In order to investigate the two H 3 + formation pathways, we obtained time-of-flight mass spectra for two distinct organic molecules: one having two methyl groups without a hydroxyl group (acetone) to confirm the first formation pathway and the other with two hydroxyl groups without having a methyl group (ethylene glycol) to confirm the second formation pathway. Figure 2 presents the mass spectra for acetone and ethylene glycol molecules upon irradiation by an intense laser field at 2.5 × 1014 W/cm2. The peak at m/z = 3 is identified as H 3 + yield. However, due to the degeneracy in m/z of H 3 + and C4+ it is imperative to confirm that there is no contribution from C4+ to the ion yield at m/z = 3. A close examination of the time-of-flight yield at m/z = 4 (see Fig. 2 insets) indicates that there are no events recorded which could be attributed to C3+, an expected precursor to the formation of C4+. Therefore, it is evident that there is no possibility to produce C4+ under these experimental conditions.

Figure 2 Truncated time-of-flight ion spectrum for (a) acetone and (b) ethylene glycol in a linearly polarized laser focus of 2.5 × 1014 W/cm2 under identical experimental conditions. Only ions relevant to this discussion (i.e. with a mass-to-charge ratio m/z < 7) are shown. Each yield is normalized with respect to the peak value of the corresponding H+ yield. Note that in both spectra, no C3+ at m/z = 4 was observed (see corresponding inset). The higher yield for forward (early time) ion signals is caused by an extraction slit as explained in the Methods: Experimental Setup section. Full size image

The absence of other H 3 + formation pathways from either of the two molecules can be intuited from their molecular structures (shown in Fig. 2). In ethylene glycol, one group of methylene hydrogens is furthest from the other group of methylene hydrogens [diagram in Fig. 2(b), shown in anti-configuration but applicable to other configurations], making the H 3 + formation via association within the two methylene groups unfeasible. In the case of acetone, however, [1,3] hydrogen migration that is followed by an associative H 3 + formation could be considered given the applicability of [1,3] H+ migration in acetone enolate30. In the current work, however, where intense femtosecond pulses are employed, electrons are initially abstracted within the optical cycles of the electric field, leaving a multiply-charged parent ion31. In this condition, the positive charge build up on the oxygen atom draws electronic density from the methyl groups to be localized mainly within the carbonyl group, which leaves the terminal methyl groups at elongated separations through which the [1,3] migration becomes less favorable compared to the associative H 3 + formation from one methyl group. Therefore, observing H 3 + from acetone dissociative ionization confirms the existence of the first formation pathway, association of three hydrogen atoms from the methyl group. Observation of H 3 + from ethylene glycol, confirms the existence of the second formation pathway, association of two methylene hydrogens with the hydrogen atom from a neighboring group.

To further investigate the two pathways for H 3 + formation under identical conditions, an organic molecule capable of reacting via both pathways has to be studied. As methanol (CH 3 OH) contains both a methyl group and a hydroxyl group, CH 3 OH and its isotopomers, CH 3 OD, CD 3 OH, and CD 3 OD, were used in this study to identify the two pathways accurately.

First we obtained a PIPICO map from dissociative ionization of CH 3 OH in a laser field of 5.0 × 1014 W/cm2. Figure 3 presents the PIPICO map for photoionization of CH 3 OH (see Supplementary Information Fig. S1 for corresponding time-of-flight mass spectrum). Observing H 3 + in coincidence with COH+/HCO+ provides evidence for H 3 + formation under strong-field dissociative ionization of CH 3 OH. The integrated yield for the pair coincidence channel of H 3 + + COH+/HCO+ is 3.3 × 10−3 events/shot. However, due to the degeneracy in m/z of COH+ and HCO+, it is not possible to distinguish between the two formation pathways from the CH 3 OH isotopomer.

Figure 3 PIPICO map from dissociative ionization of CH 3 OH. On the PIPICO map, the five vertical (dashed) lines represent the approximate center lines of the regions where H+, H 2 +, H 3 +, CH 3 +, and H 2 O+ ions are recorded. The three horizontal (dashed) lines indicate CH 3 OH+, CH 2 OH+/CH 3 O+, and COH+ /HCO+ ion regions. The contour region with an approximate slope of −1 at the intersection of the vertical H 3 + line and the horizontal COH+/HCO+ line represents the coincidence channel of H 3 +and COH+/HCO+. The logarithmic color scale depicts the event rate in units of events/shot. Full size image

