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A roaming wavepacket in the dynamics of electronically excited 2-hydroxypyridine† Lionel Poisson,*a Dhananjay Nandi,ab Benoıˆt Soep,a Majdi Hochlaf,c Martial Boggio-Pasquad and Jean-Michel Mestdagha How much time does it take for a wavepacket to roam on a multidimensional potential energy surface? This combined theoretical and pump–probe femtosecond time experiment on 2-hydroxypyridine proposes an answer. Bypassing the well-established transition state and conical intersection relaxation pathways, this molecular system undergoes relaxation into the S1 excited state: the central ring is destabilized by the electronic excitation, within B100 fs after absorption of the pump photon, then the H-atom bound to oxygen undergoes a roaming behavior when it couples to other degrees of freedom of
Received 12th July 2013, Accepted 18th October 2013
the molecule. The timescale of the latter process is measured to be B1.3 ps. Further evolution of the wavepacket is either an oscillation onto the S1 potential or a conversion into the triplet state for timescale
DOI: 10.1039/c3cp52923a
larger than B110 ps. Our work introduces a new tool for the understanding of time-resolved relaxation dynamics applied to large molecules through the roaming dynamics characterized by its strongly deloca-
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lized wavepacket on flat molecular potential energy surfaces.
Reaction mechanisms are usually described in the framework of the transition state (TS) theory.1 Whenever the number of involved internal coordinates is small, the representation of the reaction coordinate becomes visual. The original picture of unimolecular dissociation processes goes along the same line. Then, the dissociation occurs by surpassing a well identified potential barrier along a dissociation coordinate. When the barrier height is negligible, an immediate, direct dissociation takes place.2 Ten years ago, a completely novel mechanism, called the roaming mechanism (denoted hereafter as roaming), has emerged where the reaction evolves on a highly multidimensional path which minimizes the energy along each coordinate. Roaming was introduced to account for the unimolecular decomposition of H2CO3,4 and the formation of HCO + H fragments. Both state-of-the-art theoretical and experimental considerations proved that after absorption of a photon and internal conversion to the ground state, a H-atom of H2CO is a
Laboratoire Francis Perrin, CNRS-URA 2453, CEA, IRAMIS, Service des Photons Atomes et Mole´cules, F-91191 Gif-sur-Yvette Cedex, France. E-mail: [email protected] b Indian Institute of Science Education and Research (IISER)-Kolkata, Mohanpur Campus, Mohanpur, Nadia 741252, West Bengal, India c Universite´ Paris-Est, Laboratoire de Mode´lisation et Simulation Multi Echelle, UMR 8208 CNRS, 5 Boulevard Descartes 77454, Marne-la-Valle´e Cedex 2, France. E-mail: [email protected] d Laboratoire de Chimie et Physique Quantiques, IRSAMC, Universite´ de Toulouse(UPS) and CNRS, F-31065 Toulouse Cedex 4, France. E-mail: [email protected] † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c3cp52923a
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destabilized and starts roaming around the HCO moiety in a very flat region of the potential energy surface (PES). Eventually, the other H-atom is abstracted and the dissociation products H 2 + CO are formed. Strictly speaking, no true reaction coordinate can be identified in this case. Generally, TS and roaming are competing in nature. This is reflected by a bimodal distribution of the population within the ro-vibrational states of the CO products after the dissociation is completed. Since this pioneering work, it was shown that the roaming mechanism can be invoked to explain many unimolecular decays. It represents active theoretical and experimental fields of investigations in physics, chemistry and atmospheric sciences. 5,6 Applications are expected in biology (e.g., DNA damage after radiation 7), emitting dyes, 8 conjugated polymers, 9 nano-sized graphene sheets10 and more generally in all cases where molecular electronic excited states are involved. For roaming, previous studies were mainly concerned with the identification of the reaction pathways based on product analysis. It turns out that no direct real-time experimental exploration of the roaming movement exists. The only information concerning this movement stems from quasiclassical trajectory calculations.4,11 Presently, we go beyond these considerations in the sense that we explore a wavepacket evolution in the real-time domain as it accesses a roaming dynamics. We have chosen a situation where roaming occurs within an excited electronic state. Hence, the roaming wavepacket could be probed using the femtosecond time-resolved photoelectron spectroscopy (fs-TRPES) technique12 in a femtosecond pump–probe experiment on the
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2-hydroxypyridine (2-HP) molecule
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. This DNA analog is
the candidate of choice for that purpose. Indeed, it is a fluorescent molecule, which does not dissociate or isomerize when excited to the S1 state. Interestingly, we anticipate that the H-atom may be substantially destabilized by the electronic excitation and could reach roaming behavior when coupled to other degrees of freedom of the molecule. The experimental work is complemented by extensive ab initio calculations. Experimentally, the 2-HP molecule was seeded in a molecular beam and excited to the S1 state using the pump laser (264 nm, 37 880 cm1, 4.70 eV) through a p–p* transition. Although 2-pyridone, the tautomer of 2-HP, should be present as a minor compound in the beam (ratio 1 : 313–16), IR-UV double resonance studies17–19 showed that the pump at 264 nm excites essentially 2-HP with an excess energy of 1760 cm1 above the S1 ’ S0 threshold. The pump pulse creates a wavepacket. The time evolution of such a wavepacket has been probed by another laser (at 793 nm, 12 610 cm1, 1.56 eV) through multiphoton ionization after a variable time delay. The fs-TRPES technique12,20–22 with a Velocity Map Imaging (VMI) spectrometer23 is used to obtain the dynamical information on the quantum state of the system as a function of the pump–probe delay. The details of the experimental setup and technique are described elsewhere.24 It is noteworthy that the experiments with a probe at 396 nm were also performed in order to quantify the multiphoton ionization process. Through the comparison of the signals recorded at 793 and 396 nm, we certainly confirm that the results reported here with the probe at 793 nm operates through a 4-photon ionization process with a negligible 5-photon component. Theoretically, ab initio calculations were performed to determine the topology of the PESs associated with the S0, S1 and S2 states of 2-HP, using the MOLPRO quantum chemistry package.25 Geometry optimizations of critical structures were performed with the Cs symmetry constraint first, and then without any symmetry constraint at the CASSCF level of theory,26 using the correlationconsistent triple-zeta (cc-pVTZ) basis set of Dunning.27 The S0 ground state and S1(p,p*) excited state were optimized using the full valence p active space, i.e. 8 electrons are distributed in 7 orbitals (8e,7o). The S2(n,p*) requires adding the non-bonding orbital of the N atom resulting in a (10e,8o) active space. These calculations showed that for each state, one of the p orbitals localized on the hydroxyl group remains strongly doubly occupied. Thus, this orbital was removed subsequently from the active space, leaving a (6e,6o) active space to optimize S0 and S1, and a (8e,7o) active space to optimize the S2 state. In this way, convergence problems when CASSCF is performed without any symmetry constraint are avoided. The effect of leaving out this orbital from the active space was found to be small. State-averaged CASSCF(8e,7o) calculations over the three lowest singlet states were performed at the state-specific optimized geometries. To correct for the lack of dynamic electron correlation in CASSCF, MS-CASPT2 (multistate multireference second-order perturbation theory)28 and CIPT2 (coupling between multireference configuration interaction and multireference perturbation theory)29 calculations were
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performed using the previously obtained SA3-CASSCF(8e,7o) wavefunctions as a reference. A level-shift of 0.2 hartree was adopted to avoid intruder state problems in the excited-state calculations. Geometry optimizations were also performed at the MS-CASPT2 level in order to evaluate the effect of dynamic electron correlation on the ground and excited state equilibrium structures and on the potential energy landscape.
