases confirmed the energetic position of the electronicstates of the dication formed. The existence of kineticallystable (metastable) dicationic states can be inferred from

detection of the PhotoIon together with the photon fromFluorescence in COincidence (PIFCO). An example of thiswas the work of Besnard et al.29,30 which was able to confirmthe bound nature of the B 2S+ state in NO2+ and by detectingphotons of wavelength 650–900 nm, emission assigned to A2P+–X 2S+ transitions was also observed.Lundqvist et al. at Uppsala University described a novel

instrument that has been used to obtain vibrationally resolvedkinetic energy release spectra of the molecular dications:CO2+,31 O2+,32 N2

2+,33 and NO2+.34 The instrument producedmolecular dications by pulsed electron impact on the neutralgas. Fragment ions due to predissociation of the moleculardications were collected in coincidence at opposite ends oftwo 50 cm long flight tubes and detected using microchannelplates. By using energy measurements of both fragments thecenter of mass kinetic energy was eliminated by a simple calcu-lation (made in real time for each pair of fragments), resultingin a Doppler free spectrum with vibrational resolution. Similarvibrationally resolved spectra of N2

2+ and CO2+ 35 and theacetylene dication C2H2

2+ 36 were obtained using doublecharge transfer spectroscopy.In addition to techniques capable of yielding vibrationally

resolved spectra of molecular dications, special experimentshave also been developed that enable lifetimes of moleculardications to be studied at vibrational resolution. One suchexperiment relies upon double photoionization using synchro-tron radiation. The vibrational levels are determined usingpairs of threshold electrons and the resulting ions character-ized by their time of flight. In this manner lifetimes of severalstates of CO2+ have been measured and found to correspondto some microseconds.37 The second such experiment reliesupon three dimensional fragment imaging38 and enables simul-taneous measurement of kinetic energy release upon dissocia-tion and the lifetime. This technique has also been applied toCO2+ and lifetimes of two vibrational states were measuredas 670� 150 ns and 26� 5 ns for states with kinetic energyreleases of 5.713 eV and 5.841 eV respectively.The first coincidence technique to yield vibrationally

resolved spectra of molecular dications was the ThresholdPhotoElectrons in COincidence (TPEsCO) technique, of Kingand co-workers.39 The TPEsCO technique exploits the factthat near zero kinetic energy electrons can be selectivelydetected with a resolution �10 meV (81 cm�1), and has beenused to great effect to observe metastable dicationic states ofHCl, Cl2 , N2 , CO, NO, O2 and DCl.39–41 Photo-double-ioni-sation was induced using tuneable VUV from a synchrotronradiation source, near zero energy electrons were selected usinga penetrating field technique and coincidences between the twothreshold electrons discriminated against electrons due toother photoionization processes. As an example of this techni-que, we show the X 1Sþ

g , a3Pu , A

1Pu states in N22+ (Fig. 3).40

Information about the positions of the metastable vibrationalstates can be deduced from these spectra, although consider-able care should be taken in their interpretation, as we nowdiscuss.

2.2 Interpretation of vibrational spectra: nature of resonances

In calculations of vibration-rotation levels supported by dia-tomic potential energy functions it is usual to solve the radialSchrodinger equation for the potential of interest. For the caseof dications, with a barrier to dissociation, one can do this tosolve explicitly for states below the barrier, although all ofthese levels are in fact resonances within the continuum abovethe dissociation asymptote, and there can be additional reso-nances above the barrier. Above barrier resonances areobserved in scattering experiments42 and are caused by thephenomenon that (quantum mechanically) a particle can bereflected by a barrier, even if it has sufficient energy (classi-cally) to pass over it.

Fig. 2 An N1s Auger spectrum of N2 , after absorption of light froman Al Ka source at 1487 eV, which shows the X 1Sþ

g electronic dicatio-nic state with vibrational resolution. Reprinted with permission fromref. 27.

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A more satisfactory way to calculate and understand theexpected vibrational spectra for the metastable states of mole-cular dications is to calculate all vibration–rotation levels asresonances in a continuum. As an example of the applicationof this method a TPEsCO spectrum of HCl was reanalysedby some of us.43 We showed that of the five observed levels,three were below the barrier and two were above barrier reso-nances. The process leading to the observed structure is shownschematically below in Fig. 4(a). The positions of the peaks in

the spectral simulation agreed very well with those from theexperimental spectrum, with clear evidence that two of thephotoelectron coincidence peaks were continuum resonances.We display the comparison of the TPEsCO spectrum withthe simulation in Fig. 4. Subsequently, TPEsCO spectra ofDCl2+ were obtained41 and analysed in a similar manner.44

We find that in contrast to the double charge transfer intensi-ties that are well reproduced using calculated Franck–Condonintensities, the intensities in the TPEsCO spectra of NO2+ arenot well reproduced by Franck–Condon intensities.45

Having briefly considered vibrational spectra of moleculardications we now consider the two techniques that have sofar yielded spectra with rotational resolution. These two spec-troscopic techniques use very different approaches to obtainhigh resolution spectra of molecular ions. In emissionspectroscopy (section 3) many different species in a largevariety of states are formed in a plasma, and one searchesfor previously unobserved spectra that might be assigned tothe molecular dication of interest. In ion-beam spectroscopy(section 4) only the molecules of interest are selected to interactwith light from a tunable laser and a considerably more sparseset of transitions are typically seen which can be unambigu-ously assigned to the selected species.

3. Emission spectroscopy

Rotationally resolved spectra of molecular dications have beenobtained by dispersing fluorescent light from gas discharges(plasmas). Molecular ions are formed in the discharge, butthe collisions that take place between ions, neutrals and elec-trons result in a wide variety of species. Many of these speciesare created in excited states that may live long enough to fluor-esce (> 10�8 s) to a lower electronic state. An analysis of thelight emitted from such a source has the possibility of detectingspecies that have not been previously observed.

