We perform time-resolved ionization spectroscopy measurements of the excited state dynamics of CH2I2 and CH2IBr following photoexcitation in the deep UV. The fragment ions produced by ionization with a vacuum-ultraviolet probe pulse are measured with velocity map imaging, and the momentum resolved yields are compared with trajectory surface hopping calculations of the measurement observable. Together with recent time-resolved photoelectron spectroscopy measurements of the same dynamics, these results provide a detailed picture of the coupled electronic and nuclear dynamics involved. Our measurements highlight the non-adiabatic coupling between electronic states, which leads to notable differences in the dissociation dynamics for the two molecules.

The photoexcited dynamics of small molecules is of significant fundamental and practical importance. Non-adiabatic coupling between electronic states can facilitate internal conversion and the decay of excited states on ultrafast timescales1–6 and driving, e.g., photoprotection in DNA bases.7–12 The coupled motion of electrons and nuclei after photoexcitation is also important for energy and light harvesting,13–16 as well as molecular switches.17 Our understanding of these processes has been greatly accelerated by the development of new experimental probes,18,19 which allows for increasingly direct measurements of energy flow and non-adiabatic coupling.

After photoexcitation, energy is converted from electronic potential energy into nuclear kinetic energy as the wave packet evolves on the excited state surface. The wave packet can be transferred to other electronic states via Born–Oppenheimer violating terms in the molecular Hamiltonian. Time-resolved photoelectron spectroscopy (TRPES) provides a detailed picture of how the electronic potential energy is lost and can yield information on the electronic state character via Koopmans’s correlations,18,20,21 but it does not provide direct information on the nuclear kinetic energy gained as the wave packet evolves. This information can be partially acquired by infrared transient absorption spectroscopy (particularly for bound states), which probes vibrations,19 or measuring the kinetic energy of the photoions upon ionization. Relativistic ultrafast electron diffraction and hard x-ray diffraction offer the ability to directly probe the structure, but do not directly measure kinetic energy.22–24 Time-resolved photoion spectroscopy (TRPIS) with velocity map imaging of the ions provides information on the nuclear kinetic energy when the probe pulse arrives but can be complicated by the evolution of the nuclear wave packet on the cationic potential energy surface. TRPIS measurements have been used to follow the UV-driven photodissociation of CH3I, CH2IBr, CH2BrCl, and C2F3I using both resonance-enhanced multiphoton absorption and vacuum ultraviolet (VUV) absorption driven ionization as a probe.25–27 

Here, we present time-resolved ionization spectroscopy measurements with velocity map imaging (VMI) of the fragment ions, which directly probe the kinetic energy gained by the molecule as the wave packet evolves. We compare and contrast measurements in two similar systems, CH2I2 and CH2IBr, which show notable differences in the time- and energy-resolved fragment ion yields that can be interpreted in terms of trajectory surface hopping calculations of the measurement observable.28–30 While earlier time-resolved momentum imaging work on similar halogenated methanes26,31 highlighted the asymptotic distribution of kinetic energy between rotation and translation, our work concentrates on the time-dependent conversion of electronic potential energy into nuclear kinetic energy and how the dynamics differ between the two molecules of interest, complementing earlier TRPES measurements of the same two molecules.32 

Here, we describe our femtosecond time-resolved photoelectron and photoion VMI spectrometer with the TIMEPIX3 camera. Femtosecond laser pulses are obtained from an amplified Ti:Sapphire laser system (KMLab 780 nm), which produces 30 fs, 1 mJ pulses at a central wavelength around ∼780 nm, and a repetition rate of 1 kHz. The main part (∼850 μJ) of the fundamental output is used for harmonic generation, producing UV (3ω, ∼261 nm, and ℏω = 4.75 eV) pulses. A small portion of the UV output is used as the pump pulse (up to ∼3 μJ), and the remaining main part (up to ∼30 μJ) of the output is then combined with the residual fundamental in order to generate VUV (∼156 nm, ℏω = 7.92 eV) pulses through non-collinear-four-wave mixing (3ω + 3ωω = 5ω) in gas phase argon, which then is used for the probe pulse. The full pump-probe scheme has been described in detail elsewhere.33 The UV-pump and VUV-probe pulses are combined together under the interaction region of a coincidence velocity map imaging (VMI) apparatus, and we measure the momentum-resolved photoelectron and photoion yields as functions of pump-probe delays. In order to locate the pump-probe time-zero, we perform pump-probe measurements with ethylene under the same running conditions as those for CH2I2 and CH2IBr. Ethylene has a rapid decay time after VUV excitation,4,34,35 which allows one to characterize the instrument response function (IRF) as well as locate pump-probe time-zero. By fitting the ethylene signal with an exponential function convolved with a Gaussian, we acquire the time-zero and IRF of the UV-VUV cross correlation, which is ∼80 fs for the full-width-at-half-maximum (FWHM).36 