Calculation results The results of the geometry optimizations are shown in Fig. 1. A planar structure (Fig. 1b) was located for the S1(p,p*) minimum in which the bond lengths within the pyridine ring have increased relative to the ground-state planar structure (Fig. 1a). This is reminiscent of the breathing mode observed following photoexcitation of benzene in the S1(p,p*) state, for example.30 The optimized planar structure for the S1(n,p*) state (Fig. 1c) involves mainly stretching of the two C–N bonds relative to the ground-state structure, along with a shortening of one C–C bond and a lengthening of another C–C bond. This structure
Fig. 1 Optimized structures of all critical points: (a) S0 Cs minimum, (b) S1(p,p*) Cs minimum, (c) S1(n,p*) Cs saddle point, (d) S1(p,p*)/S2(n,p*) Cs MECI, (e) S1(n,p*) minimum, (f) S1(p,p*) - S1(n,p*) TS1. The normal font corresponds to state-specific (state-averaged for MECI, (d)) CASSCF optimized geometries. The bold font corresponds to MS-CASPT2 optimized geometries.
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Table 1 CASSCF, MS-CASPT2 and CIPT2 relative energies computed at the CASSCF optimized geometries. Available experimental and theoretical data from the literature are also reported. All energies are given in eV relative to the ground-state energy
Table 2 MS-CASPT2 and CIPT2 relative energies computed at the MSCASPT2 optimized geometries. All energies are given in eV relative to the ground-state energy
State CASSCF (8e,7o)
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1 0
S0(1 A 11A 0 21A 0 11A00
CIPT2 (8e,7o)
Ref. 31 Expt.
) Cs equilibrium geometry (minimum) 0 0 0 0 5.128 4.841 4.794 5.942 5.566 5.528
S1(21A 0 11A 0 21A 0 11A00 S1(21A 11A 21A 31A
MS-CASPT2 (8e,7o)
Ref. 32 CASPT2
Ref. 33 MRCI
0 4.75 5.57
0
p,p*) Cs equilibrium geometry (minimum) 0.241 0.162 0.189 4.853 4.539 4.507 4.48 4.28 5.990 5.620 5.586
CIPT2 (8e,7o)
S0(1 A ) Cs equilibrium geometry (minimum) 0 11A 0 4.760 21A 0 1 00 5.593 1A
0 4.708 5.545
S1(21A 0 p,p*) Cs equilibrium geometry (minimum) 0.236 0.267 11A 0 4.525 4.504 21A 0 5.829 5.785 11A00 4.94
n,p*) non-planar equilibrium geometry (minimum) 0.991 0.834 0.932 5.201 4.765 4.931 5.751 5.392 5.415
S1(11A00 11A 0 21A 0 11A00
MS-CASPT2 (8e,7o)
1 0
S1(11A00 n,p*) Cs equilibrium geometry (saddle point) 0.674 0.663 11A 0 5.347 5.256 21A 0 5.002 4.943 11A00
n,p*) Cs equilibrium geometry (saddle point) 0.691 0.652 0.643 5.567 5.307 5.219 5.225 5.034 4.944 5.02
proved to be a saddle point. In fact, the true minimum is found upon slight folding of the pyridine ring and moving the hydrogen of the hydroxyl group out-of-plane (Fig. 1e). Energies computed at the CASSCF and MS-CASPT2 optimized geometries are reported in Tables 1 and 2, respectively. The table sections correspond to the geometries obtained above for the S0, S1 and S2 states, as labeled in the tables. The calculated adiabatic transition energy to the S1(p,p*) state can be compared to the 0–0 band of the S1 ’ S0 electronic transition measured experimentally, when neglecting the zero-point energy correction. Table 1 shows that the CASSCF calculated value overestimates by 0.37 eV the experimental determination of Pratt and coworkers.31 As expected, this result is considerably improved by the calculations at the MS-CASPT2 and CIPT2 levels, which overestimate the experiment by only 0.06 and 0.03 eV, respectively. Using MS-CASPT2 optimized structures (Table 2), the error is further reduced to 0.05 and 0.02 eV, respectively. The accuracy of the present calculation is thus largely improved relative to that of Sobolewski and Adamowicz,32 which underestimates the experimental results by 0.2 eV. The MRCI calculation by Li et al.33 is further away (+0.46 eV). Note that if one takes into account the zero-point energy correction computed at the CASSCF level, the S1 ’ S0 electronic transition is further reduced by 0.12 eV. Based on the energetics reported in Table 1, the most important point that emerges from the calculations is that the two states S1(p,p*) and S2(n,p*) cross each other. At the (p,p*) minimum geometry, the (n,p*) state lies ca. 1.1 eV above (p,p*), whereas at the (n,p*) minimum geometry, the (p,p*) state lies ca. 0.6 eV above (n,p*). As a result, the minimum found for the (n,p*) state lies on the adiabatic S1 PES and is denoted S1(n,p*) minimum. In fact, the S1(p,p*) and S2(n,p*) states cross at a minimum-energy conical intersection (MECI)34 (Fig. 1d) located only ca. 0.1 eV above the S1(n,p*) minimum at the CASSCF level. Fig. 2 (top panel) illustrates the topology of this
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Fig. 2 Schematic potential energy landscape of the adiabatic S1 and S2 electronic states of 2-HP. The PESs are represented along two coordinates, X1 and X2, which lift the degeneracy at the S1/S2 MECI. X1 corresponds to the gradient difference vector at S1/S2 MECI and X2 combines the derivative coupling vector at S1/S2 MECI and transition vector at S1(n,p*) SP. The labels show the remarkable points of the PES. (top) Schematic view of the CASSCF landscape with the two symmetry-equivalent S1(n,p*) nonplanar minima and the two transition states (TS1). (bottom) Schematic view of the MS-CASPT2 landscape with its S1(n,p*) saddle point (SP).
PES. On each side of this MECI lie two symmetry-equivalent transition states (TS1). They connect adiabatically the (p,p*) and the (n,p*) minima on the S1 PES. These transition states are located less than 0.1 eV above the S1(n,p*) minimum at the CASSCF level. Note also that the S1(n,p*) minimum is slightly higher in energy (0.2–0.4 eV) than the S1(p,p*) minimum and is
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located at 4.76 and 4.93 eV above S0 at MS-CASPT2 and CIPT2 levels, respectively. Taking into account the zero-point energy correction computed at the CASSCF level, the S1(n,p*) is further lowered by 0.17 eV. Based on the present topology, the S1 adiabatic surface is expected to be highly anharmonic in the region of excitation by the pump laser. The pump laser will provide sufficient available energy to the system to explore the (n,p*) region of the S1 PES. It is worth noting also that at the MS-CASPT2 level (Fig. 2, bottom panel), a subtle change of topology occurs, as the S1(n,p*) non-planar shallow minimum disappears. Thus, the S1(n,p*) region of the PES is accessed from the S1(p,p*) minimum via a fairly flat plateau.
Experimental results A series of 2-D photoelectron images were recorded using a VMI spectrometer for various time delays t ranging from 600 fs to +470 ps. The corresponding 3D-distributions were reconstructed24,35 using the pBASEX inversion method.36 As an illustration, Fig. 3 represents a reconstructed image taken at pump–probe delay of 130 fs. Both of the pump and probe lasers are vertically polarized. The radial distribution reflects the velocity distribution of photoelectrons (hence the photoelectron energy) and the anisotropy of the image is a signature of their angular distribution. The expansion of the angular basis set used in the image reconstruction goes up to the 4th Legendre polynomial function.37 Accordingly, the reconstructed image is described by three matrices a(E,t), b2(E,t) and b4(E,t) according to: a(E,t)[1 + b2(E,t) P2(cos y) + b4(E,t) P4(cos y)]
(1)
where t is the pump–probe delay, E is the kinetic energy of the electrons, y corresponds to their direction with respect to the polarization of the probe laser, and P2,4(cos y) are Legendre polynomials describing the anisotropy of the electron distribution. The matrices a(E,t), a(E,t) b2(E,t) and a(E,t) b4(E,t) contain the information on the time-resolved photoelectron spectra and on the polarized component of the image at the second and fourth orders, respectively. The decomposition of
Fig. 3 Equatorial cut through the 3D photoelectron distribution after reconstruction from a 2D VMI image. The radius is proportional to the photoelectron velocity. The intensity was multiplied by the radius to enhance the Rydberg structure. The pump–probe time delay was 130 fs. Both laser polarizations are parallel, the direction being indicated on the image by the white arrow.