3.1 Emission spectroscopy of N22+

The first rotationally resolved spectrum of a molecular dica-tion was obtained in 1958 by Carroll.19 Carroll investigatedthe emission from a hollow cathode discharge through nitro-gen. The resulting spectrum showed the presence of a band sys-tem with its origin at 1589.745 A that had not been previouslyobserved. This, the first rotationally resolved spectrum of amolecular dication to be recorded, is shown in Fig. 5 below.The spectrum shows a clear alternation of intensities

between adjacent rotational lines with intensity alternation inthe ratio 2 : 1 (due to the nitrogen nuclei each having a nuclearspin of I ¼ 1 46) that proved conclusively that the emitterwas molecular nitrogen and S–S transitions within both N2

+

and N22+ were proposed as possible explanations. Hurley

and Maslen47 published a theory showing how to obtainpotential energy curves for doubly charged molecules by scal-ing potential energy curves of isoelectronic species. In order toassign the spectrum, Carroll and Hurley48 compared the

Fig. 5 The first rotationally resolved spectrum of a molecular dica-tion observed (from a discharge of molecular nitrogen) in 1958.The intensity alteration between adjacent rotational lines showed con-clusively that the spectrum was of molecular nitrogen, but the spec-trum was not definitely assigned as being due to the band system D1Sþ

u –X1Sþ

g band of N22+ until 1961.48 Reprinted with permission from

ref. 19.

Fig. 3 A TPEsCO spectrum of N2 , showing the X1Sþ

g , a3Pu , A

1Pu

states. The lower spectrum is the sum of threshold photoelectron spec-tra collected in both analysers. Reprinted with permission from ref. 40.

Fig. 4 (a) Shows the photo-double-ionisation resulting in formationof the molecular dication, including transitions to vibrational levelssupported above the barrier maximum. (b) Shows a comparisonbetween the experimental (TPEsCO) data and a simulation based onthe mechanism shown above. As can be seen definitely one, and possi-bly two, above-barrier resonances were observed in the experiment.Adapted from ref. 43.

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experimental spectrum (which was suspected to be a 0–0 band)with that expected from theory for N2

2+ (obtained by scalingthe known potential energy curves of the isoelectronic C2

molecule) and were able to positively identify the band systemas D 1Sþ

u –X1Sþ

g band of N22+.

Cossart and co-workers49 subsequently obtained furtherrotationally resolved spectra of N2

2+ in emission from thenegative glow of a nitrogen discharge with long exposure times(up to 15 h). From these spectra and their subsequent analysisthey were able to identify the (0–0) and (1–1) bands of the D1Sþ

u –X1Sþ

g electronic transition in both 14N22+ and 15N2

2+.By comparing the spectroscopic parameters of the X1Sþ

g ,v ¼ 1 state of 14N2

2+ with the lower state of transitionsobserved in the ion-beam spectra of Cosby et al.50 (see below),they were able to confirm their assignments. Also of interestwere perturbations that appeared in the (0,0) and (1,1) bandsat J ¼ 37 and J ¼ 23 respectively, which were attributed tointeractions between the X 1Sþ

g state and a low-lying 3S�g state.

3.2 Emission spectroscopy of NO2+

The initial investigations of NO2+ were by low resolution spec-troscopy. Electron impact ionisation studies,51 translationalenergy spectrometry52 and double charge transfer spectro-scopy53 together confirmed the existence of the X 2S+, A 2Pand B electronic states. Auger spectroscopy revealed the ener-gies of a further 23 electronic states.54 Coincident detectionand time of flight analysis of the two fragment N+ and O+ ionsformed by incident He(II) light at 40.8 eV provided a PIPICOspectrum28 in which two peaks corresponding to kinetic energyreleases at 4 and 6 eV from the X and A states, and one corre-sponding to 9 eV from the B state were observed.A TPEsCO spectrum by Dawber et al.40 demonstrated the

existence and relative positions of the X and A states ofNO2+ and confirmed the bound nature of the B state. In theX2S+, A2P and B2S+ electronic states 17, 7 and 4 peaks wereclearly observed whose positions were determined to within� 10 meV.Twenty nine years after the observation and assignment of

the N22+ emission spectrum by emission spectroscopy, a high

resolution spectrum of NO2+ was detected49 using a similartechnique. Spectroscopic measurements of the emission froma magnetically confined electric discharge through pure NOvapour showed a rotationally resolved optical band corre-sponding to the B 2S+–X 2S+ (0,0) transition in NO2+. Theassignment of this spectrum was aided considerably by pre-vious data from photo-ion-fluorescence coincidence (PIFCO)methods.

3.3 Emission spectroscopy of CO2+?

The molecular dication CO2+ has been of considerable impor-tance in our understanding of the dynamics of dication decay.The spontaneous predissociation of CO2+ to C+ and O+ on amicrosecond time scale was first observed in 1932.55 Despitevarious vibrationally resolved studies of lifetimes discussedabove,37,38,40 the dynamics of the predissociation of CO2+

have not been fully determined and must await the results ofhigh resolution observations where rotationally resolved life-times can be obtained from the predissociation linewidths.There have been reports of possible fluorescence of CO2+ at

546.3 nm.56 However in a more recent paper57 the assignmentof this band is doubted and it is shown that this apparentlyviolet-degraded band probably does not belong to CO2+. Inaddition, this band could not be rotationally analysed becauseof overlapping with the lines of d 3D–a 3P states of CO. It isalso suggested in57 that the possible fluorescence of CO2+

should be limited to six emission lines in a 3S+–3P transition.There have also been attempts to obtain ion beam spectra ofCO2+, which we discuss below in section 4.3.

4. Ion beam spectroscopy

Ion beam spectroscopy is very different to conventional emis-sion spectroscopy. The molecular dications are created in anion source and then extracted using electric fields into a highvacuum environment in which they can be preserved, withoutundergoing collisions, until they decay naturally (unimolecu-larly). All ions formed in the source are formed into a beamand passed through a selector (often a magnetic field) whichis used to select the molecular dications that are of interest.Spectroscopy of the molecular dications is performed by intro-ducing electromagnetic radiation to be collinear with the ionbeam. Detection of spectroscopic transitions that occur inthe ion beam has so far (for molecular dications) always beenachieved by monitoring increased fragmentation rates thatarise when population is transferred (by the transitions) froma long-lived state of the molecule to a short-lived state of themolecule. The principle is illustrated (for an infrared transitionin DCl2+) in Fig. 6.The principal advantages of ion beam spectroscopy for the

study of molecular dications are that it has very high sensitivity(in a well devised experiment the absorption of a single photoncan be detected) and that the species of interest is knownunambiguously by its mass–charge ratio (this makes isotopestudies particularly simple compared with photoelectron anddischarge spectroscopy where isotopically pure starting materi-als must be used).

