Double resonance rotational spectroscopy of He–HCO+

Thomas Salomon *a, Matthias Töpfer a, Philipp Schreier a, Stephan Schlemmer a, Hiroshi Kohguchi b, Leonid Surin cd and Oskar Asvany *a
aI. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany. E-mail: salomon@ph1.uni-koeln.de; asvany@ph1.uni-koeln.de
bDepartment of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
cInstitute of Spectroscopy RAS, Fizicheskaya Str. 5, Troitsk, Moscow 108840, Russia
dMoscow Institute of Physics and Technology, Institutskiy Per. 9, Dolgoprudny, Moscow Region 141701, Russia

Received 17th July 2018 , Accepted 21st August 2018

First published on 23rd August 2018


The ground state of He–HCO+ is investigated using a recently developed double resonance technique, consisting of a rotational transition followed by a vibrational transition into a dissociative state. In order to derive precise predictions for the rotational states, the high resolution infrared predissociation spectroscopy of the v1 C–H stretching mode is revisited. Eleven pure rotational transitions are measured via the double resonance method. A least squares fit of these transitions to a standard linear rotor Hamiltonian reveals that the semirigid rotor model cannot fully describe the loosely bound He–HCO+ complex. The novel double resonance technique is compared with other action spectroscopic schemes, and some potential future applications are presented.


1 Introduction

It is generally recognized that molecular ions play an important role in interstellar chemistry and that they are particularly valuable spectroscopic probes of the physical properties (dynamics, density, and temperature) of different regions of the interstellar medium (ISM).1 For these reasons, a large number of studies have been devoted to the characterization of ion–neutral interactions and the computation of rates of collisional (de-)excitation of abundant ions by ambient H2 and He gas. One of the most efficient tools for a reliable elucidation of intermolecular forces is high resolution spectroscopy of van der Waals complexes, because their (quasi-)bound states are very sensitive to the interaction potential.2 For complexes consisting of molecular ions and H2 or He, however, very little is known about their bound states, which mainly originate from the extremely low densities of such species under usual experimental conditions.

To date, most successful efforts have been based on the combination of laser spectroscopy and mass spectrometry. In these experiments, ion clusters are mass selected before irradiation with tunable infrared (IR), visible, or ultraviolet light, and their absorption spectra are monitored as predissociation processes after the resonant excitation by the photons.3 A wealth of information on the geometry and intermolecular vibrational energies has been obtained for the complexes He–HCO+,4 H2–HCO+,5 N2H+–He,6 N2H+–H2,7 CH3+–He,8 and N2+–He,9 using IR predissociation spectroscopy. Although the rotational structure was resolved in at least some parts of the IR photodissociation spectra, more detailed information on the molecular geometry can be provided by microwave (MW) measurements due to an advantage of higher resolution. In certain cases, it is also possible to obtain information on the intermolecular dynamics through the precisely determined centrifugal distortion constants and the hyperfine structure parameters. In contrast to IR spectroscopy, MW methods have never been applied to ionic complexes with He or H2, although there are a number of experimental investigations on relevant neutral van der Waals systems, e.g. CO–H2,10,11 CO–He,12 NH3–H2,13 or H2O–H2.14 The only exception is a novel action spectroscopic method for the rotational spectroscopy of weakly bound complexes, which has been recently developed and tested on CH3+–He.15 This method uses a double resonance consisting of a rotational transition (millimetre-wave) followed by a predissociating transition (IR), and uses the final destruction of the complex as a spectroscopic action signal.

In the present work, we apply this approach to obtain high-resolution rotational data of He–HCO+. HCO+ is particularly interesting because it is probably the most abundant molecular ion in the dense cores of interstellar molecular clouds1 and its complex with He is regarded as a reaction intermediate of the proton exchange reaction, HeH+ + CO → He + HCO+. A previous IR predissociation study4 established that He–HCO+ is linear and has a 1Σ ground state. In this work, the spectroscopic parameters of the ground state have been determined to microwave precision, thus providing the most reliable reference data for testing available He–HCO+ interaction potentials.16–18 It is shown that the floppy nature of the helium bond prevents the modelling of this apparently simple system by a standard linear rotor Hamiltonian.