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Fig. 4 Average photoelectron spectra with the probe laser tuned at 793. On the left is displayed the average signal calculated on the range 0–1.7 ps with each of the P0, P2 and P4 components of the photoelectron distribution, hence documenting a(E,t), a(E,t)b2(E,t) and a(E,t)b4(E,t), respectively. On the right is displayed the same information but averaged over delay times between 200 and 470 ps. Their relative intensity is therefore arbitrary. The dashed vertical lines guide the eyes through the spectra.
average spectra are presented on Fig. 4. It shows striking structures. One can notice that the b2(E), and b4(E) are rising with the energy. This is mainly due to the superposition of several pathways in the ionization process of the molecule, being unpolarized and of low energy. Looking at a highly polarized signal is a way to reduce the number of components and to focus on specific ionization channels. For this reason, only the corresponding spectrum, given by a(E,t) b4(E,t), is considered P hereafter. Its average aðE; tÞ b4 ðE; tÞ over various ranges of t
time delays is shown in Fig. 5. The bottom curve in Fig. 5 corresponds to an average over delay times between 200 and 470 ps whereas the same for the time delay between 0 and 1.7 ps is depicted in the middle. Both exhibit the same series of bands but the overall shape of the spectrum is different: the intensity ratio between the high energy bands and the low energy ones decreases substantially by increasing the delay time from the 0–1.7 ps range (middle curves) to the 200–470 ps range (bottom curves). These series of
Fig. 5 (top) Fit functions used for the a(E,t) b4(E,t) components of the P photoelectron spectra. (middle) Average photoelectron spectra ta(E,t) b4(E,t) associated with the P4 components of the photoelectron distribution. The average carries over delay times between 0 and 1.7 ps. The filled curves are the components from the fits. (bottom) Same as (middle) for the range going from 200 and 470 ps. (all) The vertical black dashed lines are the values expected from a Rydberg fingerprint with a d = 0.08.
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bands (0.70, 1.0, 1.19 and 1.29 eV and the barely distinguishable structures in the high energy tail of these curves) can be easily assigned with the help of Rydberg Fingerprint Spectroscopy introduced by Weber and coworkers as a tool to analyze photoelectron spectra in fs-TRPES experiments when the probe operates via multiphoton ionization.38,39 Accordingly, the present series of peaks are adequately accounted for by a Rydberg fingerprint (RF) series starting with the principal quantum number n = 4 for the 0.70 eV peak with a quantum defect of d = 0.08. This small value of d suggests that an nd Rydberg series is in action, which is coherent with the current analysis of the P4 anisotropy component of the photoelectrons. An important issue relates to the fact that the relative intensity of the RF peaks is not the same whether the photoelectron spectrum corresponds to the average of pump–probe delays in the range 0–1.7 ps (middle curve) or 200–470 ps (bottom curve). This indicates that different electronic states (this will be refined below) are probed when the delay time is varied. The simplest assumption is that two energy states are involved and that the system switches from one to the other between 0–1.7 ps and 200–470 ps. Accordingly, the curves used for fitting the P4 component of the photoelectron spectra in the top panel of Fig. 5 provide information on the RF spectrum of these two states, populated along the relaxation dynamics. Each RF is composed by a series of Gaussian peaks centered where the Rydberg resonance progression are expected for n = 4 and d = 0.08 (see above). An extra Gaussian peak centered at 2.29 eV accounts for the ionization with 5 793 nm photons. The two RF series and the extra peak were used to fit the spectra measured as a function of the delay time. The corresponding results are shown in Fig. 6. The curves running through the experimental points use a kinetic model, which assumes a sequential population transfer between four transients according to tA
tB
tC
A ! B ! C ! D
(2)
where tA, tB, tC represent the decay times from one transient to the other. Transient D is assumed to be stable at the timescale of the experiment. The values given by the fit are given in Table 3.
Fig. 6 Time dependence of the photoelectron signal. Note the change in the horizontal scale at 8 ps (0–8 ps on the left of the vertical dashed line, 8–500 ps on the right). The experimental results of various colors correspond to the RF series used to fit the photoelectron spectra (see Fig. 5). The curves running through the experimental points are fitted using the kinetic model using the parameters given in eqn (2).
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Table 3 Time decay and error bars obtained using the simultaneous fit of the three curves with a sequential model
Time
Value
tA tB tC Laser autocorrelation
106 45 fs 1.26 0.24 ps 112 44 ps 85 fs
Discussion The irregularity in the absorption spectrum of 2-HP observed by Bernstein and coworkers40 appears 500 cm1 from the band origin (more recently measured at 36 118.69 cm1 by Pratt and coworkers31). This indicates that the non-harmonic region of the S1 PES is accessible with a total energy of 36 620 cm1 or larger. The energy provided by the pump laser, 37 880 cm1, is larger than this value. Hence, the wavepacket is launched by the pump laser in a region of high anharmonicity and is expected to spread quite rapidly and to reach the regions where the initial (p,p*) character of the PES has switched to the (n,p*) character. We thus anticipate that after a delay time, the wavepacket will feature a superposition of (p,p*) and (n,p*) characters in the S1 PES. The topology of the S1 PES in Fig. 2 confirms such high anharmonicity in the region of excitation by the pump laser. Due to a MECI with the S2 PES, the S1 PES has a very peculiar shape and electronic conformation (see Fig. 2). It has the (p,p*) character near the absolute minimum and in the Franck–Condon region of excitation where the molecule is planar. Then, the wavepacket starts moving and spreading around, driven by slopes in the S1 PES. Its electronic character switches to (n,p*) outside the Franck– Condon region. The (n,p*) ‘‘dark’’ state, as denoted in the literature,17–19,31,40,41 is not associated with a stable position on the S1 PES but corresponds to a flat extended region quite far outside the Franck–Condon region of excitation, where the molecule is no more planar (Fig. 2). Importantly, these regions are accessible energetically with the currently used pump photons at 4.70 eV, at least when accounting for the zero-point energy in the ground state. As can be seen in Fig. 6, the photoelectron spectra are dominated by two nd (n Z 4) Rydberg Fingerprint (RF) series. A priori, each RF series documents a different energy state. Based on previous discussion, we can certify that these two Rydberg Fingerprint series do not probe different energy states stricto sensu but a single one, for instance S1, in two different locations of its PES where the electronic configurations are different, namely (p,p*) in the Franck–Condon region of excitation and (n,p*) after deformation of the molecule. This situation is quite amusing since it leads to probing the time evolution between ‘two quantum states’ in a relatively largesized molecular system. Such situation is well known in Atomic Physics but not in Molecular Physics. The intensity of each Rydberg series (red and green curves in Fig. 6) gives insight into the extension of the wavepacket in these regions. The signal given by the red curve in Fig. 6 is not vanishing at zero time delay and decays at positive times with the time constant tB B 1.3 ps. Likely, it is associated with the part of the wavepacket which overlaps with the Franck–Condon
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region where S1 has the (p,p*) character. Similarly, the green curve which goes up from zero with the same time constant tB documents the wavepacket when it spreads into the fairly flat region of the S1(n,p*) PES. The green and red curves run almost together at intermediate delay time, both having half the initial intensity of the red one. This indicates that about one half of the wavepacket is transferred from the region of the (p,p*) character to that of the (n,p*) character through deformation which makes 2-HP non-planar. For longer delay times, the population of both S1(p,p*) and S1(n,p*) wavepackets decays with the same time constant tC B 110 ps. Such a slow decay time could be associated with a transfer to triplet states through a standard intersystem coupling.42 At 500 ps delay, the red curve, which reflects the wavepacket in the S1(p,p*) region, goes down to zero whereas the green curve (wavepacket in the S1(n,p*) region) does not (cf. Fig. 6). As an interpretation, we believe that the wavepacket somehow oscillates between the two S1 regions and is unfilled, with a unique sink for the triplet state located somewhere in the S1(p,p*) region, whereas no sink exists in the S1(n,p*) region. Hence equilibration would refill the S1(p,p*) region from the S1(n,p*) region. We expect that either a small barrier exists between the S1(p,p*) and S1(n,p*) regions along the X1 coordinate, which would block the refill when enough energy is relaxed to other coordinates than X1, or that the plateau in the green curve corresponds to the detection of the triplet state. The second scenario is more likely to occur here. The blue curve in Fig. 6 corresponds to the ionization by a fifth probe photon. The large excess energy which is provided allows probing the molecule without much state sensitivity at all delay times. A very short timescale tA B 110 fs appears almost within the cross-correlation between the pump and probe laser pulses. It is assigned to a rapid movement of the wavepacket outside the Franck–Condon region of excitation, driven by forces towards the absolute minimum of the S1 PES which, as the Franck–Condon region of excitation, corresponds to a region of (p,p*) character. This affects specific channels which are enhanced by both an intermediate resonance in the ionization process and the strong localization of the wavepacket just after excitation. It may depopulate other ionization channels, which is not observed here. The remaining part of the blue curve is well described by the two times constants tB B 1.3 ps and tC B 110 ps. With five probe photons, it seems certain that the triplet state can be ionized. Again, this is in line with the decay of the green curve to a plateau on Fig. 6.
