Ultrafast internal conversion dynamics of highly excited pyrrole studied with VUV/UV pump probe spectroscopy

Pyrrole (C₄H₅N) has been of intense experimental^1–8 and theoretical interest^9–15 because it is considered an important building block for understanding the ultrafast dynamics of larger pyrrole-containing biomolecules, such as hemoglobin, vitamin B₁₂, chlorophyll, and tryptophan. Pyrrole exhibits rich photo-induced dynamics when excited with ultraviolet (UV) radiation. Internal conversion and dissociation have been studied extensively both experimentally and theoretically.

Experimental work on the relaxation dynamics of photoexcited pyrrole has focused on pumping the first absorption band, with time resolved studies probing the fate of molecules excited with pump wavelengths between 200 and 260 nm.^2–7 These experiments, which made use of ionization as a probe, established that the molecule undergoes rapid internal conversion and dissociation on time scales of ∼100 fs or less. Experiments that made use of velocity map imaging to measure the momentum of hydrogen ions generated by the probe pulse³ found both fast and slow H⁺, indicating dissociation on both the excited and ground state surfaces. The relative yields indicated that dissociation on the excited state dominated over internal conversion to the ground state followed by dissociation.

Several theoretical studies have examined the excited state dynamics in pyrrole. Three pathways involving conical intersections between S₁ and S₀ have been identified which are involved in nonadiabatic decay to the ground state or dissociation.^9–15 In particular dissociation along the NH bond has been found to be important in many studies. Recent theoretical work by Barbatti et al.¹⁰ using the trajectory surface hopping approach with excitation energies between 193 nm and 248 nm indicated that while excitation to the first absorption band (wavelength of 248 nm) led to N–H bond stretching and fission, excitation with higher energy to the second absorption band (wavelength of 193 nm) led to slower decay (time scales of about 200 fs) with more complicated dynamics. In this work, we consider excitation of pyrrole with pulses in the vacuum ultraviolet (VUV), corresponding to an excitation energy of about 8 eV. This corresponds to a higher excitation energy than all previous experiments and is motivated by the question of how the initial excitation influences the relaxation dynamics. Of particular interest in this study is whether the decay of the excited state is primarily due to dissociation on an excited state surface or internal conversion to the ground state. In previous work where we studied the relaxation dynamics of radical cations (uracil, 1-3 cyclohexadiene, and hexatriene) using trajectory surface hopping,¹⁶ we found that relaxation to the ground ionic state was rapid (<100 fs), taking place before dissociation. The density of states in these cations is similar to the density of states in highly excited pyrrole, and thus while excitation at lower energy resulted primarily in dissociation, we expect more competition between internal conversion and dissociation at higher energies.

We probe the excited state dynamics with a UV pulse having a ∼5 eV photon energy, which allows us to ionize from any excited state of the molecule without a background signal from the ground state. We measure a decay time from this high-lying state of approximately 200 fs.

We use a Ti:Sapphire laser (1.2 mJ, 1 kHz, 30 fs, 780 nm) to generate ultrafast UV and VUV pulses. In conjunction with a time-of-flight mass spectrometer (TOFMS), we make use of these pulses to perform pump-probe ion yield measurements on pyrrole. Gas-phase pyrrole molecules are injected into the vacuum chamber as an effusive molecular beam.

Our experimental setup can be seen in Fig. 1. The IR beam from the amplifier is split into two portions which have pulse energies of 1.1 mJ and 100 μJ. The 1.1 mJ of IR is used to create 50 μJ of UV (⁠$ℏω=4.78$ eV) light through second-harmonic-generation (SHG) followed by third-harmonic-generation (THG) in beta barium borate (BBO) crystals with a calcite delay compensator. An uncoated 1 mm thick CaF₂ window is inserted into the beam at 45° to act as a beamsplitter for the UV. The 5 μJ pulse from the front surface reflection of the CaF₂ window is used as the UV probe in our experiments. Approximately 100 nJ of fifth-harmonic (VUV) probe-pulse (⁠$λ=156$ nm, $ℏω=7.94$ eV) is generated by focusing the remaining 40 μJ of UV and 100 μJ of residual IR into an argon gas cell utilizing a non-collinear-four-wave-mixing process.^17–19 This mechanism takes advantage of phase matching at a relatively high pressure (330 Torr) of argon gas, which increases the conversion efficiency.