In Fig. 1, panel (a) shows a cartoon depiction of the experimental setup. The VMI spectrometer employs a continuous molecular beam, an electrostatic lens, a time-of-flight (ToF) tube, and a micro-channel plate (MCP) and phosphor-based position-sensitive detector. At the front of the ToF tube, an electrostatic lens consists of a standard repeller-extractor-ground electrode lens sitting inside a μ-metal sheet cylinder for magnetic shielding. At the end of the ToF, there is a position-sensitive 2D detector, consisting of two 40 mm active diameter MCPs in Chevron configuration together with a P47 phosphor screen. Both the pump and probe pulses are linearly polarized with the polarization direction perpendicular to the ToF direction. In order to detect both photoelectrons and ions with a single detector, the VMI voltages are initially negative, and then the polarity is rapidly switched immediately after detection of the electrons. Since the time between ionization and detection of the electrons is small (less than 100 ns), we can neglect the motion of the ions before the voltage on the VMI plates is switched. The molecular nozzle with a diameter of 30 μm is set parallel to the surface of repeller and extractor plates about 3 mm away from their edges. The pump and probe beams propagate parallel through the plates perpendicular to the molecular nozzle. The chamber base pressure is ∼10−7 torr, and the running pressure of the reaction chamber is kept at ∼10−6 torr. CH2I2 and CH2IBr are purchased from Sigma-Aldrich and used without further purification. A multi-functioning sample manifold is integrated into the VMI chamber, which allows for both liquid and gas samples. The manifold contains a liquid sample cell, a delivery line, and a molecular nozzle inside the reaction chamber. Several valves are used for pumping and sample pressure regulation. All of the components are made of stainless steel and copper in order to prevent leaking and contamination. CH2I2 and CH2IBr, which are liquid in room temperature, are loaded into the sample cell, pumped on while frozen (“freeze pumped”) in order to remove air from the sample, and then regulated with a precision leak valve between the sample cell and the nozzle. The pressure behind the nozzle is kept at several torr, which generates a continuous molecular beam through the nozzle to the VMI chamber.

FIG. 1.

Cartoon depictions of the experimental apparatus and potential energy curves. Panel (a) lays out the UV-pump VUV-probe apparatus with VMI detection of ions. Laser beams intersect with an effusive molecular beam (e.g., CH2I2 and CH2IBr) between VMI plates, producing photoelectrons (e) and photoions (CH2I+ and CH2Br+). With fast high-voltage switches on the VMI plates and ns time resolution on the TIMEPIX3 camera, both electrons and ions can be detected in coincidence for each laser shot. The fast time stamping camera is able to record the hit position (x, y) as well as the time-of-arrival (t) for each charged particle. The inset in the upper left corner shows an energy integrated TRPES measurement (black circles) and fittings (blue curve) of ethylene, which yields a cross correlation of 80 fs (red curve).36 This is treated as the instrument response function. Panel (b) shows a cartoon of the dissociation dynamics of CH2I2 and CH2IBr after deep UV excitation. Ground and excited states are plotted in different colors, and wave packet cartoons and arrows illustrate some of the underlying dynamics.

FIG. 1.

Cartoon depictions of the experimental apparatus and potential energy curves. Panel (a) lays out the UV-pump VUV-probe apparatus with VMI detection of ions. Laser beams intersect with an effusive molecular beam (e.g., CH2I2 and CH2IBr) between VMI plates, producing photoelectrons (e) and photoions (CH2I+ and CH2Br+). With fast high-voltage switches on the VMI plates and ns time resolution on the TIMEPIX3 camera, both electrons and ions can be detected in coincidence for each laser shot. The fast time stamping camera is able to record the hit position (x, y) as well as the time-of-arrival (t) for each charged particle. The inset in the upper left corner shows an energy integrated TRPES measurement (black circles) and fittings (blue curve) of ethylene, which yields a cross correlation of 80 fs (red curve).36 This is treated as the instrument response function. Panel (b) shows a cartoon of the dissociation dynamics of CH2I2 and CH2IBr after deep UV excitation. Ground and excited states are plotted in different colors, and wave packet cartoons and arrows illustrate some of the underlying dynamics.

Close modal

The photoelectrons or photoions are projected to the detector, and the fluorescence signal from the phosphor is recorded by a novel pixel-based time stamping camera (TIMEPIX3).37 This camera has excellent spatial and temporal resolution and can simultaneously measure the mass and 3D momentum of all charged particles in each ionization event. We note that with the current ∼1 ns time resolution, the 3D momentum measurement for ions is possible without requiring an inverse Abel transform, while for electrons, we rely on the cylindrical symmetry about the pump and probe laser polarization axes to invert the two-dimensional data since the electrons all arrive within a few nanoseconds. In contrast to a conventional frame-based camera, the measurements record the position (x and y) and time (t) for each electron or ion incident on the detector, and the pump-probe delay information for each electron or ion incident is encoded into the dataset by a systematic variation in the trigger signal to the camera. The camera’s large throughput enables a straightforward switch between low-rate coincidence and high-rate non-coincidence detection modes. In addition, as a standalone piece of equipment outside the vacuum chamber, it allows for easy exchanges, upgrades, and maintenance.

In order to interpret the experimental results and gain insights into the energetic and structural evolution of the molecules following photoexcitation, we carried out trajectory surface hopping (TSH)38 calculations of the excited state molecular dynamics. We used the results of these calculations to produce the same observables as obtained in the TRPIS measurements. The details of the TSH calculations can be found in Ref. 32. In short, we used the SHARC (Surface Hopping including ARbitrary Couplings) program,39,40 interfaced with Molcas 8.0.41 The electronic structure calculations for both molecular systems were performed with MS-CASPT2(12,8)/ano-rcc-vdzp (multi-state complete active space perturbation theory second order) based on CASSCF(12,8) (complete active space self-consistent field with 12 electrons in 8 orbitals). The state-averaging included 5 singlet/4 triplet states for CH2I2 and 3 singlet/4 triplet states for CH2IBr. Furthermore, we employed an IPEA shift of zero,42 an imaginary shift of 0.3 hartree,43 the second-order Douglas-Kroll-Hess (DKH) Hamiltonian,44 and spin–orbit couplings (SOCs) from RASSI45 and AMFI46 formalisms. Gradients were evaluated numerically with a displacement of 0.005 a.u.. The dynamics was carried out using the velocity-Verlet algorithm with a time step of 0.5 fs for the nuclear dynamics and a time step of 0.02 fs for the propagation of the electronic wavefunction using the “local diabatization” formalism.47 Energy was conserved during a hop by scaling the complete velocity vectors (not along the non-adiabatic coupling vectors since the latter were not available). Wavefunction overlaps48 were employed to compute the transition probabilities between states of the same multiplicity. An energy-based decoherence correction with a parameter of 0.1 hartree was used.49 The initial geometries and velocities for the trajectories were sampled from a Wigner distribution of the harmonic ground state potential. In this way, 10 000 geometries were produced for each molecule, and a single-point calculation at the MS-CASPT2(12,8) level of theory was performed at each of these to obtain the state energies and oscillator strengths. The initial excited states were selected stochastically,50 restricting the excitation energy window to energies around our pump pulse (between 4.62 eV and 4.67 eV).

