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Relaxation Dynamics in Photoexcited Chiral Molecules Studied by Time-Resolved Photoelectron Circular Dichroism: Toward Chiral Femtochemistry

Unravelling the main initial dynamics responsible for chiral recognition is a key step in the understanding of many biological processes. However, this challenging task requires a sensitive enantiospecific probe to investigate molecular dynamics on their natural femtosecond time scale. Here we show that, in the gas phase, the ultrafast relaxation dynamics of photoexcited chiral molecules can be tracked by recording time-resolved photoelectron circular dichroism (TR-PECD) resulting from the photoionization by a circularly polarized probe pulse. A large forward–backward asymmetry along the probe propagation axis is observed in the photoelectron angular distribution. Its evolution with pump–probe delay reveals ultrafast dynamics that are inaccessible in the angle-integrated photoelectron spectrum or via the usual electron emission anisotropy parameter (β). PECD, which originates from the electron scattering in the chiral molecular potential, appears as a new sensitive observable for ultrafast molecular dynamics in chiral systems.

toexcited chiral molecules can be tracked by recording Time-Resolved PhotoElectron Circular Dichroism (TR-PECD) resulting from the photoionisation by a circularly polarized probe pulse. A large forward/backward asymmetry along the probe propagation axis is observed in the photoelectron angular distribution. Its evolution with pump-probe delay reveals ultrafast dynamics that are inaccessible in the angle-integrated photoelectron spectrum nor via the usual electron emission anisotropy parameter (β ). PECD, which originates from the electron scattering in the chiral molecular potential, appears as a new sensitive observable for ultrafast molecular dynamics in chiral systems. Chiral species exhibit enantio-specific properties when they are embedded into a chiral medium.
For instance, chiral molecules interact with each other to form chiral complexes via the so-called chiral recognition process, this 'molecular handshake' being at the basis of stereochemistry. 1 Enantio-specific properties also arise from the interaction of chiral molecules with 'chiral light', such as Circularly Polarized Light (CPL), leading to various types of Circular Dichroism (CD). 2 As calculated 3,4 and experimentally-demonstrated, 5 CPL-induced photoionisation of randomlyoriented pure enantiomers gives rise to a forward/backward asymmetry of photoelectron emission along the photon propagation axis k, referred to as PhotoElectron Circular Dichroism (PECD). Based upon a differential measurement, this chiroptical effect can be fully described in the pure electric dipole approximation, leading to very strong asymmetries. The outgoing electron scatters in the mean chiral molecular potential involving all the other electrons -mostly the valence ones, which are the main actors of chemical reactivity. This electron scattering occurs in a space whose orientation is referenced by the circularly polarized ionising field. Despite the randomorientation of the molecules, the resulting photoelectron angular distribution shows an intense forward/backward asymmetry. The magnitude of this asymmetry, determined by the interferences be-tween the different partial waves describing the outgoing electron wavepacket, can reach the order of several percent. The sign of this asymmetry reverses with the handedness of the enantiomer (e) or the helicity of the ionising light (p). PECD is an orbital-specific effect that also depends on the final state; i.e. the photoelectron continuum. It is very sensitive to permanent -isomers, conformers, clustering -and dynamical -vibrational excitation -molecular structures. 6 As such, PECD is a useful observable to investigate dynamics in chiral molecules. So far, experiments, mostly synchrotron radiation based, have focused on the photoionisation of molecules from their ground electronic state (S 0 ) in its equilibrium geometry. Recently, a laser-based one-color Resonant Enhanced Multiphoton ionisation (REMPI)-PECD scheme involving several intermediate states has been demonstrated, however without any time resolution. [7][8][9] The possibility of observing PECD from excited states, for instance loosely bound electronic states, remains an open question. The present paper focuses on the investigation of PECD from an electronic excited state to establish the sensitivity of PECD as a probe of the ultrafast relaxation taking place in this state. To record Time-Resolved PECD (TR-PECD), a linearly polarized femtosecond pump pulse photoexcites chiral molecules and a time-delayed circularly polarized femtosecond probe pulse photoionises them.
