Strong ortho/para effects in the vibrational spectrum of Cl⁻(H₂)

Vibrational spectroscopy of weakly bound molecular and ionic complexes provides rich information on their structure and intermolecular forces.^1–3 The dihydrogen halide complexes X⁻(H₂) with X = F, Cl, Br, and I are fundamental systems that allow for precise experimental and theoretical studies.^4–9 These systems have also been of much interest for photoelectron transition state spectroscopy of the corresponding neutral reactions.^10–14 Wild et al. studied the predissociation spectra of dihydrogen halides X⁻(H₂) with X = F, Cl, Br, and I by infrared spectroscopy.^4,5 Their work focused on the intra-monomer H–H stretch vibration in the region above 3990 cm⁻¹.

In recent years, vibrational predissociation and laser-induced reaction spectroscopy in multipole radiofrequency ion traps combined with buffer gas cooling has emerged as a powerful action spectroscopic method.^3,15–21 Using this technique, Spieler et al. observed several low frequency vibrational transitions of the $Cl−35$(H₂) complex in the range of 600–1100 cm⁻¹ at 8 and 22 K.⁸ On the basis of anharmonic vibrational self-consistent field and vibrational configuration interaction calculations, the most plausible explanation for the detected bands was a combination of the fundamental Cl⁻(H₂) bending with the fundamental Cl⁻(H₂) stretching vibrations and strongly red-shifted overtones thereof. This motivated Lara-Moreno et al. to employ accurate quantum calculations of this predissociation spectrum⁹ using the potential energy surface (PES) of Buchachenko et al.⁶ Strong differences between the vibrational spectra of the two para and ortho nuclear spin isomers of Cl⁻(H₂) were found. Only one of the nuclear spin isomers, the Cl⁻(o-H₂) complex, matched the experimentally detected vibrational bands, concluded that the Cl⁻(p-H₂) complex was not seen in the experimental spectra.

In their respective ground states, the two complexes of the para form Cl⁻(p-H₂) and the ortho form Cl⁻(o-H₂) are linear and nearly degenerate with an energy difference of just 8.9 cm⁻¹.⁹ This energy difference represents the splitting that is caused by tunneling through the barrier that hinders the H₂ unit from rotating. By permutation inversion symmetry, the lower energy state correlates with the para hyperfine state of H₂, whereas the higher energy state correlates with the o-H₂ state. In higher lying vibrational levels, tunneling through the rotational barrier becomes much more important and the energy difference between para and ortho levels increases substantially.⁹ 

In this work, we present far-infrared vibrational spectra of the $Cl−35$(H₂) complex for both the previously not observed para complexes and the ortho complexes and compare them with high-level theoretical calculations. The explanation why the Cl⁻(p-H₂) features have not been found thus far is that at low temperatures, ligand exchange can take place,²² 

The energy difference ΔE = 109.8 cm⁻¹ is given by the difference of the rotational excitation of o-H₂ and the tunneling splitting of the para and ortho ground states of the complexes.⁹ Attributed to this ligand exchange, previous experiments^8,23 only detected the Cl⁻(o-H₂) bands.

The forward and backward directions of reaction (1) lead to a collision temperature-dependent para to ortho ratio of the complex. We approximate this by assuming that the exothermic and presumably barrierless forward reaction is described by the Langevin capture rate k_L, while the backward reaction is described by the product of the same capture rate k_L and a Boltzmann factor to account for the necessary activation energy ΔE. With the capture rates canceling, this leads to the para to ortho ratio

with k_B being the Boltzmann constant and T being the collisional temperature. Using normal hydrogen with a 3:1 ratio of o-H₂ to p-H₂ and a trap temperature of 22 K, this leads to a fraction of Cl⁻(p-H₂) of 3 · 10⁻⁴, which did not allow for the detection of vibrational absorption.⁸ In order to increase the fraction of Cl⁻(p-H₂) above the detection limit, in this work, we employed para-enriched hydrogen and heated the ion trap and the buffer gas to more than 40 K. With this, Cl⁻(p-H₂) fractions of up to 50% are expected.