The advantages of the TSH calculations are that these classical trajectories contain rich information, including the time-dependent electronic potentials and state indices, electronic transitions, and nuclear geometries of all the atoms. This information allows us to calculate the measurement observables and compare with the experimental results. While the same simulations were used in combination with Dyson norm calculations for TRPES24,33 and the time-dependent geometries were compared with UED,24 here we extract the kinetic energies from the geometries in order to compare with our TRPIS measurements. Ideally, the kinetic energies should be obtained from trajectories in the cationic states after gaining velocity on the neutral excited state potentials. However, such a treatment is extremely costly, and we thus make use of an approximate approach instead, where we estimate the velocities based only on the neutral excited state trajectories. We calculate classically the translational kinetic energy (TKE) of CH2I/CH2Br and I from the aforementioned trajectories.

The trajectories contain the three-dimensional geometry information of all the atoms in Cartesian coordinates for each time step, allowing for the calculation of the TKE by taking differences in the atomic positions between time steps. In both CH2IBr and CH2I2, dissociation takes place along the C–I axis, and we track the TKE of the CH2Br/I and CH2I/I fragment pairs, respectively.

In this section, we describe the experimental data analysis and results. Different from velocity map imaging with a conventional frame-based camera, we implemented a pixel-based time stamping camera (TIMEPIX3), which has ∼1 ns time resolution in order to separately measure the time of arrival and position of all different species of ions simultaneously after the photoionization process. Our measurements record the position (x and y) and time (t) for each ion incident on the micro-channel plate and phosphor detector. In this work, we conducted measurements under the same conditions for both molecules, CH2I2 and CH2IBr. The dataset recorded by the camera consists of discrete events, with the position and time information (x, y, and t) for each electron or ion detected. Each individual event recorded was assigned to a pump-probe delay step, generating a sub-dataset that contains the time and position for each fragment ion.51 In our experiments, more than 50 000 events were collected for the parent and fragment ions, which allows us to reassemble the event position information for each ion species, generating a 2D image. An inverse Abel transform was applied to the 2D image to obtain the photoion spectrum for each time delay (yield as a function of TKE and pump-probe delays). In the measurements, several fragment-ion species were detected including CH2I+2 and CH2I+ from CH2I2 and CH2IBr+, CH2Br+ and CH2I+ from CH2IBr. At each pump-probe delay, we integrated between 150 and 300 laser shots and the pump-probe measurements were repeated several hundred times. We estimated that there were about ∼2 ions (CH2I+/CH2Br+) for each laser shot around zero time delay.

In Fig. 2, panels (a) and (b) show the measured photoion translational kinetic energy distribution as a function of the pump-probe delay for CH2I+ and CH2Br+, respectively. In order to view both the dynamics near zero time delay as well as the subtle changes to the spectrum at longer delays, panels (a) and (b) are plotted using a logarithmic color scale. Both molecules show a rapid decay in the fragment ion yield with time delay (on a ∼100 fs timescale) followed by small shifts of the TKE for the remaining peaks in the spectrum for times greater than 100 fs. However, we note that the changes in the spectra after 100 fs for the two molecules are different, with the CH2I+ yield displaying a single peak that increases in TKE, while the CH2Br+ yield shows two peaks (bands) that increase in KER with time. This is highlighted in panels (c) and (d), which show the “self-normalized” spectra for CH2I+ and CH2Br+ at each individual pump-probe delay slice, respectively: as the signals beyond 100 fs are much smaller than the yields near zero time delay, we normalized the spectra shown in panels (c) and (d) at each delay individually in order to better view the TKE at a pump-probe delay larger than 100 fs. The single peak/band in CH2I+ shifts from about 0.1 eV to above 0.2 eV, whereas the peak in CH2Br+ splits into two peaks, which shift to about 0.25 eV and 0.6 eV at long delays.

FIG. 2.

Measured photoion spectra for both CH2I+ and CH2Br+ from CH2I2 and CH2IBr, respectively. Panels (a) and (b) show the time and energy dependent yield of CH2I+ and CH2Br+ with a logarithmic scale, respectively. Panels (c) and (d) show the same spectra self-normalized for each delay on a linear scale.

FIG. 2.

Measured photoion spectra for both CH2I+ and CH2Br+ from CH2I2 and CH2IBr, respectively. Panels (a) and (b) show the time and energy dependent yield of CH2I+ and CH2Br+ with a logarithmic scale, respectively. Panels (c) and (d) show the same spectra self-normalized for each delay on a linear scale.