The VUV-pulse passes through a 500 μm thick CaF₂ window into an interaction chamber, which is maintained at a pressure of 10⁻⁷ Torr. The VUV-pulse first passes under the repeller plates of our TOFMS. It is then reflected by a dichroic mirror of radius of curvature R = 268 mm. The mirror has a high reflectivity coating of > 90% at 0° for 156-160 nm light and <5% reflectivity for 260 nm and 800 nm. This enables the residual UV and IR radiation left over from VUV generation to be separated from the VUV. The reflected VUV-pulse is then focused under the TOFMS repeller plates. The 5 μJ of UV reserved for the probe is sent through the dichroic mirror and also focused under the TOFMS repeller plates.

The VUV-pump pulse excites the pyrrole molecules to a state about 0.2 eV below the ionization threshold, and the UV probe pulse captures the excited state dynamics by ionizing the molecules at different pump probe delays. The ions generated by the pump and probe pulses are detected with a microchannel plate (MCP) at the end of our TOFMS.

In order to interpret the experimental results, we performed electronic structure calculations of the neutral and ionic states of pyrrole. The ground state of pyrrole was optimized using B3LYP/6-31+G(d). The excited state energies and oscillator strengths were calculated using the equation of motion coupled cluster for excited states (EOM-EE-CCSD) and the aug-cc-pVTZ basis set. Ionic states were obtained using the equation of motion coupled cluster for ionization potentials (EOM-IP-CCSD) method and the same basis set. The Q-Chem software package was used for these calculations.²⁰ The NH bond was stretched from its equilibrium position in steps of 0.2 Å, and the excited and ionic states along this coordinate were calculated. The excited states were characterized using natural transition orbitals (NTOs) obtained from the EOM-EE-CCSD method. Molden was used for visualization of the orbitals.²¹ 

Fig. 2 shows the orbitals and the calculated potential energy surfaces along the N–H coordinate. The orbitals are NTOs obtained from diagonalizing the transition density.²² The orbitals are the eigenfunctions of the matrix and represent particle-hole pairs, while the numbers shown in the figure are the eigenvalues. The importance of a particular particle-hole excitation to the overall transition is reflected in the associated eigenvalue. When a state has more than one pair it means that it cannot be described by a single hole-particle representation in the NTO picture. States 4¹B1 and 4¹A1 are the high-lying “bright” states that are accessible with the VUV-pump pulse. Looking at their orbitals on the right-hand-side of the plot it is evident that we are driving a π → π^* transition. Orbitals describing states 1¹B2 and 1¹A2 are on the left-hand side of the plot and they show that these are π → σ^* states which are not stabilized along the NH coordinate and they can lead to dissociation. The density of states that the VUV-pulse is exciting to is very high, so one would expect very fast radiationless decay from the absorbing state to 1¹B2 or 1¹A2. By inspecting the configurations and orbitals describing the 1¹B2 and 1¹A2 states and the low lying ionic states, we see that ionization is allowed based on Koopmans’ theorem.In other words, the two lowest ionic states are described by the same valence orbitals involved in the excited states and can be accessed by removing the π^* electron. Thus, these excited states can be easily ionized with our probe. In addition to the Koopmans’ correlations, the figure makes it clear that for the range of N–H distances considered here, we are energetically able to ionize the molecule from any of the excited states, given their energies relative to the probe photon energy. Thus, the fact that the parent ion signal decays to zero at long time delays indicates that the molecule either relaxes back to the ground state or dissociates.

We note that for larger N–H bond lengths, Ref. 13 shows the ionization potential from S₁ increasing beyond our probe photon energy. Thus, our measurements cannot exclude the possibility of dissociation on S₁ despite the lack of fragment ion signal. This point is addressed further below.