4.1 The Newcastle fast ion beam spectrometer

Several ion beam spectrometers have been used to detect spec-tra of molecular dications, but they are broadly similar and sowe now describe the spectrometer that we constructed.58 Aschematic diagram of the spectrometer is shown in Fig. 7.Ions, including dications, are created in the ion source by

electron impact ionisation of a sample gas. An ion beam(dashed line in Fig. 7) is extracted from the source by a poten-tial gradient and accelerated by between 1 to 10 kV and passedinto a magnetic sector. The magnetic sector is used to select thedesired molecular dication according to its momentum tocharge ratio. Following the magnet is an interaction regionthat contains a Faraday cage constructed from a perforatedmetal tube (hereafter called the drift tube). A co-axial laserbeam (shown as a dotted line in Fig. 7) from a continuous

Fig. 6 Showing the potential energy curve for the ground electronicstate of DCl2+ and the principle of our measurements. At resonance,population is transferred from a long lived state (v ¼ 1) to a short livedstate (v ¼ 2) which results in enhanced fragmentation (in a Coulombexplosion) to yield both Cl+ and D+. The fragments are detected afterselection with an electrostatic analyser (ESA), which can also be usedto measure the well defined kinetic energy (approximately 4.75 eV)with which they were formed.

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wave CO2 laser (Edinburgh Instruments PL3) is introducedinto the mass spectrometer through infrared windows and isbrought to a coincident focus with the ion beam within thedrift tube. The laser is line tuneable with lines typicallyseparated by between 1 and 2 cm�1 (30–60 GHz), thefrequency range covered (using both 12CO2 and 13CO2) isapproximately from 880–1090 cm�1, with some gaps. In orderto achieve continuous frequency scanning, the Doppler effect isused: scanning the potential of the drift tube alters the ionbeam velocity and achieves effective frequency tuning. Insidethe drift tube spectroscopic transitions occur and result in anincrease in fragmentation of the molecular dication. Frag-ments formed in the drift tube are selected according to theirkinetic energy–charge ratio using the electrostatic analyserand detected with an off-axis deflector–electron multipliercombination. The resulting signal is processed by lock inamplification and stored on a computer as a function of drifttube voltage (and hence of effective laser frequency for thelaser frequency used). After transmission through the ESAthe ion beam (parent or fragment) must be measured.A detec-tor containing both a Faraday cup and an electron multiplierarrangement is used to allow for the wide possible variationin ion currents. The Faraday cup is on-axis with the ion beamand is used to monitor the parent ions. The fragment ions aremonitored with an off-axis electron multiplier. The total gainachievable with the electron multiplier system is typically 105.While in or out of resonance with a transition, fragment

kinetic energy spectra may be recorded. A fragment kineticenergy spectrum recorded with a transition in resonance allowsa direct measurement of the kinetic energy release of the upperstate of the transition. To record a kinetic energy spectrum, theESA voltage is scanned while the number of fragments ismonitored with the off-axis electron multiplier. The Coulombexplosion of the dications results in fragment ions. By under-standing the kinetics of the fragmentation process (see forexample58) the electrostatic analyser can be used to determinethe energy released in the Coulomb explosion.The geometry of the instrument imposes limits on the life-

times of the states that can be observed. For a spectroscopictransition to be observed the initial state must survive extrac-tion from the ion source and transmission to the drift tube; thisrequires that an initial state should have a lifetime greater thana microsecond. Similarly, the final state in the transition mustdecay within the drift tube for a signal to be observed whichlimits upper state lifetimes to be smaller than about 0.1 micro-seconds. A lower limit is from the maximum scan range overwhich a change in intensity is noticeable, this is typically1000 V, the frequency range (and hence linewidth and lifetime)

that this corresponds to must be calculated for each case, anddepends upon the excitation frequency, the beam potentialand the mass and charge of the ion concerned.Ion beam spectra of molecular dications can provide both

structural and dynamical information. The position of peakswithin the spectrum are determined by the energies of vibra-tion–rotation levels within each electronic state and the widthof each peak reflects the lifetime of each state against decay.The change of this lifetime with the various quantum numbersthat define each level can provide very detailed informationabout the dissociation process and can show whether the dis-sociation is due to tunnelling through the Coulombic barrieror by various non-adiabatic couplings. The full uses andadvantages of ion beam spectroscopy were recently discussed59

and are not further dwelt on here.

4.2 Ion beam spectroscopy of N22+

The application of ion beam spectroscopy to N22+ to elucidate

both structure and dynamics (up to 1993) was extensivelyreviewed by Larsson60 and we are therefore rather brief inthe discussion that follows. The principle of these measure-ments was resonant absorption of a visible photon, followedby unimolecular decay,

N22þðL00;v00;J 00Þ þ hn ! N2

2þðL0;v0;J 0Þ ! Nþ þNþ;

and then detection of the resulting fragment N+ ions.The first application of ion beam spectroscopy to dications

was by Cosby et al..50 As the photon energy was scanned from14,900–19,500 cm�1 five bands were observed which corre-sponded to discrete absorption from different vibrational levelsof the X state in the A 1Pu�X 1Sþ

g electronic transition. Theabsolute vibrational quantum number of the A state levelswere unassigned, but lifetime calculations indicated the twohighest levels in the A state would dissociate by tunnellingthrough the Coulombic barrier. Observation of both e and fcomponents (through P, Q and R branches) in bands thatcould be assigned to transitions to these two higher vibrationallevels added weight to this hypothesis. Observation of only Q-branch transitions to the next lowest vibrational level in the Astate implied a selective predissociation process; this was con-cluded to be electronic predissociation into the continuum of anearby 1S�

u state.Masters and Sarre61 further investigated one of the vibra-

tional bands observed by Cosby et al., that involved transitionsfrom the X 1Sþ

g v ¼ 1 state to the second highest vibrationalstate in the A state. By recording this band at high resolution

Fig. 7 A schematic diagram of the Newcastle fast ion beam spectrometer. A beam of dications is created, selected by a magnet, and interactedwith a laser beam in the drift tube. Population transfer due to the absorption of a photon results in fragmentation of the dication. Fragment ionsare selected using an electrostatic analyser (ESA), and measured with an off-axis electron multiplier. A plot of Doppler shifted frequency againstnumber of fragments gives a spectrum. The solenoid wrapped around the drift tube may be used to obtain Zeeman splitting of spectra. Adaptedfrom ref. 96.