2 Experimental methods

The experiments have been carried out on the 22-pole ion trap machine COLTRAP.19,20 HCO+ ions are created using a storage ion source by electron impact ionization of a 1[thin space (1/6-em)]:[thin space (1/6-em)]2[thin space (1/6-em)]:[thin space (1/6-em)]3 mixture of carbon monoxide (Linde 3.7) in molecular hydrogen and helium. At the beginning of each experimental cycle, an ion pulse (40 ms) is extracted from the source, mass-filtered for HCO+ (m = 29 u) and injected into the 22-pole ion trap. There, the ions are cooled down in collisions with helium gas, which has been injected into the trap for roughly 100 ms via a piezo valve. Due to the high He number density (estimated peak value n[He] ≈ 1015 cm−3) and low trap temperature (Ttrap ≈ 4 K), a few thousand He–HCO+ clusters are formed via ternary collision processes:
 
image file: c8cp04532a-t1.tif(1)
As shown in Fig. 1, typically 5000 HCO+ and 4000 He–HCO+ ions have been detected, which means that the number ratio between the complex and parent species is on the order of 1.25. On that basis, the ternary rate coefficient is estimated to be k3 ≈ 10−30 cm6 s−1, which is in very good agreement with the observations of Brünken et al.21 During the storage time of typically 700 ms, the ion ensemble is exposed to cw narrow-bandwidth (≪1 MHz) IR radiation, created using an optical parametric oscillator (OPO), leading to the subsequent IR photodissociation (IRPD) in the case of resonance:
 
image file: c8cp04532a-t2.tif(2)
At the end of the trapping period, the trap content is extracted, mass-filtered for the He–HCO+ ions (m = 33 u) and finally detected using a Daly-type detector. The predissociation spectra were recorded by counting the number of He–HCO+ complexes as a function of the OPO frequency. This frequency was measured using a wavemeter to an accuracy of about 0.001 cm−1 (=30 MHz). A laser shutter was used, allowing for a normalization s(f) = c(f)/c0 of the detected ion counts c(f) to the number c0 of the He–HCO+ ions not exposed to infrared radiation.

In the second step, the rotational-predissociation double resonance technique was applied to measure the pure rotational transitions of He–HCO+ in high resolution. The feasibility of this novel technique has only very recently been demonstrated for the CH3+–He complex.15 For this method, the beam of a mm-wave source (which is tunable, narrow-bandwidth, and locked to a rubidium atomic clock) is overlaid with the OPO beam utilizing an elliptical mirror containing a 3 mm hole (see Fig. 1 in Jusko et al.22). The frequency of the OPO is stabilized on a predissociation transition to obtain a constant IRPD signal. When the mm-wave radiation is tuned to rotational resonance, the rotational quantum state probed by the infrared transition is either populated or depopulated, depending on the combination of the two transitions (cf.Fig. 3). This leads to a modulation of the IRPD signal, by which the pure rotational transition can be recorded.


image file: c8cp04532a-f1.tif
Fig. 1 Mass spectrum of HCO+ ions stored in a 4 K He environment, illustrating that up to 5 He atoms can be attached to HCO+ in the first solvation shell.

