Ultrafast tunnel ionization enables femtosecond time-resolved dynamic measurements of the retro-Diels–Alder reactions of positively charged cyclohexene, norbornene, and dicyclopentadiene. Unlike the reaction times of 500–600 ps that are observed following UV excitation of neutral species, on the ionic potential energy surfaces, these reactions occur on a single picosecond timescale and, in some cases, exhibit vibrational coherence. In the case of norbornene, a 270 cm−1 vibrational mode is found to modulate the retro-Diels–Alder reaction.

The importance of Diels–Alder (DA) and retro-Diels–Alder (rDA) reactions in synthetic organic chemistry stems from their ability to form rings with up to four new stereocenters.1,2 The DA reaction involves bond formation between a diene and a dienophile, while the rDA reaction corresponds to the reverse reaction producing a diene and a dienophile. In the ground state, the retention of stereosymmetry through the DA and rDA reactions has suggested that they occur through a pericyclic transition state in a concerted process that follows the Woodward–Hoffmann rules.3 Interest in this reaction has spurred machine-learning prediction of major regio-, site-, and diastereoisomers in the DA reaction.4 The radical cation rDA reaction was first recognized following electron ionization (EI) in the early 1960s.5 However, the stereospecificity expected for rDA reactions was not observed in ionic species, prompting extensive studies of these important reactions in mass spectrometry.6 Here, we present a femtosecond time-resolved study of the rDA reactions in ionized cyclohexene (CHN), norbornene (NBN), and dicyclopentadiene (DCPD). Our results may shed light on the dynamics of these processes as they occur in EI mass spectrometry (EI-MS). Despite the internal energies of 10–30 eV associated with ionization and fragmentation in our studies, in some cases, evidence of coherent vibrational motion indicates that energy is not randomized on the ionic potential energy surface prior to the completion of the reaction.7,8 Here, we find that rDA reaction times in ionic species can be two orders of magnitude faster than those found in the excited states of neutral molecules. The rDA reaction in CHN is found to proceed via a statistical energy distribution process in which ring opening is followed by the loss of ethene. For NBN and DCPD, we observe coherent vibrational motion in the rDA fragment ions, suggesting that vibrational energy is not fully randomized and the reaction is a mixture of concerted and stochastic processes dictated by the presence of a strained five-membered ring.

The development of femtosecond transition-state spectroscopy9–12 made it possible to test with greater exactitude if reactions are concerted or sequential in nature. In general, a reaction can be stepwise, concerted synchronous, or concerted asynchronous, as discussed for the ultrafast molecular elimination of I2 from CH2I2.13–16 The first femtosecond studies to address the question of concertedness in the rDA reaction in neutral NBN and norbornadiene (NBD) employed two-photon excitation at 307 nm (total energy of 8.1 eV) and multiphoton ionization probing at 615 nm. The precursor mass was found to have a decay time of 160 fs, while the product mass (m/z 66) was found to have a 30-fs rise followed by a 220-fs decay.17 The reaction in NBN was revisited by Fuss et al. via one-photon excitation at 200 nm and multiphoton probing with 800-nm pulses.18 They found five time constants τi of 30, 60, 52, and 800 fs and 92 ps, with the first three being associated with departure from the FC region, traveling along the ππ* surface, while τ4 and τ5 are associated with bond rearrangement processes in the hot ground state. They suggested that the ππ* surface is crossed by the zwitterionic state, leading to two carbene products on the ground state surface. Cyclopentadiene was not detected until at least 600 ps, indicating that the rDA reaction occurs in the ground state on a hundreds-of-picosecond timescale following 200-nm excitation.