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for both 14N22+ and 15N2

2+ they were able to deduce from theisotope shift that the upper level involved was A1Pu v0 ¼ 7,providing vibrational numbering to the A state. It wasexpected, from the conclusions of Cossart and coworkers49

in emission spectra, that a perturbation would be seen atJ0 ¼ 23. However, this was not observed, implying the irregu-larities were caused within the excited 1Sþ

u state from which theemission they observed took place. The electronic potentialenergy curves involved in this study, together with some otherlow-lying curves are shown in Fig. 8.A lower than expected tunnelling rate in the 3Pg state, posi-

tioned with the potential minimum about 3.5 eV above theX1Sg state62 and calculated to support only two vibrationallevels, was observed by Szaflarski et al.63 in the 3Pg–

3Sþu

photofragment absorption spectrum. Due to the weak depen-dence of the linewidths of the transitions on N (the rotationalangular momentum quantum number of the molecule) the 3Pg

state was concluded to predissociate electrostatically through anearby repulsive state.In a reinvestigation of the A-X transition by photofragment

spectroscopy a similarly low tunnelling rate was observed byLarsson and coworkers64 for the A1Pu , v

0 ¼ 8 levels and bySundstrom and coworkers for the A1Pu , v

0 ¼ 6 levels.65 Thee and f L-doubled levels of the A state dissociated at differentrates; both levels through electronic coupling of spin–orbit ori-gin with the 3S�

u and 3Du states but in the case of the f levels anadditional electronic coupling with the 1S�

u state was deducedwhich was of gyroscopic origin.Sophisticated calculations predicted that the highest vibra-

tional level in the A 1Pu state of N22+ was v0 ¼ 8. However,

Martin and coworkers66 observed transitions to the v0 ¼ 9vibrational level by extending the photofragment investiga-tions to the blue. They observed the (9–0) and (9–1) bandswhich showed for the first time vibration-rotation levels inthe A state whose lifetimes scaled with the rotational quantumnumber N as expected for states that predissociate by tunnel-ling through the Coulombic barrier.

4.3 Ion beam spectroscopy of CO2+

Following their successful detection of an ion beam spectrumof N2

2+61 a substantial but unsuccessful search for a visibleion beam spectrum of CO2+ was undertaken by Sarre andhis co-workers.67 They monitored fragment ions while tuningthe frequency of a visible laser. Transitions between CO2+

3S+(v ¼ 0)–X3P (v ¼ 0) (using R110 laser dye – 18,273cm�1 to 18,433 cm�1 with a gap between 18,288 cm�1 and18,318 cm�1) and 3S+ (v ¼ 0)–X3P (v ¼ 1) (using R6G laser

dye) were searched for, but not found. Following their workon N2

2+64,65 and NO2+,71,72 Larsson and his co-workers alsomade an unsuccessful search for an ion beam spectrum ofCO2+, again attempting to pump from the 3P state to the3S+ state.68

It is possible that infrared spectra of CO2+ might be obtain-able using our apparatus. Some of us are currently engaged ina high level ab initio study of CO2+ to see if we might be able todetect infrared spectra.69

4.4 Ion beam spectroscopy of NO2+

The diatomic dication NO2+ is the subject of a particularlyintriguing story. Although vibrationally resolved spectra ofNO2+ are well known29,30,34,40 and rotationally resolved spec-tra of NO2+ are known from the technique of emission spec-troscopy,49 attempts to obtain ion-beam spectra of NO2+

have to date been unsuccessful in several research groups,notably those of Larsson,72 Sarre and Lineberger (personalcommunications to Larsson72) all of whom have excellenttrack records in high resolution spectroscopy of moleculardications. We shall first discuss what is known about NO2+

from theoretical calculations, before we describe the searchesfor spectra.

4.4.1 Theoretical calculations on NO2+. Several groupssince the 1960’s have performed calculations on NO2+.54,70–74

The later calculations agree well with experiments (see forexample ref. 40), notably in the predictions of the stabilityof the B 2S+ state and the number of bound vibrationallevels within the X 2S+ state.Some of us45,75 used the most recent potentials of Bennett74

to predict the characteristics of NO2+ that are relevant to aninfrared laser beam–ion beam experiment. The calculation ofthe potentials is described in detail in ref. 76. Both the X 2S+

and A 2P potentials contains a well deep enough to containseveral vibration–rotation levels which are all above the disso-ciation limit and therefore quasibound (Fig. 9). We found theenergies and tunneling lifetimes of each of these levels in orderto determine whether transitions might be observed in aninfrared ion-beam–laser-beam spectrometer. We concludedthe existence of 21 bound vibrational levels in the X stateand 10 in the A state, and predicted that 95 transitions withinthe A state (but none within the X state or from A–X) could beobserved in an infrared ion-beam/laser beam spectrometer.

4.4.2 Ion beam spectroscopy of NO2+. Pettersson et al.71

used an ion-beam/laser-beam spectrometer in conjunction

Fig. 9 Showing the lowest electronic states of NO2+ and their calcu-lated vibrational levels with zero angular momentum of rotation. Thedotted vertical lines represent the Franck–Condon ionisation regionfrom the ground state of NO. Potential energy curves courtesy ofBennett,74 as reported in ref. 75.

Fig. 8 Some low-lying potential energy curves of N22+. One of the

bands observed by Cosby et al. (labelled a1 in their work) is shown.Reprinted with permission from ref. 64.

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with an argon ion laser on the 514.5 nm (19,436 cm�1) and488.0 nm (20,491 cm�1) laser lines to photofragment massselected NO2+. After energy analysis of the ion beam, the for-ward and backward scattered fragments of N+ and O+ wereobserved on both lines. The appearance and similarity of bothpeaks at both energies suggested a DL ¼ � 1 (perpendicular)bound! free transition from the X 2S+ v0 ¼ 1 level to thecontinuum of the A 2P state, rather than a resonantbound! quasibound transition from X 2S+ v0 ¼ 0 to a quasi-bound level of the A 2P state.From the photodissociation results for NO2+ it was

expected that by lowering the photon energy and using tune-able radiation that bound!quasibound transitions could beobserved from which the increased number of resulting frag-ment ions could be detected. Petterson et al. commenced asearch based on their own theoretical calculations for theA2P–X2S+ (8,1), (9,2) and (8,2) bands using a dye laser overthe ranges centred at 536.4 nm (18,643 cm�1), 600 nm(16,666 cm�1) and 575 nm (17,391 cm�1) respectively. How-ever neither they nor two previous groups observed any dis-crete transitions.72 The results of more recent ab initiocalculations have implied that the search was conducted toofar to the red; previous calculations with smaller basis setstended to predict too low a barrier height.77 If searches wereconducted too far to the red, then the implication is that anytransitions that were pumped would have terminated in quasi-bound states that had lifetimes too great to dissociate on thetimescale of an ion beam experiment.We predicted that the 7–6 and 8–7 vibrational bands of the

A 2P state should be within our frequency and lifetime win-dows.45 We have made preliminary studies of the mass spec-trum and fragmentation of NO2+ ions in our spectrometer,and believe that the spectra should be observable if we uselaser powers greater than 1 W. We have made some prelimin-ary searches for an infrared spectrum, covering only a smallfrequency range. So far our searches have been unsuccessful.We will conduct a thorough search for the infrared spectrumof NO2+ in the near future.