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regions of the S1 PES which have (n,p*) character. There exists a fairly extended plateau, where the out-of-plane movement of the H-atom bonded to oxygen and the deformation of the ring are coupled and lead to a variety of geometrical arrangements within close energy domains. This nicely creates the conditions for a roaming movement and tB appears as the timescale for the wavepacket to reach the roaming dynamics. Finally, a decay occurs with the time constant tC, down to low lying triplet states. Since the second timescale corresponds to the access of a roaming dynamics, we conclude that the intersystem energy transfer is accessed through a roaming behavior. This mechanistic picture is another way to describe a reality approached using the theory of radiationless transitions formulated by Jortner and colleagues.42,43 This theory is a dissipative description (the Fermi Golden rule) of the evolution where an initially bright state decays into a quasicontinuum of degenerate levels weakly coupled to it. Here the roaming dynamics is very similar to a specific situation that was named the ‘strong intermediate coupling’.44 In the latter situation a rapid initial decay occurring in a subset of strongly coupled levels where the excitation lingers until the final decay could occur in the remaining set of degenerate levels. The profound similarity in the description comes from the multidimensional character of the roaming dynamics (mechanistic) and the non-radiative (dissipative) approaches. The present work represents the first study in timescale measurements for the roaming dynamics.
Conclusions The present situation is significantly different from that met in standard TRPES studies, which allowed us to probe the roaming wavepacket mechanism. In the case of the pyrazine multiphoton ionization probe45 experiment two distinct states S2(p,p*) and S1(n,p*) are detected and the dynamics of transfer from the upper state to the lower state is detailed. In the present study, two regions of different electronic configurations of the same adiabatic state are detected and the equilibration time of the wavepacket between the two regions is probed. Such situations could be more common than simply applying to the dynamics of 2-HP. Indeed, such PES topology may be frequently encountered when the density of states increases with the size of the system. Thus, roaming mechanisms that involve crossing between adiabatic PESs may become more prevalent and have a much larger impact in photochemistry than previously anticipated.
Towards roaming dynamics
Acknowledgements
Excitation by the pump laser launches a wavepacket on the S1 PES in the region where it has the (p,p*) character. Its dynamics was followed experimentally and a multiexponential evolution was observed using three different timescales tA B 110 fs, tB B 1.3 ps and tC B 110 ps, respectively. tA is assigned to the movement of the initial wavepacket outside the Franck–Condon region of excitation along the S1 PES still staying in a region of the PES where the electron configuration is dominantly in (p,p*). tB is assigned to the spread of the wavepacket towards the
D. Nandi acknowledges the financial support from the ‘‘Triangle de la physique’’ for supporting this research under project ‘‘2008062T DYNANEX’’. B.S., L.P. and J.-M.M. thank EU-ITN project ICONIC-238671 for funding.
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References 1 H. Eyring and M. Polanyi, Z. Phys. Chem., Abt. B, 1931, 12, 279. 2 P. Pechukas, Annu. Rev. Phys. Chem., 1981, 32, 159–177.
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3 D. Townsend, S. A. Lahankar, S. K. Lee, S. D. Chambreau, A. G. Suits, X. Zhang, J. Rheinecker, L. B. Harding and J. M. Bowman, Science, 2004, 306, 1158–1161. 4 J. M. Bowman and A. G. Suits, Phys. Today, 2011, 64, 33–37. 5 M. J. T. Jordan and S. H. Kable, Science, 2012, 335, 1054–1055. 6 M. P. Grubb, M. L. Warter, H. Xiao, S. Maeda, K. Morokuma and S. W. North, Science, 2012, 335, 1075–1078. 7 C. T. Middleton, K. de La Harpe, C. Su, Y. K. Law, C. E. Crespo-Hernandez and B. Kohler, Annu. Rev. Phys. Chem., Annual Reviews, Palo Alto, 2009, vol. 60, pp. 217–239. 8 E. Bremond, M. E. Alberto, N. Russo, G. Ricci, I. Ciofini and C. Adamo, Phys. Chem. Chem. Phys., 2013, 15, 10019–10027, DOI: 10.1039/C3CP43784A. 9 S. Boussaad and N. J. Tao, Nano Lett., 2003, 3, 1173–1176. 10 J. Lahiri, Y. Lin, P. Bozkurt, I. I. Oleynik and M. Batzill, Nat. Nano, 2010, 5, 326–329. 11 S. A. Lahankar, V. Goncharov, F. Suits, J. D. Farnum, J. M. Bowman and A. G. Suits, Chem. Phys., 2008, 347, 288–299. 12 A. Stolow and J. G. Underwood, Adv. Chem. Phys., 2008, 139, 497–583. 13 P. Beak and F. S. Fry, J. Am. Chem. Soc., 1973, 95, 1700–1702. 14 P. Beak, Acc. Chem. Res., 1977, 10, 186–192. 15 L. D. Hatherley, R. D. Brown, P. D. Godfrey, A. P. Pierlot, W. Caminati, D. Damiani, S. Melandri and L. B. Favero, J. Phys. Chem., 1993, 97, 46–51. 16 J. C. Poully, J. P. Schermann, N. Nieuwjaer, F. Lecomte, G. Gregoire, C. Desfrancois, G. A. Garcia, L. Nahon, D. Nandi, L. Poisson and M. Hochlaf, Phys. Chem. Chem. Phys., 2010, 12, 3566–3572. 17 Y. Matsuda, T. Ebata and N. Mikami, J. Chem. Phys., 1999, 110, 8397–8407. 18 Y. Matsuda, T. Ebata and N. Mikami, J. Chem. Phys., 2000, 113, 573–580. 19 Y. Matsuda, T. Ebata and N. Mikami, J. Phys. Chem. A, 2001, 105, 3475–3480. 20 T. Suzuki and B. J. Whitaker, Int. Rev. Phys. Chem., 2001, 20, 313–356. 21 A. Stolow, A. E. Bragg and D. M. Neumark, Chem. Rev., 2004, 104, 1719–1757. 22 T. Suzuki, Annu. Rev. Phys. Chem., 2006, 57, 555–592. 23 A. Eppink and D. H. Parker, Rev. Sci. Instrum., 1997, 68, 3477–3484.