Having the evidence of H 3 + formation, we continued our investigation using a methanol isotopomer, CH 3 OD, in order to differentiate the pathways. Figure 4 presents the PIPICO map for dissociative ionization of CH 3 OD in a laser field of 6.0 × 1014 W/cm2 (see Supplementary Information Fig. S2 for corresponding time-of-flight mass spectrum). Here we limit the discussion to three coincidence channels important to our objective (see inset in Fig. 4). Two of them arise from ionization followed by dissociation of the CH 3 OD sample. Specifically, the first two-body breakup channel is H 3 + measured in coincidence with COD+, and the second is H 2 D+ measured in coincidence with HCO+. Due to m/z degeneracy, it is possible that the first formation channel contains some coincidence events from the dissociation channel HD+ + H 2 CO+. The prominent third coincidence channel observed, which is identified as the H 3 + + COH+/HCO+ channel, is due to a CH 3 OH contamination, as the measurement for CH 3 OD was performed immediately after the CH 3 OH measurements. The integrated yield for the H 3 + channel measured in coincidence with COD+ has 2.3 × 10−4 events/shot, while the second channel, H 2 D+ + HCO+, has 4.5 × 10−5 events/ shot. An approximate event ratio of 5 to 1 for the two H 3 + + COD+ and H 2 D+ + HCO+ formation channels is evident from these coincident measurements. This indicates that the association pathway of three hydrogen atoms from the methyl group is five times more favorable than H 2 D+ formation by association of two hydrogen atoms initially bound to a carbon atom with the deuterium atom from the adjacent hydroxyl group. However, it is worth noting that the branching ratio between the two mechanisms is even higher for the CD 3 OH isotopomer, for which we measured a ratio of about 10 to 1 (see Supplementary Information Figs. S3 and S4), in contrast to previously published results based on electron impact on methanol15, which found this ratio to be 4 to 1 for CD 3 OH.

Figure 4 PIPICO map from dissociative ionization of CH 3 OD. On the PIPICO map, the six vertical (dashed) lines represent the approximate center lines of the regions where H+, H 2 +/D+, H 3 +/HD+, H 2 D+, CH 3 +, and H 2 O+ ions are recorded. The top horizontal (dashed) line indicates the COD+/H 2 CO+ ion region and the bottom horizontal line indicates the COH+/HCO+ ion region. The contour region with an approximate slope of −1 at the intersection of the vertical H 2 D+ line and the horizontal COH+/HCO+ line represents the coincidence channel of H 2 D+ + HCO+ (red colored label) while the contour region at the intersection of the vertical H 3 +/HD+ line and the horizontal COD+/H 2 CO+ line represents the coincidence channel of H 3 + + COD+ (blue colored label). The coincidence channel of H 3 + + COH+/HCO+ due to CH 3 OH contamination is visible as the contour region at the intersection of the vertical H 3 +/HD+ line and the horizontal COH+/HCO+ line. A magnified view of these three channels is given in the inset. The logarithmic color scale depicts the event rate in units of events/shot. Full size image

The absence of H 3 + formation pathways starting from a singly-charged parent ion can be intuited from time-of-flight spectra. If H 3 + is formed due to the dissociation of the singly-charged precursor (CH 3 OH+), a single peak should be visible at m/z = 3, the single peak being characteristic of dissociation into a charged and neutral fragment pair. In contrast, ion-ion repulsion would give rise to a double-peak structure. We only observe such a double-peak structure (see Supplementary Information Fig. S1), where the two peaks are from the forward and backward ejected H 3 + due to the dissociation of the doubly charged precursor (CH 3 OH2+). The formation of H 3 + from triply-charged parent cations can be ruled out by closely examining the PIPICO maps for dissociative ionization of CH 3 OH. If H 3 + is formed due to the triply-charged precursor (CH 3 OH3+), subsequent to dissociation, a prominent H 3 + + COH2+/HCO2+ coincidence channel must be visible at the approximate coordinates (1.5 µs, 3.3 µs) on the PIPICO map given in Fig. 3. Furthermore, the absence of the H 2 D+ + HCO2+ channel at (1.8 µs, 3.3 µs) and the H 3 + + COD2+ channel at (1.5 µs, 3.4 µs) in Fig. 4 provides additional evidence that the triply-charged parent cations do not contribute significantly to the formation of H 3 +. In addition, we checked for three-body breakup of CH 3 OH, for example, and observed no trace of H+ + H 3 + + CO+ or H 3 + + C+ + OH+, therefore supporting the claim that H 3 + is produced following double ionization. However, it is important to note that due to experimental uncertainties, any minute contribution to H 3 + production from singly- or triply-charged precursor states cannot be completely ruled out at our present signal to noise ratio.