Close modal

A common feature in the fragment ion spectra shown in Fig. 2 is the increasing TKE of the peaks for both CH2I+ and CH2Br+. This is consistent with the conversion of electronic potential energy into nuclear kinetic energy as the wave packet launched by the pump pulse makes its way out on the dissociative potential. However, there is a significant difference between the two cases in that we observe two peaks in the CH2Br+ spectrum at delays beyond 100 fs, whereas there is only one in the CH2I+ spectrum.52 This difference can be interpreted in terms of our structure and dynamics calculations, which were also used to interpret previous time-resolved photoelectron spectroscopy results for the same two molecules.32 With the absorption of a deep UV photon (4.75 eV), both molecules are excited to a cluster of excited states including both bound (cyan) and dissociative states (blue and red). Figure 3 shows the potential energy for relevant neutral and cationic states as well as the state populations as function of time for both CH2I2 and CH2IBr.53 In panels (a) and (b), the calculated potential energy of the molecule is plotted as (one of) the C–I bond(s) is stretched, and all of the other bond lengths and angles are kept fixed. For CH2IBr, the excited neutral states are all directly dissociative, whereas for CH2I2, it is a mixture of bound and dissociative states. CH2IBr undergoes direct dissociation, with dissociation taking place on two groups of states that asymptotically converge to CH2Br+/I and CH2Br+/I*, with I* corresponding to the spin–orbit excited state of the iodine atom. In contrast, the excitation in CH2I2 is mainly to bound states, and internal conversion takes place before dissociation along states that asymptotically converge to CH2I+/I and CH2I+/I*. It is the internal conversion from initially bound states to the dissociative states that drives the differences in the fragment ion spectrum for the two molecules.

FIG. 3.

Calculated potential energy curves and excited state populations. In panels (a) and (b), we show the calculated spin-adiabatic potential energy curves as a function of the C–I distance for several neutral and ionic states for CH2I2 and CH2IBr, respectively. Different groups of neutral states are highlighted with different colors. Panels (c) and (d) show the calculated neutral state populations as a function of time from the TSH calculations for CH2I2 and CH2IBr, respectively. The color coding for the groups of neutral states is the same for panels (a)–(d). States 2–8 are maroon, states 9–12 are dark blue, and states 13–17 are light blue.

FIG. 3.

Calculated potential energy curves and excited state populations. In panels (a) and (b), we show the calculated spin-adiabatic potential energy curves as a function of the C–I distance for several neutral and ionic states for CH2I2 and CH2IBr, respectively. Different groups of neutral states are highlighted with different colors. Panels (c) and (d) show the calculated neutral state populations as a function of time from the TSH calculations for CH2I2 and CH2IBr, respectively. The color coding for the groups of neutral states is the same for panels (a)–(d). States 2–8 are maroon, states 9–12 are dark blue, and states 13–17 are light blue.

Close modal

Based on Fig. 3, one might expect that there are two peaks in the fragment ion spectra for both molecules since both molecules have two groups of dissociative states that asymptotically approach two different energies separated by about 1 eV. For CH2I2, the population is dominated by the higher group of dissociative states with a ratio of 3.75 for the populations of the higher and lower asymptotic states after 150 fs. In contrast, for CH2IBr, both states are roughly equally populated. A natural question is that whether the difference in the measurements of the two systems aforementioned is due to the different populations between the two groups of states for CH2I2 and CH2IBr, respectively, or whether there is another reason.

In order to directly compare our TSH calculations with the experimental measurements, we have carried out a detailed analysis on the kinetic energies of the fragments for both molecules. For each trajectory, the TKE of the I atom and CH2Br/CH2I as well as the rotational kinetic energy (RKE) were calculated at each time step. For both CH2I2 and CH2IBr, the TKE of all the radicals and RKE of CH2I and CH2Br were evaluated from each individual trajectory. In Fig. 4, we show the calculated TKE of CH2I and CH2Br, compared with the measured TKE of CH2I+ and CH2Br+. As discussed above, there is a significant potential energy difference between the lower and higher asymptotic groups of dissociative states, so one expects that higher energy states lead to lower kinetic energy, while lower energy states results in higher kinetic energy. In order to check this point, we averaged the calculated TKE from each trajectory by considering the excited state index at each delay step. In Fig. 4, panels (a) and (b) show the simulated TKE of CH2I and CH2Br radicals as a function of time by averaging the trajectories from the lower and higher asymptotic spin–orbit coupling state. The averaged TKE distribution from trajectories correlated with the lower and higher asymptotic are plotted in thick red and blue lines, respectively. The simulations were convolved with a 80 fs FWHM Gaussian function in order to take into account the IRF associated with the measurements. The pink and cyan shaded areas indicate the standard deviation (STD) among the ensemble of trajectories and serve as a measure of the statistical uncertainty associated with the calculations.

FIG. 4.

Time-resolved translational kinetic energies from calculations and measurements for CH2I2 and CH2IBr. Panels (a) and (b) show the calculated TKE for CH2I and CH2Br radicals as function of time from CH2I2 and CH2IBr trajectories, respectively. Panels (c) and (d) show the measured TKE for CH2I+ and CH2Br+, respectively, as a function of pump-probe delay, taken from the location of the peaks from panels (c) and (d) in Fig. 2. The calculated results have been convolved with a 80 fs (FWHM) Gaussian function to account for the instrument response function. In panels (c) and (d), the orange shading indicates the early pump-probe delay region affected by the changes to the TKE, which are due to the evolution in the cationic potential and the experimental signal deconvolution.

FIG. 4.

