The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans’ correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

The canonical π−π* transition in the linear polyenes is very widely studied because it leads to the process of cis-trans isomerisation. The electronic spectroscopy of linear polyenes began with the pioneering work of Hudson and Kohler1 and is well understood.2–5 Polyenes typically have a bright state of 1B character, prepared by the π−π* HOMO to LUMO transition. The singly excited 11B state is typically very short lived and internally converts to the lower lying dark 21A state which has multireference character. This conversion of electronic to vibrational energy through conical intersections is the origin of the large amplitude vibrational motions which lead to cis-trans isomerisation.6 Ethylene, H2C=CH2, is the smallest molecule exhibiting cis-trans isomerisation upon π−π* excitation. Its internal conversion dynamics involve H atom transfer, isomerization, and a twisted-pyramidalized (Tw-Py) conical intersection,7,8 a feature which also appears in the linear polyenes. Ethylene’s ultrafast C=C dynamics represent a local chemical moiety, which we termed a dynamophore,9 wherein localized dynamics can occur in all unsaturated hydrocarbons. The excited state nuclear dynamics of linear polyenes can be characterized as a competition between (i) the Tw-Py dynamics at a single C=C double bond (localized dynamics) and (ii) the bond-alternation dynamics, preserving π-system delocalization which maintains planarity (delocalized dynamics). The latter process is related to the appearance of fluorescence in longer-chain polyenes and their reduced rates of internal conversion to the ground electronic state. The smallest linear polyene, trans-1,3-butadiene (BD), bridging the gap between ethylene and the longer polyenes, exhibits dynamical aspects of each. In Paper I and Paper II,10 we present detailed time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy and ab initio multiple spawning (AIMS) studies of the π−π* excited state dynamics of BD.

As discussed in Paper II,10 the electronic structure of BD has long presented computational challenges, with the relative ordering of its two lowest excited states—11Bu vs. 21Ag—being a source of controversy. The most accurate ab initio computations predict a vertical excitation energy of 6.2 eV to the 11Bu state, characterized as the HOMO → LUMO transition, and 6.4 eV to the dark, doubly excited 21Ag state.11–13 However, the 21Ag potential energy surface displays steep gradients along the bond-alternation and torsional coordinates, such that the putative minimum on this surface lies below that of the 11Bu state.14,15 This suggests the presence of conical intersections near the 11Bu Franck-Condon (FC) region in BD, consistent with the observed lack of fluorescence. This is in contrast to the longer polyenes wherein the dark doubly excited 21A electronic state lies below the bright 1B state in the Franck-Condon region.

In Fig. 1, we present the previously recorded high resolution UV absorption spectrum of BD.16 The extreme breadth of the absorption band is immediately apparent, suggesting ultrafast dephasing. At the 11Bu origin, the peak at 216 nm (5.74 eV, dashed vertical line) has (from a fit to a sum of Lorentzians) a half-width at half-maximum (HWHM) of 377 cm−1. This corresponds to a phenomenological Lorentzian dephasing time of about 14 fs, consistent with the lack of fluorescence. The dotted curve is a reflection of the red side spectral line shape through the 216 nm vertical, giving a sense of the apparent width of the absorption band. The extreme width of this origin band has been a focus of many prior theoretical studies.17 More recently, it was shown that the inclusion of out-of-plane modes is essential18,19 in order to model the observed width of the absorption spectrum. In the experiments described below, we pumped BD at its 11Bu origin with a fs UV pulse centred at 216 nm.

FIG. 1.

The UV absorption spectrum of trans-1,3-butadiene in the region of its π−π* transition to the bright S2 11Bu state, modified from Ref. 16. The apparent origin is at 216 nm. Although a vibrational progression is seen, there is an extreme broadening of the UV transition due to ultrafast excited state dynamics. A fit to a sum of Lorentzians yields a width of 377 cm−1 and a phenomenological lifetime of about 14 fs. The excited state dynamics generating this apparent broadening is a central subject in this paper, Paper I, and the following companion theory paper, Paper II.10 

FIG. 1.

The UV absorption spectrum of trans-1,3-butadiene in the region of its π−π* transition to the bright S2 11Bu state, modified from Ref. 16. The apparent origin is at 216 nm. Although a vibrational progression is seen, there is an extreme broadening of the UV transition due to ultrafast excited state dynamics. A fit to a sum of Lorentzians yields a width of 377 cm−1 and a phenomenological lifetime of about 14 fs. The excited state dynamics generating this apparent broadening is a central subject in this paper, Paper I, and the following companion theory paper, Paper II.10 

Close modal

The excited state dynamics of BD following excitation to the 11Bu state has equally been a subject of much discussion. As summarized by Levine and Martinez20 and the references therein, competing views struggled over many years as to whether BD was more ethylene-like (ionic/charge transfer, localized dynamics) or more polyene-like (covalent/radicaloid, delocalized dynamics). Using a balanced treatment of the 11Bu and 21Ag states, Levine and Martinez unified these competing views and showed that both mechanisms are active in BD. They found two conical intersection pathways from the 11Bu Franck-Condon region: one that involves the commonly accepted “covalent” bond-alternation coordinate, leading to the 21Ag state; the other, an “ionic” ethylene-like Tw-Py conical intersection which leads to the ground state.20 The ultrafast decay of the bright state presumably involves both paths, but a quantitative determination of the branching would require still higher levels of electronic structure theory. The first direct measures of the 11Bu excited state used time-resolved mass spectrometry, pumping at 200 nm and probing via non-resonant multiphoton ionization, estimated a 35 fs lifetime for the 11Bu state21 and a subsequent multi-component sub-100 fs decay process.22 A time-resolved multi-dimensional (time-, energy-, angle-resolved) coincidence imaging spectroscopy study of BD excited at 200 nm revealed further details.23 Here we apply the time-resolved photoelectron spectroscopy (TRPES) method, a powerful probe of ultrafast excited state non-adiabatic dynamics in polyatomic molecules.24–31 Although not related to 11Bu dynamics, two-photon excitation of BD—which directly prepares the dark 21Ag state—was previously studied using TRPES.32,33

In Fig. 2, we present the energy level scheme and π orbital occupations for the TRPEPICO experiments reported here. The singly excited S2 11Bu state was pumped by a fs pulse at 216 nm (5.75 eV) to its vibronic origin. It undergoes ultrafast non-adiabatic processes which include the doubly excited S1 21Ag state, itself subsequently returning on ultrafast time scales to the S0 11Ag ground state with high internal energy. The highly transient S1 21Ag state has never been directly detected during internal conversion. As described below, we probed these processes via time-resolved photoionization using a fs 267 nm pulse.

FIG. 2.

A depiction of the electronic states, π electron orbital occupancies, energetics, and Koopmans’ correlations involved in the pump-probe photoelectron spectroscopy of excited state dynamics in trans-1,3-butadiene, C4H6. The S0(1 1Ag) ground state HOMO is a single configuration. Upon UV excitation, a π electron is promoted to the LUMO, forming the single configuration S2(11Bu) excited state. Due to ultrafast excited state non-adiabatic dynamics, the initial S2 state rapidly internally converts to the lower lying S1(2 1Ag) state. The latter is comprised of three dominant configurations, two of which are doubly excited. The Koopmans’ allowed photoionization correlations are as indicated: S2(11Bu) → D0(2Bg) + e and S1(2 1Ag) → D1(2Au) + e. Dynamics in the bright S2(11Bu) state are probed by single photon ionization, a (1 + 1′) process producing the photoelectron band ε1. Dynamics in the dark S1(2 1Ag) state are probed by two photon ionization, a (1 + 2′) process producing the photoelectron band ε2. Near the origin of the cation D1(2Au) state, a unimolecular fragmentation channel producing C3H3+ + CH3 is shown. As discussed in  Appendix C, this means that ionizing transitions to the D1 excited state will very likely be detected as a C3H3+ daughter ion.

FIG. 2.

A depiction of the electronic states, π electron orbital occupancies, energetics, and Koopmans’ correlations involved in the pump-probe photoelectron spectroscopy of excited state dynamics in trans-1,3-butadiene, C4H6. The S0(1 1Ag) ground state HOMO is a single configuration. Upon UV excitation, a π electron is promoted to the LUMO, forming the single configuration S2(11Bu) excited state. Due to ultrafast excited state non-adiabatic dynamics, the initial S2 state rapidly internally converts to the lower lying S1(2 1Ag) state. The latter is comprised of three dominant configurations, two of which are doubly excited. The Koopmans’ allowed photoionization correlations are as indicated: S2(11Bu) → D0(2Bg) + e and S1(2 1Ag) → D1(2Au) + e. Dynamics in the bright S2(11Bu) state are probed by single photon ionization, a (1 + 1′) process producing the photoelectron band ε1. Dynamics in the dark S1(2 1Ag) state are probed by two photon ionization, a (1 + 2′) process producing the photoelectron band ε2. Near the origin of the cation D1(2Au) state, a unimolecular fragmentation channel producing C3H3+ + CH3 is shown. As discussed in  Appendix C, this means that ionizing transitions to the D1 excited state will very likely be detected as a C3H3+ daughter ion.

Close modal

As discussed in  Appendix B, Koopmans’ ionization correlations for BD are completely analogous to those in the four C=C linear polyene 2,4,6,8-decatetraene (DT).34 Specifically, as shown in Fig. 2, the S2 11Bu state correlates with the D02Bg cation ground state, whereas the S1 21Ag correlates with the D12Au cation first excited state. As in the previous study of decatetraene,34 the S2 11Bu state is probed via single photon (1 + 1′) photoionization, whereas the S1 21Ag state is probed via two-photon (1 + 2′) photoionization. The single photon ionization valence shell photoelectron spectrum of BD was previously studied in detail.35 Shown in Table I are the orbital configurations, single photon Koopmans’ ionization channels, and cation state energies for BD. At our total (1 + 2′) photon energy of 15.0 eV, the D0–D4 cation states are vertically accessible from the BD ground state. Due to geometric distortions in excited states, the D5 state may become adiabatically accessible via (1 + 2′) ionization.

TABLE I.