3 Ro-vibrational spectroscopy

The v1 C–H stretching mode of He–HCO+ was observed first in an octopole ion guide by Nizkorodov, Maier and Bieske in 19954 using a pulsed OPO system with a bandwidth of 0.02 cm−1. In order to obtain rotational predictions better than 30 MHz, the v1 C–H stretching mode was re-investigated using COLTRAP. Due to the nominal trap temperature of 4 K, only the ro-vibrational transitions from P(11) to R(9) were detected in the spectral range between 3070 and 3083 cm−1. A part of the IRPD spectrum is shown in Fig. 2. In these measurements, special care has been taken to limit the IR power to well below 1 mW for the strong transitions in order to avoid saturation of the IRPD signal. Even though the IRPD spectrum appears to possess the regular structure expected for a linear molecule, some infrared transitions are perturbed and accompanied by additional lines, which is in good agreement with the observations of Nizkorodov et al.4 In the case of obviously perturbed transitions, only one of the two pairs with a common upper state in the P- and R-branch was remeasured in order to be able to form combination differences in the ground state. As the measured lineshapes are dominated by Doppler broadening and lifetime broadening (the laser bandwidth and pressure broadening are negligible), the observed lines were fitted with Voigt profiles. The obtained line centers are summarized in Table 1. As can be seen, a systematic shift of roughly 0.02 cm−1 exists between our values and those of Nizkorodov et al. We attribute this to a residual of the Doppler correction applied for the ions flying through the octopole ion guide of the former experiment (the ions had an energy of 8 eV4). In contrast, the cryogenic trapping method presented in this work excludes Doppler shifts. Based on our observations summarized in Table 1, an improved prediction for the vibrational ground state has been achieved. Due to the perturbation for v1 = 1, first, the parameters for v1 = 0 have been determined by a combination difference fit, and with those parameters fixed, the parameters for v1 = 1 have been fitted. All parameters extracted for our ro-vibrational work are given in Table 2 and compared to the former measurements.
image file: c8cp04532a-f2.tif
Fig. 2 Part of the IRPD spectrum of the v1 C–H stretching mode of the He–HCO+ complex observed using COLTRAP. The magnified image shows a dedicated measurement of the J = 1 ← 2 transition with the IR power limited to below 1 mW in order to avoid saturation effects. The data points were normalized to the He–HCO+ counts that have not been exposed to infrared radiation.
Table 1 P and R branch transitions in the v1 band of He–HCO+, compared to former measurements by Nizkorodov, Maier and Bieske.4 All quantities are given in cm−1. The fitted precision is given in parentheses. Our overall accuracy is 0.001 cm−1
J′ ← J′′ This work Nizkorodov et al.4
10 ← 11 3070.02218(2) 3070.005
9 ← 10 3070.51426(2) 3070.496
8 ← 9 3070.78556(3) 3070.767
7 ← 8 3071.70051(1) 3071.688
6 ← 7 3072.26598(2) 3072.247
5 ← 6 3072.84264(2) 3072.826
4 ← 5 3073.469(7) 3073.456
4 ← 5 3073.399(7) 3073.389
3 ← 4 3074.008(4) 3073.991
2 ← 3 3074.59146(1) 3074.578
1 ← 2 3075.17376(1) 3075.150
0 ← 1 3075.755(4) 3075.733
1 ← 0 3076.91449(2) 3076.899
2 ← 1 3077.49138(1) 3077.476
3 ← 2 3078.06705(2) 3078.044
4 ← 3 3078.68377(2) 3078.663
5 ← 4 3079.21160(1) 3079.199
6 ← 5 3079.78637(1) 3079.764
7 ← 6 3080.36893(1) 3080.354
8 ← 7 3080.59918(5) 3080.582
9 ← 8 3081.46840(1) 3081.446
10 ← 9 3082.11226(2) 3082.092


Table 2 Molecular parameters for the ground state and the v1 C–H stretching mode of He–HCO+. The parameters for v1 = 0 are obtained by a combination difference fit to a standard linear rotor Hamiltonian. These values are kept fixed to determine the perturbed vibrationally excited state. The uncertainties are given in parentheses
Parameter v 1 = 0 v 1 = 1
This work
ν/cm−1 3076.3374(12)
B/MHz 8698.6(6) 8668.4(8)
D/MHz 0.316(16)
Nizkorodov et al.4
ν/cm−1 3076.313(10)
B/MHz 8694.0(60) 8688.0(300)
D/MHz 0.30(2)


The negligible laser bandwidth and the low kinetic temperature of the ions in our experiment allow us to determine the lifetime in the v1 dissociating state. Typical ro-vibrational transitions recorded using COLTRAP at 4 K exhibit Doppler lineshapes corresponding to temperatures on the order of 12 K.19,23–26 In order to determine the lifetime, pseudo-Voigt profiles with fixed Doppler contributions at the given temperature were fit to the observations. The Lorentzian contributions of the Voigt fits typically have a FWHM on the order of 68 MHz, corresponding to a lifetime of ≈2.34 ns in the v1 vibrational state. The predissociation lifetime was discussed by Nizkorodov et al., who estimated a lower limit of 250 ps.4 They explained that the small coupling between the v1 mode and the He–proton stretching mode results in the long lifetime. The linear structure with the He atom bound to the proton side and a low harmonic frequency (90 cm−1) of the He–proton stretching mode, both of which were indicated by their analysis of the spectroscopic constants, would cause fast predissociation in the v1 = 1 state unless the C–H vibrational energy transfer to the He dissociation coordinate is highly restricted. We suppose that the isolation of the He–proton bond from the intramolecular vibrational modes originates from a peculiar potential curve in the long range region. The He–proton bond length is estimated to be 2.00 Å, which is longer than those in analogous He–molecular ion complexes.4 The signatures of unusual long-range interactions of the He–proton bond are also indicated in the molecular constants for the vibrational ground state, which will be described based on the results of pure rotational spectroscopy in the next section.