Experiments on CHN by Diau et al. found the rise and decay times of the product ion to be 15 and 150 fs, respectively.19 Fuss et al. carried out experiments on CHN and measured four time constants τi of 20, 47, 43, and 350 fs, associated with departure from the FC state, traveling along the ππ* surface. Bond rearrangement was initiated within the fourth time constant to form ground state cyclopentyl-carbene, with butadiene formation not occurring until 500 ps.20 Subsequent analysis of the femtosecond results from Zewail and Fuss by Wilsey and Houk, backed by ground- and excited-state potential energy surfaces using complete active space self-consistent field (CASSCF) theory and the 6-31G* basis set, concluded that the 1(ππ*) excited states of CHN and NBN can readily reach the conical intersection from which ground state carbene products are formed.21,22 More recent results on CHN based on velocity map imaging following excitation at 193 nm confirm that the rDA reaction occurs from high vibrational levels of the electronic ground state following internal conversion from a higher-lying electronic state initially populated by photoexcitation.23 Femtosecond time-resolved experiments were performed on DCPD by Goswami et al. using a weak 800-nm pump and a stronger 800-nm probe, with pulse intensities below the ionization threshold. Their transient data showed biexponential decay components associated with the C10H12+ ion (35 and 240 fs) and those associated with the C5H6+ ion (36 and 280 fs).24 Given the likely four-photon excitation based on their power dependence, the dynamics observed are those associated with a Rydberg state that decays via conical intersections to the ground state in ∼250 fs. These measurements are likely sensitive to high-energy intermediates and not products, in analogy to the experiments on CHN and NBN by Fuss.18,20

In strong-field ionization,25–27 the laser field ionizes molecules and can accelerate electrons to tens of eV in energy. These electrons may return to rescatter with the originating atom or molecule, given that the sign of the field oscillates with the optical period. This return may occur within the same optical cycle (2.67 fs for 800-nm photons) as the “birth” time or in subsequent cycles for a multi-cycle pulse. While first demonstrated in smaller systems, decades of studies of strong-field rescattering and high-harmonic generation (HHG) have demonstrated the prevalence of these phenomena in polyatomic molecules.28–36 Femtosecond 800-nm pulses with a peak intensity of 1 × 1014 W/cm2 can tunnel ionize large polyatomic molecules with ionization potentials (IPs) ranging from 8 to 10 eV and create high-energy electrons that can deposit much of their energy back into the molecule upon rescattering. The maximum kinetic energy of returning electrons is ∼3.2 Up,37 where Up is the ponderomotive energy. For the above laser parameters, this maximum energy is about 19 eV. We suggest that the dynamics observed following ultrafast strong field ionization as performed here may shed light on the fragmentation processes occurring in EI-MS, given that the ultrafast vertical excitation driven by the 70-eV EI-MS electrons quickly leads to single or multiple ionization, followed by fragmentation and vibrational energy distribution occurring on fs-to-ns timescales. Here, we focus on the time-resolved rDA reaction dynamics in CHN, NBN, and DCPD following strong-field ionization.

The experimental apparatus employed in this study has been described in detail elsewhere.38 Briefly, a 1-kHz, 40-fs, 800-nm laser beam is split into pump and probe pulses. The temporal delay is controlled by a translation stage (Aerotech, ANT130L). The pump and probe pulses are recombined and focused into the interaction region by an f = 300-mm achromatic lens. The pump intensity is tuned to optimize ion yields while avoiding the saturation of the larger mass-to-charge species. The peak intensity of the pump is 1 × 1014 W cm−2, and the calibration of the laser intensity has been performed using the N22+/N2+ and Ar2+/Ar+ ion yield ratios.39,40 The wavelength, intensity, and pulse duration of the pump correspond to a Keldysh parameter γ of ∼0.9 (assuming a 9-eV ionization potential [IP]), thus favoring tunnel ionization.41 The IPs of CHN, NBN, and DCPD are 8.94, 8.6, and 8.8 eV, respectively. In this intermediate ionization regime, some combination of tunnel and multiphoton ionization likely occurs.42 We have, however, also utilized higher pump intensities, ranging from 2 to 6 × 1014 W cm−2 (γ ∼ 0.6 down to 0.4). These higher intensities resulted in similar fragmentation patterns and retrieved time constants (see Tables S1 and S2 in the supplementary material).