Single photon orbital ionization channels and associated energies for BD.35 

Neutral stateOrbital configurationEnergy (eV)
S0(1 1Ag)(3ag)2 (3bu)2 (4ag)2 (4bu)2 (5bu)2 (5ag)2 (6ag)2 (6bu)2 (7ag)2 (1au)2 (1bg)20.00
Cation stateIonization channel
D0(2Bg1bg−1 9.07 
D1(2Au1au−1 11.39 
D2(2Ag7ag−1 ∼12 
D3(2Bu6bu−1 13.16 
D4(2Ag6ag−1 ∼13.5 
D5(2Ag5ag−1 15.17 
D6(2Bu5bu−1 ∼15.7 
Neutral stateOrbital configurationEnergy (eV)
S0(1 1Ag)(3ag)2 (3bu)2 (4ag)2 (4bu)2 (5bu)2 (5ag)2 (6ag)2 (6bu)2 (7ag)2 (1au)2 (1bg)20.00
Cation stateIonization channel
D0(2Bg1bg−1 9.07 
D1(2Au1au−1 11.39 
D2(2Ag7ag−1 ∼12 
D3(2Bu6bu−1 13.16 
D4(2Ag6ag−1 ∼13.5 
D5(2Ag5ag−1 15.17 
D6(2Bu5bu−1 ∼15.7 

Importantly, the D12Au cation state is unstable with respect to unimolecular decay, with an energetic threshold shown by the red dashed line in Fig. 2. It undergoes spontaneous methyl elimination to yield the C3H3+ daughter ion.36 As discussed in  Appendix C, the internal energy dependence of fragmentation pathways of BD cations was previously studied in detail36–39 using single photon ionization Photoelectron-Photoion Coincidence (PEPICO) spectroscopy, yielding appearance energies (AEs) and breakdown curves for the ion fragments involved. The observed fragmentation channels and AEs are given in Table II.

TABLE II.

Observed fragmentation channels and appearance energies for single photon ionization of BD.35,38,39 The channels are labeled as to their temporal Group (vide infra, Fig. 7).

FragmentationAppearance
Parent ionchannelenergy (eV)Group
 →C4H5+ (53 amu) + H 11.72 (b) 
 →C4H4+ (52 amu) + H2 13.11 (b) 
 →C4H3+ (51 amu) + H2 + H 15.2 (c) 
C4H6+(54 amu) →C3H3+ (39 amu) + CH3 11.50 (b) 
 →C2H4+ (28 amu) + C2H2 12.44 (b) 
 →C2H3+ (27 amu) + C2H2 + H 15.1 (c) 
 →C2H2+ (26 amu) + C2H2 + H2 15.1 (c) 
FragmentationAppearance
Parent ionchannelenergy (eV)Group
 →C4H5+ (53 amu) + H 11.72 (b) 
 →C4H4+ (52 amu) + H2 13.11 (b) 
 →C4H3+ (51 amu) + H2 + H 15.2 (c) 
C4H6+(54 amu) →C3H3+ (39 amu) + CH3 11.50 (b) 
 →C2H4+ (28 amu) + C2H2 12.44 (b) 
 →C2H3+ (27 amu) + C2H2 + H 15.1 (c) 
 →C2H2+ (26 amu) + C2H2 + H2 15.1 (c) 

Comparing Tables I and II, it is seen that photoionization to the (vibrationally excited) D12Au cation state will be correlated with the appearance of the C3H3+ daughter ion. This indicates, as discussed in detail below, that TRPEPICO measurements will be helpful in clarifying the time-resolved photoelectron spectra of BD excited state dynamics.

In Fig. 3, we present a cartoon which conceptually illustrates the expected initial vibrational motions, C—C twist and C—C stretch, on the UV pumped S2 11Bu state. Shown on the right are molecular models of the planar S0 ground state and the twisted (upper) and pyramidalized (lower) geometries associated with the excited states. Time- and energy-resolved photoionization (TRPES) to the Koopmans’ correlated D0 cation ground state should thus be sensitive to the excited state vibrational motions on the S2 11Bu potential, via the time evolution of the D0 photoelectron spectrum.

FIG. 3.

A cartoon of the excited state motions expected to be involved in the excited state dynamics of planar trans-1,3-butadiene, excited to its bright S2(11Bu) state. This π−π* transition reduces the bond order in the excited state, leading to a stretching and large amplitude twisting about the C—C bonds. Twisting in the excited state also leads to conversion of the originally sp2 hybridized C atoms to sp3, leading to a pyramidalization of the C—H bonds. These two motions (twisting and pyramidalization) are shown by the ball-and-stick figures in the excited states. Upon twisting, the system encounters a conical intersection with the dark S1(2 1Ag) state, leading to an ultrafast non-adiabatic transition.

FIG. 3.

A cartoon of the excited state motions expected to be involved in the excited state dynamics of planar trans-1,3-butadiene, excited to its bright S2(11Bu) state. This π−π* transition reduces the bond order in the excited state, leading to a stretching and large amplitude twisting about the C—C bonds. Twisting in the excited state also leads to conversion of the originally sp2 hybridized C atoms to sp3, leading to a pyramidalization of the C—H bonds. These two motions (twisting and pyramidalization) are shown by the ball-and-stick figures in the excited states. Upon twisting, the system encounters a conical intersection with the dark S1(2 1Ag) state, leading to an ultrafast non-adiabatic transition.

Close modal

This paper is organized as follows. We first present a detailed description of the pulsed molecular beam TRPEPICO experiment, based on a large bore permanent magnet bottle dual time-of-flight (TOF) design, and the fs laser systems employed. In Sec. III, we describe our data analysis methods and their limitations, particularly when large amplitude motions are involved. We then present our experimental time-resolved mass spectrometry, TRPES, and TRPEPICO results for BD excited at 216 nm. These are discussed and compared in detail, and our phenomenological conclusions are presented. We report the first direct observation of the elusive dark S1 21Ag state of BD. We also consider, using a simple model, the excited state motions responsible for the extreme width of the BD UV absorption spectrum. In the following theory Paper II,10 we present detailed AIMS simulations of both the excited state non-adiabatic dynamics and, importantly, the experimental TRPES and TRPEPICO spectra. These reveal details of the ultrafast dynamical processes occurring in the excited state dynamics of the smallest linear polyene, 1,3-butadiene.

We describe our femtosecond time-resolved PEPICO magnetic bottle spectrometer experiments. Femtosecond laser pulses were obtained from a fs Ti:sapphire regenerative amplifier (Coherent, Legend, 800 nm). Part of the output (∼700 μJ) was used for harmonic generation to produce 267 nm laser pulses. A second part (∼700 μJ) was used to pump a travelling wave optical parametric amplifier system (TOPAS) (Light Conversion) system. The idler from the TOPAS was doubled in a β-barium borate (BBO) crystal and sum-frequency mixed with 800 nm (∼460 μJ) pulses in a second BBO crystal. The resulting sum frequencies were then doubled in a third BBO crystal to generate 216 nm. The fs UV pulses were individually recompressed using vacuum ultraviolet (VUV) grade CaF2 prism pairs, combined collinearly on a dichroic mirror, and then gently focused using an f/250 spherical reflective Al mirror to intersect a seeded molecular beam in the interaction region of a novel magnetic bottle PEPICO spectrometer, shown in Fig. 4 and described below. Typical pulse energies were ∼25 nJ for the 216 nm pump and ∼1.5 μJ for the 267 nm probe. Time delays between pump and probe pulses were scanned using a computer-controlled stepper motor. The temporal cross correlation (CC) between the 216 nm (hv1 = 5.74 eV) and 267 nm (hv2 = 4.64 eV) fs pulses was 155 ± 10 fs, determined in situ using (1 + 1′) photoionization of nitric oxide (NO). This also served to determine the photoelectron kinetic energy calibration. The cross correlation for a (1 + 2′) photoionization process was 130 ± 10 fs. Approximately 1% trans 1,3-butadiene (BD, Matheson, 99.9%) seeded in 1 bar helium was expanded continuously through a 100 μm pinhole. The 216 nm fs pump pulse excited the molecules from their ground state into the optically bright S21Bu state, whereupon the delayed fs 267 nm probe pulse produced photoelectrons via one-photon or two-photon probe ionization. The accepted ionization potential (IP) of trans 1,3-butadiene is 9.072 ± 0.007 eV.40 For (1 + 1′) photoionization, the total photon energy (hv1+hv2) was 10.37 eV, an excess energy of 1.30 eV above the IP. For (1 + 2′) photoionization, the total photon energy (hv1+2hv2) was 15.0 eV, an excess energy of 5.93 eV above the IP. Photoelectron spectra arising from the pump and probe laser pulses at negative time delays (i.e., probe preceding the pump) were subtracted in order to correct for background photoelectrons generated from single color multiphoton ionization. Pump-probe time delays were scanned 155 times and co-added so as to minimize any small effects due to temporal and/or spatial laser drift.

FIG. 4.

A depiction of the Photoelectron-Photoion Coincidence (PEPICO) apparatus used in these experiments. A molecular beam introduced cold BD molecules to the interaction region of a dual time-of-flight (TOF) magnetic bottle PEPICO spectrometer. Photoelectrons are collected along the e-TOF, yielding the energy-resolved photoelectron spectrum, whereas coincident ions are collected along the i-TOF, yielding the mass spectrum. The PEPICO spectrum is recorded as a function of the femtosecond pump-probe time delay Δt. For a detailed description of the permanent magnet large bore bottle, see the text.

FIG. 4.

A depiction of the Photoelectron-Photoion Coincidence (PEPICO) apparatus used in these experiments. A molecular beam introduced cold BD molecules to the interaction region of a dual time-of-flight (TOF) magnetic bottle PEPICO spectrometer. Photoelectrons are collected along the e-TOF, yielding the energy-resolved photoelectron spectrum, whereas coincident ions are collected along the i-TOF, yielding the mass spectrum. The PEPICO spectrum is recorded as a function of the femtosecond pump-probe time delay Δt. For a detailed description of the permanent magnet large bore bottle, see the text.

Close modal

Our molecular beam ultrahigh vacuum PEPICO spectrometer (P < 5 × 10−10 mbar) was built around a large bore 20-pole permanent magnet “magnetic bottle” design. As seen in Fig. 4, there are two collinear time-of-flight (TOF) spectrometers: a 30 cm TOF for photoelectrons [electron time-of-flight (e-TOF) for electron energy resolution] and a 50 cm TOF for photoions (i-TOF Wiley-McLaren design, for ion mass resolution), allowing for simple PEPICO and ion-electron covariance measurements. The large bore (0.75 cm ID) magnetic bottle design was based on magnetic field simulations using the Los Alamos Accelerator Code Group’s finite element package “Poisson Superfish.”41 The twenty individual rectangular bar magnets (gray rectangles) were Ni-coated Nd—Fe—B (Sumitomo NEOMAX 38 VH) with dimensions 5 × 5 × 30 mm and magnetization direction along the radial 5 mm dimension. In our design, these twenty radially magnetized bar magnets were mounted vertically and distributed evenly around a 1 cm bore cylindrical cone soft iron (Fe) core (inner cone, lined dark blue) which strongly focused the magnetic field to 0.2 T at the top of the magnet unit. A solenoidal coaxial field (10 G) was applied along the 30 cm e-TOF tube, completing the “bottle” and thereby guiding the electrons toward their detector. An outer steel core (large outer cylinder, lined light blue) served to further increase the divergence of magnetic field lines at the laser-molecule interaction point, located 4.5 mm above the magnet unit. The interaction point was chosen to be just beyond the field maximum, on the “downhill” slope of the magnetic field gradient. This is the so-called “magnetic mirror” mode which serves to collect a very large solid angle (in this design, 80%) of emitted electrons (green trajectory) at the expense of slightly poorer energy resolution. The magnetic field line distribution was experimentally measured using a SENIS (Baar, Switzerland) magnetic field Hall transducer. As can be seen in Fig. 5, the measured magnetic field closely matches that of the simulation. At the laser interaction point, the field strength is 0.175 T and the field gradient has a 1/e length of 10 mm. Importantly, our design has a relatively large and uniform collection volume (∼2 mm diameter) for photoelectrons and a large 0.75 cm ID open bore for collection of photoions in the opposite direction. A 1 mm wall thickness Mu-metal cylinder (Magnetic Shield Corp., 1000x field reduction) shielded the e-TOF from stray external magnetic fields. The photoelectrons pass through two home-made 98% open area gold wire (20 μm ϕ, 2 × 2 mm grid) meshes (dotted light blue lines) before entering the e-TOF. A 92% open area gold-coated Cu mesh (Buckbee-Mears) is in front of the 40 mm OD triple-stack MCP detector (Burle): the measured overall photoelectron detection efficiency was 40% for kinetic energies up to 5 eV. The measured kinetic energy resolution, determined via (1 + 1′) photoionization of NO, was ΔE/E = 0.16 at 1 eV.