Key features of this two-color two-photon experiment are schematised in Figure 1.
The target molecule we investigate here is the fenchone (C 10 H 16 O), a bicyclic ketone whose rigid structure ensures the existence of a single conformer. Fenchone has been extensively studied by VUV-PECD with and without coincidence detection, 10,11 by multiphoton, 12 above threshold or tunnel ionisation 9 PECD as well as by absorption circular dichroism. 13 However, none of these experiments was time-resolved, and all of them probed a molecule in its ground electronic state defined by its equilibrium geometry, with a possible contribution from the excited states in the REMPI-PECD experiments. The absorption spectrum of fenchone is characterized by a weak valence band around 4.6 eV, followed by strong Rydberg bands starting around 6 eV. 13 We chose to excite the molecules to their first Rydberg state (3s) in order to drastically change the initial orbital of the outgoing electron compared to the ground state, as illustrated in Figure 1. The pump pulse spectrum is centred at 6.17 eV with a 30 meV full width half maximum bandwidth (201 nm, 80 fs duration if Fourier-transform-limited). The probe (403 nm, 35 meV with 70 fs duration) is chosen to photoionise the system ∼0.6 eV above the vertical ionisation threshold (IP v =8.72 eV), in the energy range where the largest VUV PECD has been measured (15%). 10 Since the pump pulse is linearly polarized, the sensitivity to chirality only comes into play in the ionisation step, via the helicity of the probe pulse.
The photoelectron images are collected by a velocity map imaging detector for alternating probe helicities at each pump-probe delay, as described in the Experimental Methods section and the S.I. The momentum distribution of the photoelectrons (angular resolved photoemission spectrum ARPES) for a probe helicity p = ±1 (Left/Right) and one given enantiomer (e) is defined by a function ARPES (p,e) (ϕ, θ , E kin ) with θ the photoelectron ejection angle with respect to the probe propagation axis k, ϕ its azimuthal angle and E kin its kinetic energy. When a cylindrical symmetry in the emission angle ϕ of the photoelectron is achieved along an axis parallel to the detector, the and can be retrieved from its VMI 2D-projection PROJ (p,e) (θ , E kin ) by using a p-Basex analysis for instance. 14 As the P even Legendre polynomials are symmetric along the optical axis k, the B even coefficients encode the angular distribution of the standard photoelectron image: the PES is the angle-integrated photoelectron intensity B 0 (E kin ) and the anisotropy parameter b 2 (E kin ) = −β /2 (with β , the usual anisotropy parameter retrieved for a linearly polarized photoionisation). These even parameters do not depend on the laser helicity (p) or enantiomer (e). The P odd Legendre polynomials are antisymmetric along k, consequently the B (p,e) odd (E kin ) coefficients are non-zero only for chiral molecules photoionised by elliptically polarized light (p = 0) and encode the PECD. In a 2-photon ionisation, the sum of Legendre polynomials is expected to go up to P 4 (cos(θ )), with a drastically reduced B 4 in a (1+1') resonant ionisation.
