Introduction

Spectra of molecular dications (doubly positively charged molecules) with better than vibrational resolution have proved difficult to obtain. The first dication to be measured with rotational resolution was N₂²⁺
(1958), the second was NO²⁺ (1987) and our measurements of  DCl²⁺  in 1995 were the third. The timescales involved give a good idea of the experimental difficulties involved in determining highly resolved spectra of these species. 

Molecular dications are metastable and extremely chemically reactive and are the subject of growing interest. The molecular bonding causes unusual potential energy (hereafter pe) curves that have a minimum and a barrier to dissociation into two charged fragments;examples of such curves are shown in figure one. Vibrational levels, all of which are metastable, may be supported above the dissociation limit. The lower levels can be extremely long lived, whereas the upper levels may dissociate within picoseconds. Calculation of the lifetime of dications in different energy levels is even now (2011) a difficult problem, and the subject of theoretical development and research. If population is transferred from long lived levels, to short lived levels the resulting "Coulomb explosion" releases considerable kinetic energy (several eV / dication).

The shape of dication pe curves suggests that the barrier may result from an avoided crossing but sophisticated calculations show that it is more often better thought of as resulting from competition between Coulomb and valence forces. It was initially believed that dications would dissociate by tunneling through the barrier (which would cause J-dependent linewidths), For our measurements of DCl²⁺ this is correct because transitions originate in an essentially unperturbed ground electronic state of the dication. However, for earlier high resolution spectra of N₂²⁺measurements showed that in the lower vibrational levels of the first excited electronic state the dissociation was caused by electronic predissociation (with no J-dependence of linewidths). Ab-initio calculations are not yet routinely able to predict the observed structure and lifetimes of dications and it seems that the region close to the top of the barrier (which is that probed by fast ion beam spectroscopy) is the most demanding part of the pe curve to calculate accurately.

Achievements of the Research

Our most important objective, to obtain dication spectra, was been achieved; we observed many vbration rotation transitions of the doubly charged molecule DCl²⁺. As theoretical support we calculated accurate ab initio pe functions for the lowest four electronic states of DCl²⁺.

Outline of Experiment

In the fast ion beam spectrometer that we developed, ions were formed in an electron impact ion source and accelerated into a magnetic sector where the dication of interest was selected. The selected dications formed a beam that was collinear with a laser beam from a line tuneable CO/CO₂ laser (lines typically separated by 1-2 cm-1). For light dications almost complete frequency coverage could be obtained by Doppler shifting the ions using retarding or accelerating voltages applied to the "drift tube". At resonance, population was moved from one state to another with a different predissociation lifetime, consequently the number of fragment ions formed was increased. The fragment ions were selected with an electrostatic analyzer and detected with an electron multiplier. A plot of fragment ion intensity against Doppler shifted frequency yields the spectrum.

We decided that the ideal candidate dication for study would have one light and one heavy nucleus. A because the fragments which are monitored with the electrostatic analyzer are far removed from the parent peak. The consequence of the above equations is that a dication which fragments to one light and one heavy fragment will display three convenient properties. (i) Although the fragments have half the charge of the parent, the masses are not close to half the parent mass and hence will be transmitted at far removed electrostatic analyzer voltages; this avoids the problem of overlapping the parent beam. (ii) The resolution of the analyzer is fixed and given by dE/E, because the light fragment forward-backward scattering pattern appears at low energy (small E) it is well resolved and this aids kinetic energy analysis. (iii) The heavy fragment is not well resolved by the analyzer and so shows essentially no splitting; the resulting high collection efficiency presents an ideal way of monitoring increased fragmentation on resonance.

With these considerations in mind we decided to examine the species DCl²⁺, a light- heavy diatomic with many predicted transitions in our wavenumber range (HCl²⁺ only had one predicted transition).

The mass spectrometry of DCl²⁺.

The magnetic analyzer following the ion source transmitted ions with a specific mass/charge ratio. We could be certain that we were examining DCl²⁺ because both the isotopes D³⁵Cl²⁺ and D³⁷Cl²⁺ have odd masses and hence appeared at half integer mass/charge (37/2 and 39/2). In addition to this, the expected pattern of intensity is 3:1 for the ³⁵Cl and ³⁷Cl isotopes respectively and this was clearly observed.

The infrared spectrum of DCl²⁺.