4.5 Ion beam spectroscopy of DCl2+

The hydrogen chloride dication was first observed in a massspectrometer by Thorburn in 1959.78 Since then there havebeen many low resolution studies.39,79–83

4.5.1 Theoretical calculations on HCl2+. Calculations ofHCl2+ properties have included the energies of the lowestvalence state of HCl2+ in 3S, 1D, 1S, 3P and 1P symmetries,84

these were used to unambiguously assign several transitions inan Auger spectrum of HCl; potential energy curves for the3S�, 1D and the repulsive 3P state of HCl2+;85 tunnelling ratesfor vibrational levels in the 3S�, 1D and 1S+ states of HCl2+ aswell as predissociation rates arising from spin-orbit interactionbetween the latter two levels and the 3P state and of a fourthnon-repulsive state, c5S�.86 Bennett and McNab87 used MRCIcalculations to produce potential energy curves for the fourlowest electronic states. They showed that the quality of thecalculation (i.e. basis set size) had a considerable bearing uponthe height of the potential barrier. The barrier height decreasedas the size of the basis sets was increased, it was therefore con-cluded that the potentials represented upper limits for the truewell depths. Most recently Ellingsen et al. have performed fullyrelativistic configuration interaction calculations for HCl2+.88

Using the Bennett and McNab potential for HCl2+ some ofus calculated theoretical infrared spectra of HCl2+ and DCl2+

to see what spectra might be observable with our experiment.The accuracy of the Bennett and McNab potential was estab-lished by using it to synthesise existing vibrationally resolvedTPEsCO spectra of HCl2+43 (see section 2.2) and DCl2+.89

For HCl2+ the predicted infrared spectrum consisted of very

broad lines that are not ideally suited to our experiments(see section 4.6 below). However, we predicted an extensiveinfrared spectrum for the deuterium isotopomer DCl2+ asshown in Fig. 10.We found that the v ¼ 2–1 band vibrational system of the

ground electronic state X 3S� was predicted to lie within thefrequency and lifetime windows for our experiment, and thatthe transitions had a transition dipole of about 0.7 D.kThe rotational structure shown in Fig. 10 is appropriate for

a 1S–1S transition, but the transitions for DCl2+ are 3S–3Stransitions. The two unpaired electrons that give rise to thetriplet state interact with each other directly (a spin–spin inter-action) and indirectly through spin–orbit/orbit–spin inter-actions via excited electronic states; the combination of theseinteractions gives rise to a spin-splitting term with constant lin the Hamiltonian which causes individual rotational levels(signified by the N quantum number) to split into three(labelled with the J quantum number). There is also a spin-rotation term with constant g. We express the coupling ofthe angular momenta as

J ¼ N þ S:

and as S ¼ 1, J takes the values N+1, N and N� 1. The finestructure energy level diagram and stick spectrum for a P-branch (DN ¼ �1) 3S�–3S� transition is shown in Fig. 11.Hyperfine interactions split the DCl2+ 3S–3S spectra still

further. Hyperfine energy splittings are due to magnetic andelectrostatic interactions between the nuclei and the electronsof the molecule.The magnetic moment of the chlorine nucleus is much larger

than that of the deuterium nucleus and we are able to observehyperfine splittings due to the chlorine nucleus, but not thedeuterium nucleus. We therefore only need consider the chlor-ine nuclear spin in any calculations and we express the

Fig. 10 Simulated spectrum of Dv ¼ 1 vibrational bands within theX 3S� state of DCl2+. The calculated transition frequencies and rela-tive intensities are shown in the lower part of the spectrum. The rangethat can be observed by experiment is about 900–1100 cm�1 and thisrange is indicated on the figure by vertical lines. Whether a spectrumcan be observed with our technique depends crucially upon lifetimes(linewidths), and the lifetimes of both the upper and lower states ineach transition are shown above the relevant transition frequency(these are reminiscent of Fortrat diagrams, because the tunnelling line-widths are J-dependent). For a transition to be observed the lower statelifetime must be greater than 10�6 s (below the line on part (b) of thefigure), and the upper state lifetime must be between 10�6 s and5�10�10 s (between the horizontal lines on part (c) of the figure). Byinspection we see that only the v ¼ 2–1 band fulfils these criteria,although if the calculations of lifetimes are slightly in error then sometransitions of the v ¼ 3–2 band might be observable together withsome high-J levels of v ¼ 1–0.

k 1 D (1 debye)� 3.33564� 10�30 C m.

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coupling of the angular momenta as

F ¼ J þ ICl:

Chlorine has a nuclear spin of 3/2. Each fine structure levelwith J > 1 is therefore split into four, with the F quantumnumber taking values,

F ¼ J þ 32 ;J þ 1

2 ;J � 12 ;J � 3

2

The magnitude and sign of hyperfine constants depend on theelectronic wavefunction, nuclear spins and nuclear moments,and even the signs of hyperfine constants in simple moleculesrequire detailed ab initio calculations for their interpretation.A direct calculation (diagonalization of the Hamiltonian

and transition matrices) assuming values of the relevant con-stants can be used to produce simulated spectra. We have cal-culated such spectra for DCl2+ using ab initio (where available)and estimated (where necessary) values of constants. Each ofthe fine structure transitions shown above is split by hyperfineinteractions into distinctive patterns of lines that can be usedto help the assignment of the observed transitions.

4.5.2 Observed spectra of DCl2+. Some of us first observedan infrared transition of D35Cl2+ in December 1996, and ofD37Cl2+ some days later. We have since recorded extensivespectra for both isotopomers. We first determined the electronicstate involved in the spectra by recording a kinetic energy spec-trum of fragment D+ ions (see Fig. 12) while an infrared transi-tion was in resonance. The Coulomb explosion of the upperstate resulted in a kinetic energy release of between 4.9 and6.0 eV: this compares very well with the expected kinetic energyrelease for the X 3S� electronic state, and is fairly conclusiveproof that it is this state in which the spectrum originates.Part of the infrared spectrum of DCl2+ is shown in Fig. 13.