The dynamics of all the different products following ultrafast ionization are followed by a weak 800-nm pulse. The probe pulse is polarized at the “magic” angle (54.7°) relative to the pump pulse to minimize the influence of rotational dynamics on the measurements. The probe is attenuated to about 3 × 1013 W cm−2 until signals for large negative times and large positive times are equal, where “negative” or “positive” means that the probe pulse arrives earlier or later than the pump pulse, respectively. No ion signal is produced by the probe alone. The probe disrupts the chemical reaction of interest only while the chemical transformation is happening, preventing its completion. The ability to deplete the product of interest can thus be tracked with femtosecond time resolution. Once the product is formed, the product can no longer be depleted by the weak probe pulse. It is worth noting that disruptive probing, as described here and used in previous experiments,7,9,38,43,44 is very different from multiphoton ionization probing as used in the studies by Zewail, Fuss, and Goswami.17–24 Multiphoton ionization of neutral species is strongly favored by hot intermediates, which in those experiments were observable only for time delays of <350 fs. In our experiments, the pump pulse causes ionization and fragmentation, and the weak probe pulse can only disrupt the product yield if it arrives before such a product is formed. Therefore, disruptive probing provides information about the timescale of product formation, which in our case can extend to hundreds of picoseconds. The effectiveness of disruptive probing has been confirmed by experiments on the formation of H3+ following strong-field excitation and electron rescattering in alcohols. The times measured corresponded quite closely to molecular dynamics simulations from our group,8,9,38,44 as well as from an independent experiment and theory effort.45 

The samples, CHN, NBN, and DCPD, were degassed by several freeze–pump–thaw cycles before the sample vapor is introduced into the interaction region through a needle valve. During all the measurements, the pressure of the mass spectrometer is kept below 5 × 10−6 Torr. When the sample needle valve is closed, the background pressure drops quickly to the range of 10−8 Torr, and the base pressure is in the range of 10−9 Torr. Our measurements are performed using a Wiley–McLaren time-of-flight (TOF) mass spectrometer,46 in which ions are detected using a Chevron-configuration microchannel plate detector. The TOF signals are digitized using an oscilloscope (LeCroy, WaveRunner 610Zi). A 1-mm slit after the interaction is used to mitigate focal-volume averaging effects, given a Rayleigh length of about 1.8 mm. For every time delay in one time-resolved scan, a TOF spectrum is obtained by averaging over 1000 laser shots. Each time-resolved plot is the average of several hundred iterations of a time-resolved scan, and thus, every data point is an average of more than 75 000 laser shots.

The mass spectra of the compounds obtained by femtosecond tunnel ionization (blue) and via EI-MS (red) are shown in Figs. 1(a)1(c). In the spectra, we identify the molecular ion with an arrow and the main product of the rDA reaction with an asterisk. For CHN, in addition to the butadiene radical cation (m/z 54) resulting from the rDA reaction, we also observe the loss of a methyl radical, leaving a five-carbon species (m/z 67), and the dissociation of the molecule into two C3H5 ions (m/z 41). For NBN and DCPD, the main rDA product is the cyclopentadiene radical cation. The maximum energy of the returning electrons is about 3.2 Up. For a 1 × 1014 W cm−2-pump pulse, this corresponds to about 19 eV, whereas for a 6 × 1014 W cm−2-pump pulse, the maximum return energy is about 110 eV (see Fig. S1 in the supplementary material, where electron returning energies are calculated for a number of laser peak intensities). A significant fraction of the electron energy may be imparted to the parent ion through rescattering. Moreover, the fragment ions observed provide indications of returning electron energy and the internal energy of the molecular ions after rescattering. EI-MS measurements have shown that fragments m/z = 93, 79, and 66 from NBN, for example, have appearance energies ranging from about 9 to 11 eV.47 EI-MS and photoionization measurements for CHN48–54 have shown the appearance energies of fragments m/z = 82, 67, 54, and 39 from about 9 to 13 eV. Due to the presence of these fragments in our measurements, we can estimate the internal energy of the molecules following electron rescattering to be at least ∼15 eV. As shown in Fig. 1(c), for DCPD, the fragmentation pattern observed following electron rescattering is remarkably similar to the pattern observed following EI-MS, indicating a similar internal energy based on the concept of “thermometer ions.”55 While the internal energy may be controlled following femtosecond laser ionization by adjusting the pump laser intensity and wavelength, no such effort was made here to replicate the internal energy following EI-MS.

FIG. 1.

EI-MS spectra from the NIST database (red) and strong-field ionization (blue) spectra for (a) CHN, (b) NBN, and (c) DCPD together with the molecular scheme. The two bonds that are broken during the rDA reaction are indicated by a dashed red line. The molecular ion is indicated by an arrow and the main product of the rDA reaction by an asterisk.

FIG. 1.