FIG. 5.

Measurement of the axial (black squares) and radial (arrows) variation of the magnetic field (B) for the magnetic bottle shown in Fig. 4. The maximum field strength is 0.2 T. A full simulation of the B field is shown, for the axial direction, as a solid line. The agreement is good. The dashed horizontal line, indicating the laser axis from where the photoelectrons originate, is located 4.5 mm above the magnet face. This is downhill from the field maximum, meaning that the bottle spectrometer is operated in the magnetic mirror mode which enhances collection efficiency. At the interaction point, the field strength is 0.175 T and the field gradient has a 1/e length of 10 mm. For details, see the text.

FIG. 5.

Measurement of the axial (black squares) and radial (arrows) variation of the magnetic field (B) for the magnetic bottle shown in Fig. 4. The maximum field strength is 0.2 T. A full simulation of the B field is shown, for the axial direction, as a solid line. The agreement is good. The dashed horizontal line, indicating the laser axis from where the photoelectrons originate, is located 4.5 mm above the magnet face. This is downhill from the field maximum, meaning that the bottle spectrometer is operated in the magnetic mirror mode which enhances collection efficiency. At the interaction point, the field strength is 0.175 T and the field gradient has a 1/e length of 10 mm. For details, see the text.

Close modal

Referring again to Fig. 4, once all photoelectrons have passed both 98% transmission grids (∼185 ns after ionization) and are drifting along the e-TOF, a +0.5 kV pulse is applied to the middle grid (the upper grid, the entrance to the e-TOF, remained grounded, thereby shielding the drifting photoelectrons from the ion extraction voltage pulse), pushing the photoions (red trajectory) toward the magnet bore and the i-TOF. A cylindrical semiconductor tube (purple) provides, in a meshless and uniform manner, the second electric field gradient required for the Wiley-McLaren space-focusing condition. The drift tube was typically floated at +2 kV. Beneath this, a half-cylindrical deflection plate (steel blue, voltage V) removes the transverse molecular beam velocity component of the photoions and an Einzel lens (not shown) further down the 50 cm i-TOF focuses ion trajectories (red) onto a second 40 mm OD triple-stack MCP detector (Burle). The measured overall photoion collection efficiency was 37%. The TOF mass resolution was measured to be ΔM = 1 amu at 100 amu.

Often, in the analysis of TRPES data S(εk, t), a 2D global least-squares method (e.g., Levenberg-Marquardt) is employed to fit all photoelectron kinetic energies εk and time delays t simultaneously. Thus, the S(εk, t) surface is globally fitted to

S(εk,t)=g(t)iDi(εk)et/τi,
(1)

where the Di(εk) are the time independent decay associated spectra (DAS), the energy-resolved amplitudes of fit components having time constants τi. The convolution with g(t), the Gaussian cross-correlation function, accounts for the instrumental response. A given Di(εk) is related to the energy-resolved photoionization cross section σi(εk) of the ith state.

Importantly, there is a critical assumption underlying such 2D global fitting. It is that the Di(εk) are themselves time-independent in form and only their contribution (amplitude) varies with time. Physically, this demands that the Franck-Condon spectrum associated with the dynamical behavior of a given state remains “frozen” during the kinetics. In other words, the excited state molecular structure is nearly frozen (i.e., small amplitude motions) during the dynamics of state i but appears as a different, nearly frozen, structure for the dynamics of state j. As detailed previously, 2D global fitting gives meaningful results if the molecules do not undergo rapid large amplitude motions in the excited state.42,43 Large amplitude deformations of the molecular frame will, typically, cause the instantaneous vertical IP to vary during such dynamics, as Franck-Condon factors will typically force transitions to increasingly higher-lying vibrational states of the cation as a function of time. Since, in BD, the excited neutral and cation ground state potentials are anti-parallel along these large amplitude coordinates (e.g., torsion), the Franck-Condon envelope of a given channel will “sweep” toward lower εk as a function of time and, therefore, 2D global fitting may not yield physically meaningful results. There are, however, ways to mimic this effect within a 2D global fitting framework. The “time zero” is normally fixed to be the centroid of the Gaussian cross-correlation function g(t). We previously employed a phenomenological method to account for rapid large amplitude motions by allowing the “time zero” of the fitting routine to be a free variable.9 The variation of the “time zero” fit parameter as a function of εk can be used as a phenomenological measure of large amplitude motion in the excited state. This is discussed in more detail in Sec. IV D.

In the present case of BD, as discussed in detail in Sec. IV, we did observe a significant and rapid sweep of εk toward lower energy within a given photoelectron band (specifically, that associated with the initial S2 state). For BD, 2D global fitting fails in a specific region of the TRPES spectrum. In the following companion paper (Paper II),10 we present full ab initio simulations of the non-adiabatic dynamics in the excited states and the calculation of time-resolved observables (i.e., TRPES, TRPEPICO) from these dynamics in order to directly compare experiment with theory. Nevertheless, we employ here the floating “time zero” method discussed above in order to characterize phenomenological aspects of large amplitude motions in the excited states of BD: these are discussed in Sec. IV.

In Fig. 6, we present time-resolved mass spectra (TRMS) for pump-probe photoionization of excited state dynamics in BD. The C4H6+ parent ion mass is 54 amu. The small mass peak at m/e = 55 is due to the 1% natural abundance of 13C. It can be seen that there are hydrogen loss channels (m/e = 50-53), methyl (m/e = 39), and further hydrogen loss (m/e = 36-38) channels, and a group associated with the loss of two carbon atoms (m/e = 26-28). Two fragments, C3H3+ (m/e = 39) and C2H3+ (m/e = 27), are highlighted for reasons discussed below. It can be seen that, relative to the parent ion signal (m/e = 54), the other mass channels are delayed and have varying time dependencies. We have observed that these time-dependences fall into three distinct groups, shown in Fig. 7. The first group, (a), containing the C4H6+ (m/e = 54) parent ion alone, is shown as the blue trace. All other signals are delayed with respect to this. The second group, (b), exemplified by C3H3+ (m/e = 39, black trace), also contains the following fragment ions: C4H5+ (m/e = 53), C4H4+ (m/e = 52), and C2H4+ (m/e = 28). The third group, (c), exemplified by C2H3+ (m/e = 27, purple trace), also contains the fragment ions C4H3+ (m/e = 51) and C2H2+ (m/e = 26). It can be seen that all fragment ion channels show a non-zero signal (offset) persisting out to long time delays (exceeding the time range of the experiment): the ratio of this offset to the transient peak is significantly larger for group (c).

FIG. 6.

Time-resolved mass spectra for BD pumped at 216 nm and probed at 267 nm. The parent ion, C4H6+ (m/e = 54), is seen to rise promptly and decay very rapidly. Various fragmentation channels are seen in the mass spectrum. In the C4Hn+ region, H atom loss channels are seen. In the C3Hn+ region, a dominant methyl loss channel, producing C4H3+ (m/e = 39), is seen and is delayed with respect to the parent ion. Various fragments seen in the C2Hn+ region, such as C2H3+ (m/e = 27), are also delayed with respect to the parent ion. For details, see the text.

FIG. 6.

Time-resolved mass spectra for BD pumped at 216 nm and probed at 267 nm. The parent ion, C4H6+ (m/e = 54), is seen to rise promptly and decay very rapidly. Various fragmentation channels are seen in the mass spectrum. In the C4Hn+ region, H atom loss channels are seen. In the C3Hn+ region, a dominant methyl loss channel, producing C4H3+ (m/e = 39), is seen and is delayed with respect to the parent ion. Various fragments seen in the C2Hn+ region, such as C2H3+ (m/e = 27), are also delayed with respect to the parent ion. For details, see the text.

Close modal
FIG. 7.

Normalized time-dependence of the mass spectra shown in Fig. 6. These are arranged into three groups according to their time-dependence. Group (a) contains only the parent ion C4H6+ (m/e = 54). It rises with the laser cross correlation and decays very rapidly, with no offset at long time delays. Group (b) contains four fragment ions, of which C4H3+ (m/e = 39) is a prominent member, and has a clearly delayed rise with respect to Group (a). The group (b) channels also decay rapidly and have a long time delay offset. Finally, the group (c) channels contain three fragment ions, of which C2H3+ (m/e = 27) is an example, and are even further delayed and have an even larger long time delay offset. This type of behavior is suggestive of a sequential kinetic mechanism: (a) → (b) → (c). The offsets seen in groups (b) and (c) at long time delays are due to dissociative photoionization (into several channels) of the “hot” ground state neutral subsequent to its internal conversion.

FIG. 7.

Normalized time-dependence of the mass spectra shown in Fig. 6. These are arranged into three groups according to their time-dependence. Group (a) contains only the parent ion C4H6+ (m/e = 54). It rises with the laser cross correlation and decays very rapidly, with no offset at long time delays. Group (b) contains four fragment ions, of which C4H3+ (m/e = 39) is a prominent member, and has a clearly delayed rise with respect to Group (a). The group (b) channels also decay rapidly and have a long time delay offset. Finally, the group (c) channels contain three fragment ions, of which C2H3+ (m/e = 27) is an example, and are even further delayed and have an even larger long time delay offset. This type of behavior is suggestive of a sequential kinetic mechanism: (a) → (b) → (c). The offsets seen in groups (b) and (c) at long time delays are due to dissociative photoionization (into several channels) of the “hot” ground state neutral subsequent to its internal conversion.