The predissociation spectrum of $Cl−35$(H₂) is recorded using the cryogenic 22-pole ion trap instrument FELion located at the Free Electron Lasers for Infrared eXperiments (FELIX) Laboratory at Radboud University, The Netherlands.¹⁸ Chlorine anions are produced in an ion storage source²⁴ by dissociative electron attachment to CCl₂F₂ diluted in helium. The ions are then mass filtered by a quadrupole and loaded into the cryogenic 22-pole ion trap. The trap is temperature variable from 4 to 41.5 K. We use a pulsed buffer gas of para-enriched H₂ seeded in helium to form $Cl−35$(H₂) ions by three-body collisions and cool them in subsequent collisions. The fraction of p-H₂ is estimated to be at least 97%, given the hydrogen temperature and pressure at production and the delay time between production and use in the experiment. The ion complexes are expected to thermally equilibrate with the buffer gas in the trap on a millisecond time scale. The complex formation efficiency increases when the temperature decreases, in agreement with recent measurements of the ternary rate coefficient for Cl⁻(H₂) formation.²⁵ When comparing the signal of trapped Cl⁻(H₂) with that of trapped Cl⁻, we observe that the complex formation is significantly less efficient with p-H₂ compared to normal H₂, which contains 75% o-H₂. At 41.5 K, we note complex fractions of ≈0.5% and 5.3% with para-enriched H₂ and normal H₂, respectively.

Vibrational predissociation is initiated by pulses of the free electron laser FEL-2. In the range from 450 to 800 cm⁻¹, FEL-2 delivers varying pulse energies from 20 to 35 mJ inside the trap at 10 Hz repetition rate with a macropulse duration of a few microseconds. The calculated binding energy of Cl⁻(p-H₂) and Cl⁻(o-H₂) is 416.5 cm⁻¹ and 526.3 cm⁻¹, respectively.⁹ Thus, absorption of a single photon can already lead to predissociation. The FEL-2 is optimized for narrow bandwidth, reaching typical rms widths of about 0.2%–0.4% of the center value¹⁸ or about 6 cm⁻¹ (FWHM) for the present experiment. The measured ion depletion signal is normalized to laser pulse energy and the number of pulses and corrected for drifting source conditions.

Two kinds of quantum calculations are performed. First, a rotationally adiabatic calculation is done in order to obtain the potential energy curves and the vibrational levels of Cl⁻(p-H₂) and Cl⁻(o-H₂) shown in Fig. 1 for the total angular momentum J = 0. This is an approximate calculation since the non-adiabatic couplings are neglected, but it provides a clear scheme of the major transitions. Second, accurate calculations as described by Lara-Moreno et al.,⁹ including all necessary values of J, are done in order to obtain the stick spectrum shown in Fig. 2. The adiabatic potential curves for the doubly degenerate bending motion v₂ are shown in Fig. 1 as a function of the Cl⁻–H₂ distance. They support the corresponding eigenvalues and eigenfunctions for the stretching motion v₁. l₂ is the projection of the vibrational angular momentum along the principal axis of the linear equilibrium structure. The H₂ stretching mode v₃ has also been included in the calculation. Since v₃ = 0 throughout this work, we omit v₃ in the following.

In Fig. 1, the para and ortho ground state levels with (v₁, $v2l2$⁠) = (0,0⁰) are separated by the 8.9 cm⁻¹ tunneling splitting, as discussed above. The potential well is deeper for Cl⁻(o-H₂), resulting in a higher dissociation energy compared to Cl⁻(p-H₂) and in its higher abundance in a low-temperature ensemble. Figure 1 also shows possible dipole-allowed vibrational bands for the para and ortho levels, indicated by the colored arrows. The para vibrational bands are found at significantly lower photon energies than the corresponding ortho bands.

The single photon vibrational predissociation spectrum of $Cl−35$(H₂) produced from p-H₂ is shown in Fig. 2(a) at three different temperatures. The 14 K spectrum has already been measured by Spieler et al.; it shows only the one strong band at 773 cm⁻¹ that matches the band measured for complexes produced from normal H₂.⁸ This vibrational transition does not belong to $Cl−35$(p-H₂) but is assigned to the overtone transition (0,2⁰) ← (0, 0⁰) of Cl⁻(o-H₂), which we refer to as a (0,2⁰) transition below.⁹ Its calculated vibrational spectrum is shown in red in Fig. 2(b). The spectrum is produced by folding the different rovibrational transitions of the P and R branches with the estimated free electron laser (FEL) spectral width of 6 cm⁻¹ (FWHM).

Raising the trap temperature to 30.5 and 41.5 K, two additional vibrational bands appear at lower frequencies near 500 and 600 cm⁻¹, respectively. These vibrational bands agree well with the calculated spectrum for Cl⁻(p-H₂) [blue transitions in Fig. 2(b)], again folded with the spectral width of the FEL. These two bands are therefore assigned to transitions to the (0, 2⁰) and (1, 2⁰) bands of Cl⁻(p-H₂). For the calculated spectrum, a 41.5 K rotational temperature and a para to ortho ratio of the complex of 1:1 have been used. All observed vibrational bands are Σ-type (Δ l₂ = 0) overtone transitions with Δv₂ = 2. For combination bands that involve a joint excitation of the v₁ mode, the intensity and thus the transition dipole moment decrease as expected in this case. The Δv₂ = 1 fundamental transition, while strongly dipole allowed, lies below the binding energy of the Cl⁻(H₂) complex and is therefore unobservable in predissociation spectroscopy.

