The H6+ cation was generated in a pulsed-discharge supersonic expansion of hydrogen and mass-selected in a time-of-flight spectrometer. Its vibrational spectrum was measured in the region of 2050–4550 cm−1 using infrared photodissociation with a tunable OPO/OPA laser system. The H6+ photodissociates, producing H5+, H4+, and H3+ fragments; each of these fragment channels has a different spectrum. Computational studies identify two low-lying isomers described in previous work, whose energies were evaluated at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. A D2d species having an H2+ cation bridging between two perpendicular H2 molecules is the global minimum structure. A Cs structure with an H3+ core ion bound to both H2 and an H atom lies 4.0 kcal mol−1 higher in energy. Anharmonic vibrational spectra were computed for each of these isomers with second-order vibrational perturbation theory (VPT2) in combination with density functional theory at the B2PLYP/cc-pVTZ level. The comparison between experimental and predicted spectra confirms the presence of both the D2d and Cs structures and explains the spectra in different fragmentation channels. Although we find reasonable agreement between the experiment and the spectra predicted by VPT2 computations, a more sophisticated computational approach is needed to better understand this complex system.

Hydrogen ions have been known in mass spectrometry since the discovery of H3+ by Thomson in 1911.1 This well-known cation has a cyclic D3h structure and a low proton affinity (100.9 kcal mol−1), allowing its use as a protonating agent in chemical ionization mass spectrometry.2 High-resolution infrared spectroscopy of H3+ by Oka and co-workers3 made its detection possible in the interstellar medium,4 which confirmed that it is one of the most abundant ions in the universe.5 Protonation of small neutral molecules by H3+ underlies many reaction pathways leading to more complex molecules in space.5–12 At higher pressures, ionization of hydrogen produces larger Hn+ cluster ions, primarily in the form of odd-numbered Hn+ ions believed to have H3+ at their core.13,14 Even-numbered hydrogen cations were not identified experimentally until the 1980s.15,16 Although computations predicted that the even-numbered hydrogen ions would have binding energies similar to those of the odd-numbered species,17 they are produced only in minute quantities because the abundant H3+ acts as a “seed” for cluster growth. Thus, there is still little experimental information about the structures of the even-numbered hydrogen ions. Here, we present the first infrared spectrum of H6+, allowing its structure to be determined.

Because H3+ has a symmetric D3h structure and no dipole moment, as well as no low-lying excited states, it cannot be studied with microwave or UV-visible spectroscopy. Spectroscopy on this ion and its clusters has therefore been limited to the infrared region. Infrared photodissociation spectra of the odd-numbered hydrogen cluster ions were first reported by Lee and co-workers in the hydrogen stretching region near 4000 cm−1.18 Our group later extended the frequency range of these measurements and included the corresponding deuterated species.19–21 These ions were initially postulated to consist of H3+ cations with successive H2 units clustering around this core. This was confirmed for the H7,9+ ions,21 but H5+ was found to have a symmetrically shared proton-bound dimer (PBD) structure.19,20 Although computations on H5+ predict a double well potential with two equivalent C2v minimum energy structures, the zero-point energy lies above this barrier, resulting in the symmetric D2d ground state. Since our report on the spectroscopy of H5+ and D5+, these cations have been the subject of several computational studies examining their anharmonic vibrational interactions.22–36 

Previous experimental work on the even-numbered hydrogen cations is limited. Bowers and co-workers reported the first detection of H4+ as a fragment from collisional dissociation of H5+.15 Shortly thereafter, the same group utilized a coaxial drift tube source to generate Hn+ cluster ions.16 Although the odd-numbered clusters still dominated the mass spectrum, even-numbered (n = 4, 6, 8, 10) cations were also produced; of these, H6+ was the most abundant. Hn+ ions were also studied in solid para-hydrogen (p-H2) matrices.37–42 Electron spin resonance (ESR) in this environment complemented by computational chemistry suggested that H6+ has an H2+ radical cation core.41,42 More recently, large even-numbered Hn+ (up to n = 120) cations were generated in helium nanodroplets.43 

Computational studies at various levels of theory have been performed on the small even-numbered hydrogen cluster cations, with particular emphasis on H6+.17,42–45 Wright and Borkman initially suggested that H6+ has a structure with an H3+ core.17 Later work using higher levels of theory found a structure with D2d symmetry, having an H2+ core bridging two neutral hydrogen molecules.42–45 These studies also found a nearby H–H3+–H2 minimum with Cs symmetry. The most recent work employed full correlation interaction and extrapolated energies to the complete basis set limit using focal point analysis (FCI/CBS), confirming that the D2d structure is the ground state and that the Cs isomer is only +4.2 kcal mol−1 higher in energy.45 These isomers are connected by a transition state lying +5.2 kcal mol−1 above the ground state. A quartet D3h state was found at much higher (+106.9 kcal mol−1) energy. Unfortunately, only harmonic vibrational spectra have been predicted for H6+ thus far.