As a test and characterization of the apparatus, we recorded the VUV/UV pump-probe signal for ethylene, which has been studied in earlier work and has a very rapid decay.^23–25 These results are shown alongside those for pyrrole in Fig. 3. The parent ion yield for pyrrole, C₄H₅N⁺, as a function of VUV/UV pump-probe delay is shown as diamonds. At negative delays the UV-probe pulse comes before the VUV-pump pulse, while for positive delays the VUV pulse comes first. For the simplest fit we assume a mono-exponential decay to describe the molecular dynamics. In order to account for the finite duration of our pump and probe pulses (which have a Gaussian temporal profile), we use a Gaussian convolved with a decaying exponential as our fitting function.

In Fig. 3 the triangles represent VUV-pump UV-probe data for $C2H4+$ from ethylene, and the red curve represents the ethylene data fit to a mono-exponential decay convolved with a Gaussian. The $C2H4+$ data fit yields an exponential decay constant of $37±5$ fs with $χ2=1.2$ (all χ² values quoted in the text are reduced χ² values). Ethylene pump-probe data were collected and refitted for various VUV/UV pulse durations and the resulting spread in the decay constant was used to determine our uncertainty. The VUV excitation of ethylene has been previously studied by Allison²⁴ and Farmanara²³ where they recorded time constants of $τ=21±4fs$ and $τ=40±20fs$⁠, respectively. Our decay constant being consistent with previously recorded values serves as both a test of our experimental apparatus as well as an indication of where zero time delay is in the pump-probe measurement, since the ethylene decay time is significantly shorter than our pulse duration.

Looking at the fit in panel (a) of Fig. 3, it is obvious that the mono-exponential pyrrole fit does not describe our data well after 400 fs. The residual plot, Fig. 3 panel (a) inset, for the pyrrole pump-probe data fit to a mono-exponential clearly has structure, and the fit has a $χ2=2.3$⁠, indicating that the fit does not accurately reflect the measurement.

Panel (b) of Fig. 3 shows that a dual exponential function fits the data well with a $χ2$ value of 1.2. The decay constants are 68 fs and 253 fs instead of the 162 fs obtained from the mono-exponential fit. Fig. 3 panel (b) inset is the residual plot for the dual-exponential fit. The residual is randomly distributed, indicating that we have a good fit to our data and that a double exponential decay provides a reasonable description of our measurement.

A dual-exponential fit implies a two stage process indicating two time scales for internal conversion or internal conversion followed by dissociation. In order to determine whether the decay of the parent ion involves dissociation, we monitored the fragment ion yield. The most relevant fragment ion is C₄H₄N⁺, as dissociation along the N–H coordinate is the most likely to occur.^2–4 Our calculation of the energy levels along the N–H stretching coordinate indicates that the 4.8 eV probe photon energy should be enough to ionize the molecule as it is dissociating along the N–H coordinate. In addition, our calculations of the molecular orbitals for the neutral and cation along the dissociation coordinate indicate that ionization along the dissociation coordinate is not forbidden by Koopmans’correlations. However, in the TOFMS we do not see any distinct C₄H₄N⁺ peak, suggesting that there is no dissociation. In order to allow for the possibility of a small amount of C₄H₄N⁺ being formed but overwhelmed by the C₄H₅N⁺ signal in the TOFMS, we binned the lower mass end of the C₄H₅N⁺ peak with a large enough window so we could capture the C₄H₄N⁺ peak, if it were there. Fig. 4 shows that any C₄H₄N⁺ fragment which is formed has the same decay dynamics as the parent ion (C₄H₅N⁺), indicating that the fragment ion is formed after ionization rather than in the neutral. If the molecule were evolving on a dissociative potential after rapid internal conversion, one would expect to see a delayed peak in the fragment dissociation yield.

While our calculation of the energy levels along the N–H stretching coordinate suggests that the 4.8 eV of photon energy should be enough to ionize the C₄H₄N⁺ fragment as it is dissociating, as an extra precaution we performed pump probe measurements for higher UV pulse energies, such that we could ionize any neutral fragments formed with an ionization potential higher than the UV photon energy via two photon absorption. These measurements yielded the same results, giving further evidence that there is negligible dissociation compared with internal conversion to the ground state.