EI-MS spectra from the NIST database (red) and strong-field ionization (blue) spectra for (a) CHN, (b) NBN, and (c) DCPD together with the molecular scheme. The two bonds that are broken during the rDA reaction are indicated by a dashed red line. The molecular ion is indicated by an arrow and the main product of the rDA reaction by an asterisk.

Close modal

The time-resolved ion yields of C4H6+ (CHN) and C5H6+ (NBN and DCPD) following the strong-field ionization are shown in Fig. 2. The three traces are fitted to the following function:

(1)

Here, n is the number of exponential terms, each with amplitude Ai and time constant τi. A positive or negative Ai value corresponds to a decaying or a rising exponential function, respectively. Furthermore, m is the number of cosine components that describe the oscillatory behavior, each with angular frequency ωj and phase shift φj. The parameter τdamp represents the damping time of the oscillations. The exponential components modulated by the oscillations are multiplied by the Heaviside function H(t), and this product is convolved with the instrument response function IRF(t). The full-width-at-half-maximum (FWHM) of the IRF(t) is about 80 fs for all the traces in this work. The very sharp peak at zero time delay exhibits a fast exponential decay (τ < 15 fs), corresponding to the overlap between pump and probe pulses in time.

FIG. 2.

The time-resolved yield of the main rDA reaction product ions for (a) CHN, (b) NBN, and (c) DCPD following ultrafast ionization. The experimental data points, connected by a blue line, are normalized such that the yield at negative time delays is unity. The best-fit results are plotted as a red solid line, and the insets are zoomed in on the regions in the dashed green boxes to highlight the behavior near time zero.

FIG. 2.

The time-resolved yield of the main rDA reaction product ions for (a) CHN, (b) NBN, and (c) DCPD following ultrafast ionization. The experimental data points, connected by a blue line, are normalized such that the yield at negative time delays is unity. The best-fit results are plotted as a red solid line, and the insets are zoomed in on the regions in the dashed green boxes to highlight the behavior near time zero.

Close modal

The fitting parameters are summarized in Table I. For C4H6+ from CHN, shown in Fig. 2(a), three exponential terms are found, a 0.84 ± 0.11-ps decay, a 23.5 ± 7.6-ps rise, and a slower 131 ± 55-ps rise. As shown in Figs. 2(b) and 2(c), C5H6+ from NBN also exhibits three exponential components, a 0.30 ± 0.02-ps decay, a 0.89 ± 0.07-ps rise, and a slower 7.30 ± 0.67-ps rise. These exponential terms are modulated by an oscillation frequency of 270.4 ± 0.3 cm−1, with a damping time of 2.49 ± 0.40 ps. For C5H6+ from DCPD, shown in Fig. 2(c), we retrieve two exponential components, a 0.43 ± 0.02-ps rise and a 10.3 ± 0.6-ps slow rise. These are modulated by oscillation frequencies of 65.7 ± 5.7 and 107 ± 7 cm−1, extracted using the maximum entropy method.56 The retrieved damping time for these oscillations is 0.15 ± 0.02 ps. As mentioned above, we have repeated the measurements using higher pump intensities, ranging from 2 to 6 × 1014 W cm−2 (γ ∼ 0.6 down to 0.4). At these higher energies, the energy of the returning electron is higher (see Fig. S1 in the supplementary material). Data obtained at higher pump intensities resulted in similar fragmentation patterns and retrieved time constants, consistent with the data shown in this manuscript (see Tables S1 and S2 and Fig. S2 in the supplementary material).

TABLE I.

Fitting parameters based on Eq. (1). The numbers in parentheses are the percent contributions of the exponential rise terms. The angular frequencies of the oscillations have been converted to wavenumbers.

