Capturing electron-driven chiral dynamics in UV-excited molecules

The temporal resolution provided by attosecond technologies developed in the past 23 years gives access to some of the fastest electronic dynamics of matter on their natural timescale. Seminal pump–probe experiments using attosecond light pulses have revealed valence electron dynamics in atoms¹⁶, autoionization dynamics in molecules¹⁷, photoionization delays in solids¹⁸, as well as electron-driven charge migration in simple ionized biomolecules^9,19. In all of these cases, the intrinsically high photon energy of the attosecond light sources inevitably leads to ionization of the target, which has restricted the measurements to ultrafast dynamics of cationic states.

When aiming to investigate the ultrafast light-induced electron dynamics of chiral molecules in their neutral states, the pump pulse must thus have a photon energy below the ionization threshold and a broadband energy spectrum that can trigger coherent electron motion among several electronic states, and a time duration that ensures prompt excitation before any nuclear motion can take place, together with sufficient temporal resolution. The low ionization potential of most molecular systems thus restricts the choice of the pump pulse wavelength to the UV and vacuum-UV ranges, that is, to a spectral region that cannot trigger intricate high-order, strong-field multiphoton-driven processes^20,21 that rarely occur with natural light sources. When these requirements are met, measurements with high time resolution are possible using pump–probe spectroscopic techniques that are highly sensitive to chirality, such as TR-PECD^12,15 recently used to probe nuclear dynamics, internal conversion and photoionization delays in chiral molecules^{11,12,13,14,22}.

We use ultrashort UV pump pulses^23,24 in combination with circularly polarized near-infrared (NIR) probe pulses to study coherent electronic dynamics in chiral neutral molecules with unprecedented temporal resolution. We apply the chiroptical method of TR-PECD to investigate electron-driven chiral interactions in neutral methyl lactate (C₄H₈O₃). Figure 1a,b shows an overview of the experimental approach. First, a linearly polarized UV pulse promptly launches a coherent electronic wave packet just below the ionization threshold in (S)-methyl lactate by means of a two-photon transition. Then, a time-delayed circularly polarized NIR probe triggers ionization from the transient wave packet, providing an exceptional instrument response function of 2.90 ± 0.06 fs (Extended Data Fig. 1). For each pump–probe delay t, the 2D-projected photoelectron angular distributions (PADs) S^(h)(ε, θ, t) are collected with a velocity map imaging spectrometer (VMIS), for both left (h = +1) and right (h = −1) circular polarizations of the probe pulse. ε and θ stand for the kinetic energy and direction of ejection of the photoelectron in the (x, z) VMIS detection plane, respectively. The chiroptical response is characterized by a photoelectron circular dichroism (PECD) image defined as the normalized difference \({\rm{PECD}}\left(\varepsilon ,\theta ,t\right)=2\frac{{S}^{\left(+1\right)}\left(\varepsilon ,\theta ,t\right)-{S}^{\left(-1\right)}\left(\varepsilon ,\theta ,t\right)}{{S}^{\left(+1\right)}\left(\varepsilon ,\theta ,t\right)+{S}^{\left(-1\right)}\left(\varepsilon ,\theta ,t\right)}\), subsequently fitted using a pBasex inversion algorithm¹¹. Snapshots of the measured PECD(ε, θ, t) are presented in Fig. 1c. The signal reaches values of up to 10%, typical for PECD and about two orders of magnitude higher than the analogously defined g factor generally obtained in circular dichroism^25,26. Low-energy electrons (ε ≤ 100 meV; see white dashed circles) are preferentially emitted in the θ = 180° backward hemisphere at t = 5 fs and preferentially ejected forward at t = 11 fs. Their main direction of ejection reverses again at t = 17 fs. Higher-energy electrons (ε > 100 meV) are more likely emitted forward than backward for t ≥ 11 fs, but the magnitude of their asymmetry depends on t.

a, A few-femtosecond linearly polarized UV pulse excites an ensemble of randomly oriented chiral molecules, creating an electronic wave packet of Rydberg states by means of two-photon absorption. The dynamics is probed by means of one-photon ionization by a time-delayed circularly polarized NIR pulse. The probing step leads to the ejection of photoelectrons along the light-propagation axis defined along the z direction and the resulting angular distribution is recorded by a VMIS. b, The red and blue structures show the temporal evolution of the coherent electron density in the excited neutral molecule: the chiral evolution of the photoexcited Rydberg wave packet leads to a reversal of the 3D photoelectron angular distribution at two distinct time delays, t and t + Δt, captured by the measurements. c, For each time delay, an image is recorded for both left and right circular polarization of the probe pulse. The differential image PECD(ε, θ, t), defined in the main text, is shown for time delays of 5, 11,17 and 26 fs for photoelectrons with kinetic energies from 25 to 300 meV along the radial coordinate. The white dashed circles identify the photoelectrons below 100 meV that experience an ultrafast reversal of their emission direction in the laboratory frame.