The spectrum shown is a single fine structure component splitby hyperfine interactions. Our simulated spectra showed thatthe pattern of hyperfine structure seen (two weak lines, threemedium intensity lines and one intense line) is typical of oneof the main (intense) triplet fine structure transitions.With our current ion source and ion optics the frequency

coverage that we can obtain using Doppler tuning about the

individual lines of the CO2 laser is about 50% of the rangefrom 880 cm�1 to 1090 cm�1 for D35Cl2+. The ranges thatwe have scanned for D35Cl2+ are shown in Fig. 14.In addition to the strong triplet lines that we have detected

(such as that shown in Fig. 13) we have also observed someof the much weaker satellite lines. The satellite transitions haveDJ ¼ 0, DN ¼ �1. These satellite lines are split by hyperfinestructure. An example of such a spectrum, and its energy leveldiagram is shown below in Fig. 15.We know we are examining a 3S�–3S� spectrum, but what

of the vibrational assignment? By comparing our theoreticalspectra with the strongest lines in our observed spectrum wedecided that we are almost certainly examining P- and R-branch transitions of the v ¼ 2–1 band of DCl2+. Fig. 16shows the comparison between theoretical and experimentallyobserved transitions. In order to achieve the agreementbetween the observed and calculated spectra shown in Fig.16 above it was necessary to shift the band origin of the theo-retical spectrum (1015.4 cm�1) by �21.1 cm�1. The agreementbetween the calculated and measured spectra is reasonable(considering that no theoretical allowance for the triplet orhyperfine structure was made).We initially thought that with the vibrational band estab-

lished, the rotational analysis of the spectrum would be

Fig. 11 The fine structure energy level diagram and stick spectrumfor a P-branch transition. The rotational selection rule for a P-branchtransition is DN ¼ �1. The strongest transitions (unbroken arrows) inthe energy level diagram correspond to the selection rule DJ ¼ �1 andthe weaker transitions (broken arrows) correspond to the selection ruleDJ ¼ +1,0. Standard spectroscopic notation is given beneath. The lineintensities (relative to the strongest line) are given in the stick spec-trum. Hyperfine structure splits each fine structure component stillfurther, with characteristic patterns. A similar energy level diagramand stick spectrum may be drawn for an R-branch transition, corre-sponding to DN ¼ +1.

Fig. 12 A typical ESA spectrum for D+ ions which arise from theupper state of a resonant transition in D35Cl2+. Forward and back-ward scattered D+ fragments are seen. The transformation from labframe kinetic energy to centre of mass kinetic energy release is illu-strated by the upper and lower scales. Adapted from ref. 22.

Fig. 13 Part of the infrared spectrum of D35Cl2+. The spectrumshown was recorded by scanning the drift tube by 500 V at a sourcepotential of 3200 V using a CO2 laser line at a frequency of 951.1923cm�1. The structure observed is a single fine structure component ofthe n ¼ 2–1 vibration-rotation band; the six lines are due to resolved35Cl (I ¼ 3/2) nuclear hyperfine structure.

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straightforward. However, as shown in Fig. 14, we have nospectral coverage in the wavenumber region that is believedto correspond to the band origin. This gives rise to a classicproblem in spectroscopic analysis,90 that many different rota-tional assignments are possible, each of which results in anequally good fit using different rotational constants. One crudecheck that we have on the relative ordering of the J quantumnumbers is the expected increase in linewidth with J.The measured linewidths of individual lines in the spectrum

of DCl2+ can be simply inverted to yield information of thelifetimes of the states of the transitions. From Heisenberg’suncertainty principle we have G ¼ (1/Tupper + 1/Tlower)/2p,where G is the natural linewidth (full width at half maximumof the Lorentzian function) and T is the associated lifetime.However, the upper state lifetime is so much smaller thanthe lower state lifetime that we can assume that G ¼1/(2pTupper).A graph of measured and calculated linewidths is shown in

Fig. 17. The measured linewidths may be power broadened(although we attempt to guard against this by making ourmeasurements at the lowest powers that enable the measure-ment) and may contain unresolved hyperfine structure. Theminimum observable linewidth is set by the energy distributionthat emerges from the ion source (about 10 eV). The measuredlinewidths therefore represent an upper limit to the true line-widths. The theoretical linewidths are for a 1S state, rather

than a 3S state. Therefore, for each theoretical frequency wehave indicated the range over which the linewidth may beexpected to appear with an error bar of �10 cm�1 (�l).The R-branch head is the most obvious feature of the

measured linewidths, lying at about 1048 cm�1. A shift of�21.1 cm�1 was required to bring the measured and calculatedbranch heads into agreement (as done above in Fig. 16). Thefew lines around 950 cm�1 with much larger than expectedlinewidth may belong to the R-branch of the v ¼ 3–2 vibra-tional band. A similar diagram can be drawn for theD37Cl2+ data.The calculated and measured linewidths agree quite well,

especially at around 1048 cm�1, allowing for the shift of thetheoretical spectrum. This is further evidence that we areindeed observing the v ¼ 2–1 band of D35Cl2+. For this assign-ment to be incorrect, our calculated linewidths would need tobe in error by about 10�3 (see Fig. 10).Some of our observed spectra have a characteristic ‘‘quar-

tet ’’ hyperfine structure (illustrated above in Fig. 15) of fourclosely spaced transitions of monatonically increasing inten-sity, and weaker transitions between them. Our simulationsshow that this hyperfine structure is characteristic of thesatellite transitions PQ32 ,

RQ23 etc. which for a P-branch(DN ¼ �1) transition are shown in Fig. 11 by dashed arrows.The total angular momentum of the states involved in the tran-sition changes from F to F� 3. The relative intensities of lines

Fig. 14 Showing the ranges scanned for D35Cl2+. We have achievedabout 35% coverage of the range from 880–1090 cm�1.

Fig. 15 The hyperfine structure energy level diagram and spectrumfor a P-branch quartet transition. The rotational and fine structureselection rules for a P-branch hyperfine quartet transition areDN ¼ �1 and DJ ¼ 0. The strongest transitions (unbroken arrows)in the energy level diagram correspond to the hyperfine selection ruleDF ¼ 0 and the weaker satellite transitions (broken arrows) corre-spond to DF ¼ �1.