CHNNBNDCPD
τdecay (ps) 0.84 ± 0.11 0.30 ± 0.02 ⋯ 
τrise1 (ps) 23.5 ± 7.6 (47%) 0.89 ± 0.07 (75%) 0.43 ± 0.02 (74%) 
τrise2 (ps) 131 ± 55 (53%) 7.30 ± 0.67 (25%) 10.3 ± 0.6 (26%) 
ν̃1 (cm−1⋯ 270.4 ± 0.3 65.7 ± 5.7 
ν̃2 (cm−1⋯ ⋯ 107 ± 7 
τdamp (ps) ⋯ 2.49 ± 0.40 0.15 ± 0.02 
CHNNBNDCPD
τdecay (ps) 0.84 ± 0.11 0.30 ± 0.02 ⋯ 
τrise1 (ps) 23.5 ± 7.6 (47%) 0.89 ± 0.07 (75%) 0.43 ± 0.02 (74%) 
τrise2 (ps) 131 ± 55 (53%) 7.30 ± 0.67 (25%) 10.3 ± 0.6 (26%) 
ν̃1 (cm−1⋯ 270.4 ± 0.3 65.7 ± 5.7 
ν̃2 (cm−1⋯ ⋯ 107 ± 7 
τdamp (ps) ⋯ 2.49 ± 0.40 0.15 ± 0.02 

The vibrational coherence observed for NBN is further analyzed, as shown in Fig. 3. To extract the oscillatory component, we fix Bj at 0 when fitting the traces of the product ion (C5H6+) and molecular ion (C7H10+) to Eq. (1). The residuals of this fitting, shown in Fig. 3(a), correspond to the oscillating components of the signals. We find that the product and molecular ion oscillations are out of phase. The Fourier analysis of the residuals allows us to identify a frequency centered at 270.4 ± 0.3 cm−1 for both the molecular ion and product. Zero padding is applied to the experimental data before the fast Fourier transform (FFT) to ensure an appropriate number of data points without artificially decreasing the frequency resolution. A similar out-of-phase behavior was observed for DCPD and the rDA product, not shown.

FIG. 3.

Coherent vibrational motion with a period of 123.4 fs observed in the molecular ion and the main rDA reaction product for NBN. (a) Fitting residuals of the product ion (C5H6+) and molecular ion (C7H10+) yields based on Eq. (1) with Bj fixed at zero for the rDA reaction in NBN. (b) Fast Fourier transform of the residuals shown in (a), with zero padding to 2048 data points. The out-of-phase nature of the oscillations implies a direct link between the two species as discussed in the text.

FIG. 3.

Coherent vibrational motion with a period of 123.4 fs observed in the molecular ion and the main rDA reaction product for NBN. (a) Fitting residuals of the product ion (C5H6+) and molecular ion (C7H10+) yields based on Eq. (1) with Bj fixed at zero for the rDA reaction in NBN. (b) Fast Fourier transform of the residuals shown in (a), with zero padding to 2048 data points. The out-of-phase nature of the oscillations implies a direct link between the two species as discussed in the text.

Close modal

We find that the rDA reaction in CHN, NBN, and DCPD ionic species is hundreds of times faster than the rDA reaction in excited-state neutral molecules. For the neutral species, the reaction was initiated by 4–6-eV photons, whereas in our case, it was initiated by strong-field tunnel ionization and possible electron rescattering, depositing energies up to 19 eV. Studies on the UV-excited neutral species have concluded that the rDA process takes place in the ground state potential.17–22 Here, the process most likely takes place in the ground state of the cation, as discussed below. We reach this conclusion based on the observation that polyatomic molecules, upon near-threshold tunnel ionization, are found primarily in the ionic ground state and their internal energy is determined by the change in geometry between the neutral and ionic ground states.8 

One of the key questions regarding rDA processes has been determining if the process is concerted, namely, if both C–C bonds break in a single kinetic step. In general, it is natural to associate concerted processes with reaction timescales that are comparable to a single vibrational oscillation. Zewail and co-workers concluded that the rDA reaction involves both concerted and sequential reaction pathways.17,19,21 However, subsequent experiments18,20 and calculations22 questioned this conclusion, given that the product was not observed until 500–600 ps later. The question of concertedness in rDA reactions as they occur in mass spectrometry has been addressed by analyzing the conservation of orbital symmetry.6 The conclusion from that study was that the reaction mechanism depends on substituents and likely occurs by both concerted and stepwise mechanisms.6 

For CHN, the rDA product (C4H6+, m/z 54) exhibits an induction time of ∼840 fs, a period of time before the probe pulse causes a depletion in the reaction pathway. Product formation takes place in ∼80 ps and shows no evidence of coherent vibrational motion. We thus conclude that the rDA reaction in CHN most likely follows a stepwise process. The first step is either the opening of the CHN ring or the formation of a cyclopentyl-carbene radical cation,57,58 and subsequently, a second bond breaks to form C4H6+. The lower energy path, corresponding to the loss of a methyl radical, is a preferred reaction pathway following EI-MS.53 In our experiments, the ion count for this pathway (m/z 67) is slightly lower than that observed in EI-MS. The loss of the methyl pathway shows an induction time of ∼360 fs, likely associated with H-atom bond rearrangement, leading to the formation of a five-member ring,53 and a biexponential decay with fast 2-ps and slow 21-ps components associated with the formation of the cyclopentyl cation and CH3 (data not shown).