Once the two H 3 + formation pathways were identified, we looked at the time-resolved yields for H 3 + formation from CH 3 OH molecules in order to ascertain the formation time.

Figure 5 presents the time-dependent variation of the H 3 + yield as a function of pump-probe delay over a time period of 1.5 ps. For negative times, the H 3 + yield is independent of time delay. As the pump and probe pulses overlap, the yield reaches a maximum. Once the probe pulse lags behind the pump pulse, the yield goes through a minimum followed by an exponential rise prior to reaching a plateau. This time dependence of the yield can be described as follows. At negative time delays, when the probe pulse arrives earlier than the pump pulse, the formation of the precursor state, i.e. CH 3 OH2+, is solely due to the pump pulse. Due to its low intensity, the probe pulse is not capable of forming the precursor by itself, and since it arrives before the pump pulse, it cannot alter the precursor state formed by the pump pulse either. Thus, the H 3 + yield remains constant during negative delays. Once the pulses overlap, at t = 0, the peak intensity of the combined pump and probe pulses increases to a maximum, causing an overall increase in the H 3 + yield. However, when the probe pulse lags behind the pump pulse, the total yield first goes through a minimum before it recovers over a certain time reaching a plateau. The minimum is due to depletion of the precursor (i.e. further ionization and/or fragmentation of the precursor state created by the pump) caused by the probe pulse arriving immediately after the pump. As the arrival time of the probe pulse is further delayed from the pump pulse, the depletion becomes less prominent. The formed H 3 + are minimally disturbed by the probe pulse32. Therefore, the time scale for the H 3 + yield recovery is related to the lifetime of the precursor state, thus providing a time scale for the formation of H 3 +. The corresponding time scale can be extracted from the pump-probe transient by fitting a suitable exponential curve to the rising edge of the curve. Here we used a fit given by y = y 0 + A exp(−t/τ) where A is the amplitude, y 0 is the offset, and τ is the time constant. For the curve given in the inset of Fig. 5, the time constant is τ = 98 ± 4 fs, assuming a 95% confidence level for fit parameters. This indicates a fast H 3 + formation time, on the order of 100 femtoseconds, in contrast to previous studies19, 20, in which the formation lifetimes of the trihydrogen molecular ions were estimated indirectly through the anisotropy in the measured angular distributions of fragment ions. It is important to keep in mind that the H 3 + yield measured here has contributions from both formation pathways. It is worth noting that an attempt to determine the formation times of the two pathways through a bi-exponential fit was not successful. The most likely reason for this is that the formation times only differ by ~50–100 fs, therefore, the ~40-fs time resolution of the experimental setup leads to a non-converging bi-exponential fit. However, as H 3 + formation via the first channel is more favorable than the second, the time constant given above will more accurately represent the dominant channel.

Figure 5 Normalized H 3 + yield (blue solid line) from dissociative ionization of CH 3 OH as a function of applied time delay between the pump and probe pulses. Normalization was performed with respect to the yield at negative time delays. (Inset) Magnified view of the normalized yield in the region of the dashed rectangle is shown together with an exponential fit (black solid line). Full size image

In order to obtain timing information for both H 3 + formation channels, we studied the dissociative ionization of the methanol isotopomer, CH 3 OD. Figure 6 presents the time-resolved yield for H 3 + from the first formation channel together with H 2 D+ from the second channel. Following an exponential fit described previously, the transient for the H 3 + formation channel indicates a time constant of 119 ± 3 fs while the H 2 D+ formation channel has a larger time constant of τ = 244 ± 25 fs. However, due to m/z degeneracy (m/z = 3 for H 3 + and HD+), the former channel may have an additional contributing channel, i.e. the HD+ formation channel. We took this into account by performing a double exponential fit given by y = y 0 + A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ) and found that τ 1 = 97 ± 14 fs and τ 2 = 182 ± 54 fs with an amplitude ratio of A 1 /A 2 = 4.6. This supports our assumption regarding the existence of an additional (degenerate) channel. By carefully analyzing the ion yields at m/z = 1, 2, and 3 for mass spectra from CH 3 OH and CH 3 OD, it was evident that the majority of the yield at m/z = 3 for CH 3 OD is due to H 3 + as the contribution from HD+ is minor. Therefore, by considering the amplitude difference, A 1 > A 2 , it is evident that the channel indicated by the subscript 1 manifests the formation of H 3 +. The time constants for H 3 + formation obtained from CH 3 OH and CH 3 OD are identical within the measurement uncertainties and 2.5 times faster than the time constant for H 2 D+ formation, indicating that the association of three hydrogen atoms from the methyl group is a faster process compared to the association of two hydrogen atoms bound to the carbon atom with the deuterium atom from the neighboring hydroxyl group. However, the delay in formation time for the second pathway is partly attributed to orientation and an isotope effect33, as further discussed in the subsequent section.