Fig. 17 A graph of measured (open circles) and calculated linewidths(full squares with valid ranges indicated) for all measured transitionsof D35Cl2+. The measured linewidths represent an upper limit to thetheoretical linewidth.

Fig. 16 A comparison of measured transition frequencies and widthswith the theoretical spectrum of the v ¼ 2–1 band as predicted above.The theoretical spectrum has been generated without any considera-tion of structure due to unpaired electron spin, so each theoretical lineshown will be split into six components due to spin splitting and thenfurther split by hyperfine structure. Adapted from ref. 22.

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belonging to a single rotational (DN) transition can be exactlycalculated using angular momentum theory.91 We have there-fore been able to use the relative intensities of the hyperfinepatterns to help to assign their angular momentum quantumnumbers.92 Analysis of our observed quartet spectra formedthe basis for a preliminary assignment of the D37Cl2+ spec-trum.The quartet spectra were used in a preliminary determina-

tion of the hyperfine constants.92 First-principles calculationsof the Fermi contact constants for the deuterium and chlorinenuclei as a function of bond length for DCl2+92 showed thatthere is only a weak dependence on bond length and vibra-tional state for DCl2+. The vibration-rotation dependencewas therefore ignored in our preliminary determination ofthe experimental hyperfine constants, that is the hyperfineinteractions were treated as small perturbations of the widelyspaced terms.The hyperfine parameters comprising the Fermi contact

interaction (bF), the axial dipole–dipole interaction (c) andthe electric quadrupole interaction (eq0Q) essentially controlthe magnitude of the hyperfine splittings within the quartetstructures. The uncertainties in our transition wavenumbersare of the order of 0.006 cm�1 (180 MHz). However, wheremultiple lines are observed in a single scan (such as a quartet)reproducibility is excellent, and the predominant uncertaintyin the relative wavenumbers (separations) between lines isdetermined only by the accuracy with which line centres canbe measured by fitting a suitable line shape function i.e., towithin 20 MHz).In this preliminary work92 we were able to determine values

for the hyperfine constants directly in a linear least square fit.Values for the Fermi contact constant, bF and the axial dipole–dipole interaction, c were obtained from this analysis; how-ever, attempts to include the electric quadrupole interactionterm, eq0Q in the fit produced physically unrealistic magni-tudes for the constants and this was therefore set to zero.Our current estimates for the hyperfine parameters in the X

3S� electronic states of DCl2+ (ignoring vibrational and rota-tional dependence) are for D37Cl2+: bF ¼ 140(21) MHz,c ¼ �75(21) MHz and eq0Q ¼ undetermined, for D35Cl2+

bF ¼ 162 (30) MHz, c and eq0Q undetermined.These values are very insensitive to the exact assignment of

the quartet patterns, which may still be in error. The measuredFermi contact (isotropic hyperfine) constant (bF) is in goodagreement with first-principles calculations.92 The positive signof the experimentally determined bF constant is supported bythe fact that the sign of the constant in the isoelectronic mole-cule PD is also positive for the phosphorus nucleus.93

Ignoring vibration–rotation effects, the isotope shifts for thehyperfine constants are expected to be in the ratio of thenuclear magnetic moments of the 35Cl and 37Cl nuclei as bothhave the same nuclear spin, that is in the ratio m(35Cl)/m(37Cl) ¼ 1.2.94 As can be seen, the Fermi contact constantsthat were determined agree well with this prediction and wecan therefore estimate the dipole–dipole interaction forD35Cl2+ to be c ¼ �90 (25) MHz. We are now in the unusualposition, for infrared spectroscopists, of having determinedhyperfine constants, but not the fine structure constants.Our attempts to arrive at a consistent assignment and deter-

mination of fine structure constants for both isotopomers ofDCl2+ have so far proved unsuccessful. In our measured spec-tra the exact position of the band origin, v0 , is unknown but itlies within a wavenumber range (990–1021 cm�1) that is notaccessible to us with our current light sources. Attempts toassign the spectrum and obtain least-squares fit estimates ofthe band origin and the fine and hyperfine structure molecularconstants have therefore been made using an incomplete set ofline positions. In order to arrive at a definitive assignment andfit of the DCl2+ spectra, we need additional information. Wehave chosen to use the Zeeman splitting of lines to help us

determine the absolute angular momentum quantum numbersinvolved in transitions.

4.5.3 Zeeman spectroscopy of DCl2+. As well as helping usto assign our spectrum, magnetic properties of molecules are ofinterest in their own right (see for example95). An example of aZeeman split infrared spectrum of DCl2+ is shown in Fig. 18.The lower spectrum is a quartet of lines (due to hyperfine inter-actions) with the F quantum number (for total angularmomentum including nuclear spin) increasing in units of onefrom left to right across the spectrum;96 the F-quantumnumber is the same in both upper and lower states92 for thisspectrum. From the Zeeman split spectrum shown (recordedat a field of 60.67 G) and others recorded at higher fieldsit was deduced that the lowest F-transition was split into14 ¼ 4F components (not all components are resolved), whichshows unambiguously that the F-quantum numbers in boththe lower and upper state were 7/2, 9/2, 11/2 and 13/2 fromleft to right as shown.

4.5.4 Summary of results on DCl2+. We have obtained highresolution (hyperfine resolved) spectra of both the D35Cl2+

and D37Cl2+ isotopomers of HCl2+ over the range 880–1090cm�1, with about 35% frequency coverage. Our first assign-ments in the observed spectra were of characteristic ‘quartet ’patterns which correspond to the weak transitions PQ12 etc.From the characteristic intensity patterns in the spectra wewere able to determine a range of N quantum numbers fromwhich each spectrum might originate. We were able to arriveat a consistent set of assignments for these hyperfine quartets,which enabled an accurate determination of the hyperfine con-stants in both of the isotopomers, and which were consistentwith the expected isotope shift between the isotopomers.Despite our best efforts, we have not yet been able to unam-

biguously assign the infra-red spectra of DCl2+. We are pre-sently in the somewhat unusual position of having measuredwell determined hyperfine constants but not yet being able todetermine the fine structure constants. In order to arrive atan unambiguous assignment of the data we have decided tomake Zeeman splitting measurements of some lines, hopefullyto arrive at definite assignments of the total angular momenta(F-quantum numbers) involved in some transitions. So far wehave only made one such measurement, but we will soon re-measure enough lines to make the spectroscopic assignmentproblem tractable.