Close modal

The time dependence of each group is non-trivial and requires fitting with both rising and decaying exponential components in order to adequately represent these data. Due to the intuitive expectation that the excited state dynamics follow a sequential S2(1Bu) → S1(2 1Ag) → S0(1 1Ag) mechanism and that the groups (a)–(c) in Fig. 7 appear sequentially, we employed a sequential kinetic model for a global fit to the data. Due to the time-dependences seen in groups (a)–(c) and the significant long-time offset observed in group (c), it is tempting to associate group (a) with the decay of the initially prepared S2(1Bu) state, group (b) with the formation and subsequent decay of the S1(2 1Ag) state, and group (c) offset with the final appearance of the “hot” S0(1 1Ag) ground state “product.” As will be discussed in a Sec. IV C (see Fig. 10 and associated discussion), the reason why both group (b) and group (c) ions have a long time offset is because the “hot” ground state neutral formed by internal conversion can undergo dissociative photoionization into both of these fragment ion groups. The time evolution of the initial parent ion into group (b) and then to group (c) fragment ions shown in Fig. 7 is suggestive of a sequential mechanism. The results of a fit to a sequential model S2(1Bu) → S1(21Ag) → S0(1Ag) yielded estimated lifetimes. The fit determined that group (a) can be uniquely assigned to the decay of S2(1Bu), whereas groups (b) and (c) each have contributions from both S1(2 1Ag) and S0(1 1Ag). The decay time of the initial S2(1Bu) state was found to be 28 ± 10 fs, the lifetime of the intermediate S1(2 1Ag) dark state was found to be 31 ± 10 fs, and the long lifetime (apparent offset) of the “hot” ground state was represented by a time constant of 10 ps. As detailed in  Appendix A, we believe that it is difficult to develop an unambiguous mechanism for the excited state wavepacket dynamics in BD based on ion yields alone. As discussed in Sec. IV C, TRMS alone cannot distinguish two pathways: (i) ionization to a cation excited state followed by spontaneous fragmentation, from (ii) ionization to the cation ground state followed by photofragmentation of the ion. An example of the latter would be a (2 + 1′) channel where two-photon ionization of the neutral ground state by the pump laser is subsequently fragmented by the probe laser. These two pathways can produce the same fragment ion, and a TRPES or TRPEPICO measurement is required to disentangle them. In our experiments, the pump laser fluence was reduced to the extent that two-photon ionization of the neutral ground state was negligibly small. More generally, we previously showed that in some cases TRMS can be very misleading29 and may only be properly re-interpreted once the more differential TRPES measurements are known. Therefore, although there is clear evidence for a sequential mechanism, the fitted values of the TRMS time constants cannot be considered as quantitative and we do not report them as being the lifetimes of the states involved. In Secs. IV B and IV C, we investigate the use of more differential probes, specifically TRPES and TRPEPICO.

In Fig. 8, we present TRPES spectra for BD (under the same conditions as for TRMS). In Fig. 8(a), we show the full photoelectron kinetic energy spectrum out to 10 ps delay, using a time axis which is linear up to 1 ps and then logarithmic from 1-10 ps. In the following, we will use the adiabatic state labels S2, S1, and S0 for notational convenience. The energetic thresholds for various processes are indicated by dashed lines. The energy limit for (1 + 1′) processes is 1.30 eV (red line) above the D0 origin (adiabatic IP). The energy limit for (1 + 2′) processes is 5.93 eV (red line) above the D0 origin. The (1 + 2′) transition which leaves the ion in its electronically excited D1 state has an energy limit of 3.61 eV (green line). For later reference, the dissociative ionization channel forming the C3H3+ fragment has an energy threshold of 2.4 eV (grey line) with respect to the (1 + 2′) energy limit.

FIG. 8.

Time-resolved Photoelectron Spectroscopy (TRPES) of BD pumped at 216 nm and probed at 267 nm. The time axis is linear in the −0.5–1.0 ps range and logarithmic in the 1–10 ps range. (a) The red dashed vertical line (1.30 eV) indicates the energetic limit for (1 + 1′) photoionization. In this region, only the ion ground state D0(2Bg) + e channel is open. The red dashed vertical line at 5.93 eV indicates the energetic limit for (1 + 2′) photoionization to the D0(2Bg) state. The energetic limit for forming the ion D1(2Au) electronically excited state, via a (1 + 2′) process, is shown as the green dashed vertical line (3.61 eV). At 2.40 eV above the IP [the D0(2Bg) origin], a unimolecular fragmentation channel producing C3H3+ + CH3 becomes open, as shown in Fig. 2. This fragmentation channel is only accessible for a (1 + 2′) process. The black dashed vertical line indicates the threshold for this channel, shifted by 2.40 eV relative to the (1 + 2′) energy limit at 5.93 eV. (b) The data from (a) are replotted with a logarithmic intensity scale, revealing all contributions to the TRPES signals. (c) A 2D global fit to a sequential kinetic model S2 → S1 → S0 describes the data very well. The expected Koopmans’ correlations S2(11Bu) → D0(2Bg) and S1(2 1Ag) → D1(2Au) are clearly reflected in these data, supporting the assignments. For details, see the text.

FIG. 8.

Time-resolved Photoelectron Spectroscopy (TRPES) of BD pumped at 216 nm and probed at 267 nm. The time axis is linear in the −0.5–1.0 ps range and logarithmic in the 1–10 ps range. (a) The red dashed vertical line (1.30 eV) indicates the energetic limit for (1 + 1′) photoionization. In this region, only the ion ground state D0(2Bg) + e channel is open. The red dashed vertical line at 5.93 eV indicates the energetic limit for (1 + 2′) photoionization to the D0(2Bg) state. The energetic limit for forming the ion D1(2Au) electronically excited state, via a (1 + 2′) process, is shown as the green dashed vertical line (3.61 eV). At 2.40 eV above the IP [the D0(2Bg) origin], a unimolecular fragmentation channel producing C3H3+ + CH3 becomes open, as shown in Fig. 2. This fragmentation channel is only accessible for a (1 + 2′) process. The black dashed vertical line indicates the threshold for this channel, shifted by 2.40 eV relative to the (1 + 2′) energy limit at 5.93 eV. (b) The data from (a) are replotted with a logarithmic intensity scale, revealing all contributions to the TRPES signals. (c) A 2D global fit to a sequential kinetic model S2 → S1 → S0 describes the data very well. The expected Koopmans’ correlations S2(11Bu) → D0(2Bg) and S1(2 1Ag) → D1(2Au) are clearly reflected in these data, supporting the assignments. For details, see the text.

Close modal

The TRPES of Fig. 8 reveals the key features of excited state dynamics in BD. Figure 8(b) shows the same data as in Fig. 8(a) but now with a logarithmic photoelectron intensity scale, revealing all large and small amplitude photoionization channels in one plot. We first discuss the energy region below the 1.30 eV (1 + 1′) limit. We recall that the D1 electronic origin is 2.32 eV above the IP. Therefore, in this region, only the D0 ground state is energetically accessible. As illustrated by the orbital occupancy drawings in Fig. 1, the bright S2(11Bu) state is a single configuration which corresponds to a canonical ππ* HOMO → LUMO excitation. By contrast, the dark S1(2 1Ag) state contains multireference character (Fig. 2), with three approximately equal contributions from HOMO → LUMO+1 (left configuration), HOMO−1 → LUMO (middle configuration), and a (π*)2 double (right configuration) excitation. The electronic configurations of the cation are also shown in Fig. 2 (see also Table I) where it can be seen that the expected Koopmans’ correlations are S2(11Bu) → D0(2Bg) + e and S1(2 1Ag) → D1(2Au) + e. We therefore assign this prompt (i.e., rising at Δt = 0) photoelectron band, which has an energy cutoff exactly where expected for (1 + 1′) S2 → D0 ionization, to the excited state dynamics of the initially prepared S2(11Bu) state.

In the energy region between 1.30 and 3.61 eV, there appears a delayed rise photoelectron band which has an energy cutoff exactly where expected for (1 + 2′) S1 → D1 ionization. We therefore assign this photoelectron band to the excited state dynamics of the dark S1(2 1Ag) state which appears following internal conversion of the initially prepared S2(11Bu) state. This assignment is further supported by arguments present in the following paragraph. It can be seen that the 3.6 eV photoelectron band also decays rapidly, as would be expected for an intermediate configuration in a sequential kinetic process.

As discussed in  Appendix B, there are parallels in the ionization dynamics of the two double-bonded BD with the previously studied four double-bonded polyene all trans 2,4,6,8-decatetraene (DT).34 This strongly supports our assignment that the (1 + 1′) band corresponds to the S2(1 1Bu) → D0 + e channel and the (1 + 2′) bands corresponds to the S1(2 1Ag) → D1 + e channel. Therefore, based on the above, we claim to have directly detected and determined the lifetime of the famously elusive dark S1(2 1Ag) during the internal conversion of BD.

In Fig. 8(c), we present the results of 2D global fitting (as described in Sec. III) to the experimental data of Fig. 8(a). It can be seen that, using a sequential kinetic model S2 → S1 → S0, 2D global fitting reasonably describes the data. The quality of the fit is good and the essential dynamic features—the rapid decay of S2, the growth and then rapid decay of S1 and, finally, the appearance of the “hot” S0 ground state—are captured by this analysis. The 2D fit yields a (98% confidence interval) lifetime of 23 ± 4 fs for the bright S2(1 1Bu) state and 42 ± 4 fs for the dark S1(2 1Ag) state. We note that these values are in statistical agreement with the corresponding fits to the ion yields discussed above.

In Fig. 9, we present an expanded view of Figs. 8(a) and 8(c), focussing on the low energy region corresponding to (1 + 1′) photoionization of S2. In the upper left panel, we show the experimental data, whereas in the lower left panel we show the 2D global fit. Even in this expanded view, the quality of the fit seems good. However, on the right side of Fig. 9, we plot the residuals of the 2D fit (experiment minus fit). The red indicates a positive value, and the blue indicates a negative value. It can be seen that the fit errors are not statistically distributed in this (1 + 1′) region. We note that the 2D global fit residuals in all other regions (not shown) are of very high quality and show no statistical bias. Therefore, there is a clear systematic error in the 2D global fit in the lowest energy (1 + 1′) range. Specifically, at longer time delays, the fit does not capture the rising signal. As discussed above, this is due, to the fit constraint that the decay associated spectra are time independent. The systematic error seen in Fig. 9 (right) indicates that this fails to some degree and that there is a tilt of the S2 photoelectron spectrum toward lower kinetic energy with time. This is a clear indication that there is rapid large amplitude motion in the Franck-Condon region of the bright S2(1 1Bu) state. This tilt of the S2 photoelectron spectrum, the large amplitude motion associated with it, and the relation of these to the apparent breadth of the UV absorption spectrum are discussed in Sec. IV D.

FIG. 9.