Time-resolved translational kinetic energies from calculations and measurements for CH2I2 and CH2IBr. Panels (a) and (b) show the calculated TKE for CH2I and CH2Br radicals as function of time from CH2I2 and CH2IBr trajectories, respectively. Panels (c) and (d) show the measured TKE for CH2I+ and CH2Br+, respectively, as a function of pump-probe delay, taken from the location of the peaks from panels (c) and (d) in Fig. 2. The calculated results have been convolved with a 80 fs (FWHM) Gaussian function to account for the instrument response function. In panels (c) and (d), the orange shading indicates the early pump-probe delay region affected by the changes to the TKE, which are due to the evolution in the cationic potential and the experimental signal deconvolution.

Close modal

As shown in panel (a), which is the case of CH2I2, the TKE of CH2I from both groups increases as a function of time, and the two groups end up with a roughly equal amount of energy by 300 fs. In panel (b), we plot the simulated TKE for CH2Br averaged for both lower and higher asymptotic states as a function of time. In contrast to the CH2I results, the TKE of the two groups separate from each other, with the trajectories that come out on the lower asymptotic state having a higher amount of kinetic energy and trajectories that come out on the higher asymptotic state having lower kinetic energies as expected. Again in panel (a), the standard deviations are larger than the difference between the averaged TKEs for the two groups of trajectories. In contrast, the difference between the two groups is larger than the standard deviation in the case of CH2IBr, leading to a clear separation.

These observations are in agreement with the experimental measurements, as shown in panels (c) and (d) of Fig. 2. For CH2I2, both the calculated and measured TKE only show one peak, which increases in energy from about 0.1 eV to about 0.2 eV in the first few hundred femtoseconds. Comparing panels (b) and (d), one also sees that there is an agreement between the measurement and calculations for CH2IBr; in that, the spectrum separates into two separate peaks whose energy increases with time in the first few 100 femtoseconds. An additional feature in panels (c) and (d) of Fig. 2 is the oscillation of the peak energy as a function of time, especially after 300 fs. These oscillations correspond to the halogen–carbon stretching in the CH2Br or CH2I fragment upon dissociation. However, this is not the main focus of this work.

Figures 3 and 4 illustrate several important points. The simulations capture the main features in the photoion spectra for both CH2I2 and CH2IBr, and measurement and calculation agree on the time scales for the changes in the spectra. However, we note that the calculations in panel (b) of Fig. 4 for CH2IBr do not perfectly agree with the measurements as shown in the panel (d). In the calculations, the TKE for both groups of trajectories are rising faster during the early times (<150 fs) than that in the measurements. This is also true for the case of CH2I2, as shown in panels (a) and (c). This discrepancy is partially due to the fact that, upon ionization, the fragments have to climb out of the bound state well in the cation at early pump-probe delays—see panels (a) and (c) of Fig. 3. Thus, the experimentally measured TKE does not increase substantially until the wave packet on the neutral state moves out to distances at which the cationic potential becomes flat—around 3.5 Å. This results in a decrease of the kinetic energy of the fragment ion gain from neutral states. This is not taken into account in the calculations, and thus, one expects the calculation to show the TKE rising faster than in the measurements, as we observe in Fig. 4. We also note that the TKE of the two peaks in the CH2Br spectrum are further apart than those from the calculation, and this is due to the fact that the energy difference of the averaged cationic spin–orbit channels increases. The lower asymptotic states [states 2-8, red curves in panel (b) of Fig. 3] in the neutral are mostly Koopmans or Dyson correlated with the lower states of the cation. Accordingly, the higher asymptotic states (states 9-12, blue curves) are mostly correlated with the higher states in the cation. Considering the energy difference between the higher branch of the lower cationic channel and the higher cationic channel (but also the energy difference of the average channels), one can see that this energy difference increases. This effect is not considered in the calculations and leads to the peak separations shown in Fig. 4 being underestimated in comparison with the experiment. The  Appendix contains some analyses of how evolution in the cationic potential affects the TKE for different pump-probe delays.

Another contribution to the discrepancy between the experiment and theory in Fig. 4 is imperfections in the subtraction of the VUV pump UV probe contribution to the yield near zero time delay. As the VUV absorption cross section is significantly larger than the UV absorption cross section, there are many ions generated by first VUV absorption followed by UV ionization in the region where there is some overlap between pump and probe pulses. This contribution is subtracted from our data but leads to some systematic errors in the measured TKE for delays less than 100 fs. A detailed discussion of the subtraction is provided in the  Appendix, Subsection A.

Before turning to detailed analysis of what drives the differences in the dynamics for the two molecules, we compare the calculated and measured branching ratio Φ* = [CH2Br/I*]/([CH2Br/I*] + [CH2Br/I]) for the two spin orbit channels ([CH2Br/I*] and [CH2Br/I]) in CH2IBr. In the CH2IBr calculation, the ratio is evaluated from the number of trajectories that live on the lower and higher asymptotic states. The calculated ratio is about 0.47, while the measured ratio is about 0.48, demonstrating excellent agreement. Earlier measurements that used multiphoton ionization as a probe found a ratio of about 0.41, which is in reasonable agreement with our measurements and calculations.26 In the case of CH2I2, while the measurements could not resolve the two kinetic energies peaks, the branching ratio could be extracted from the calculations by checking the time-dependent state populations. As shown in panel (c) of Fig. 3, the branching ratio, Φ* = [CH2I/I*]/([CH2I/I*] + [CH2I/I]), is about 0.78 after 150 fs when the populations are stable. However, we note that the branching ratio is likely overestimated due to trajectories crashing at slightly different rates on the different groups of states.