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24 E. Gloaguen, J. M. Mestdagh, L. Poisson, F. Lepetit, J. P. Visticot, B. Soep, M. Coroiu, A. Eppink and D. H. Parker, J. Am. Chem. Soc., 2005, 127, 16529–16534. 25 H.J. Werner andP.J. Knowles, http://www.molpro.net, 2010. 26 P. J. Knowles and H. J. Werner, Chem. Phys. Lett., 1985, 115, 259–267. 27 J. T. H. Dunning, J. Chem. Phys., 1989, 90, 1007. ´s, 28 J. Finley, P. Malmqvist, B. O. Roos and L. Serrano-Andre Chem. Phys. Lett., 1998, 288, 299–306. 29 P. Celani, H. Stoll, H. J. Werner and P. J. Knowles, Mol. Phys., 2004, 102, 2369–2379. 30 I. J. Palmer, I. N. Ragazos, F. Bernardi, M. Olivucci and M. A. Robb, J. Am. Chem. Soc., 1993, 115, 673–682. 31 D. R. Borst, J. R. Roscioli and D. W. Pratt, J. Phys. Chem. A, 2002, 106, 4022–4027. 32 A. L. Sobolewski and L. Adamowicz, J. Phys. Chem., 1996, 100, 3933–3941. 33 Q. S. Li, W. H. Fang and J. G. Yu, J. Phys. Chem. A, 2005, 109, 3983–3990. 34 D. R. Yarkony, Rev. Mod. Phys., 1996, 68, 985–1013. 35 L. Poisson, P. Roubin, S. Coussan, B. Soep and J. M. Mestdagh, J. Am. Chem. Soc., 2008, 130, 2974–2983. 36 G. A. Garcia, L. Nahon and I. Powis, Rev. Sci. Instrum., 2004, 75, 4989–4996. 37 A. V. Baklanov, L. M. C. Janssen, D. H. Parker, L. Poisson, B. Soep, J. M. Mestdagh and O. Gobert, J. Chem. Phys., 2008, 129, 214306. 38 J. L. Gosselin and P. M. Weber, J. Phys. Chem. A, 2005, 109, 4899–4904. 39 N. Kuthirummal and P. M. Weber, J. Mol. Struct., 2006, 787, 163–166. 40 M. R. Nimlos, D. F. Kelley and E. R. Bernstein, J. Phys. Chem., 1989, 93, 643–651. 41 H. Ozeki, M. C. R. Cockett, K. Okuyama, M. Takahashi and K. Kimura, J. Phys. Chem., 1995, 99, 8608–8612. 42 M. Bixon and J. Jortner, J. Chem. Phys., 1968, 48, 715–726. 43 J. Jortner, S. A. Rice and R. M. Hochstrasser, Adv. Photochem., 1969, 7, 149–309. 44 F. Lahmani, A. Tramer and C. Tric, J. Chem. Phys., 1974, 60, 4431–4447. 45 J. K. Song, M. Tsubouchi and T. Suzuki, J. Chem. Phys., 2001, 115, 8810–8818.
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PAPER
Cite this: Phys. Chem. Chem. Phys., 2014, 16, 581
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A roaming wavepacket in the dynamics of electronically excited 2-hydroxypyridine† Lionel Poisson,*a Dhananjay Nandi,ab Benoıˆt Soep,a Majdi Hochlaf,c Martial Boggio-Pasquad and Jean-Michel Mestdagha How much time does it take for a wavepacket to roam on a multidimensional potential energy surface? This combined theoretical and pump–probe femtosecond time experiment on 2-hydroxypyridine proposes an answer. Bypassing the well-established transition state and conical intersection relaxation pathways, this molecular system undergoes relaxation into the S1 excited state: the central ring is destabilized by the electronic excitation, within B100 fs after absorption of the pump photon, then the H-atom bound to oxygen undergoes a roaming behavior when it couples to other degrees of freedom of
Received 12th July 2013, Accepted 18th October 2013
the molecule. The timescale of the latter process is measured to be B1.3 ps. Further evolution of the wavepacket is either an oscillation onto the S1 potential or a conversion into the triplet state for timescale
DOI: 10.1039/c3cp52923a
larger than B110 ps. Our work introduces a new tool for the understanding of time-resolved relaxation dynamics applied to large molecules through the roaming dynamics characterized by its strongly deloca-
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lized wavepacket on flat molecular potential energy surfaces.
Reaction mechanisms are usually described in the framework of the transition state (TS) theory.1 Whenever the number of involved internal coordinates is small, the representation of the reaction coordinate becomes visual. The original picture of unimolecular dissociation processes goes along the same line. Then, the dissociation occurs by surpassing a well identified potential barrier along a dissociation coordinate. When the barrier height is negligible, an immediate, direct dissociation takes place.2 Ten years ago, a completely novel mechanism, called the roaming mechanism (denoted hereafter as roaming), has emerged where the reaction evolves on a highly multidimensional path which minimizes the energy along each coordinate. Roaming was introduced to account for the unimolecular decomposition of H2CO3,4 and the formation of HCO + H fragments. Both state-of-the-art theoretical and experimental considerations proved that after absorption of a photon and internal conversion to the ground state, a H-atom of H2CO is a
Laboratoire Francis Perrin, CNRS-URA 2453, CEA, IRAMIS, Service des Photons Atomes et Mole´cules, F-91191 Gif-sur-Yvette Cedex, France. E-mail: [email protected] b Indian Institute of Science Education and Research (IISER)-Kolkata, Mohanpur Campus, Mohanpur, Nadia 741252, West Bengal, India c Universite´ Paris-Est, Laboratoire de Mode´lisation et Simulation Multi Echelle, UMR 8208 CNRS, 5 Boulevard Descartes 77454, Marne-la-Valle´e Cedex 2, France. E-mail: [email protected] d Laboratoire de Chimie et Physique Quantiques, IRSAMC, Universite´ de Toulouse(UPS) and CNRS, F-31065 Toulouse Cedex 4, France. E-mail: [email protected] † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c3cp52923a
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destabilized and starts roaming around the HCO moiety in a very flat region of the potential energy surface (PES). Eventually, the other H-atom is abstracted and the dissociation products H 2 + CO are formed. Strictly speaking, no true reaction coordinate can be identified in this case. Generally, TS and roaming are competing in nature. This is reflected by a bimodal distribution of the population within the ro-vibrational states of the CO products after the dissociation is completed. Since this pioneering work, it was shown that the roaming mechanism can be invoked to explain many unimolecular decays. It represents active theoretical and experimental fields of investigations in physics, chemistry and atmospheric sciences. 5,6 Applications are expected in biology (e.g., DNA damage after radiation 7), emitting dyes, 8 conjugated polymers, 9 nano-sized graphene sheets10 and more generally in all cases where molecular electronic excited states are involved. For roaming, previous studies were mainly concerned with the identification of the reaction pathways based on product analysis. It turns out that no direct real-time experimental exploration of the roaming movement exists. The only information concerning this movement stems from quasiclassical trajectory calculations.4,11 Presently, we go beyond these considerations in the sense that we explore a wavepacket evolution in the real-time domain as it accesses a roaming dynamics. We have chosen a situation where roaming occurs within an excited electronic state. Hence, the roaming wavepacket could be probed using the femtosecond time-resolved photoelectron spectroscopy (fs-TRPES) technique12 in a femtosecond pump–probe experiment on the
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2-hydroxypyridine (2-HP) molecule
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. This DNA analog is