In the present study, H6+ was generated in the gas phase via a pulsed-discharge supersonic expansion of hydrogen gas doped with water as an electron scavenging agent.46 Consistent with previous work, we find that the Hn+ clusters are dominated by the odd-numbered species. However, small amounts of even-numbered clusters are also produced (see mass spectrum in Fig. S1 of the supplementary material). H6+ was mass-selected in a home-made time-of-flight spectrometer, and a tunable infrared OPO/OPA laser beam was introduced for photodissociation of the clusters at the turning point of the reflectron.47,48 Its photofragmentation spectrum was measured in the 2050–4550 cm−1 region.

Infrared excitation of the H6+ cation resulted in dissociation, producing the H5+, H4+, and H3+ fragment ions with wavelength-dependent yields. Power-dependent studies of these signals ensured as much as possible that each is the result of single photon absorption. The loss of an H2 molecule or the production of the known stable H3+ cation is not surprising, but the H5+ fragment channel corresponds to the loss of a single hydrogen atom, which is unexpected. Figure 1 shows the spectra of the H6+ cluster cation measured in each of the H5+, H4+, and H3+ fragment channels. The linewidths detected for all of these spectra are broader than the laser linewidth (1−2 cm−1) and presumed to result from a combination of predissociation and rotational profiles of the vibrational bands. In the upper trace, the yield for the H5+ fragment exhibits only two features: a strong band at 3397 cm−1 and a weak, broad band at 3790 cm−1. The second trace for the H4+ fragment produces a weaker spectrum with a more complex pattern. The intensity scale here is multiplied by a factor of three compared with the upper trace. The two main bands from the H5+ spectrum are again present, and the 3397 cm−1 peak is still the most intense feature. Other new bands appear at 2522, 3120, 3909, and 4420 cm−1, and there is a shoulder on the high energy side of the 3397 cm−1 band. The band at 3790 cm−1 was broad in the H5+ fragment spectrum but is sharper in the H4+ channel. The bottom trace shows the photofragmentation yield of H3+, which is weaker still. Its intensity is multiplied by a factor of six compared with that of the upper spectrum. The strong band at 3397 cm−1 is no longer present, but several of the broad features here overlap with bands seen in the H4+ fragment spectrum. The most intense feature here is a band at 3515 cm−1, which overlaps with a weak shoulder on the high energy side of the 3397 cm−1 band in the H4+ channel. The positions and relative intensities of the 3515, 3909, and 4204 cm−1 features are reminiscent of bands seen previously in the infrared spectrum of the H5+ cation.19 

FIG. 1.

Infrared photodissociation spectra of the H6+ ion recorded in the three fragmentation channels (H5+, H4+, and H3+). Dashed vertical lines are provided to show the common features in different channels. The second trace is multiplied by a factor of three in intensity compared with the top trace, and the lower spectrum is multiplied by a factor of six compared with the top trace.

FIG. 1.

Infrared photodissociation spectra of the H6+ ion recorded in the three fragmentation channels (H5+, H4+, and H3+). Dashed vertical lines are provided to show the common features in different channels. The second trace is multiplied by a factor of three in intensity compared with the top trace, and the lower spectrum is multiplied by a factor of six compared with the top trace.

Close modal

Our computational work optimized the structures of H6+ at the MP2/cc-pVTZ level and refined the energetics at the CCSD(T)/cc-pVTZ level using the Gaussian09 package.49 We found the same two low-lying D2d and Cs isomers identified before, with only slight differences in relative energies compared with the previous work (Table I). We focus our vibrational spectroscopy on these two low-lying isomers, as other structures were documented previously to be much less stable.45 As a first approach, we employed harmonic theory with scaled vibrations (Fig. S11 of the supplementary material). The most intense vibration predicted for the D2d isomer in the region of the experiment is the out-of-phase H–H stretch of the two external hydrogens (νH2a) (the in-phase stretch of these two hydrogens, νH2s, is not IR active). The harmonic prediction for this frequency of 3865 cm−1 (964.6 km mol−1) was reduced to 3672 cm−1 with a scaling factor of 0.950. No other bands are predicted in this region with significant intensity. A strong vibration corresponding to a “shuttling” motion of the central H2+ with respect to the external H2 units is predicted near 1000 cm−1, but this is below the dissociation limit and therefore cannot be detected in our experiment. A single strong band at high energy is consistent with expectations for the high symmetry D2d isomer, and it also matches the general appearance of the spectrum in the upper trace of Fig. 1, but the predicted frequency is much higher than that observed. The scaled harmonic spectrum for the Cs isomer has more bands, but likewise none match the experimental frequencies. Based on the known importance of anharmonic effects in the spectrum of the related H5+ cation,19,20 we expect that anharmonic theory is necessary to describe these spectra.