Details of 2D global fitting to the data from Fig. 8(a), emphasizing the short time dynamics (0–200 fs) probed by the S2(11Bu) → D0(2Bg) transition (0–1.3 eV). Linear time and intensity scales are used. The fit residuals, shown right, indicate a systematic error where red indicates positive (blue negative) residuals. Importantly, the fit residuals throughout the rest of the 2D fit regions show no systematic deviations. As discussed in the text, the observed deviation is due to large amplitude motion in the initial S2(11Bu) state which is not captured by 2D global fitting models.

FIG. 9.

Details of 2D global fitting to the data from Fig. 8(a), emphasizing the short time dynamics (0–200 fs) probed by the S2(11Bu) → D0(2Bg) transition (0–1.3 eV). Linear time and intensity scales are used. The fit residuals, shown right, indicate a systematic error where red indicates positive (blue negative) residuals. Importantly, the fit residuals throughout the rest of the 2D fit regions show no systematic deviations. As discussed in the text, the observed deviation is due to large amplitude motion in the initial S2(11Bu) state which is not captured by 2D global fitting models.

Close modal

In Fig. 10, we present TRPEPICO spectra for BD (under the same conditions as for TRPES). In Fig. 10(a), we present the total (uncorrelated) electron kinetic energy spectrum out to 10 ps delay, using a linear time axis for 0-1 ps and logarithmic time axis for 1-10 ps, and a linear photoelectron intensity scale. These are the same data presented in Fig. 8(a) and correspond to all photoelectrons irrespective of which photoion they are coincident with. For Figs. 10(b)–10(d), the time axis is linear, emphasizing the short time scale dynamics. In Fig. 10(b), we show the TRPEPICO spectrum for electrons coincident with the C4H6+ parent ion [group (a) of Fig. 7]; in Fig. 10(c), the spectrum coincident with the C3H3+ fragment ion [in group (b) of Fig. 7]; and in Fig. 10(d), for the C2H3+ fragment ion [in group (c) of Fig. 7]. Shown are the kinetic energy limits for (1 + 1′) ionization to D0 at 1.3 eV (red dash) and for (1 + 2′) ionization to D1 at 3.6 eV (green dash). The dissociative ionization channel forming the C3H3+ fragment38 has an (1 + 2′) energy threshold of 3.5 eV (gray dash): in other words, (1 + 2′) photoelectrons with kinetic energy less than 3.5 eV will lead to parent ion fragmentation, forming C3H3+, but with a rate that depends on internal energy.

FIG. 10.

Time-resolved Photoelectron-Photoion Coincidence Spectroscopy (TRPEPICO) of BD pumped at 216 nm and probed at 267 nm. In (a), the time axis is linear in the −0.5–1.0 ps range and logarithmic in the 1–10 ps range, whereas in (b)–(d) a linear time axis is used in the −0.5–0.6 ps range. A linear intensity scale is used throughout. The red dashed line (1.3 eV) indicates the energetic limit for (1 + 1′) S2(11Bu) → D0(2Bg) photoionization. The green dashed line (3.6 eV) indicates the energetic limit for (1 + 2′) S1(2 1Ag) → D1(2Au) photoionization. The black dashed line (3.5 eV) indicates the threshold of the unimolecular decay channel C4H6+ → C3H3+ + CH3 (for which the decay rate is internal energy dependent). The purple dashed line (3.15 eV) indicates the C4H6+ cation internal energy at which the parent cannot survive the ∼200 ns transit time in the Wiley-McLaren extraction region (see Fig. 4). Electron kinetic energies below this value mean that the parent ion fragments in the extraction region and must be detected as C3H3+. (a) Total electron TRPEPICO correlated with all ion masses. This is the same data as presented in Fig. 8(a). (b) TRPEPICO correlated with the C4H6+ parent ion, revealing the dominant (1 + 1′) S2(11Bu) → D0(2Bg) transition. A small time delayed parent ion signal is seen near 3.6 eV, corresponding to the S1(2 1Ag) → D1(2Au) transition. Parent C4H6+ ions with internal energies corresponding to photoelectrons between the green and purple lines survive the transit of the extraction region and are detected as the parent ion mass. (c) TRPEPICO correlated with the C3H3+ fragment ion, revealing the dominant time-delayed (1 + 2′) S1(2 1Ag) → D1(2Au) transition. As discussed in  Appendix C, this fragment appears only for photoelectron energies less the purple dashed line, corresponding to internal energies at which the parent ion cannot survive the extraction region transit time. In the 0–1.3 eV region, the C3H3+ fragment ion is seen but with a photoelectron spectrum corresponding to the S2(11Bu) → D0(2Bg) transition. This is due to post-ionization photodissociation of the C4H6+ parent. A significant contribution is also seen at long time delays and low electron energies. This is due to dissociative photoionization of the “hot” S0 neutral molecule formed by internal conversion. (d) TRPEPICO correlated with the C2H3+ fragment ion. As indicated in Table II, this high energy fragment requires a total energy of around 15 eV. Therefore, this channel is due to two-photon post-ionization photodissociation of the C4H6+ parent and C3H3+ fragment ions, echoing the dynamics seen in both panels (b) and (c). The dissociative photoionization contribution from “hot” S0 appears more prominently and over a broader energy range in this channel. In panels (b)–(d), a dashed black line in the low energy region indicates the centroid of the S2(11Bu) → D0(2Bg) photoelectron band. It is clearly negatively sloped toward lower energies, indicating a “sweep” of the Franck-Condon spectrum due to large amplitude motion during the dynamics. For further details, see the text.

FIG. 10.

Time-resolved Photoelectron-Photoion Coincidence Spectroscopy (TRPEPICO) of BD pumped at 216 nm and probed at 267 nm. In (a), the time axis is linear in the −0.5–1.0 ps range and logarithmic in the 1–10 ps range, whereas in (b)–(d) a linear time axis is used in the −0.5–0.6 ps range. A linear intensity scale is used throughout. The red dashed line (1.3 eV) indicates the energetic limit for (1 + 1′) S2(11Bu) → D0(2Bg) photoionization. The green dashed line (3.6 eV) indicates the energetic limit for (1 + 2′) S1(2 1Ag) → D1(2Au) photoionization. The black dashed line (3.5 eV) indicates the threshold of the unimolecular decay channel C4H6+ → C3H3+ + CH3 (for which the decay rate is internal energy dependent). The purple dashed line (3.15 eV) indicates the C4H6+ cation internal energy at which the parent cannot survive the ∼200 ns transit time in the Wiley-McLaren extraction region (see Fig. 4). Electron kinetic energies below this value mean that the parent ion fragments in the extraction region and must be detected as C3H3+. (a) Total electron TRPEPICO correlated with all ion masses. This is the same data as presented in Fig. 8(a). (b) TRPEPICO correlated with the C4H6+ parent ion, revealing the dominant (1 + 1′) S2(11Bu) → D0(2Bg) transition. A small time delayed parent ion signal is seen near 3.6 eV, corresponding to the S1(2 1Ag) → D1(2Au) transition. Parent C4H6+ ions with internal energies corresponding to photoelectrons between the green and purple lines survive the transit of the extraction region and are detected as the parent ion mass. (c) TRPEPICO correlated with the C3H3+ fragment ion, revealing the dominant time-delayed (1 + 2′) S1(2 1Ag) → D1(2Au) transition. As discussed in  Appendix C, this fragment appears only for photoelectron energies less the purple dashed line, corresponding to internal energies at which the parent ion cannot survive the extraction region transit time. In the 0–1.3 eV region, the C3H3+ fragment ion is seen but with a photoelectron spectrum corresponding to the S2(11Bu) → D0(2Bg) transition. This is due to post-ionization photodissociation of the C4H6+ parent. A significant contribution is also seen at long time delays and low electron energies. This is due to dissociative photoionization of the “hot” S0 neutral molecule formed by internal conversion. (d) TRPEPICO correlated with the C2H3+ fragment ion. As indicated in Table II, this high energy fragment requires a total energy of around 15 eV. Therefore, this channel is due to two-photon post-ionization photodissociation of the C4H6+ parent and C3H3+ fragment ions, echoing the dynamics seen in both panels (b) and (c). The dissociative photoionization contribution from “hot” S0 appears more prominently and over a broader energy range in this channel. In panels (b)–(d), a dashed black line in the low energy region indicates the centroid of the S2(11Bu) → D0(2Bg) photoelectron band. It is clearly negatively sloped toward lower energies, indicating a “sweep” of the Franck-Condon spectrum due to large amplitude motion during the dynamics. For further details, see the text.

Close modal

In Fig. 10(b), we show the TRPEPICO spectrum for photoelectrons coincident with the C4H6+ parent ion. The dominant band has a sharp cutoff at 1.3 eV (red dash). As discussed above, this is assigned to the S2(1 1Bu) → D0 channel and therefore probes the excited state dynamics of the initially prepared 1Bu state. Since C4H6+ is stable at internal energies below 1.3 eV, this channel is detected as the parent ion. It can be seen that this channel rises promptly at Δt = 0 and rapidly decays with a lifetime matching that obtained from the data of Fig. 8. Also observed in Fig. 10(b) is a much weaker photoelectron band with an energy cutoff at the (1 + 2′) D1 threshold of 3.6 eV. Due to the sharp cutoff at 3.6 eV, we assign this channel to (1 + 2′) ionization of the dark S1(2 1Ag) state. Supporting this assignment, it can be seen that this channel is delayed in time relative to the S2(1 1Bu) channel. The rise time of the small band near 3.6 eV matches that expected from the sequential kinetic model fit to the data of Fig. 8. It can be seen in Fig. 10(b) that the grey dashed line, which indicates the lowest energy threshold for parent ion fragmentation (forming C3H3+) is just below the D1 origin. This means that BD ions formed at the D1 origin will not fragment and must therefore arrive at the i-TOF detector (see Fig. 4) as the parent ion. Concomitantly, parent ions with more internal energy (i.e., electrons slower than ∼3.1 eV) should fragment and therefore cannot be detected as the parent ion. As detailed in  Appendix C, this “transition region” between parent ion and fragment ion detection is shown as a purple dashed line in Fig. 10. It can be seen that the coincident parent ion signal in Fig. 9(b) “fades” in quite reasonable agreement with this estimate. These arguments further support our assignment of the 3.6 eV photoelectron band as being due to the S1(2 1Ag) → D1 channel.