In order to understand what drives the difference between the two molecules in more detail, we examine the hopping statistics from the TSH calculations. The trajectories include hundreds of hops between different electronic states, and we sorted these hops into two different types based on their initial and final state indices. As shown in panels (a) and (b) of Fig. 3, there are three different groups of excited states for both CH2I2 and CH2IBr, including dissociative ones that asymptotically approach the spin–orbit ground and excited states of I (I/I*) for large C–I distances, as well as a group of bound states. It is the hops between different groups of states that result in significant changes of energy or the electronic state character, whereas the hops within each group of states do not involve such substantial differences. Thus, the hops across groups play the essential role on the determination of the undergoing dynamics. Here, in Fig. 5, we show the hopping statistics between groups for both CH2I2 and CH2IBr. The hops were binned into 20 fs windows, and the number of hops were divided by the total number of trajectories in order to obtain the hopping rate per trajectory.

FIG. 5.

Hopping rates for CH2I2 and CH2IBr. In this figure, panel (a) shows the hopping rate for CH2I2, whereas panel (b) illustrates the hopping rate for CH2IBr. Only the hops between different groups of states are included, whereas the hops between states in the same group are excluded. The number of hops is divided by the number of trajectories in each 20 fs time window in order to obtain the hops per trajectory as a function a time.

FIG. 5.

Hopping rates for CH2I2 and CH2IBr. In this figure, panel (a) shows the hopping rate for CH2I2, whereas panel (b) illustrates the hopping rate for CH2IBr. Only the hops between different groups of states are included, whereas the hops between states in the same group are excluded. The number of hops is divided by the number of trajectories in each 20 fs time window in order to obtain the hops per trajectory as a function a time.

Close modal

In Fig. 5, panels (a) and (b) show the hopping rate for CH2I2 and CH2IBr as a function of time. For CH2I2, the hopping rate stays relatively high out to about 100 fs, whereas for CH2IBr, the hops are concentrated in the first 20 fs. The extended hopping in CH2I2 leads to the overlap of the TKE for fragments dissociating on the two spin–orbit asymptotes for I (I and I*) since molecules do not dissociate on one group of states or the other but rather on a mixture of the two groups. In contrast, for CH2IBr, the asymptotic state on which the molecule dissociates is determined early in the dissociation dynamics, leading to a well-defined separation in the TKE for the two I/I* asymptotes. Thus, it is clear that it is the different non-adiabatic dynamics during dissociation that lead to the differences in the measured TKE for the two different molecules.

In conclusion, the excited state dynamics of CH2I2 and CH2IBr driven by photoexcitation in the deep UV were studied with VUV ionization and velocity map imaging of the fragment ions. The measurements were interpreted with TSH calculations of the excited state dynamics. The evolution of the measured fragment ion spectra highlighted the conversion of electronic potential energy into nuclear kinetic energy. Differences in the dynamics between the two molecules could be attributed to non-adiabatic dynamics during dissociation. These results highlight the ability of UV-pump VUV-probe experiments with velocity map imaging in conjunction with TSH calculations to provide a detailed picture of the coupled electronic nuclear dynamics involved in excited state molecular dynamics.

We gratefully acknowledge support from the Department of Energy under Award No. DEFG02-08ER15984 for carrying out the measurements and from the National Science Foundation under Award No. 1806294 for the interpretation of the measurements. This project was partly supported by the Government of Hungary and the European Regional Development Fund under Grant No. VEKOP-2.3.2-16-2017-00015. The computational results presented have been achieved, in part, using the Vienna Scientific Cluster (VSC).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

A. Measurement and analysis details

In many molecules, the absorption cross section in the VUV can be stronger than in the VUV, complicating the measurements near zero time delay. As both the pump and probe pulses have finite pulse durations, there can be overlapping contributions from dynamics driven by the pump pulse (pump-probe) and dynamics driven by the probe pulse (probe-pump) when the two pulses overlap. As seen from our early TRPES measurements with the same pump and probe photon wavelengths,32 the VUV driven signal dominates over the UV driven signal for both CH2I2 and CH2IBr. This issue needs to be also addressed for the photoion measurements. In Fig. 6, panels (a) and (b) plot the measured photoion spectra for fragments CH2I+ and CH2Br+, respectively. Note that the maximum ion yields occur for slightly negative delay times, consistent with the fact that the VUV absorption cross section is larger than the UV absorption cross section. In order to isolate the UV induced dynamics, it is useful to decompose the signal into UV and VUV driven dynamics by performing a global 2D fit.

FIG. 6.

Time-resolved CH2I2 and CH2IBr photoion spectra and global fitting analysis. Panels (a) and (b) show the measured photoion spectra as a function pump-probe delay and translational kinetic energy for CH2I+ and CH2Br+, respectively. A 2D global fitting analysis was applied in order to decompose the measurements into UV and VUV driven components. Panels (c) and (d) show measured and fitted energy integrated yields for CH2I+ and CH2Br+, respectively.

FIG. 6.

Time-resolved CH2I2 and CH2IBr photoion spectra and global fitting analysis. Panels (a) and (b) show the measured photoion spectra as a function pump-probe delay and translational kinetic energy for CH2I+ and CH2Br+, respectively. A 2D global fitting analysis was applied in order to decompose the measurements into UV and VUV driven components. Panels (c) and (d) show measured and fitted energy integrated yields for CH2I+ and CH2Br+, respectively.