When comparing the absolute frequency positions of the measured and calculated vibrational bands, one finds a red shift of about 8 cm⁻¹ for the (0, 2⁰) band and about 12 cm⁻¹ for the (1, 2⁰) band (see Table I). We attribute this red shift of about 2% to the overall accuracy of the potential energy surface.

Not only the transition frequency but also the line profiles agree well for the measured and calculated bands. For the lowest frequency band of Cl⁻(p-H₂), even the contours of the P and R branches of the transition are resolved in both the measured bands at 30.5 and 41.5 K. From the calculated stick spectrum, it can be seen that the R branch has a much more compressed structure than the P branch. This shows that the upper vibrational level has a smaller rotational constant or that the Cl⁻(H₂) complex expands upon vibrational excitation. The calculated rotational constants for the (0, 0⁰) ground state and the (0, 2⁰) excited state are B″ = 0.838 cm⁻¹ and B′ = 0.765 cm⁻¹, respectively. The ground state constant compares well with the experimental value $Bexp′′=0.8555(8)$ cm⁻¹ determined by Wild et al. from the rotationally resolved band of the H₂ stretching vibration v₃.²³ 

The difference between the para (0, 2⁰) and ortho (0, 2⁰) bands stems from the tunneling splitting between the geometric structures of the hindered H₂ rotation along the bending coordinate of Cl⁻(H₂). The difference between these two bands is about 260 cm⁻¹, which can be compared to a few hertz in systems such as $Ag35107$Cl(H₂)²⁶ or a few wavenumbers in the system of OH(D₂).²⁷ 

By comparing the intensity of the measured bands with the calculated bands, we can extract the ortho to para ratio of the Cl⁻(H₂) complexes. The area of the para (0, 2⁰) and ortho (0, 2⁰) bands is normalized by the area of the corresponding calculated bands, resulting in the para:ortho ratios for the trapped ions given in Table II. These ratios are compared with the kinetic model described above, which is also shown in Table II. As an input to the kinetic model, a para:ortho ratio of the hydrogen buffer gas of about 100 for 30.5 K and 40 for 41.5 K is approximated based on the reconversion of p-H₂ to o-H₂ that occurs over time.²⁸ The relative increase with the temperature of the experimental ratio is well captured by the kinetic model. The absolute values are found to be 3.6–3.8 times smaller than the ratios estimated from the kinetic model. This could stem from the additional para to ortho conversion of the H₂ gas, before or while it is entering the ion trap.

In conclusion, far-infrared vibrational spectroscopy of the two nuclear spin isomers Cl⁻(p-H₂) and Cl⁻(o-H₂) has been performed in the range of 450–800 cm⁻¹. Using elevated trap temperatures and an enriched p-H₂ buffer gas, we have created a para:ortho ratio of the Cl⁻(H₂) complex of up to 0.24, despite the ligand exchange reaction with o-H₂. This allowed us to detect two vibrational bands in Cl⁻(p-H₂) with peak positions at 510(1) and 606(1) cm⁻¹.

The experimental spectra have been compared with the calculated spectra, computed with an accurate quantum approach. The two main bands can be assigned to transitions from the vibrational ground state to the (0, 2⁰) and (1, 2⁰) states. The positions and the line profiles of the calculated bands, folded with the spectral width of the laser, agree very well with the measured band profiles. While the linear complexes of Cl⁻(p-H₂) and Cl⁻(o-H₂) are nearly degenerate in the ground state, in the excited state, they show an energy difference of about 260 cm⁻¹. This difference illustrates the strong tunneling splitting of the hindered H₂ rotation along the bending coordinate of Cl⁻(H₂).

We thank the FELIX team for their support of this experiment. This work was supported by the Austrian Science Fund (FWF) (Project No. I2920-N27) and the Doctoral Program Atoms, Light and Molecules (Project No. W1259-N27). The research leading to this result was supported by the project CALIPSOplus (Grant Agreement No. 730872) from the EU Framework Program for Research and Innovation HORIZON 2020 and also by the “Agence Nationale de la Recherche” project COLD HMINUS. The operation of the 22-pole trap was partially funded by the DFG via the DFG Gerätezentrum “Cologne Center for Terahertz Spectroscopy” (Grant No. DFG SCHL 341/15-1). We also acknowledge the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) for the support of the FELIX Laboratory.