In Fig. 10(c), we show the TRPEPICO spectrum for photoelectrons coincident with the C3H3+ fragment ion. There are two regions of interest, one below 1.3 eV (red dash) and the other below 3.6 eV (green dash). We discuss the higher energy region first. This photoelectron band is delayed with respect to the S2 band seen in Fig. 10(b) and has a rise time matching the S1 photoelectron band of Fig. 10(b). It also has a rise time and decay matching, quantitatively, that of the S1 band of Fig. 8. Interestingly, this band has an energy onset not at the 3.6 eV (green dash) limit expected for the S1(2 1Ag) → D1 channel but, rather, at lower energy, approximately at the “transition region” energy (purple dash) discussed in the paragraph above. Ions associated with photoelectrons above the purple line will be detected as the C4H6+ parent ion [Fig. 10(b)]. However, ions associated with photoelectrons having kinetic energies below the purple line will likely fragment rapidly enough to be detected as the C3H3+ fragment, as detailed in  Appendix C. This supports the assignment of this photoelectron band as being due to the S1(2 1Ag) → D1 channel. Finally, we note that the C3H3+ fragment belongs to group (b) in Fig. 7. As discussed in the TRMS section, the group (b) ions exhibit the behavior of a transient intermediate in a sequential kinetic scheme. This confirms our direct detection of the transient S1(2 1Ag) state of BD.

We now discuss the lower energy photoelectron band in Fig. 10(c) which has a cutoff at the (1 + 1′) limit of 1.3 eV. As discussed above, these (1 + 1′) ionizing transitions do not produce a fragment ion. Therefore, this band in Fig. 10(c) must be due to post-ionization photodissociation. The S2 photoelectron band of Fig. 10(b) produces a parent ion. However, after the photoelectron has departed (on sub-cycle time scales), the parent ion may persist in the probe laser field long enough to absorb a second probe photon, undergoing a resonant electronic transition D0(2Bg) → D3(2Bu), thus acquiring an additional 4.6 eV of internal energy. Following ultrafast internal conversion, the vibrationally “hot” cation dissociates producing a fragment, in this case C3H3+. However, since the photoelectron had already departed, this fragment ion has as its coincident partner a photoelectron associated with the S2(1 1Bu) → D0 channel, thus explaining the lower energy photoelectron band of Fig. 10(c). It is important to note that only PEPICO spectroscopy can readily distinguish post-ionization photodissociation from direct dissociative ionization. Time-resolved mass spectra, as shown in Figs. 6 and 7, inadvertently convolve these differing dynamical processes, confounding a clear view of the excited state dynamics.

Finally, we note that in Fig. 10(c) there is a weak coincident photoelectron signal at low kinetic energies which persists out to long time delays. This channel is therefore a contributor to the long-lived photoelectron signals seen in the logarithmic plot of Fig. 10(a). Since this featureless photoelectron band does not match those of either the S2 → D0 or S1 → D1 transitions, or post-ionization photodissociation of cations formed in these channels, they must have another origin. We propose that this long-lived signal is due to photoionization of the “hot” S0 ground state formed, as expected, via internal conversion from the dark S1(2 1Ag) state.

In Fig. 10(d), we show the TRPEPICO spectrum for photoelectrons coincident with the C2H3+ fragment ion. As shown in Table I, this high energy fragment has an appearance energy (AE) at the 15 eV energy limit for (1 + 2′) ionization and belongs to group (c) of Fig. 7. There are three regions of interest: a short-lived band below 1.3 eV, a transient band below the “transition region” cutoff (purple dash) near 3.1 eV, and a long-lived diffuse band at low kinetic energies. The first two are assigned to post-ionization photodissociation of the ions produced by the S2 → D0 and S1 → D1 photoionization channels discussed for Figs. 10(b) and 10(c). The latter (long-lived) channel is considerably stronger in Fig. 10(d). It matches the temporal [far exceeding the S1(2 1Ag) lifetime], fragmentation [highest energy fragmentation channel (c)], and photoelectron spectral behavior (broad, featureless) expected for (1 + 2′) photoionization of the “hot” S0 ground state.

In Figs. 10(b)–10(d), we also show a dashed black line indicating the centroid of the low energy (S2) band as a function of photoelectron kinetic energy. It can be seen that these bands slope toward lower kinetic energy, relative to the horizontal Δt = 0 line, at longer time delays. This indicates large amplitude motion on the S2(1Bu) potential surface. Significantly, this motion occurs while retaining zeroth order S2(1Bu) electronic character—in other words, before reaching a 1Bu1Ag conical intersection. This important point will be discussed in more detail below.

In Fig. 10(c), we show photoelectrons coincident with the C3H3+ fragment ion [group (b) of Fig. 7]. The region of interest below 1.3 eV is assigned to post-ionization photodissociation of the ions produced by the (1 + 1′) S2 → D0 transition, as discussed above. Interestingly, by comparing the tilted dashed black centroid line with the horizontal Δt = 0 line, we can see that these post-ionization photodissociation ions are delayed with respect to the analogous tilted line for the parent ion signal shown in Fig. 10(b). This means that the parent ion photodissociation channel producing C3H3+ requires some vibrational evolution on the cation D0 potential before the fragment signal is maximized. This preferentially selects out of the photoelectrons coincident with the parent ion [Fig. 10(b)], those that are somewhat delayed, as these more favourably produce the C3H3+ fragment. This delay is perhaps unsurprising, as time-resolved photodissociation of neutral molecules has been previously used in a pump-probe scheme, but with neutral photofragment detection as a probe.44 

The region of interest between 1.3 and 3.1 eV is assigned to the (1 + 2′) S1 → D1 transition, as discussed for Fig. 10(c). The dotted black (nearly horizontal) line marks the centre of this S1 band and it is clearly delayed with respect to that of the S0 band (dashed black). This, combined with its rapid decay, strongly supports the sequential kinetic scheme. Interestingly, the slope of the (nearly) horizontal dotted black line (S1) is different from the slope of the dashed black line (S2). This indicates that vibrational energy spreads much more rapidly in S1 than in S2. This is unsurprising, given that the greatly increased excess vibrational energy in S1 should lead to faster intramolecular vibrational energy redistribution (IVR) within that state.

In Fig. 10(d), we show photoelectrons coincident with the C2H3+ fragment ion [group (c) of Fig. 7]. This high energy fragment has an AE of 15 eV (Table I) and requires extensive internal energy in the BD cation. There are two post-ionization photodissociation processes appearing in the C2H3+ channel, as discussed above. Again, there is a delay between the D0 post-ionization photodissociation channel and the data in Fig. 10(c). There is photoelectron intensity, spread over a broad energy range, at longer time delays for the C2H3+ channel. This further supports the assignment that the photoelectron signals at long time delays (Figs. 7 and 9), and the group (c) fragment ions (Fig. 7) probe the vibrationally hot ground state neutral following the sequential internal conversion pathway S2 → S1 → S0.

As discussed above, due to the slope of the Franck-Condon spectrum in the (1 + 1′) region, 2D global fitting of the TRPES and TRPEPICO spectra may not yield accurate results: the decay associated spectrum (DAS) for the S2 → D0 transition does not retain a time independent form Di(εk). Ab initio excited non-adiabatic state dynamics and simulated “on-the-fly” TRPES spectra will be presented and discussed in detail in the following Paper II,10 allowing a direct “zero-adjustable-parameter” comparison of experiment with theory. In the following, however, we independently extract some information directly from the experimental data alone regarding the dynamical evolution of the excited state wavepacket on the S2 potential surface.

In Fig. 11, we present a more detailed analysis of the slope of the Franck-Condon spectrum and its relation to large amplitude motion within a given zeroth order electronic state (e.g., S2 11Bu). In Fig. 11(a), we show the dashed lines at 1.3 (red), 3.6 (green), and 5.9 (red) eV associated with the various energetic limits discussed above. In Fig. 11(a), we replot the photoelectron data of Fig. 10(a) but now normalize each kinetic energy slice to unit intensity. This helps to reveal the temporal behavior of each of the various channels, independent of their amplitude. In order to focus on the short time dynamics, in Fig. 11(b), we replot this using a narrower time range of 50–150 fs. For each kinetic energy slice, we fit the photoelectron band to a Gaussian function of time and determined the centroid. The locus of all centroid points is shown as the white line in Fig. 11(b). This line shows the motion of the effective “time zero” point (effectively, the sweep of the Franck-Condon spectrum) as a function of time delay. In Fig. 11(c), we plot separately the locus of Gaussian centroids, showing their behavior as a function of time and photoelectron kinetic energy. In a ballistic picture of localized Gaussian wavepacket motion, the rate of change of photoelectron kinetic energy with time delay, dεk/dt, within a given photoelectron band, should relate to the rate of change of the molecular geometry as viewed by the cation potential surface. The energy region above ∼5.5 eV corresponds to very small signals and is dominated by Poisson noise: we do not consider this region further here. We have divided the plot into two regions, labeled I and II, corresponding to the regions between the known energy limits (dashed lines) for the various channels. In region I, the average slope dεk/dt = −40 meV/fs. This region rises promptly with the pump laser pulse and, as discussed above, corresponds to the S2 → D0 transition. Therefore, we suggest that this slope corresponds to the rapid motion of the initially prepared wavepacket out of the vertical Franck-Condon region. Due to the geometry change between S0 and S2, we believe that the steepest gradient at the Franck-Condon point of the S2(1Bu) potential will be along the bond-alternation coordinate. However, the largest amplitude motion will be along the torsional coordinate and it is due to displacements along this mode that (higher frequency C=C stretch) vibrational revivals in the nuclear autocorrelation function are strongly attenuated, leading to significant broadening of the absorption spectrum. Some of these vibrational motions are depicted in Fig. 3. We note that the instantaneous vertical IP (i.e., the instantaneous εk) reflects the instantaneous difference potential between the neutral and cation states involved and, therefore, the geometry dependence of both neutral and cationic potentials determines dεk/dt. In BD, this difference potential increases monotonically via displacements along the torsional mode, whereas motion along the bond alternation coordinate will result in a smaller modulation of the IP. Thus, the slope dεk/dt is mostly sensitive to nuclear dynamics involving large amplitude torsional motion. In the following, we assume displacements along the torsional coordinate are chiefly responsible for the slope in region I.

FIG. 11.

(a) The photoelectron spectrum of Fig. 10(a) is split into two regions separated by a black vertical dashed line. The energy-resolved photoelectron spectrum is divided into thin bins (slices) of width 0.1 eV. Within each bin, the photoelectron intensity is normalized, allowing for comparison of the time-dependent behavior within each region. (b) The data from (a) are plotted over a small time range (−0.05–0.2 ps), revealing the fastest excited state dynamics. Within each bin, the centroid of the normalized photoelectron band is given by the white solid line. It can be seen that these clearly vary with energy. (c) The centroid of the photoelectron bands is plotted (blue squares) as a function of energy and time delay. In region I, a linear fit (red dashed line) yields a slope of −40 meV/fs. In region II, the behavior is more complex and cannot be fit with a single slope. Rather, three different slopes (−400 meV/fs, −100 meV/fs, −40 meV/fs) are used to indicate the trends (green dashed lines). The light gray solid lines indicate the expectations (hyperbolic functions) of a simple model of wavepacket motion on an inverted harmonic surface. As shown in Fig. 10, region I corresponds to (1 + 1′) S2(11Bu) → D0(2Bg) and region II below 4 eV corresponds to (1 + 2′) S1(2 1Ag) → D1(2Au) photoionization. These data indicate that large amplitude motion leads to a “sweep” of the Franck-Condon spectrum. For details, see the text.