TABLE I.

Relative energies from CCSD(T)/cc-pVTZ single points at the MP2/cc-pVTZ minimized geometry with MP2 harmonic ZPE corrections and binding energies (kcal mol−1) for hydrogen atoms and molecules to Hn+. The superscript signifies a transition state.

Cluster (geometry)Relative energy–H (kcal/mol)–H2–(H + H2)
H6+ (D2d0.0 5.2 7.1 10.8 
H6+ (Cs4.0 1.2 3.1 6.8 
H6+‡ (Cs4.4 … … … 
H5+ … 103.8 5.6 142.8 
H4+ … 3.7 39.1 103.4 
H3+ … 137.3 99.6 … 
Cluster (geometry)Relative energy–H (kcal/mol)–H2–(H + H2)
H6+ (D2d0.0 5.2 7.1 10.8 
H6+ (Cs4.0 1.2 3.1 6.8 
H6+‡ (Cs4.4 … … … 
H5+ … 103.8 5.6 142.8 
H4+ … 3.7 39.1 103.4 
H3+ … 137.3 99.6 … 

To further investigate this system, we performed second-order vibrational perturbation theory (VPT2) at the DFT/B2PLYP/cc-pVTZ level. The spectrum obtained for H6+ in the H5+ fragment channel is compared with the predicted VPT2 spectra for the two relevant D2d and Cs isomers in Fig. 2. As shown, the single strong band predicted for the νH2a vibration of the D2d isomer at 3464 cm−1 is in much better agreement with the experimental band at 3397 cm−1. Because the H5+ fragment channel is by far the most intense, and because of this acceptable agreement with theory, we conclude that the ground state of the H6+ ion has the D2d structure that is predicted to be most stable. Unfortunately, anharmonic theory fails to explain the weak band at 3790 cm−1. However, on the basis of the frequency interval, we can assign this as a combination of the in-phase H2 stretch with the asymmetric H2 bend (νH2s+νH2ba), which is predicted at 3787 cm−1. There are no bands in this fragmentation channel which match the resonances predicted for the Cs isomer. The H5+ fragment is therefore only produced by dissociation of the most stable D2d structure.

FIG. 2.

The H5+ fragmentation channel of H6+ compared with the spectra predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory.

FIG. 2.

The H5+ fragmentation channel of H6+ compared with the spectra predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory.

Close modal

Figure 3 shows the spectrum in the H4+ fragmentation channel compared with the anharmonic vibrational patterns for the two isomers. As noted above, the 3397 cm−1 band and the weaker 3790 cm−1 band seen in the H5+ fragment appear again here. The other features in this spectrum may therefore arise from another isomer, and indeed, there is some overlap between the bands detected and those predicted for the Cs structure. The experimental band at 2522 cm−1 matches reasonably well with the band predicted at 2589 cm−1 and assigned to the mixed character of a combination of the H3+ twist with the lower energy H3+ asymmetric ring deformation mode (νtw + νrd2) and the combination of the two ring deformation modes (νrd1 + νrd2). The band at 3120 cm−1 approximately matches that predicted at 3019 cm−1 and is assigned to the H3+ symmetric breathing mode (νb). Although the 3790 cm−1 band was already seen and assigned earlier in the H5+ channel, it is sharper and more intense here and the 3790/3909 cm−1 doublet matches well in spacing and relative intensities to the doublet predicted at 3965/4071 cm−1. It is therefore possible that a different resonance is giving intensity to the 3790 cm−1 band in this spectrum. If this is the case, it would be assigned to the fundamental of the H2 stretch (νH2) predicted at 3965 cm−1 and the 3909 cm−1 band would correspond to the combination of the free hydrogen atom stretch with the H3+ breathing mode predicted at 4071 cm−1H + νb). The weak feature at 4418 cm−1 matches reasonably well with the band predicted at 4464 cm−1 and assigned to the combination of the H3+ twisting mode with the H3+ breathing mode (νtw + νb). Altogether, the H3+ symmetric breathing mode shows strong coupling with other modes throughout the spectrum. Because of the reasonable agreement here between the bands predicted and observed, it appears that the Cs isomer is also present, albeit with lower concentration than the D2d isomer. Apparently, both of these isomers dissociate to produce the H4+ fragment.