For NBN, we observed very different dynamics. First, we observe the induction time of ∼300 fs, faster than in CHN, and second, we observe the presence of vibrational coherence in both the molecular and rDA product ions. The rDA reaction time (∼2.5 ps) is >30 times faster than in CHN. The vibrational coherence enhances or decreases the yield depending on the phase of the oscillations, demonstrated by the out-of-phase behavior between the molecular and product ions shown in Fig. 3. It is tempting to associate the observed vibrational coherence with a concerted process. The association between vibrational coherence in the product and a concerted chemical reaction was first made in connection to the reaction CH2I2 → CH2 + I2.13,14 In a sense, the dynamics are reminiscent of the dissociation of excited state NaI, which depends on a Landau–Zener crossing from the ionic to the covalent potential.59–61 The modulation depth of the vibrational coherence observed for NBN in Fig. 2(b) accounts for only 30% of the depletion. We thus consider the rDA reaction in NBN to take place through both a concerted process in which the two C–C bonds are broken in a single kinetic step and a sequential process in which there is some time between the two bond-breaking events.

Quantum chemical studies of the dissociation of the NBN radical cation were carried out to look for vibrational Raman/IR modes that might help explain the striking 270 cm−1 coherent fragmentation modulation described above (see Tables S3 and S4 in the supplementary material).62 Notably, a strong 275 cm−1 vibration was computed at the EDF2/6-31+G* level of theory, a method specifically designed to cost effectively predict molecular vibrational modes.63 The analogous wavefunction-based method MP2/6-31G* found the same mode at 265 cm−1 after scaling.64,65 Importantly, this vibrational mode, which corresponds to the compression of the angle between the HC=CH and H2C–CH2 bridges, is likely to be strongly excited upon ionization; relaxation from the ground state structure of NBN to the radical cation entails geometry changes that mimic this mode. Electron loss from the olefinic π-bonding orbital (the HOMO) weakens and lengthens the π bond (from 1.35 to 1.43 Å in the MP2/6-31G* geometries) while compressing the angle between the HC=CH and H2C–CH2 bridges and shortening and lengthening side bonds as shown in Fig. 4. These distortions are also essentially the same as the initial bonding changes expected upon the cleavage of the ethylene radical cation and the cyclopentadiene radical cation. Thus, the 270 cm−1 vibration is strongly coupled to the rDA reaction coordinate.

FIG. 4.

MP2/6-31G* calculated equilibrium geometries for NBN and the radical cation, highlighting the geometry changes occurring as the nascent cation moves toward equilibrium. The distortions observed are close to the motions seen in the calculated 265 cm−1 vibrational mode. The bond extensions (red) and bond contractions (blue) are consistent with the extensions and contractions expected during a retro-Diels–Alder reaction as indicated in the bottom scheme.

FIG. 4.

MP2/6-31G* calculated equilibrium geometries for NBN and the radical cation, highlighting the geometry changes occurring as the nascent cation moves toward equilibrium. The distortions observed are close to the motions seen in the calculated 265 cm−1 vibrational mode. The bond extensions (red) and bond contractions (blue) are consistent with the extensions and contractions expected during a retro-Diels–Alder reaction as indicated in the bottom scheme.