Figure 6 Normalized H 3 + (red solid line) and H 2 D+ (orange solid line) yields from dissociative ionization of CH 3 OD as a function of pump-probe delay. Normalization was performed with respect to the yields at negative time delays (see Fig. 5). Exponential fits corresponding to the H 3 + and H 2 D+ yields are shown by black solid and dashed lines, respectively. Full size image

To further compare the formation times for different H 3 + creation channels and to explore the effect of isotope substitution, we carried out time-resolved measurements for CD 3 OD, acetone, and ethylene glycol (Fig. 7). Following a similar fitting procedure as mentioned before, we obtained time constants for each trihydrogen cation formation channel. For CD 3 OD, the D 3 + formation indicates a time constant of 132 ± 5 fs. For acetone, the time constant for H 3 + formation is 131 ± 10 fs, and for ethylene glycol, it is 142 ± 5 fs. The effect of isotope substitution on formation time is apparent when making a direct comparison between the time constants obtained for CH 3 OH and CD 3 OD, as the time constant for the latter shows a ~34% increase. For acetone, the time constant is larger than that of CH 3 OH, even though the more plausible pathway for H 3 + formation is the association of three hydrogen atoms from the methyl group. This could be attributed to differences in the precursor state. In comparison to H 3 + formation times from CH 3 OH and CH 3 OD, the H 3 + yield from ethylene glycol indicates a longer formation time. This is in agreement with our model, as the sole pathway for H 3 + formation from ethylene glycol entails an association of the hydroxyl hydrogen with two methylene hydrogens.

Figure 7 Normalized H 3 + and D 3 + yields from dissociative ionization of different organic molecules as a function of pump-probe delay. Shown in the figure are H 3 + from ethylene glycol (orange solid line), H 3 + from acetone (green solid line), and D 3 + from CD 3 OD (magenta solid line). Normalization was performed with respect to the yields at negative time delays (see Fig. 5). Corresponding exponential fits are shown by black lines. Full size image

Trihydrogen cation formation times obtained in this study are summarized in Table 1, arranged in ascending order of formation time. The fast formation times correspond to the first pathway involving the three hydrogen atoms bound to the carbon atom, while the last two entries correspond to the slow channels, which comprise the pathway involving the hydrogen from the hydroxyl group associating with two hydrogens from an adjacent carbon atom. The H 2 D+ formation from CH 3 OD was found to be the slowest. This is in part because the HCOD2+ ion needs to rotate in order to expose the hydroxyl proton to the roaming H 2 molecule; some slowing could also be due to the heavier deuteron involved. In comparison to that reaction, H 3 + formation from ethylene glycol via formation pathway 2 occurs faster due to the favorable orientation of the hydroxyl protons, which are pointing at the nascent roaming H 2 molecule.

Table 1 Summary of formation times obtained for trihydrogen cation production from methanol isotopomers, acetone, and ethylene glycol. Full size table

The kinetic energy release (KER) during a dissociation process provides additional insight into the mechanism34. Figure 8 presents the KER distributions calculated from the position and time information of the two ions measured in coincidence following a standard COLTRIMS approach35, 36.

Figure 8 Kinetic energy release (KER) during the formation of trihydrogen cations at different focal intensities for dissociative ionization of CH 3 OH and CH 3 OD. All H 3 + formation channels (black curves) represent a Gaussian distribution with a mean of 5.00 eV and a standard deviation of 0.62 eV, while H 2 D+ formation channels (red curves) have a similar distribution with a mean of 5.48 eV and a standard deviation of 0.69 eV. Full size image

It is evident from these KER distributions that regardless of the originating molecule or the laser intensity, similar fragments exhibit almost identical KER. However, a comparison between the H 3 + + COD+ and H 2 D+ + HCO+ dissociation channels from the same precursor molecule, CH 3 OD2+, indicates an increase in the KER with the latter pathway (H 2 D+ formation). This increase in KER for the H 2 D+ formation channel can be attributed, based on conservation of energy and momentum arguments, to the higher thermodynamic stability of the HCO+ fragment compared to the COD+ fragment. This difference in stability has been predicted to be 1.63 eV at the CCSD(T)/CBS(V + C) + ZPE level of theory for the non-deuterated molecules37. Thus, a fraction of this excess energy appears to be converted to additional kinetic energy in the recoiling fragments of the H 2 D+ + HCO+ dissociation channel. We anticipate a fraction of the remaining energy ends up as internal rotational and vibrational energy of the products. KER analysis confirms that the H 2 D+ formation occurs via abstraction of the deuterium atom directly from oxygen, and not through H-migration.