FIG. 3.

The H4+ fragmentation channel of H6+ compared with the spectra predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory.

FIG. 3.

The H4+ fragmentation channel of H6+ compared with the spectra predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory.

Close modal

Figure 4 shows the spectrum in the H3+ fragment channel compared with the anharmonic spectra predicted for the Cs isomer and with the spectrum measured previously for the H5+ cation.19 As shown in Fig. 1, none of these bands match those in the H5+ fragment spectrum, but several match those in the H4+ fragment spectrum, i.e., bands at 2522, 3909, and 4204 cm−1. The very weak feature at 3120 cm−1 in the H4+ fragment spectrum is a more intense and better resolved doublet at 3099/3152 cm−1 in the H3+ fragment spectrum. The shoulder near 3500 cm−1 in the H4+ fragment spectrum is a well-resolved band at 3515 cm−1 and the most intense feature in the H3+ fragment spectrum. As noted above for the H4+ fragment spectrum, some of these bands match with those predicted for the Cs isomer. However, the smooth profile of the progression of bands in the H3+ channel does not match the qualitative appearance of the band intensities predicted. Additionally, there is nothing predicted that can explain the most intense 3515 cm−1 feature. From the computed frequencies, this feature could be assigned to either the overtone of the H3+ core ion ring deformation mode (2νrd1) or a combination of the core H3+ ion breathing mode with the second ring deformation mode (νb + νrd2). However, it is clear that the present level of VPT2 anharmonic theory is still not adequate to describe this spectrum. Table II provides a summary of the vibrational bands observed in different mass channels and the frequencies predicted by theory.

FIG. 4.

The H3+ fragmentation channel of H6+ compared with the spectrum predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory and with the previously measured spectrum of H5+.19 

FIG. 4.

The H3+ fragmentation channel of H6+ compared with the spectrum predicted by VPT2 computations at the B2PLYP/cc-pVTZ level of theory and with the previously measured spectrum of H5+.19 

Close modal
TABLE II.

Measured vibrational bands (cm−1) compared with the anharmonic computations at the B2PLYP/cc-pVTZ VPT2 level.

ExperimentTheory
(fragment(intensity,
channel)km/mol)Assignment
2522 (H4,3+2589 (532.5), 2585 (72.9) Cstw + νrd2),Csrd1 + νrd2
3099 (H3+  
3120 (H4+3019 (237.3) Csb
3152 (H3+  
3397 (H5,4+3464 (1129.4) D2d (νH2a
3515 (H3+3546 (10.4), 3567 (2.6) Cs (2νrd1), Csb + νrd2
3790 (H5,4+3787 (0.002) D2d (νH2s+νH2ba
3909 (H4,3+3965 (116.6) Cs (νH2
4204 (H3+4071 (198.0) CsH + νb
4420 (H4+4464 (21.1) Cstw + νb
4483 (H3+  
ExperimentTheory
(fragment(intensity,
channel)km/mol)Assignment
2522 (H4,3+2589 (532.5), 2585 (72.9) Cstw + νrd2),Csrd1 + νrd2
3099 (H3+  
3120 (H4+3019 (237.3) Csb
3152 (H3+  
3397 (H5,4+3464 (1129.4) D2d (νH2a
3515 (H3+3546 (10.4), 3567 (2.6) Cs (2νrd1), Csb + νrd2
3790 (H5,4+3787 (0.002) D2d (νH2s+νH2ba
3909 (H4,3+3965 (116.6) Cs (νH2
4204 (H3+4071 (198.0) CsH + νb
4420 (H4+4464 (21.1) Cstw + νb
4483 (H3+  

It is useful to note the similarity of the spectrum found here for H6+ in the H3+ channel to that of the H5+ cation.19 At the same level of theory employed here, H5+ has a localized H3+–H2 structure like that suggested here for the sub-structure of the Cs isomer of H6+, even though higher levels of anharmonic theory show that it actually has a delocalized H2–H+–H2 PBD structure when zero-point energy is considered.19 As shown in Fig. 4, the spectrum in the H3+ channel looks remarkably similar to the one we have measured previously for H5+.19 Bands in the H5+ spectrum at 3520, 3904, and 4232 cm−1 correspond closely in both position and relative intensities to those in the H3+ fragment spectrum of H6+ at 3515, 3909, and 4204 cm−1. The strong band at 3520 cm−1 in the H5+ spectrum is the out-of-phase H–H stretch of the external H2 units, analogous to the strong vibration discussed earlier for this vibration in the D2d isomer of H6+. It therefore seems likely that the Cs isomer of H6+ actually has a more symmetrical PBD H5+ ion sub-structure that is attached to a single, weakly bound hydrogen atom rather than containing the distinct H3+ and H2 units. Although the anharmonic theory does not capture the band positions or intensities well, the similarity to the H5+ spectrum also suggests that a Cs-type isomer is present. Higher levels of theory will be necessary to confirm this.