FIG. 11.

(a) The photoelectron spectrum of Fig. 10(a) is split into two regions separated by a black vertical dashed line. The energy-resolved photoelectron spectrum is divided into thin bins (slices) of width 0.1 eV. Within each bin, the photoelectron intensity is normalized, allowing for comparison of the time-dependent behavior within each region. (b) The data from (a) are plotted over a small time range (−0.05–0.2 ps), revealing the fastest excited state dynamics. Within each bin, the centroid of the normalized photoelectron band is given by the white solid line. It can be seen that these clearly vary with energy. (c) The centroid of the photoelectron bands is plotted (blue squares) as a function of energy and time delay. In region I, a linear fit (red dashed line) yields a slope of −40 meV/fs. In region II, the behavior is more complex and cannot be fit with a single slope. Rather, three different slopes (−400 meV/fs, −100 meV/fs, −40 meV/fs) are used to indicate the trends (green dashed lines). The light gray solid lines indicate the expectations (hyperbolic functions) of a simple model of wavepacket motion on an inverted harmonic surface. As shown in Fig. 10, region I corresponds to (1 + 1′) S2(11Bu) → D0(2Bg) and region II below 4 eV corresponds to (1 + 2′) S1(2 1Ag) → D1(2Au) photoionization. These data indicate that large amplitude motion leads to a “sweep” of the Franck-Condon spectrum. For details, see the text.

Close modal

In the high energy side of region II below ∼5.5 eV, we have reproduced the dεk/dt = −40 meV/fs sloped line obtained from the linear fit to region I. Although much noisier, this slope is also roughly consistent with the data in the region above 5.5 eV which corresponds to a (1 + 2′) S2 → D0 ionization process, as discussed above (see Fig. 8). This region therefore reveals the same S2(1Bu) large amplitude vibrational dynamics via a (1 + 2′) process that region I reveals via a (1 + 1′) process and is not discussed further here.

In region II, we do not see a simple behavior for the slopes dεk/dt as a function of time. We can roughly divide region II into three ranges: one from 1.3 to 2.8 eV, the next from 2.8 to 3.8 eV, and the last from 3.8 to 5.0 eV. In the higher energy range, which appears simultaneously with region I, we replot the −40 meV/fs line from region I. Although much noisier, the same slope line roughly captures the trend. In the middle range, slightly delayed with respect to region B, we again treat the behavior as quasi-linear and find a slope of dεk/dt = −100 meV/fs. In the lowest energy range, which appears at longer time delays, we find a quasi-linear slope of dεk/dt = −400 meV/fs. The latter two slopes represent a much greater dεk/dt than seen in region I. This means that the photoelectron band in region II is broadening energetically much more rapidly with time delay than that in region I. We remind that region II below 4 eV corresponds to the (1 + 2′) photoionization process S1 → D1. In our sequential kinetic model, the photoelectrons at 3.6 eV kinetic energy correspond to ionization of the S1(1Ag) wavepacket prepared by internal conversion from the S2(1Bu) state. We suggest that the increased slope dεk/dt in the energy range from 3.6 eV to 2.8 eV is due to the greatly increased rate of internal vibrational energy flow following internal conversion to the S1(1Ag) state. This should lead to a significantly increased rate of IVR. In fact, as the wavepacket evolves further (i.e., longer time delays) on the S1(1Ag) potential, it is seen that the rate dεk/dt increases further to −400 meV/fs, approximately 10x the rate seen in region I. This suggests that the rate of IVR on S1(1Ag) increases with time over this period. This is consistent with what is expected for vibrational dynamics following rapid internal conversion and is discussed in greater detail in the following companion theory paper, Paper II.10 

The sweep in the Franck-Condon spectrum can be directly correlated with motion along an effective large amplitude coordinate, tentatively assigned to an out-of-plane torsional mode. We argue that it is precisely this motion (upon excitation to S2 11Bu) which leads to irreversible decay of the nuclear autocorrelation function: it is this motion which is responsible for the phenomenological breadth of the UV absorption band of BD. Without relying on theory (Paper II10), we now develop an internally consistent argument—based on our data alone—that the width of the UV absorption spectrum is due to large amplitude motion. In the following, we show that the increase in the instantaneous vertical IP due to large amplitude wavepacket motion in the S2 11Bu state can be observed via the time-dependent shift of the Franck-Condon (FC) spectrum in the TRPES. This result can be combined with a very simple model in order to extract the motion of the initial wavepacket from the FC region, thereby offering a mechanistic explanation of the observed extreme width of the lowest UV absorption band of BD.

As illustrated in Fig. 12, we consider an oversimplified but nevertheless instructive model of frozen Gaussian wavepacket dynamics in the FC region of the S2 11Bu. We assume that the curvatures along the relevant large amplitude (torsional) coordinate of the D0 cationic ground and S0 neutral ground state potential energy surfaces are each harmonic and quite similar. This is a reasonable assumption, given the lack of a torsional vibrational progression seen in this mode in the He(i) photoelectron spectrum. In such a situation, the nuclear autocorrelation function for the decay of the initial S2 11Bu wavepacket from the FC region would appear very similar, whether correlated with respect to the neutral S0 vibrationless ground state (related to the absorption spectrum) or the cation D0 vibrationless ground state. Thus, the slope of the instantaneous vertical IP observed in the TRPES can be used as a proxy for visualizing the differential displacements—along the large amplitude (torsional) mode—between the S2 11Bu and D0 cation states. Since, in our model, the D0 and S0 states are parallel along this torsional coordinate, this measure—by proxy—relates to the decay of the nuclear autocorrelation function with respect to the S0 ground state. It is this latter quantity which is responsible for the width of the UV absorption spectrum.

FIG. 12.

A cartoon summarizing the excited state dynamics of BD, as probed by the (1 + 1′) and (1 + 2′) TRPEPICO measurements in our experiments. Due to large amplitude motion (torsion) on the S2 potential, the initially prepared wavepacket rapidly moves away from the Franck-Condon region, producing the −40 meV/fs sloped S2 → D0 photoelectron band seen in region I of Fig. 11(c). This motion is the origin of the extreme width of the BD absorption spectrum. At larger displacements (later times), the conical intersection with S1 is reached and the Koopmans’ correlations and energetic considerations favour (1 + 2′) photoionization to the D1 state, region II of Fig. 11(c). At these ion internal energies, the unimolecular decay channel producing C3H3+ is open. Due to the rapidly increasing internal energy, the photoelectron spectrum in region II shows a large and increasing slope with time delay. For details, see the text.

FIG. 12.

A cartoon summarizing the excited state dynamics of BD, as probed by the (1 + 1′) and (1 + 2′) TRPEPICO measurements in our experiments. Due to large amplitude motion (torsion) on the S2 potential, the initially prepared wavepacket rapidly moves away from the Franck-Condon region, producing the −40 meV/fs sloped S2 → D0 photoelectron band seen in region I of Fig. 11(c). This motion is the origin of the extreme width of the BD absorption spectrum. At larger displacements (later times), the conical intersection with S1 is reached and the Koopmans’ correlations and energetic considerations favour (1 + 2′) photoionization to the D1 state, region II of Fig. 11(c). At these ion internal energies, the unimolecular decay channel producing C3H3+ is open. Due to the rapidly increasing internal energy, the photoelectron spectrum in region II shows a large and increasing slope with time delay. For details, see the text.

Close modal

As seen in Fig. 12, upon excitation to the S2 11Bu state, a frozen Gaussian wavepacket (black) evolves on an inverted harmonic surface. This inverted potential is merely a cartoon picture but one which represents an effective imaginary frequency responsible for removing wavepacket density from the initial Franck-Condon region. During this effective motion (horizontal axis), the vertical IP increases as a function of time [region I in Fig. 11(c)] until it exceeds the energy of a single probe photon. In this cartoon picture, the ballistic motion of the frozen Gaussian wavepacket maps the instantaneous vertical IP. The classical equations of motion for position x(t) and momentum p(t) on an inverted harmonic potential are given by the hyperbolic functions,

x(t)=x0sinh(ω1t)+p0cosh(ω1t),
(2)
p(t)=x0cosh(ω1t)+p0sinh(ω1t),
(3)

where ω1 is the harmonic (negative) curvature of the inverted potential along the effective coordinate and x0 and p0 are the Gaussian initial position and momentum obtained from the S0 ground state v = 0 Wigner distribution. In this simple picture, the vertical energy difference between the S2 11Bu and D0 states monotonically follows the effective coordinate x(t), thus determining the instantaneous vertical IP as a function of time. Rather than attempting to extract meaningful parameters from such an oversimplified model, we simply wish to see if the variation of vertical IP with time delay matches the expectations (functional form) of a large amplitude motion. To proceed, we self-consistently fit both regions I and II to the data in Fig. 11(c) in order to obtain a phenomenological x(t). This fit is shown as the light grey curve overlapping the data in Fig. 11(c). It can be seen that the hyperbolic form is consistent with the variation in vertical IP seen in both regions. This supports the argument that the initial slopes of the photoelectron bands in regions I and II are due to a large amplitude effective motion. We assume that this motion contains a significant torsional component.

Importantly, via this cartoon, we can propose a mechanistic explanation of the much debated extreme width of the UV absorption spectrum of BD as seen in Fig. 1. We emphasize that the apparent width is not due to non-adiabatic dynamics in the FC region–i.e., the rapid development of S1 21Ag character within the FC region. Rather, it is due large amplitude (mostly torsional) motion within the S2 11Bu state which rapidly moves the initial wavepacket away from the FC region. As discussed in detail in the following companion paper, Paper II,10 large amplitude torsional motion does indeed lead to a conical intersection between S2 and S1, but at a large torsional displacement (away from the FC region), thus generating an apparent irreversibility45 in the nuclear autocorrelation function.