Close modal

Vertical ionization of the NBN molecule generates the radical cation in a non-equilibrium geometry. To explore the excess distortion energy this difference would leave in the cation, NBN and its radical cation were modeled at the G3(MP2) level of theory to compute the vertical (9.14 eV) and 0–0 (8.86 eV) ionization potential values.66 These may be compared with the literature values of 9.2 and 8.6–8.8 eV.67 Thus, upon initial formation, the radical cation would have an additional internal energy of 0.3–0.5 eV with respect to its equilibrium geometry. The rDA cleavage of the ethylene + cyclopentadiene radical cation is uphill in enthalpy by roughly the same amount (1.0 ± 0.3 eV) as for the neutral dissociation. However, considering the fragmentation from one to two particles, the free energy cost is substantially lower (+0.43 eV) at ambient temperatures, so this excess internal energy represents a significant extra contributor to enable the rDA reaction pathway.

Using the dynamic features of the Q-chem quantum chemistry package,62 a small number of quasiclassical molecular dynamics simulations using the EDF2/6-31+G* model were run to examine the flow of vibrational energy in the ionized NBN. This approach sets up initial atom velocities by putting vibrational energy into each normal mode, with the vibrational levels populated according to a Boltzmann distribution for the simulation temperature. The trajectory is then propagated according to classical mechanics.68 Starting from the geometry of neutral NBN, as expected based on the above descriptions, but using the Hessian matrix obtained for the radical cation, the analysis of the motions found the 275 cm−1 mode of the cation to be activated at a level corresponding to multiple quanta of energy, roughly equal to 0.3–0.5 eV cited above. More striking was that during nearly the full 1200 fs of the simulation, this mode remained substantially more excited than most of the other vibrational modes in the ion. It appears that the strong coupling of the geometry change upon ionization to this particular vibration, together with the high symmetry and rigidity of the norbornene molecule, leads to particularly slow intramolecular vibrational energy redistribution, preserving the oscillations that alternately carry the structure closer and farther from the ideal geometry for the rDA dissociation of the ethylene fragment.

Finally, the reaction dynamics of DCPD are similar to those found for NBN. The reaction time is ∼3.0 ps, and we observe coherent vibrational motion in the product ion [see Fig. 2(c)]. Similar to NBN, the motion of the product is out of phase with that of the molecular ion. However, for DCPD, the dephasing is much faster with one clear oscillation period of ∼300 fs. It is likely that the lower symmetry compared to NBN and the participation of additional low-frequency vibrational modes result in faster vibrational dephasing. Once again, based on the observation of coherent vibrational motion and the modulation depth in the depletion, we must conclude that the rDA reaction in the DCPD radical cation occurs via both concerted and sequential bond breaking mechanisms.

In conclusion, comparing the strong-field-induced rDA reactions in CHN, NBN, and DCPD radical cations, we find that the reaction is sequential in CHN and occurs via a mixture of sequential and concerted mechanisms in NBN and DCPD. The main difference between these compounds is the presence of a five-membered ring that contributes structural strain in NBN and DCPD. In addition, NBN and DCPD have an already formed cyclopentadiene ring, which upon dissociation constitutes a highly stable leaving group. These two factors improve the chances for a concerted process. In contrast to the UV-initiated rDA studies, we find that rDA reactions in radical cations are two-orders of magnitude faster and, in the cases of NBN and DCPD, involve coherent vibrational motion that may be associated with a concerted rDA mechanism. Future pursuits will include mimicking the conditions present in EI-MS by taking advantage of strong-field tunnel ionization and electron rescattering as an in situ source of high-energy electrons. Here, we have made no attempt to match the intramolecular energies that are reached in EI-MS because our focus is to elucidate the dynamics of the rDA reaction upon ionization of CHN, NBN, and DCPD. We hope our findings will encourage more detailed molecular dynamics simulations of the rDA reaction in NBN and DCPD. Similarly, we hope our findings will inspire femtosecond time-resolved x-ray or electron diffraction studies capable of following the structural changes associated with the rDA reaction.

See the supplementary material for (1) the calculated energy of the returning electron following strong field ionization, (2) data obtained for NBN and CHN at higher pump intensities, and (3) for tables containing the calculated Raman/IR frequencies for the NBN radical cation and for ground state neutral NBN.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Atomic, Molecular, and Optical Sciences Program, under Award Number SISGR (Grant No. DE-SC0002325). We thank Sarah Zenas in our group for proofreading this manuscript.

S.L., B.J., and M.D. contributed equally to this work. J.E.J. performed quantum chemistry computations and made important contributions to the interpretation of results and writing of the manuscript.

The data that support the findings of this study are available within the article and its supplementary material.

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Supplementary Material