Fig. 18 The lower part of the figure shows a single fine structurecomponent of the infra-red spectrum of D35Cl2+, split into four bynuclear hyperfine interaction with the chlorine nucleus. The upper halfof the figure shows the same spectrum recorded with an axial magneticfield of 60.7 G; Zeeman splitting of the lines can clearly be seen.Adapted from ref. 96.

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4.6 Ion beam spectroscopy of H37Cl2+

We made a preliminary study of H37Cl2+ with our apparatus.Transition frequencies, widths and intensities for the X 3S�

state of H37Cl2+ were calculated with LEVEL97 from theab initio potential energy surface and transition dipole momentfunction calculated by Bennett and McNab.87 Several transi-tions in both the 2–1 and 1–0 bands are within the frequencyrange of the CO2 laser. A theoretical spectrum over thefrequency range of interest is reproduced in Fig. 19. Thewidths of the most intense transitions that fall within the fre-quency range of the CO2 laser used far exceed the range overwhich the laser can be Doppler tuned.To scan these very broad ranges (several cm�1) a pointwise

frequency scanning approach was used. The total photodisso-ciation rate was measured at intervals of approximately 1cm�1 by using a fixed accelerating potential and differentCO2 laser lines. This approach was successfully used by Car-rington et al. in measurements of broad lines in HeH+.98

The measured photodissociation rates were normalised withrespect to parent beam current and incident laser power. Wehoped that peaks in normalised photodissociation intensitywould be observed across several CO2 lines, but the resultswere inconclusive.

5. Discussion

We have considered in detail the only three molecular dica-tions, N2

2+, NO2+ and DCl2+, for which rotationallyresolved spectra are available, together with some discussionof unsuccessful searches for a high resolution spectrum ofCO2+ by discharge spectroscopy and ion beam spectroscopy,and for an ion beam spectrum of NO2+. The rotationallyresolved spectra of molecular dications have been obtainedboth by examining the light from gas discharges, and byion beam spectroscopy using laser light sources and indirectmethods of detecting the absorption of radiation. Despitethe intrinsic difficulty of these experiments, good experimentaldata is now available with which to benchmark calculations ofdication properties. In obtaining the high resolution data, lowresolution information from other spectroscopic techniqueshas proved to be invaluable in guiding searches, but as we haveshown, the inversion of low resolution spectroscopic data mustbe performed with particular care for dication spectra.The next obvious challenges to dication spectroscopists are

to obtain rotationally resolved spectra of polyatomic dicationsand of thermodynamically stable molecular dications. We now

discuss the possibility of making such measurements with ionbeam spectroscopy.Spectra of polyatomic molecular dications will become

increasingly difficult to obtain by ion beam spectroscopy asthe size of the molecular dications is increased because thetotal ion current available from a source is distributed acrossall levels that are populated in the ionisation process. Poly-atomic molecules have many more levels than diatomic mole-cules, and therefore the population of any individual statemay become too small to be of use as the number of energylevels increases. It will probably be possible to probe tri-atomic or tetra-atomic molecular dications, but larger molecu-lar dications may not be readily observable by ion beamspectroscopy.To obtain ion beam spectra of thermodynamically stable

molecular dications will be particularly challenging. Falcinelliand co workers11 formed stable monohalide dications of bar-ium, strontium, calcium and magnesium by electron impacton effusive beams containing the neutral molecules that weregenerated using high-temperature ovens and differential pump-ing. Ion beams formed in this way are usually rather weak andare not ideal for ion beam spectroscopy. More promising arethe thermodynamically stable dications XeNe2+ and SiF2+.XeNe2+ was first identified by reaction of Xe2+ and Ne in adrift tube11 and subsequently has been formed by electronimpact ionization of the van der Waals dimer of NeXe.14

The dication SiF2+ was formed by photodissociation ofSF4 .

13 It is likely that specially constructed ion sources wouldbe necessary for us to form high current beams of these dica-tions in our apparatus. The detection techniques so far usedin ion beam spectroscopy of molecular dications rely uponthe formation of fragment ions to enable high detection sensi-tivities. There are many techniques that can be used to obtainion beam spectra of stable molecular ions (for a review see ref.59), but many of them have far lower intrinsic sensitivity thatdetection of fragment ions formed by predissociation.Two other techniques could certainly be used to obtain valu-

able spectroscopic information on molecular dications; spec-troscopy in ion storage rings and in ion traps. Very littlespectroscopy has so far been performed in ion storage ringsand to the best of our knowledge the only molecular spectrato be studied so far were of CO+ 99 and N2

+.100 Theearly application of ion storage rings to determine the lifetimesof long lived states of CO2+ 18 has not been followed up byspectroscopic measurements. Spectroscopy of molecular ionsin traps has a rich history, including the first spectroscopicmeasurements of the simplest molecule, H2

+.101 To the best ofour knowledge, no spectroscopy of molecular dications has yetbeen accomplished using ion trap techniques.Photoelectron spectroscopy has already been applied to

dication spectroscopy with vibrational resolution by investi-gating double photo ionisation. The limiting factor in the reso-lution is the linewidth of the light source used, which iscurrently light generated from a synchrotron. If high intensitynarrow linewidth tunable light sources were to become avail-able in the far or extreme ultraviolet, then photoelectron (dou-ble photoionisation) spectroscopy of dications would probablybecome the most widely applicable technique. It is also possi-ble to investigate dications by single photoionisation of mole-cular ions (see for example ref. 102), but this then gives rise tothe difficulty that the target molecular ion sample necessarilyhas very low density.The next challenge for us is to further our work on Zeeman

spectroscopy of molecular dications, and to use the spectrathus generated to help us to arrive at a global fit of ourDCl2+ data. We then intend to perform extensive searchesfor infrared spectra of NO2+ and CO2+; we will be particularlypleased if we are able to find spectra of these molecular ions,which have proved so elusive to measurement using otherion beam spectrometers.

Fig. 19 Theoretical transition intensities for the 2–1 and 1–0 bands ofthe X 3S� state of H37Cl2+ (note the logarithmic intensity scale).

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Acknowledgements

We are grateful to EPSRC and to the Research Committeeof the University of Newcastle upon Tyne for their generoussupport of this work, IMcN is grateful to Professors A. S.Dickinson, J. M. Brown and G. Duxbury for helpful discus-sions, PK is grateful to the School of Natural Sciences, Univer-sity of Newcastle upon Tyne, for a studentship.

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