Close modal

We applied a two-dimensional bilateral global least-squares fit to the measured photoion spectra36,54 in order to extract the UV driven contribution from the measured signal. Here, we briefly describe the process. We define Y(t; ϵk) to be the differential photoion yield as a function of pump-probe (or probe-pump) delay and ion kinetic energy for the UV (or VUV) driven dynamics. In general, Y(t; ϵk) is globally fitted to

Y(t;ϵk)=G(t)iSi(ϵk)et/τi,
(A1)

where Si(ϵk) are the time independent decay related spectra and G(t) represents the Gaussian cross correlation function associated with the IRF. The energy-resolved amplitudes of the fitting components have decay constants τi, assuming that the population of the excited states follows an exponential decay. If the underlying dynamics involve Photoionization from more than one excited state (e.g., i = 1, 2, …), one can establish kinetic models in the global fitting where more than one decay constant could be extracted from the fitting. The total ion yield is then convolved with G(t), the Gaussian cross correlation function that represents the instrument response function (IRF) for the apparatus. In the case of CH2I2 and CH2IBr, we fit the measured signal toward both positive and negative delays, corresponding to the UV and VUV driven dynamics, respectively. As in our previous work on CH2I2 using TRPES,32 we fit the data with a single exponential function for each side of zero delay. Both the exponential functions start from time-zero but decay in opposite directions. The sum of the two functions is then convolved with the IRF. Thus, Eq. (A1) can be simplified and rewritten as

Y(t;ϵk)=G(t)(S(ϵkVUV)et/τVUV|t<0+S(ϵkUV)et/τUV|t>0).
(A2)

Since the bilateral fitting is very sensitive to both the time-zero position and the IRF, we made use of pump-probe measurements with ethylene (for which the decay dynamics are very rapid) in order to locate the time-zero and determine the IRF of the experiment. The ethylene pump-probe measurements were conducted with the same running conditions as for CH2I2 and CH2IBr.

The fit returns the amplitudes of the time-independent spectra as well as the decay constants of both UV and VUV driven signals, which allows us to reconstruct the fitted 2D spectra for either UV or VUV driven dynamics. In Fig. 2, panels (a) and (b) in the main text show the time resolved UV driven spectra for CH2I+ and CH2Br+ with the VUV driven dynamics subtracted using the fitting approach described above.

B. Details of the theoretical calculation

In this section, we present the calculated absorption spectra, the dissociation energies, a detailed analysis of two exemplary trajectories for each molecule, and an analysis of the effect of the cationic dynamics on the measured TKE.

Figure 7 shows the comparison between the calculated absorption spectra from this work and the measured spectra in the literature.55,56 One can see that the calculations capture the main features of the absorption spectrum below 5.5 eV relevant to the experiments. There is some disagreement between the measured and calculated spectra in terms of the relative peak heights for CH2I2, but the number of peaks and their locations are in good agreement for both molecules. The agreement for CH2I2 can be improved when including more states in the calculation [see the gray line in panel (a) of Fig. 7], but the important states in this study—states 1–12 (dark red and dark blue channels in Fig. 3)—remain unaffected by such a change.

FIG. 7.

Calculated and measured absorption spectra for CH2I2 and CH2IBr. Panels (a) and (b) compare the calculated (left y-axis) and measured (right y-axis) absorption spectra in the deep UV region for CH2I2 and CH2IBr, respectively. The red lines indicate the calculated spectra using the same number of states used for the trajectory calculations, while the blue lines show the measured absorption cross section with absolute values reproduced from Refs. 55 and 56. For CH2I2, the gray line showcases the calculated spectra when more states (10 singlet and 9 triplet states instead of 5 singlet and 4 triplet states for the red line) are included. All spectra are normalized to the peak at ∼4 eV.

FIG. 7.

Calculated and measured absorption spectra for CH2I2 and CH2IBr. Panels (a) and (b) compare the calculated (left y-axis) and measured (right y-axis) absorption spectra in the deep UV region for CH2I2 and CH2IBr, respectively. The red lines indicate the calculated spectra using the same number of states used for the trajectory calculations, while the blue lines show the measured absorption cross section with absolute values reproduced from Refs. 55 and 56. For CH2I2, the gray line showcases the calculated spectra when more states (10 singlet and 9 triplet states instead of 5 singlet and 4 triplet states for the red line) are included. All spectra are normalized to the peak at ∼4 eV.

Close modal

In addition to calculating the absorption spectra, we estimated the dissociation limit for different dissociative channels (CH2X + I, CH2X + I*, and CH2X* + I, where X represents I or Br) for both CH2I2 and CH2IBr, as shown in Table I. The energies were computed at the same MS-CASPT2 level of theory as used for the dynamics simulations (see Sec. III). The geometries of the parent and fragments were determined by density functional theory at the B3LYP/aug-cc-pVTZ-PP level of theory. Zero-point energies are neglected. For the CH2X* + I channels, the geometries of the ground state CH2X species were used, and thus, the dissociation energies for these channels are somewhat overestimated. They are, however, so much higher than the available energy after photoexcitation that dissociation into these channels can be excluded.

TABLE I.

Dissociation energies for different dissociation channels of CH2IBr and CH2I2. FC indicates the Franck–Condon geometry.