In the present experiment, the linear pump polarization as well as the circular probe polarization are defined by quantification axes perpendicular to each other and both parallel to the detector axis. The pump excitation along a well defined transition dipole induces a loss of isotropy in the molecular target, that breaks the ϕ cylindrical symmetry required to retrieve the ARPES distribution from its VMI 2D-projection PROJ. Nevertheless, in fenchone, this cylindrical symmetry is almost restored in the 'difference'-image, defined as PROJ (+1,e) (θ , E kin ) − PROJ (−1,e) (θ , E kin ), To extract PECD, which manifests itself as an asymmetry in the photoelectron yield emitted in the forward or backward hemisphere along the optical axis k for a given enantiomer and for a given light helicity, normalisation by the PES needs to be done. The normalisation of B i observables yields the b i coefficients (Eq. 1). As shown in the SI, the break of cylindrical symmetry prevents access to the 'true' B 0 (E kin ) via a p-Basex analysis of the 'sum'-image , defined as PROJ (+1,e) (θ , E kin ) + PROJ (−1,e) (θ , E kin ) and called (LCP + RCP) images in Figure 1. Nevertheless we will still use a p-Basex analysis on this (LCP + RCP) 'sum'-image to obtain B 0 (E kin ), and we use this coefficient to normalise the B (p,e) odd (E kin ) coefficients from which we calculate a circular dichroism of the 2D photoelectron projection. The quantity we calculate, PECD, is thus not strictly the same as the PECD usually defined in the litterature and that have been all recorded without a break of cylindrical symmetry. For (1R)-(-)-fenchone (e = −1), these definitions are : This yields, in terms of Legendre coefficients : With the cylindrical symmetry breaking : (1) odd andB even coefficients are extracted from these images. A significant forward PECD, (i.e.) preferential emission of the photoelectron in the k direction, is observed on the 'difference'-images, demonstrating that loosely bound electronic excited states in chiral molecules can lead to strong asymmetric photoionisation when driven by CPL. We also see that the 'sum'-images show a preferential emission along the pump polarization. In order to obtain a time-dependence of this anisotropy, we use also theB 2 (E kin ) coefficient extracted from the p-Basex analysis of these 'sum'-images. Similarly to theb odd coefficients, normalisation ofB 2 byB 0 is required to obtainb 2 . Note thatb 2 coefficient cannot be quantitatively used to evaluate the anisotropy of the ARPES, but it will show the same temporal evolution. Thẽ   decreases faster in only 1.4 ps. Using Eq. 1, the PECD has the same sign and a similar magnitude, to that observed at that same total energy in single-photon VUV photoionisation (9.3 eV) 10 even though the ionisation process is different. In the experiments of ref. 10, the outgoing electron was scattered from the HOMO orbital in the ground electronic state potential, while here, the outgoing electron is emitted from the 3s Rydberg wavefunction and scatters further from the ionic core.  Table 1 summarizes the time constants extracted from the fits (see SI). When the population in 3s state starts to be less than 10% (delay≥7ps), the normalisation by a smallB 0 increases the dispersion of the normalised coefficients.
What are the dynamics revealed by these different timescales ? The absorption of the pump pulse creates a vibrational wavepacket in the 3s Rydberg state. This wavepacket will undergo vibrational relaxation dynamics towards the equilibrium geometry of the 3s state as illustrated in Figure 4(a). In addition, vibronic couplings may occur, leading to internal conversion towards either the lowest valence state (S 1 ) or the ground state (S 0 ) as shown in Figure 4(c). Nothing is known about these two ultrafast processes. In the present excitation scheme, the vibrational energy in both S 1 (∼1.6 eV) and S 0 (∼6 eV) is too high to get significant Franck-Condon factors at only ∼0.5 eV above the IP v . The probe energy is thus not high enough to photoionise molecules vibrationnally excited in S 0 or in S 1 . Table 1: Time constants extracted from the fits of the normalised Legendre polynomial coefficientsb (−1) i andb 2 dependences shown in Figure 3. The uncertainties correspond to a 50% confidence bounds.

Observables Time constant in ps Converging value of theb
Consequently, the 3.28 psB 0 decay mirrors the lifetime of the 3s Rydberg state and the internal conversion timescale from 3s to the lower valence states. Theb 1 coefficient is mostly determined by the Rydberg-electron continuum transition dipole moment whileb 3 being a higher order term, will depend on the anisotropy of excitation created by the pump pulse. Similarly a β time-dependence within a given electronic state is, in general, also associated to a decay of the anisotropy of excitation created by the pump. 15,16 The calculations presented in the SI predict that the 3s-S 0 transition dipole moment is aligned along the C1-C3 axis, as shown on Figure 4(a).