the candidate of choice for that purpose. Indeed, it is a fluorescent molecule, which does not dissociate or isomerize when excited to the S1 state. Interestingly, we anticipate that the H-atom may be substantially destabilized by the electronic excitation and could reach roaming behavior when coupled to other degrees of freedom of the molecule. The experimental work is complemented by extensive ab initio calculations. Experimentally, the 2-HP molecule was seeded in a molecular beam and excited to the S1 state using the pump laser (264 nm, 37 880 cm1, 4.70 eV) through a p–p* transition. Although 2-pyridone, the tautomer of 2-HP, should be present as a minor compound in the beam (ratio 1 : 313–16), IR-UV double resonance studies17–19 showed that the pump at 264 nm excites essentially 2-HP with an excess energy of 1760 cm1 above the S1 ’ S0 threshold. The pump pulse creates a wavepacket. The time evolution of such a wavepacket has been probed by another laser (at 793 nm, 12 610 cm1, 1.56 eV) through multiphoton ionization after a variable time delay. The fs-TRPES technique12,20–22 with a Velocity Map Imaging (VMI) spectrometer23 is used to obtain the dynamical information on the quantum state of the system as a function of the pump–probe delay. The details of the experimental setup and technique are described elsewhere.24 It is noteworthy that the experiments with a probe at 396 nm were also performed in order to quantify the multiphoton ionization process. Through the comparison of the signals recorded at 793 and 396 nm, we certainly confirm that the results reported here with the probe at 793 nm operates through a 4-photon ionization process with a negligible 5-photon component. Theoretically, ab initio calculations were performed to determine the topology of the PESs associated with the S0, S1 and S2 states of 2-HP, using the MOLPRO quantum chemistry package.25 Geometry optimizations of critical structures were performed with the Cs symmetry constraint first, and then without any symmetry constraint at the CASSCF level of theory,26 using the correlationconsistent triple-zeta (cc-pVTZ) basis set of Dunning.27 The S0 ground state and S1(p,p*) excited state were optimized using the full valence p active space, i.e. 8 electrons are distributed in 7 orbitals (8e,7o). The S2(n,p*) requires adding the non-bonding orbital of the N atom resulting in a (10e,8o) active space. These calculations showed that for each state, one of the p orbitals localized on the hydroxyl group remains strongly doubly occupied. Thus, this orbital was removed subsequently from the active space, leaving a (6e,6o) active space to optimize S0 and S1, and a (8e,7o) active space to optimize the S2 state. In this way, convergence problems when CASSCF is performed without any symmetry constraint are avoided. The effect of leaving out this orbital from the active space was found to be small. State-averaged CASSCF(8e,7o) calculations over the three lowest singlet states were performed at the state-specific optimized geometries. To correct for the lack of dynamic electron correlation in CASSCF, MS-CASPT2 (multistate multireference second-order perturbation theory)28 and CIPT2 (coupling between multireference configuration interaction and multireference perturbation theory)29 calculations were
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performed using the previously obtained SA3-CASSCF(8e,7o) wavefunctions as a reference. A level-shift of 0.2 hartree was adopted to avoid intruder state problems in the excited-state calculations. Geometry optimizations were also performed at the MS-CASPT2 level in order to evaluate the effect of dynamic electron correlation on the ground and excited state equilibrium structures and on the potential energy landscape.
Calculation results The results of the geometry optimizations are shown in Fig. 1. A planar structure (Fig. 1b) was located for the S1(p,p*) minimum in which the bond lengths within the pyridine ring have increased relative to the ground-state planar structure (Fig. 1a). This is reminiscent of the breathing mode observed following photoexcitation of benzene in the S1(p,p*) state, for example.30 The optimized planar structure for the S1(n,p*) state (Fig. 1c) involves mainly stretching of the two C–N bonds relative to the ground-state structure, along with a shortening of one C–C bond and a lengthening of another C–C bond. This structure
Fig. 1 Optimized structures of all critical points: (a) S0 Cs minimum, (b) S1(p,p*) Cs minimum, (c) S1(n,p*) Cs saddle point, (d) S1(p,p*)/S2(n,p*) Cs MECI, (e) S1(n,p*) minimum, (f) S1(p,p*) - S1(n,p*) TS1. The normal font corresponds to state-specific (state-averaged for MECI, (d)) CASSCF optimized geometries. The bold font corresponds to MS-CASPT2 optimized geometries.
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Table 1 CASSCF, MS-CASPT2 and CIPT2 relative energies computed at the CASSCF optimized geometries. Available experimental and theoretical data from the literature are also reported. All energies are given in eV relative to the ground-state energy
Table 2 MS-CASPT2 and CIPT2 relative energies computed at the MSCASPT2 optimized geometries. All energies are given in eV relative to the ground-state energy
State CASSCF (8e,7o)
State
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1 0
S0(1 A 11A 0 21A 0 11A00
CIPT2 (8e,7o)
Ref. 31 Expt.
) Cs equilibrium geometry (minimum) 0 0 0 0 5.128 4.841 4.794 5.942 5.566 5.528
S1(21A 0 11A 0 21A 0 11A00 S1(21A 11A 21A 31A
MS-CASPT2 (8e,7o)
Ref. 32 CASPT2
Ref. 33 MRCI
0 4.75 5.57
0
p,p*) Cs equilibrium geometry (minimum) 0.241 0.162 0.189 4.853 4.539 4.507 4.48 4.28 5.990 5.620 5.586
CIPT2 (8e,7o)
S0(1 A ) Cs equilibrium geometry (minimum) 0 11A 0 4.760 21A 0 1 00 5.593 1A
0 4.708 5.545
S1(21A 0 p,p*) Cs equilibrium geometry (minimum) 0.236 0.267 11A 0 4.525 4.504 21A 0 5.829 5.785 11A00 4.94
n,p*) non-planar equilibrium geometry (minimum) 0.991 0.834 0.932 5.201 4.765 4.931 5.751 5.392 5.415
S1(11A00 11A 0 21A 0 11A00
MS-CASPT2 (8e,7o)
1 0
S1(11A00 n,p*) Cs equilibrium geometry (saddle point) 0.674 0.663 11A 0 5.347 5.256 21A 0 5.002 4.943 11A00
n,p*) Cs equilibrium geometry (saddle point) 0.691 0.652 0.643 5.567 5.307 5.219 5.225 5.034 4.944 5.02
proved to be a saddle point. In fact, the true minimum is found upon slight folding of the pyridine ring and moving the hydrogen of the hydroxyl group out-of-plane (Fig. 1e). Energies computed at the CASSCF and MS-CASPT2 optimized geometries are reported in Tables 1 and 2, respectively. The table sections correspond to the geometries obtained above for the S0, S1 and S2 states, as labeled in the tables. The calculated adiabatic transition energy to the S1(p,p*) state can be compared to the 0–0 band of the S1 ’ S0 electronic transition measured experimentally, when neglecting the zero-point energy correction. Table 1 shows that the CASSCF calculated value overestimates by 0.37 eV the experimental determination of Pratt and coworkers.31 As expected, this result is considerably improved by the calculations at the MS-CASPT2 and CIPT2 levels, which overestimate the experiment by only 0.06 and 0.03 eV, respectively. Using MS-CASPT2 optimized structures (Table 2), the error is further reduced to 0.05 and 0.02 eV, respectively. The accuracy of the present calculation is thus largely improved relative to that of Sobolewski and Adamowicz,32 which underestimates the experimental results by 0.2 eV. The MRCI calculation by Li et al.33 is further away (+0.46 eV). Note that if one takes into account the zero-point energy correction computed at the CASSCF level, the S1 ’ S0 electronic transition is further reduced by 0.12 eV. Based on the energetics reported in Table 1, the most important point that emerges from the calculations is that the two states S1(p,p*) and S2(n,p*) cross each other. At the (p,p*) minimum geometry, the (n,p*) state lies ca. 1.1 eV above (p,p*), whereas at the (n,p*) minimum geometry, the (p,p*) state lies ca. 0.6 eV above (n,p*). As a result, the minimum found for the (n,p*) state lies on the adiabatic S1 PES and is denoted S1(n,p*) minimum. In fact, the S1(p,p*) and S2(n,p*) states cross at a minimum-energy conical intersection (MECI)34 (Fig. 1d) located only ca. 0.1 eV above the S1(n,p*) minimum at the CASSCF level. Fig. 2 (top panel) illustrates the topology of this
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Fig. 2 Schematic potential energy landscape of the adiabatic S1 and S2 electronic states of 2-HP. The PESs are represented along two coordinates, X1 and X2, which lift the degeneracy at the S1/S2 MECI. X1 corresponds to the gradient difference vector at S1/S2 MECI and X2 combines the derivative coupling vector at S1/S2 MECI and transition vector at S1(n,p*) SP. The labels show the remarkable points of the PES. (top) Schematic view of the CASSCF landscape with the two symmetry-equivalent S1(n,p*) nonplanar minima and the two transition states (TS1). (bottom) Schematic view of the MS-CASPT2 landscape with its S1(n,p*) saddle point (SP).