Dissoc. channelDissoc. energy (eV)
CH2BrI → CH2Br + I 2.091 
CH2BrI → CH2Br + I* 2.957 
CH2BrI → CH2Br* + I 6.446 
CH2I2 → CH2I + I 2.141 
CH2I2 → CH2I + I* 3.004 
CH2I2 → CH2I* + I 5.675 
CH2BrI+ (FC) → CH2Br+ + I 0.964 
CH2I2+ (FC) → CH2I+ + I 1.100 
Dissoc. channelDissoc. energy (eV)
CH2BrI → CH2Br + I 2.091 
CH2BrI → CH2Br + I* 2.957 
CH2BrI → CH2Br* + I 6.446 
CH2I2 → CH2I + I 2.141 
CH2I2 → CH2I + I* 3.004 
CH2I2 → CH2I* + I 5.675 
CH2BrI+ (FC) → CH2Br+ + I 0.964 
CH2I2+ (FC) → CH2I+ + I 1.100 

Figure 8 shows the total energy, translational kinetic energy (TKE), potential energy, and state index as a function of time for two exemplary trajectories from each molecule. Panel (a) plots the time-dependent total energy (kinetic, T + potential, V) and potential energy (denoted V), whereas panel (c) underneath shows the state indices and TKE for CH2I2. Panels (b) and (d) show the same for CH2IBr. As the legends show, one trajectory ends up in the spin–orbit coupling ground state channel (CH2X + I, states 2-8) and another trajectory ends up in the excited state channel (CH2X + I*, states 9-12). While the two trajectories for CH2I2 end up on states with different potential energies, they lead to very similar TKE because of hopping between potentials as the molecule dissociates, redistributing kinetic energy also to rotation and vibrations of the molecular fragment. This is in contrast to CH2IBr, for which the TKE for the two trajectories is quite different because the trajectories do not hop between groups of states that lead to different potential energies after about 20 fs.

FIG. 8.

Surface hopping trajectories for CH2I2 and CH2IBr. Energies and state indices for two representative trajectories of CH2I2 and CH2IBr. Panel (a) plots the time-dependent total energy and potential energy (V in the legend), whereas panel (c) underneath shares the same x axis with panel (a), showing the state indices and TKEs. Panels (a) and (c) showcase the trajectories for CH2I2, whereas panels (b) and (d) are for CH2IBr. In the legend, T represents kinetic energy and V represents potential energy.

FIG. 8.

Surface hopping trajectories for CH2I2 and CH2IBr. Energies and state indices for two representative trajectories of CH2I2 and CH2IBr. Panel (a) plots the time-dependent total energy and potential energy (V in the legend), whereas panel (c) underneath shares the same x axis with panel (a), showing the state indices and TKEs. Panels (a) and (c) showcase the trajectories for CH2I2, whereas panels (b) and (d) are for CH2IBr. In the legend, T represents kinetic energy and V represents potential energy.

Close modal

For both CH2I2 and CH2IBr, the lower-lying cationic states are bound states. A natural question is how these bound-state potential wells affect the kinetic energy release upon ionization. In Fig. 9, panel (a) shows the cationic state potential when averaged over the lower states that can be accessed by the pump and probe pulse energies as well as the well depth for both CH2I2 and CH2IBr. One can see that the depth is on the order of 2 eV, which can have a significant effect on the kinetic energy after ionization (if ionization happens at a location within the well). In order to evaluate this effect, we examine the (dissociative) C–I distance as a function of time from the trajectories, as shown in panel (b). With this information, we are able to calculate the net kinetic energy, including the energy gained on the neutral states and lost in the cationic states as a function a C–I distance or time. Panels (c) and (d) show a comparison of the translational kinetic energy (TKE) for CH2I and CH2Br with or without the consideration of dynamics in the cation, respectively. It is clear that in the first 50 fs, the cationic bound states do have a significant effect on the final kinetic energy: The TKE changes quite a bit when one includes the cationic dynamics. However, after about 50 fs, the wave packet on the neutral states reaches a point where the cationic potential is almost flat and the molecule barely loses energy on the cationic state after ionization. Thus, the TKE is roughly the same as if one only considers the neutral state dynamics, i.e., the molecule does not lose a significant amount of kinetic energy in the cation.

FIG. 9.

Kinetic energy of CH2I+ and CH2Br+ with and without compensation for dynamics in the cation. Blue colored lines (using left hand y-axis) in panel (a) showcase the averaged potential energies of the cationic bound state of CH2I2 and CH2IBr shown in panels (c) and (d) of Fig. 3, respectively. By the right hand y-axis, the red colored lines show the well depth of the cationic state potential, which is the energy difference from the FC region to where the potential becomes flat. Panel (b) depicts the dissociating C–I bond length as a function of time for a trajectory of CH2I2 and CH2IBr. Panels (c) and (d) show a comparison of the TKE for CH2I2 and CH2IBr with and without accounting for the cationic potential.

FIG. 9.

Kinetic energy of CH2I+ and CH2Br+ with and without compensation for dynamics in the cation. Blue colored lines (using left hand y-axis) in panel (a) showcase the averaged potential energies of the cationic bound state of CH2I2 and CH2IBr shown in panels (c) and (d) of Fig. 3, respectively. By the right hand y-axis, the red colored lines show the well depth of the cationic state potential, which is the energy difference from the FC region to where the potential becomes flat. Panel (b) depicts the dissociating C–I bond length as a function of time for a trajectory of CH2I2 and CH2IBr. Panels (c) and (d) show a comparison of the TKE for CH2I2 and CH2IBr with and without accounting for the cationic potential.

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While our measurements allow for direct reconstruction of the full 3D momentum of each fragment ion based on the measured (x, y, t), we can also perform an inverse Abel transform on an ensemble of ion measurements, integrating over t values for a given ion species. This can sometimes be advantageous, producing higher momentum resolution than available from the timing information, and is the approach that we took in the measurements presented here.

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We also note that there are some modulations in the CH2I+ TKE which are consistent with C-Br stretching, but do not focus on these dynamics in this work.

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