The fact that the pyrrole measurements cannot be fitted to a single exponential decay while the ethylene data can implies that there is not a single rate limiting step in the case of pyrrole (see  Appendix B for an analysis of possible kinetic models for this system). Given that the relaxation of pyrrole to the ground state starting with an internal energy of 8 eV involves many more states than the relaxation after 5 eV excitation, it is not surprising that there is more than one time scale involved.

We make use of a newly developed VUV-pump UV-probe apparatus to study the ultrafast relaxation of highly excited pyrrole. Electronic structure calculations help interpret the measurements, which show a two step decay process with time constants of 68 fs and 253 fs. While earlier measurements that pumped the first absorption band at around 5 eV found a mix of dissociation and internal conversion, we find that the decay of the excited state and our ionization signal is driven largely by rapid internal conversion to the ground state.

We gratefully acknowledge the support from the Department of Energy under Award Nos. DE-FG02-08ER15984 and DE-FG02-08ER15983.

In order to determine the error in our decay constant for the ethylene pump probe data, we tested how the error of our individual fits compared to systematic errors in the experiment. To check this, we varied the pulse duration of our beams and evaluated how the extracted decay constant of ethylene varied.

We moved the grating separation of a pulse compressor in our amplifier to change our pulse durations in our interaction chamber and reperformed experiments on ethylene at each position. For each grating position we refit our data and from the fit we extracted the FWHM of the convolution of the pump and probe pulse and the decay constant of the molecule. For each individual fit we varied the decay constant, τ, re-minimized the fitting parameters, determined at what values of τ did $χ2$ change by one, and used this as our individual data point error bar.

Fig. 5 shows the results of this compressor scan. It is evident that the spread in the data points is significantly larger than the individual error bars. The individual error bars from the fit vary from $≈±1$ to ±2 fs, whereas the standard deviation in all the data points is ±5 fs, which we take as a more realistic indication of our uncertainty. We note that the distribution of decay constants about the mean is not completely random but shows a slight trend with pulse or cross correlation duration. This indicates that our measurement of the decay time for ethylene might be a slight overestimate based on our pulse duration, which is larger than the measured decay time.

The pump probe data for pyrrole show a clear dual exponential nature. In order to develop a physical interpretation of this double exponential decay, we consider several kinetic models. These models are shown in Fig. 6. In these models, ks are the decay constants between two states and correspond to $1/τ$ values in the text.

In Fig. 6(a) we have the simplest scheme that has two different decay channels from the same state. The population in N₁ can be ionized by the probe to produce the parent ion. The total ionization yield is proportional to the population in N₁, which is

In this model N₁(0) is the initial population in N₁. This model yields a single exponential, hence it cannot explain the double exponential nature of our pyrrole data.

We then consider Fig. 6(b). Here we have an effective three-level model for the dynamics, where decay from the initial excited state to an intermediate state gives one time scale, while decay of this intermediate state to the ground state gives the second. Both the initial excited state and intermediate state can be ionized by the probe pulse to produce the parent ion. In this simple picture, the total ionization yield is proportional to the sum of the populations, N, in the intermediate and initial states, N₁ and N₂, with

This model would seem to explain the fit to a double exponential with two distinct decay constants. But, when we constrain our fit to Eq. (B2), and the amplitudes are not allowed to evolve freely, the fit cannot capture the dynamics.

Finally, we consider Fig. 6(c) where we have two parallel decays (5 level system). Here we consider that the initial excited state, N₁, can decay via two channels, N₂ and N₃. From N₂ the system decays into N₄ and from N₃ the system decays into N₅. Again, we assume the total ionization yield is proportional to the sum of the populations, N, in the intermediate and initial states N₁, N₂, and N₃. In this model, the combined signal, N, is

This model, even with the constrained amplitudes, fits our data very well. This model gives values $τ1$ = 293 fs, $τ2$ = 84 fs, $τ3$ = 290 fs, and $τ4$ = 70 fs with a $χν2$ of 1.3.

While this model fits our data well, the real dynamics are undoubtedly much more complicated. These kinetic models show that the double exponential nature which we see in the pyrrole data cannot be accurately described by the simple pictures seen in Figs. 6(a) and 6(b). This is not surprising, considering the complexity of pyrrole’s relaxation dynamics with many states involved.