PES. On each side of this MECI lie two symmetry-equivalent transition states (TS1). They connect adiabatically the (p,p*) and the (n,p*) minima on the S1 PES. These transition states are located less than 0.1 eV above the S1(n,p*) minimum at the CASSCF level. Note also that the S1(n,p*) minimum is slightly higher in energy (0.2–0.4 eV) than the S1(p,p*) minimum and is
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located at 4.76 and 4.93 eV above S0 at MS-CASPT2 and CIPT2 levels, respectively. Taking into account the zero-point energy correction computed at the CASSCF level, the S1(n,p*) is further lowered by 0.17 eV. Based on the present topology, the S1 adiabatic surface is expected to be highly anharmonic in the region of excitation by the pump laser. The pump laser will provide sufficient available energy to the system to explore the (n,p*) region of the S1 PES. It is worth noting also that at the MS-CASPT2 level (Fig. 2, bottom panel), a subtle change of topology occurs, as the S1(n,p*) non-planar shallow minimum disappears. Thus, the S1(n,p*) region of the PES is accessed from the S1(p,p*) minimum via a fairly flat plateau.
Experimental results A series of 2-D photoelectron images were recorded using a VMI spectrometer for various time delays t ranging from 600 fs to +470 ps. The corresponding 3D-distributions were reconstructed24,35 using the pBASEX inversion method.36 As an illustration, Fig. 3 represents a reconstructed image taken at pump–probe delay of 130 fs. Both of the pump and probe lasers are vertically polarized. The radial distribution reflects the velocity distribution of photoelectrons (hence the photoelectron energy) and the anisotropy of the image is a signature of their angular distribution. The expansion of the angular basis set used in the image reconstruction goes up to the 4th Legendre polynomial function.37 Accordingly, the reconstructed image is described by three matrices a(E,t), b2(E,t) and b4(E,t) according to: a(E,t)[1 + b2(E,t) P2(cos y) + b4(E,t) P4(cos y)]
(1)
where t is the pump–probe delay, E is the kinetic energy of the electrons, y corresponds to their direction with respect to the polarization of the probe laser, and P2,4(cos y) are Legendre polynomials describing the anisotropy of the electron distribution. The matrices a(E,t), a(E,t) b2(E,t) and a(E,t) b4(E,t) contain the information on the time-resolved photoelectron spectra and on the polarized component of the image at the second and fourth orders, respectively. The decomposition of
Fig. 3 Equatorial cut through the 3D photoelectron distribution after reconstruction from a 2D VMI image. The radius is proportional to the photoelectron velocity. The intensity was multiplied by the radius to enhance the Rydberg structure. The pump–probe time delay was 130 fs. Both laser polarizations are parallel, the direction being indicated on the image by the white arrow.
584 | Phys. Chem. Chem. Phys., 2014, 16, 581--587
Fig. 4 Average photoelectron spectra with the probe laser tuned at 793. On the left is displayed the average signal calculated on the range 0–1.7 ps with each of the P0, P2 and P4 components of the photoelectron distribution, hence documenting a(E,t), a(E,t)b2(E,t) and a(E,t)b4(E,t), respectively. On the right is displayed the same information but averaged over delay times between 200 and 470 ps. Their relative intensity is therefore arbitrary. The dashed vertical lines guide the eyes through the spectra.
average spectra are presented on Fig. 4. It shows striking structures. One can notice that the b2(E), and b4(E) are rising with the energy. This is mainly due to the superposition of several pathways in the ionization process of the molecule, being unpolarized and of low energy. Looking at a highly polarized signal is a way to reduce the number of components and to focus on specific ionization channels. For this reason, only the corresponding spectrum, given by a(E,t) b4(E,t), is considered P hereafter. Its average aðE; tÞ b4 ðE; tÞ over various ranges of t
time delays is shown in Fig. 5. The bottom curve in Fig. 5 corresponds to an average over delay times between 200 and 470 ps whereas the same for the time delay between 0 and 1.7 ps is depicted in the middle. Both exhibit the same series of bands but the overall shape of the spectrum is different: the intensity ratio between the high energy bands and the low energy ones decreases substantially by increasing the delay time from the 0–1.7 ps range (middle curves) to the 200–470 ps range (bottom curves). These series of
Fig. 5 (top) Fit functions used for the a(E,t) b4(E,t) components of the P photoelectron spectra. (middle) Average photoelectron spectra ta(E,t) b4(E,t) associated with the P4 components of the photoelectron distribution. The average carries over delay times between 0 and 1.7 ps. The filled curves are the components from the fits. (bottom) Same as (middle) for the range going from 200 and 470 ps. (all) The vertical black dashed lines are the values expected from a Rydberg fingerprint with a d = 0.08.
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bands (0.70, 1.0, 1.19 and 1.29 eV and the barely distinguishable structures in the high energy tail of these curves) can be easily assigned with the help of Rydberg Fingerprint Spectroscopy introduced by Weber and coworkers as a tool to analyze photoelectron spectra in fs-TRPES experiments when the probe operates via multiphoton ionization.38,39 Accordingly, the present series of peaks are adequately accounted for by a Rydberg fingerprint (RF) series starting with the principal quantum number n = 4 for the 0.70 eV peak with a quantum defect of d = 0.08. This small value of d suggests that an nd Rydberg series is in action, which is coherent with the current analysis of the P4 anisotropy component of the photoelectrons. An important issue relates to the fact that the relative intensity of the RF peaks is not the same whether the photoelectron spectrum corresponds to the average of pump–probe delays in the range 0–1.7 ps (middle curve) or 200–470 ps (bottom curve). This indicates that different electronic states (this will be refined below) are probed when the delay time is varied. The simplest assumption is that two energy states are involved and that the system switches from one to the other between 0–1.7 ps and 200–470 ps. Accordingly, the curves used for fitting the P4 component of the photoelectron spectra in the top panel of Fig. 5 provide information on the RF spectrum of these two states, populated along the relaxation dynamics. Each RF is composed by a series of Gaussian peaks centered where the Rydberg resonance progression are expected for n = 4 and d = 0.08 (see above). An extra Gaussian peak centered at 2.29 eV accounts for the ionization with 5 793 nm photons. The two RF series and the extra peak were used to fit the spectra measured as a function of the delay time. The corresponding results are shown in Fig. 6. The curves running through the experimental points use a kinetic model, which assumes a sequential population transfer between four transients according to tA
tB
tC
A ! B ! C ! D
(2)
where tA, tB, tC represent the decay times from one transient to the other. Transient D is assumed to be stable at the timescale of the experiment. The values given by the fit are given in Table 3.
Fig. 6 Time dependence of the photoelectron signal. Note the change in the horizontal scale at 8 ps (0–8 ps on the left of the vertical dashed line, 8–500 ps on the right). The experimental results of various colors correspond to the RF series used to fit the photoelectron spectra (see Fig. 5). The curves running through the experimental points are fitted using the kinetic model using the parameters given in eqn (2).