Our calculations led us to believe that the infra-red spectrum of DCl²⁺ in its ground electronic state (triplet sigma) should be fairly extensive within the wavenumber and lifetime ranges available to us. These calculations agreed quite closely with previous (less sophisticated) ab-initio work, but appear to be at odds with the recent photoelectron spectra obtained by McConkey et al.. Their photoelectron spectrum of HCl²⁺ was vibrationally resolved and appears to show five vibrational levels in the ground electronic state. Our calculations predicted only three vibrational levels. This discrepancy was resolved once we realized that HCl dication displays "above barrier" resonances. 

We have recorded hundreds of vibration-rotation transition in D³⁵Cl²⁺ and D³⁷Cl²⁺ and made preliminary assignments. Better assignments of the data await significant improvements in ab-initio theory. The basis-sets with which we made our calculations (nearly twenty years ago!) have barely been improved upon. The complete recording and analysis of the infrared spectrum of DCl²⁺  in the range available to us was substantially completed. A preliminary communication was published as a Journal of Chemical Physics Communication (108, 1761-1764 (1998). In order to be certain that the first transitions we found were genuine we confirmed that:

(a) that the transition disappears when the laser is off (it does),

(b) that the transitions disappears when adjacent laser lines are used (it does),

(c) that the transition is observable at different combinations of accelerating and retarding voltages (it is),

(d) that the transition can be observed by monitoring both D+ and Cl+ fragments (it can).

(e) that the "on-resonance" kinetic energy release spectrum shows a centre of mass kinetic energy release appropriate for the ground state (it does).

Assignment of the spectrum

We originally believed that a full analysis of the infrared spectrum of DCl²⁺ would be straightforward as we have four "tools" to aid our spectroscopic assignment: linewidths (tunneling lifetimes), rotational progressions, vibration-rotation isotope effects, and measurements of the kinetic energy of fragmentation. Nevertheless, the spectrum has not yet been fully assigned.

Theory shows that the tunneling lifetimes of dications are less sensitive to rotational level than those of normal molecules. For DCl²⁺ the lifetime changes from 7x10-8s at J=10 to 2x10-10s at J=20. The insensitivity to angular momentum arises because the potential barrier is mostly due to Coulomb repulsion between the two charge centers. The practical result of this is that we expect to be able to observe rotational progressions of lines (one is not usually so fortunate in fast ion beam work) which will be amenable to traditional methods of analysis.

The tunneling lifetimes of the states involved in these spectroscopic transitions determine the measured linewidths. Calculations show that a small change in the vibration- rotation energy of the upper state results in extremely small changes in the calculated lifetimes. Consequently, we expect to use the measured linewidths as an aid in our initial assignment; the widths should be a good guide to the barrier width (and hence energy beneath the top of the potential barrier) confining the upper level of the transition.

Each transition that is measured releases fragments with considerable kinetic energy. The geometry of the instrument is such that only fragments scattered within 3 milli-steradians about the beam axis are detected. The resultant forward-backward scattering pattern for D+ fragments from DCl²⁺ is shown in figure four. By narrowing the acceptance angle of the ESA the resolution can be increased sufficiently to enable the energy release to be compared with calculations of absolute vibration-rotation energy levels as an aid to assignment.

Isotopic substitution shifts vibration-rotation transition wavenumbers in a well understood manner. DCl²⁺is available in two isotopes (the natural abundance ratios for Chlorine result in an observed 3:1 mix of D³⁵Cl²⁺: D³⁷Cl²⁺ in the ion beam) and we have recorded spectra of both. As the difference between the reduced masses is small, we observe pairs of lines (one for each isotope). The measured shift between isotopes is direct evidence of the vibration-rotation band involved.

We do not yet have sufficient data to assign the rotational structure unambiguously, but we are certain that we are measuring transitions in the 2-1 vibrational band. The transitions are very intense, and vary in intensity by over four orders of magnitude. We can easily see the strongest transitions using laser powers of a few milli Watts, and arrangements are in progress to attempt to record the spectrum with diode lasers.

Many of the lines that we see in the spectrum are in a characteristic grouping of four closely spaced transitions. This is due to hyperfine structure. Such structure arises because of the interactions between electron spin (S), the rotation of the nuclear framework (R), the rotation of the electrons (L) and the nuclear spins (ID=1, ICl=3/2); the largest hyperfine interaction is probably the fermi contact-interaction, which we estimate to be 200 MHz. We have programmed a perturbation Hamiltonian with which to calculate this hyperfine structure based on the triplet sigma hamiltonian of Carrington et al.. Because it is possible to resolve the hyperfine structure in some lines of the spectrum we expect to learn more about the molecular physics of the bond in DCl²⁺ than has hitherto been possible for any molecular dication.

Conclusion

We located the first infrared spectrum of a molecular dication and were able to substantially increase theoretical understanding of these species.