In addition to the spectral patterns seen here, it is interesting to consider the photodissociation dynamics that lead to the three different fragmentation channels. To investigate this, we have computed the energies of all relevant structures for this system (H6+D2d, H6+Cs, H6+‡Cs, H5+, H4+, H3+, H2+, H2, and H) at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. Although higher levels of theory are available from previous work (FCI/CBS level),45 not all of the observed dissociation pathways were included in that study. The resulting energies, which agree well with those reported in previous work by Hao et al.,45 are presented in Table I and shown schematically in Fig. 5. Our computations are detailed in the supplementary material.

FIG. 5.

Potential energy diagram calculated at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory, including harmonic ZPE corrections. The dashed red line indicates the excitation energy at the strongest band in the H5+ fragment ion channel, and the red vertical arrows show the energy level attained with this excitation for the different isomers.

FIG. 5.

Potential energy diagram calculated at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory, including harmonic ZPE corrections. The dashed red line indicates the excitation energy at the strongest band in the H5+ fragment ion channel, and the red vertical arrows show the energy level attained with this excitation for the different isomers.

Close modal

As shown in Fig. 5, the fragmentation pathways of H6+ include the loss of a neutral hydrogen atom, a neutral dihydrogen molecule, or both. Elimination of a neutral H3 molecule is not considered as this species is not stable in its ground state.50 The energy of a photon at 3397 cm−1 (9.7 kcal mol−1) corresponding to the strong resonance in the H5+ fragment spectrum is indicated as a dashed red line, with vertical arrows indicating the light absorbed here for the D2d and Cs isomers. It is evident that a photon exciting the 3397 cm−1 band of the D2d isomer has enough energy to access either the H5+ + H or the H4+ + H2 dissociation channels, but not the H3+ + H2 + H channel. However, excitation of the D2d ground state likely requires isomerization to the Cs structure before dissociation to the H5+ + H channel can take place. As shown, the transition state allowing this isomerization is also energetically accessible. Thus, although the elimination of a hydrogen atom as a photofragment is not usually expected, it makes sense when these energetics are considered. Excitation of the Cs isomer in this same energy region is sufficient to access all three possible dissociation channels.

The D2d isomer of H6+ therefore dissociates into both of the energetically possible channels, but the Cs isomer only dissociates into the two higher energy paths. Its spectrum does not occur in the H5+ fragment channel, even though the loss of a hydrogen atom to produce H5+ seems dynamically reasonable. Perhaps the excess energy here always causes the additional fragmentation. We did not see any fragmentation in the lower frequency infrared (800–2000 cm−1) region where the Cs isomer could conceivably dissociate into this lower energy pathway. However, the resonances predicted are weak and our laser power is much lower here. An additional consideration is the possibility of kinetic energy release in the photofragments because of the excess energy available. If this occurs, some fraction of these light fragment ions could be ejected from the beam, reducing the number detected. This uncertainty makes it difficult to quantify the amounts of the two isomers present or the branching ratios of the fragment ions.

In summary, we have successfully generated the H6+ cation in the gas phase and measured its infrared photodissociation from 2050 to 4550 cm−1. Three photofragments are produced (H5+, H4+, and H3+) which exhibit different spectra. Computational studies identify the D2d and Cs isomers described previously, whose energetics provide a reasonable mechanism to explain the dissociation patterns. The measured vibrational patterns are not reproduced well by scaled harmonic theory, but are in somewhat better agreement with patterns predicted by VPT2 anharmonic theory. The simple spectrum in the most abundant H5+ fragment channel confirms that there is a greater concentration of the D2d isomer that is predicted to be the most stable. The more complex patterns in other mass channels, together with their similarity to the spectrum of the related H5+ cation, suggest that a smaller amount of the Cs isomer is also present. More sophisticated treatment of the anharmonicity, particularly for the Cs isomer, is highly desirable to confirm the vibrational assignments for this system. Future work will include the corresponding deuterated ions and higher energies in the near-IR.

See supplementary material for a mass spectrum of the hydrogen clusters and the complete details of the computational work.

The authors gratefully acknowledge funding for this research by the National Science Foundation (M.A.D. Grant No. CHE-1464708). J.P.W. acknowledges the Alexander von Humboldt Foundation for a Feodor Lynen Postdoctoral Fellowship.

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