4 Rotational spectroscopy

We started our rotational measurements by optimizing our mm-wave setup using the well-known rotational transitions of HCO+.27–29 For this, an action spectroscopic technique was used that exploits the dependence of the ternary attachment of the helium atoms (eqn (1)) on the rotational quantum state.21,26,30,31 In the present case, we counted the number of formed He–HCO+ complexes as a function of the mm-wave frequency (without any IR radiation), and a dip in the counts indicated the hindrance of their formation by the rotational excitation of the naked HCO+. Our obtained values for the center frequencies of the two rotational transitions of HCO+, based on seventeen and six individual measurements of their Doppler shapes, respectively, are summarized in Table 3. A comparison of our values to the best direct laboratory measurements (no predictions taken into account) confirms our frequency calibration, and demonstrates that cryogenic ion trap techniques operating under vacuum conditions (thus avoiding pressure shifts) are capable of improving the values obtained with conventional absorption in discharge cells.
Table 3 Observed rotational transitions of HCO+ measured with the method of state-dependent He attachment, and comparison to the best direct laboratory measurements. All quantities are given in MHz with uncertainties in parentheses
J′ ← J′′ This work Former work
2 ← 1 178[thin space (1/6-em)]375.0683(11) 178[thin space (1/6-em)]375.0563(81)27
3 ← 2 267[thin space (1/6-em)]557.6366(29) 267[thin space (1/6-em)]557.619(10)29


In the next step, we used the double resonance technique, which proved to be very powerful in the case of CH3+–He,15 to measure the rotational lines of He–HCO+. Both double resonance combinations as depicted in Fig. 3 (cases A and B) were applied. Based on predictions made using the molecular parameters given in Table 2, the rotational transitions listed in Table 4 were detected. Most of the time, the trap temperature was kept fixed at 4 K, whereas it was increased up to 10 K for the highest J states in order to increase the population of those states. Even though the infrared power was attenuated well below 1 mW, the IRPD signals of the low J states easily went into saturation. Hence, depopulating those probed levels (case B in Fig. 3) in the double resonance scheme was the preferred approach. Also, care was taken to avoid broadening and skewing of the rotational lines observed at excessive mm-wave power. Obeying these conditions, the rotational transitions have a pure Doppler lineshape without any Lorentzian contribution (the rotational states are very long-lived) and the corresponding Doppler temperatures approach a typical Trot ≈ 12 K.


image file: c8cp04532a-f3.tif
Fig. 3 Example for the double resonance technique applied to the He–HCO+ complex. The infrared laser is stabilized on a predissociation transition (red arrow). When the mm-wave (blue arrows) is tuned into rotational resonance, the quantum level probed by the infrared transition is either populated (case A) or depopulated (case B), depending on the choice of the rotational transition. In the shown example measurements, black squares are single measurement cycles, the red curve is the average, and the blue curve is a Doppler fit.
Table 4 Observed and calculated rotational transitions of the He–HCO+ complex measured with the double resonance method. All quantities are given in MHz with uncertainties in parentheses
J′ ← J′′ Obs. Calc. Obs.–calc.
1 ← 0 17[thin space (1/6-em)]395.1112
2 ← 1 34[thin space (1/6-em)]782.5930
3 ← 2 52[thin space (1/6-em)]154.8930(7) 52[thin space (1/6-em)]154.8910 0.0024
4 ← 3 69[thin space (1/6-em)]504.5481
5 ← 4 86[thin space (1/6-em)]824.3164(14) 86[thin space (1/6-em)]824.3172 −0.0002
6 ← 5 104[thin space (1/6-em)]107.0922(4) 104[thin space (1/6-em)]107.0930 −0.0013
7 ← 6 121[thin space (1/6-em)]345.9633(13) 121[thin space (1/6-em)]345.9577 0.0032
8 ← 7 138[thin space (1/6-em)]534.1142
9 ← 8 155[thin space (1/6-em)]664.8274
10 ← 9 172[thin space (1/6-em)]731.3559(3) 172[thin space (1/6-em)]731.3544 0.0016
11 ← 10 189[thin space (1/6-em)]726.8475(5) 189[thin space (1/6-em)]726.8532 −0.0051
12 ← 11 206[thin space (1/6-em)]644.3117(16) 206[thin space (1/6-em)]644.3115 0.0023
13 ← 12 223[thin space (1/6-em)]476.4892(21) 223[thin space (1/6-em)]476.4649 0.0224
14 ← 13 240[thin space (1/6-em)]215.7559(13) 240[thin space (1/6-em)]215.7092 0.0455
15 ← 14 256[thin space (1/6-em)]853.9714(4) 256[thin space (1/6-em)]853.9718 −0.0004
16 ← 15 273[thin space (1/6-em)]382.4879(24) 273[thin space (1/6-em)]382.4837 0.0041