The smallest linear polyene, trans-1,3-butadiene, bridges the gap between ethylene and the longer polyenes, exhibiting dynamical aspects of each. Its dynamics following π−π* excitation to the bright S2 11Bu state have long been a controversial subject. Using a balanced treatment of the non-adiabatically coupled S2 11Bu and S1 21Ag states, Levine and Martinez previously proposed20 that both ethylene-like and polyene-like mechanisms are active in BD. In this paper (Paper I), we presented detailed time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy studies of the π−π* excited state dynamics of BD. Specifically, we excited BD with a fs pulse at 216 nm, corresponding to the apparent origin of its π−π* HOMO to LUMO transition. The evolving excited state wavepacket was subsequently photoionized with a delayed probe pulse at 267 nm using either a one photon (1 + 1′) or a two-photon (1 + 2′) process: the emitted photoelectrons were analyzed as to their kinetic energy spectrum as a function of time. Due to the specific electronic structure of the neutral and ionic states of BD, the complementary Koopmans’ correlations are S2(11Bu) → D0(2Bg) + e and S1(2 1Ag) → D1(2Au) + e. This favoured the separation of the TRPES spectra associated with the bright and dark states. Furthermore, due to an open fragmentation channel lying near the D1(2Au) origin, the pump-probe preparation of vibrationally excited D1 unavoidably leads to post-ionization fragmentation forming C3H3+. Using the TRPEPICO method, we correlated photoelectrons with either the parent ion or a fragment ion, allowing for disentangling of these ionization channels. Using 2D global fitting to a sequential kinetic model S2 → S1 → S0, we could represent the data with a good quality (98% confidence) fit. The essential dynamic features—the rapid decay of S2, the growth and then rapid decay of S1, and, finally, the appearance of the “hot” S0 ground state—were all seen in this analysis. This allowed us to report the first direct observation of the famously elusive S1(2 1Ag) state of BD during its ultrafast internal conversion. The 2D global fit yielded lifetimes of 23 fs for the bright S2(1 1Bu) state and 42 fs for the dark S1(2 1Ag) state.

A detailed analysis of the residuals of the global fits revealed a systematic error due to extensive large amplitude motion in the Franck-Condon region. 2D global fitting assumes a time-independent form of the decay associated spectra. In the case of large amplitude motion, this constraint may lead either to poor fits or, worse, to a misinterpretation of the dynamics. We presented a purely phenomenological analysis of this large amplitude motion which leads to a time dependence (slope) of the photoelectron spectrum associated with a given channel. In particular, by analyzing the slope of the photoelectron spectrum in the region of the S2(11Bu) → D0(2Bg) + e transition (region I), we were able to determine that the initially prepared wavepacket rapidly leaves the Franck-Condon region due to large amplitude (predominantly torsional) motions but, importantly, while retaining zeroth order S2(1 1Bu) electronic character. This allowed us to propose a clear dynamical mechanism for the extreme breadth of the trans-1,3-butadiene UV absorption spectrum. We emphasize that the origin of this breadth is not due to strong non-adiabatic coupling to S1 within the Franck-Condon region. Rather, it is large amplitude (torsional) motion on the zeroth order S2 potential which rapidly moves the wavepacket from the Franck-Condon region. As will be detailed in the following paper, Paper II,10 the S2-S1 conical intersection is indeed encountered but at larger values of the torsional angle (i.e., not in the Franck-Condon region). This subsequent conical intersection along the large amplitude torsional coordinate leads to the apparent irreversibility of the wavepacket dynamics, thereby broadening the UV absorption spectrum.

The following paper, Paper II,10 presents detailed ab initio multiple spawning (AIMS) calculations of the same wavepacket dynamics in trans-1,3-butadiene. This method permits on-the-fly calculations of observables, in this case the TRPES and TRPEPICO spectra. These are compared with the experimental results of Paper I. This comparison also reveals the intramolecular motions and non-adiabatic crossings which underlie the TRPES and TRPEPCIO results. As suggested by the results presented here and by Paper II,10 we believe that the combination of TRPES (and its imaging and coincidence variants) with AIMS theory is particularly powerful at revealing details of the dynamics involved in the complex non-adiabatic processes of polyatomics molecules.

A.S. and M.S.S. thank the NSERC Discovery Grant program for financial support. The authors thank Rune Lausten (NRC), Paul Hockett (NRC), Christian Evenhuis, and Hongli Tao for helpful discussions and Marc Smits (AMSL) for the magnet design simulations. This work was supported in part by the AMOS program within the Chemical Sciences, Geosciences and Biosciences Division of the Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy.

It is important to note that the TRMS of Fig. 6 offers no direct spectroscopic identification of the neutral S2(1Bu), S1(2 1Ag), or S0(1 1Ag) states of BD. Rather, these TRMS channels comprise various processes in the molecular ionization continuum. As illustrated in Fig. 2, we expect that there will be both one-photon probe (1 + 1′) and two-photon probe (1 + 2′) processes, meaning that there could be several open channels for BD cation fragmentation, with differing timedependences.

The fragmentation data presented in Figs. 5 and 6 may originate from (i) neutral excited state dynamics prior to ionization or (ii) post-ionization photodissociation of a cationic state, or both. In the first process, direct ionization of electrons from lower lying molecular orbitals would lead, via Koopmans’ correlations, to the formation of cation excited states which may subsequently spontaneously fragment. In the second process, direct ionization to the cation ground state followed (within the same probe pulse) by absorption of further probe photons would also lead to the formation of cation excited states which subsequently fragment. From TRMS measurements alone, it is very difficult to discern these two ion fragmentation processes.

The fragmentation channels shown in Table II are labeled (right column) in terms of which Fig. 7 group they belong to. It can be seen that the lower AE (11.4–13.1 eV) channels (53, 52, 39, 28 amu) all belong to group (b), whereas the higher AE (∼15 eV) channels (51, 27, 26 amu) belong to group (c). We remind that the total (1 + 1′) photon energy is 10.37 eV and the total (1 + 2′) photon energy is 15.0 eV, indicating that no fragment channels are open for (1 + 1′) photoionization: these fragment channels must all arise from (1 + 2′) processes. The dominant fragment is the low energy methyl loss channel forming C3H3+, corresponding almost exactly to the origin of the D1 state. The other group (b) channels below 15 eV may correspond to ionizing transitions to the D2–D4 cation states. From energetic considerations alone, the group (c) channels may require significant geometric distortion in order to be adiabatically accessible via a (1 + 2′) process. This may potentially involve the D5 cation state.

The channel forming C3H3+ was further analyzed,37,38 and a two-well Rice–Ramsperger–Kassel–Marcus (RRKM) unimolecular decay mechanism was established.38 Briefly, the BD parent ion formed by an ionizing transition to the D1 (or higher) cation state undergoes rapid internal conversion (kIC > 1011 s−1)46 to form a vibrationally “hot” D0 ground state. Once in the cation ground state, it overcomes a 2.0 eV isomerization barrier to form the 3-methylcyclopropene cation which subsequently fragments via methyl loss, forming C3H3+, at a dissociation threshold of 2.4 eV above the adiabatic IP, with a rate that depends steeply on the excess energy above threshold. This means that vibrationally hot C4H6+ cations with internal energies just above 2.4 eV may not dissociate rapidly enough within the extraction region of the Wiley-McLaren i-TOF to be detected as the C3H3+ fragment: these would fragment during their μs transit of the i-TOF drift tube and would therefore retain the TOF arrival of the C4H6+ parent ion. However, due to the steep energy dependence of the dissociation rates,37,38 at slightly higher internal energies, these would fragment within the TOF extraction region and thus be detected as C3H3+.

The orbital configurations of the neutral and ionic states and corresponding Koopmans’ correlations in BD are homomorphic with those of the longer linear polyene all-trans 2,4,6,8-decatetraene (DT), previously studied in detail.34,47 A key difference is that in DT there is much less large amplitude motion in the excited states: the adiabatic state labels S2 and S1 are arguably better defined. In DT, the single configuration bright S2(11Bu) correlates upon ionization to the D0 ground state, whereas the multi-configurational dark S1(2 1Ag) correlates upon (1 + 1′) ionization to the D1 electronically excited state. This favourable type of Koopmans’ ionization correlation was termed “complementary.”47 In this prior TRPES study,34 the S2 photoelectron band decayed on a 380 fs time scale—the lifetime of the DT bright S2 state—and the S1 photoelectron band rose on the same (380 fs) time scale and subsequently decayed on a ∼2 ps time scale. Both the S2 and S1 states were probed by (1 + 1′) photoionization and the switching as a function of time between the energetically open S2 → D0 and S1 → D1 ionization channels represents the direct observation of non-adiabatic charge and vibrational energy flow during internal conversion. Of relevance to the present study, when the excited state of DT was probed instead via (1 + 2′) ionization [where the (1 + 1′) energy was chosen to be above D0 but below D1], a low kinetic energy band due to (1 + 1′) S2 → D0 ionization was observed along with a time-delayed, higher kinetic energy band due to (1 + 2′) S1 → D1 ionization. In DT, the observed switching from (1 + 1′) to (1 + 2′) ionization as a function of time was directly related47 to the non-adiabatic change in electronic configuration S2 → S1. The dark S1 state could not energetically access the D1 continuum via a (1 + 1′) process. Instead, it made an optical transition to superexcited states (quasi-bound high lying Rydberg states) lying above D0 but which converge to the D1 threshold. Upon absorption of a second probe photon, these superexcited states are directly photoionized into the D1 continuum. In this case, the competition between vibrational autoionization of these superexcited states and second photon absorption favours the latter process. For the S2 state, the (1 + 1′) ionization into D0 is direct and further photon absorption (i.e., above threshold ionization, ATI) cannot compete.

Following (1 + 2′) photoionization of BD, as the cation internal energy increases (slower electrons), the C3H3+ fragment channel opens, but with a dissociation rate that depends on internal energy. For internal energies just above threshold, the rate will be slow enough that parent ions will enter the drift tube and therefore be detected at the parent ion TOF. At high internal energies, the parent ion will fragment rapidly within the extraction region of the i-TOF and cannot therefore be detected at the parent ion TOF. This explains why, in Fig. 10(b), no (1 + 2′) photoelectrons are coincident with the C4H6+ ion in the energy range below, say, 3 eV. The transition from the parent ion to fragment ion TOF is, of course, due to the internal energy dependence of the ion dissociation rate and will not give a very sharp transition energy, but rather a transition region. Nevertheless, we can roughly estimate this transition region energy as follows. As discussed in Sec. II, in the PEPICO detection mode, we applied a “wait time” of ∼185 ns, letting the kinetic electrons escape the interaction region before applying a high voltage pulse to extract the ions. Using the known applied voltages and internal dimensions of the field regions of our PEPICO spectrometer, and a ∼10 ns rise time for the high voltage pulse, we estimate that a C4H6+ parent ion would enter the field-free TOF drift region in about 650 ns. As such, it would necessarily be detected as the parent ion. Converting to a rate, 650 ns would correspond to a dissociation rate of 1.5 × 106 s−1. Referring to the previous experimentally determined BD ion fragmentation rates, we estimate that a fragmentation rate of 1.5 × 106 s−1 corresponds to a “single-photon equivalent” energy of about 11.85 eV.38,39 Converting to electron kinetic energy in Fig. 10, this corresponds to a (1 + 2′) kinetic energy of about 3.15 eV. Roughly speaking, this means that parent ions with less internal energy (i.e., electrons faster than ∼3.1 eV) should be detected as the parent ion. Concomitantly, parent ions with more internal energy (i.e., electrons slower than ∼3.1 eV) should fragment and therefore not be detected as the parent ion. This “transition region” energy is shown as a purple dashed line in Fig. 10. It can be seen that the coincident parent ion signal in Fig. 9(b) “fades” in quite reasonable agreement with this estimate.

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