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Table 3 Time decay and error bars obtained using the simultaneous fit of the three curves with a sequential model
Time
Value
tA tB tC Laser autocorrelation
106 45 fs 1.26 0.24 ps 112 44 ps 85 fs
Discussion The irregularity in the absorption spectrum of 2-HP observed by Bernstein and coworkers40 appears 500 cm1 from the band origin (more recently measured at 36 118.69 cm1 by Pratt and coworkers31). This indicates that the non-harmonic region of the S1 PES is accessible with a total energy of 36 620 cm1 or larger. The energy provided by the pump laser, 37 880 cm1, is larger than this value. Hence, the wavepacket is launched by the pump laser in a region of high anharmonicity and is expected to spread quite rapidly and to reach the regions where the initial (p,p*) character of the PES has switched to the (n,p*) character. We thus anticipate that after a delay time, the wavepacket will feature a superposition of (p,p*) and (n,p*) characters in the S1 PES. The topology of the S1 PES in Fig. 2 confirms such high anharmonicity in the region of excitation by the pump laser. Due to a MECI with the S2 PES, the S1 PES has a very peculiar shape and electronic conformation (see Fig. 2). It has the (p,p*) character near the absolute minimum and in the Franck–Condon region of excitation where the molecule is planar. Then, the wavepacket starts moving and spreading around, driven by slopes in the S1 PES. Its electronic character switches to (n,p*) outside the Franck– Condon region. The (n,p*) ‘‘dark’’ state, as denoted in the literature,17–19,31,40,41 is not associated with a stable position on the S1 PES but corresponds to a flat extended region quite far outside the Franck–Condon region of excitation, where the molecule is no more planar (Fig. 2). Importantly, these regions are accessible energetically with the currently used pump photons at 4.70 eV, at least when accounting for the zero-point energy in the ground state. As can be seen in Fig. 6, the photoelectron spectra are dominated by two nd (n Z 4) Rydberg Fingerprint (RF) series. A priori, each RF series documents a different energy state. Based on previous discussion, we can certify that these two Rydberg Fingerprint series do not probe different energy states stricto sensu but a single one, for instance S1, in two different locations of its PES where the electronic configurations are different, namely (p,p*) in the Franck–Condon region of excitation and (n,p*) after deformation of the molecule. This situation is quite amusing since it leads to probing the time evolution between ‘two quantum states’ in a relatively largesized molecular system. Such situation is well known in Atomic Physics but not in Molecular Physics. The intensity of each Rydberg series (red and green curves in Fig. 6) gives insight into the extension of the wavepacket in these regions. The signal given by the red curve in Fig. 6 is not vanishing at zero time delay and decays at positive times with the time constant tB B 1.3 ps. Likely, it is associated with the part of the wavepacket which overlaps with the Franck–Condon
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region where S1 has the (p,p*) character. Similarly, the green curve which goes up from zero with the same time constant tB documents the wavepacket when it spreads into the fairly flat region of the S1(n,p*) PES. The green and red curves run almost together at intermediate delay time, both having half the initial intensity of the red one. This indicates that about one half of the wavepacket is transferred from the region of the (p,p*) character to that of the (n,p*) character through deformation which makes 2-HP non-planar. For longer delay times, the population of both S1(p,p*) and S1(n,p*) wavepackets decays with the same time constant tC B 110 ps. Such a slow decay time could be associated with a transfer to triplet states through a standard intersystem coupling.42 At 500 ps delay, the red curve, which reflects the wavepacket in the S1(p,p*) region, goes down to zero whereas the green curve (wavepacket in the S1(n,p*) region) does not (cf. Fig. 6). As an interpretation, we believe that the wavepacket somehow oscillates between the two S1 regions and is unfilled, with a unique sink for the triplet state located somewhere in the S1(p,p*) region, whereas no sink exists in the S1(n,p*) region. Hence equilibration would refill the S1(p,p*) region from the S1(n,p*) region. We expect that either a small barrier exists between the S1(p,p*) and S1(n,p*) regions along the X1 coordinate, which would block the refill when enough energy is relaxed to other coordinates than X1, or that the plateau in the green curve corresponds to the detection of the triplet state. The second scenario is more likely to occur here. The blue curve in Fig. 6 corresponds to the ionization by a fifth probe photon. The large excess energy which is provided allows probing the molecule without much state sensitivity at all delay times. A very short timescale tA B 110 fs appears almost within the cross-correlation between the pump and probe laser pulses. It is assigned to a rapid movement of the wavepacket outside the Franck–Condon region of excitation, driven by forces towards the absolute minimum of the S1 PES which, as the Franck–Condon region of excitation, corresponds to a region of (p,p*) character. This affects specific channels which are enhanced by both an intermediate resonance in the ionization process and the strong localization of the wavepacket just after excitation. It may depopulate other ionization channels, which is not observed here. The remaining part of the blue curve is well described by the two times constants tB B 1.3 ps and tC B 110 ps. With five probe photons, it seems certain that the triplet state can be ionized. Again, this is in line with the decay of the green curve to a plateau on Fig. 6.
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regions of the S1 PES which have (n,p*) character. There exists a fairly extended plateau, where the out-of-plane movement of the H-atom bonded to oxygen and the deformation of the ring are coupled and lead to a variety of geometrical arrangements within close energy domains. This nicely creates the conditions for a roaming movement and tB appears as the timescale for the wavepacket to reach the roaming dynamics. Finally, a decay occurs with the time constant tC, down to low lying triplet states. Since the second timescale corresponds to the access of a roaming dynamics, we conclude that the intersystem energy transfer is accessed through a roaming behavior. This mechanistic picture is another way to describe a reality approached using the theory of radiationless transitions formulated by Jortner and colleagues.42,43 This theory is a dissipative description (the Fermi Golden rule) of the evolution where an initially bright state decays into a quasicontinuum of degenerate levels weakly coupled to it. Here the roaming dynamics is very similar to a specific situation that was named the ‘strong intermediate coupling’.44 In the latter situation a rapid initial decay occurring in a subset of strongly coupled levels where the excitation lingers until the final decay could occur in the remaining set of degenerate levels. The profound similarity in the description comes from the multidimensional character of the roaming dynamics (mechanistic) and the non-radiative (dissipative) approaches. The present work represents the first study in timescale measurements for the roaming dynamics.
Conclusions The present situation is significantly different from that met in standard TRPES studies, which allowed us to probe the roaming wavepacket mechanism. In the case of the pyrazine multiphoton ionization probe45 experiment two distinct states S2(p,p*) and S1(n,p*) are detected and the dynamics of transfer from the upper state to the lower state is detailed. In the present study, two regions of different electronic configurations of the same adiabatic state are detected and the equilibration time of the wavepacket between the two regions is probed. Such situations could be more common than simply applying to the dynamics of 2-HP. Indeed, such PES topology may be frequently encountered when the density of states increases with the size of the system. Thus, roaming mechanisms that involve crossing between adiabatic PESs may become more prevalent and have a much larger impact in photochemistry than previously anticipated.
Towards roaming dynamics
Acknowledgements
Excitation by the pump laser launches a wavepacket on the S1 PES in the region where it has the (p,p*) character. Its dynamics was followed experimentally and a multiexponential evolution was observed using three different timescales tA B 110 fs, tB B 1.3 ps and tC B 110 ps, respectively. tA is assigned to the movement of the initial wavepacket outside the Franck–Condon region of excitation along the S1 PES still staying in a region of the PES where the electron configuration is dominantly in (p,p*). tB is assigned to the spread of the wavepacket towards the
D. Nandi acknowledges the financial support from the ‘‘Triangle de la physique’’ for supporting this research under project ‘‘2008062T DYNANEX’’. B.S., L.P. and J.-M.M. thank EU-ITN project ICONIC-238671 for funding.
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