Finally, we also tested the action spectroscopic method of the state-dependent He attachment on He–HCO+. We assumed that if it is possible to detect the rotational transitions of HCO+ by hindering the formation of He–HCO+, it should also be possible to detect the rotational transitions of He–HCO+ by hindering the formation of He2–HCO+ when He–HCO+ is irradiated with a resonant mm-wave beam. Knowing the exact frequencies for the J = 3 ← 2 and J = 10 ← 9 transitions of He–HCO+ (Table 4), we tested our assumption. We failed to detect any signal after long integration times. Similarly, we failed to detect any rotational signal for CH3+–He,15 though the double resonance technique worked perfectly. The most probable reasons for these non-detections are the smaller partition functions for the heavier species and the similarity of the He attachment rates for the rotational states connected by rotational transitions in the case of He–HCO+ and CH3+–He. We have to conclude that for the rotational investigation of ion–noble gas complexes in ion traps, the action spectroscopic method of choice is the double resonance presented here.

With eleven very accurate rotational transitions for He–HCO+ given in Table 4, a least squares fit of the pure rotational transitions to a standard linear rotor Hamiltonian was performed and the obtained parameters are listed in Table 5. The determined B and D values agree well with those of the preliminary IR combination difference fit of this work and those reported by Nizkorodov, Maier and Bieske4 (see Table 2), but their accuracies are improved by a few orders of magnitude in the present study. As illustrated in Table 5, it has turned out to be necessary to include five orders of centrifugal distortion constants (D, H, L, M, N) to reach an rms that is typical for a semi-rigid rotor fit (≈10 kHz). This behaviour, also observed for CH3+–He,15 can be traced back to the floppy nature of the weak bond with the helium atom. Indeed, the pure rotational spectra of the stronger bound Ar–HCO+ and Kr–HCO+ complexes32,33 observed earlier under jet-cooled conditions by Fourier transform microwave (FTMW) spectroscopy could be fitted with standard deviations better than experimental uncertainties (10 kHz) using only the B and D constants.

Table 5 Molecular parameters of He–HCO+ obtained by fitting the observed pure rotational transitions to a standard linear Hamiltonian involving 5 orders of centrifugal distortion constants. The weighted average uncertainty of the fit is still only on the order of 10σ, giving rise to the assumption that the standard linear Hamiltonian is not a good approximation for such a rather floppy molecule. All quantities are given in MHz with uncertainties in parentheses
Parameters v 1 = 0
B 8698.1947(16)
D 0.318741(46)
H/10−5 10.03(6)
L/10−7 −2.681(39)
M/10−10 4.0(1)
N/10−13 −3.2(1)


These findings provide important information on the He–proton interaction potential of He–HCO+. The B and D constants are related to the shape of the potential minimum. A harmonic analysis based on the B and D constants was already applied by Nizkorodov et al.4 to estimate the force constant (1.64 N m−1) and vibrational frequency (90 cm−1) of the He–proton stretching mode. The slow convergence of the higher order centrifugal terms for the rotational energy levels of He–HCO+ points to a large deviation from a harmonic-type function in the radial coordinate of the He motion, as well as large amplitude motions along the angular coordinate. In fact, the available ab initio potential energy surfaces for this system16,18 show that the angular portion of the potential is fairly flat. A long range interaction along the He–proton stretching coordinate is likely to explain both the anharmonicity around the potential minimum and the long predissociation lifetime.

5 Outlook

The application of the rotation-predissociation double resonance scheme to He–HCO+ and CH3+–He demonstrates the effectiveness of this novel method. A natural extension of these investigations is the more strongly bound complexes CH3+–Ne and CH3+–Ar, as well as HCO+–H2.5 Even more advantages can be expected when applying this method to ionic complexes containing quadrupole nuclei, e.g. NH2+–He, N2+–He, DCO+–He or ND2+–He. The hyperfine structure can be resolved in these cases, providing additional information on the internal dynamics of the complexes. Further future target systems include fundamental complexes such as CH+–He,26 H3+–He24 or H2+–He.34 In particular, the latter complex is interesting as it is a very fundamental system (3 nuclei, 3 electrons). Being fairly strongly bound, it may have played an important role in the early universe, and it still plays an important role in astrochemistry as the intermediate collision complex in fundamental He–H2+ scattering. It is thus of utmost importance to elucidate its potential energy surface, not only by ab initio computations35 and collisional experiments,36 but also by high-resolution rotational spectroscopy.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) via grant AS 319/2-2 and SCHL 341/15-1 (“Cologne Center for Terahertz Spectroscopy”). The contribution of L. S. to this work (project idea, data analysis and writeup) was financed by the Russian Science Foundation grant No. 17-12-01395. H. K. is supported by the Yamada Science Foundation and JSPS KAKENHI Grant No. 15KT0065.

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