The free rotations of the excited molecules induce a loss of the anisotropy of excitation, over a timescale defined by the moments of inertia of the molecules and the rotational temperature of the gas. 17 The moments of inertia of the asymmetrical top fenchone have been calculated from the S 0 geometry to I x,y,z =1159, 1555 and 1876 amu.bohr 2 with the axis represented on Figure 4(a). The decay time due to the anisotropy loss is typically 1/3 of the dephasing time of the rotational periods (I y /(kT rot )), i.e. between 1.4 and 2.4 ps for T rot ∼10-30 K as expected for an Even-Lavie pulsed valve source. 17,18 This is consistent with the 1.4 ps decay measured onb (−1) 3 and the 2 ps onb 2 , confirming the sensitivity of these two observables to the average laboratory-frame alignment created by the pump transition. Here, the 3s-S 0 dipole moment is almost aligned along the I y rotational axis. To assign the time-dependence ofb (−1) 3 andb 2 due to I x and I z rotations with similar periods than I y , is a challenging task beyond the scope of this letter. This would require a systematic study for different relative polarizations of the pump and probe pulses to extract the spherical tensor components of the photoionisation matrix element.
Beyond these global picosecond dynamics, two different mechanisms can be inferred from This interpretation requires theoretical support with calculations of TR-PECD that include vibrations, this is far beyond the present state-of-the-art. In particular, our results indicate that PECD would be very sensitive to the initial vibrational states, while previous investigations only considered the effect of vibrational excitation of the final cationic state. 19,22 The PECD from the 3s Rydberg state (∼14.6 ± 3.3%) is as strong as the PECD recorded from the ground electronic state (15.4%). The PECD magnitude obtained at large delays is rather impressive, considering that the 3s outgoing Rydberg electron scatters less often in the inner part of the molecular potential but more often at distance further from the chiral carbons compared to an electron outgoing from the HOMO ground state orbital. This shows that the phases of partial wavefunctions can be determined by their values far from the ionic core and that PECD is thus a very long range probe of the whole molecular potential, as already observed in one-photon PECD, for instance in clusters. 23,24 At the same time, by using a pump step, partial alignment is achieved and by exciting a Rydberg state, a smaller number of angular momentum components are required to describe the photoelectron continuum. It would be interesting to investigate these two latter conditions to determine their respective impact on the large asymmetry that is observed here.
In conclusion, we have shown that a large PECD (>10%) could be observed in photoionisation In particular, odd coefficients, such asb 1 which is fully proportional to the sine of dephasing between adjacent outgoing waves, 25 are much more sensitive to the whole molecular potential than even parameters such asB 0 . TR-PECD provides new and richer opportunities to template molecular dynamics in chiral systems in comparison to previous time-resolved Angle-Resolved PES on achiral samples involving only PES and the classical β anisotropy parameter. The ability to probe complex ultrafast relaxation in chiral systems opens up concrete possibilities for the investigation of molecular dynamics such as transient chirality or nuclear motions involved in chiral recognition.
These results present a stepping stone for time-resolved chirality and more generally to establish a femtochemistry based on circular polarizations.

Experimental and computational methods
An Even-Lavie valve is used as a pulsed enantiopure fenchone source with helium as carrier gas to avoid cluster formation. The experiment was performed using the Aurore laser system at CELIA, which delivers 20 mJ, 25 fs, 800 nm pulses at 1 kHz. Only 2 mJ is used in the present experiment.
The presented results are obtained by scanning the pump-probe delays typically 16 times and at each delay, one helicity image is a record over 45000 laser shots. For each scan, two background images corresponding to the probe pulse alone in each helicity are recorded and subtracted to each image of each delay for a given helicity. This background subtraction is required for the longest pump-probe delay when the signal reaches zero (see Figure S4 of the SI). High-level quantum chemistry calculations, using Gaussian 09, Molpro and GAMESS-US quantum chemistry packages, have been performed on the ground and first five electronic excited states of fenchone in order to help in the interpretation of the experimental data. All the computational details and results can be found in Supporting Information.

Supporting Information Available
Details of the calculations of the geometry and energies of the excited states, the experimental setup, the adiabatic ionisation potential deduced experimentally by the energy balance of the PES, the effect of breaking cylindrical symmetry and the fitting procedures used in Figure 3.
This material is available free of charge via the Internet at http://pubs.acs.org/.

Author Information
The authors declare no competing financial interests.