Theoretical Results

First principles molecular dynamics simulations for the formation of H 3 + from a doubly charged methanol molecule based on the single reference configuration interaction singles and doubles (CISD) method have previously been reported38. The CISD trajectories revealed two distinct H 3 + formation pathways. In these pathways, a neutral H 2 molecule is initially ejected and then later reacts with the CHOH2+ to form H 3 + either along with the formyl cation (CHO+) or the isoformyl cation (COH+). The isoformyl cation formation mechanism, which does not involve the hydroxyl hydrogen in the H 3 + formation, was found to be about an order of magnitude more probable. In our experiments, CHOH2+ and CHOD2+ were detected in the respective mass spectra (see Supplementary Information Figs. S1 and S2). This observation confirms the ejection of neutral H 2 from CH 3 OH2+. Here we assess the validity of involvement of the neutral H 2 molecule in the production of H 3 + from the doubly charged methanol.

For our simulations we used the multireference complete active space self-consistent field method with 12 active electrons in 12 active orbitals (CASSCF(12/12)) to investigate the H 3 + formation mechanism. This method is a more flexible treatment of the electronic structure than the single reference CISD method, giving a balanced treatment of regions of the potential energy surface corresponding to closed shell and radical electronic configurations. A summary of the final outcome of the trajectories is provided in Table 2.

Table 2 Summary for the final products of the CASSCF trajectories after 150 fs. Full size table

We observe that the ejection of one proton from the methyl side accounts for about half of the trajectories. Moreover, the production of diatomic hydrogen was observed in a large percentage either as neutral H 2 or cationic H 2 +. Interestingly, H 2 + was not predicted in the earlier CISD work38, but is observed experimentally in high yield and in coincidence with the formation of CHOH+ (Fig. 3). The preferential formation of H 2 + + CHOH+ compared to the H 2 + CHOH2+ pathway in the current trajectories is consistent with the fact that the biradical system is more thermodynamically stable by 1.86 eV, as calculated at the complete basis set-atomic pair natural orbital (CBS-APNO) level of theory37. In most of the trajectories that form dihydrogen, either neutral or charged, the dihydrogen molecule moves far away from the other fragment, making H 3 + formation impossible. However, when H 3 + formation is observed, it occurs only after the formation of neutral H 2 in two distinct mechanisms that resemble what was previously found in the early CISD work38. In the predominant mechanism, H 2 roams near CHOH2+ and then abstracts a methyl proton to form H 3 + and COH+. The 50–130 fs timescale of this process observed in our simulations matches our experimental observations. The second mechanism involves a roaming H 2 molecule which abstracts a hydroxyl proton to form H 3 + and CHO+. This trajectory was observed only once out of 1000 trajectories, and occurred at about 130 fs. The relatively low occurrence of H 3 + + CHO+ in our simulations can be explained in part by the fact that the time scale associated with this mechanism is comparable to our total 150 fs simulation window (see Fig. 6). Moreover, a review of the trajectory indicates this pathway depends on the relative distance/orientation of the hydroxyl proton. Our relatively short simulations may not be a good measure of the relative occurrence of this slower mechanism. It is worth noting that the predicted dominance of the formation of H 3 + along with COH+ is thermodynamically unfavorable compared to the second pathway (H 3 + + CHO+) by 1.63 eV as reported at the CCSD(T)/CBS(V + C) + ZPE level of theory39. Yet, the thermodynamic stability of CHO+ compared to COH+ is clearly reflected upon the ejection of separate H+ and H 2 in our trajectories. The simulations predict a ratio of H 3 + to H+ of 7%, which is in good agreement with the experimental mass spectra of methanol.

Several snapshots from two of the H 3 + formation trajectories are shown in Fig. 9. These two examples represent the two different H 3 + formation pathways. Videos of these two trajectories are provided online as Supplementary Video S1 and Supplementary Video S2. The Mulliken charges for each of the two hydrogen atoms that are forming H 2 as well as the three hydrogen atoms forming H 3 + are also shown in Fig. 9, to demonstrate that neutral H 2 roaming is essential for the formation of H 3 +. Note that for the second pathway shown in Fig. 9(b), a longer roaming time is observed when the more distant hydroxyl proton is involved.