The PECD(ε, θ, t) images provide quantitative fingerprints of an ultrafast dynamics taking place on the few-femtosecond timescale. To further characterize the temporal evolution of the observed dynamics, we decompose the PAD images in series of Legendre polynomials, \({S}^{\left(h\right)}\left(\varepsilon ,\theta ,t\right)={\sum }_{n=0}^{6}{b}_{n}^{\left(h\right)}\left(\varepsilon ,t\right){P}_{n}\left(\cos \theta \right)\), and calculate the multiphoton PECD (MP-PECD)²⁷, defined as the normalized difference of electrons emitted in the forward and backward hemispheres for h = +1, as \({\rm{MP}} \mbox{-} {\rm{PECD}}\left(\varepsilon ,t\right)=2{\beta }_{1}^{\left(+1\right)}\left(\varepsilon ,t\right)-\frac{1}{2}{\beta }_{3}^{\left(+1\right)}\left(\varepsilon ,t\right)+\frac{1}{4}{\beta }_{5}^{(+1)}\left(\varepsilon ,t\right)\), in which \({\beta }_{n}^{\left(+1\right)}\left(\varepsilon ,t\right)=\frac{{b}_{n}^{\left(+1\right)}\left(\varepsilon ,t\right)}{{b}_{0}^{\left(+1\right)}\left(\varepsilon ,t\right)}\) (see Methods and Extended Data Figs. 2 and 3). \({\beta }_{1}^{\left(+1\right)}\left(\varepsilon ,t\right)\) refers to the isotropic part of the asymmetry in each hemisphere, whereas \({\beta }_{3}^{\left(+1\right)}\left(\varepsilon ,t\right)\) encodes anisotropic features owing to pump excitation^11,28, leading to the angular shaping of the PECD illustrated in Fig. 1c. \({\beta }_{5}^{(+1)}\left(\varepsilon ,t\right)\) has been found to be negligible in our measurements. Figure 2a shows MP-PECD(ε, t) and its \({b}_{1}^{(+1)}(\varepsilon ,t)\) component is shown in Fig. 2b. The results are shown for (S)-methyl lactate and a mirroring symmetric measurement in (R)-methyl lactate clearly confirms the chiral character of the Rydberg-induced dynamics, with minor discrepancies owing to slightly lower enantiopurity and statistics (Extended Data Fig. 4). We observe that the unnormalized MP-PECD(ε, t) behaviour in Fig. 2a closely matches \({b}_{1}^{(+1)}(\varepsilon ,t)\) in Fig. 2b, indicating that the anisotropic effects included in \({\beta }_{3}^{(+1)}\left(\varepsilon ,t\right)\) play a minor role. The MP-PECD can be partitioned into three kinetic energy ranges, as identified in Fig. 2a,b. Between 25 and 100 meV, the photoelectron emission asymmetry reverses in about 7 fs (see Fig. 2c). A clear modulation of the asymmetry remains over several tens of femtoseconds, which is also observed at higher ε between 100 and 300 meV (Fig. 2d) and 300 and 720 meV (Fig. 2e). These modulations are also visible in the time-resolved photoelectron yield b₀(ε, t), albeit their contrast is considerably weaker (Extended Data Fig. 5). This highlights the capabilities of TR-PECD, which relies on differential measurements, over conventional photoelectron spectroscopy. In the following, we aim at assigning the origin of the fast temporal modulation of the asymmetry, which could involve electronic and/or nuclear degrees of freedom.

a–e, Temporal evolution of the unnormalized MP-PECD in (S)-methyl lactate (a) and corresponding \({b}_{1}^{(+1)}\) coefficient (b). The white lines identify three different kinetic energy ranges of photoelectrons: 25–100 meV (c), 100–300 meV (d) and 300–720 meV (e). The standard error of the mean over five measurements is shown by the shaded areas. The solid blue lines show the fit of the oscillations from t = 0 fs (see the corresponding Fourier analysis in Fig. 3c,e). The change of sign in c identifies a reversal of the photoelectron emission direction in the laboratory frame.

Source Data

We modelled the experiment including both the two-photon UV excitation and the NIR photoionization steps as sequential perturbative processes, within the frozen-nuclei approximation. A detailed description of the theoretical model is provided in Methods. The electronic spectrum of methyl lactate and the two-photon excitation amplitudes are obtained through time-dependent density functional theory²⁹. Ionization from the excited states is described using the continuum multiple scattering Xα approach^30,31.

We present the results of our calculations in Fig. 3. The pump pulse populates excited states mainly originating from excitation of the highest occupied molecular orbital (HOMO) of the methyl lactate ground state (see  Supplementary Information section 1 and Supplementary Fig. 2). Figure 3a shows the two-photon excitation cross-section associated with almost pure HOMO excitation to Rydberg states. Subsequent photoionization by the probe pulse leads to the emission of photoelectrons with kinetic energies ε = 250 and 500 meV. These ε values are representative of the second and third energy ranges discriminated in the experimental data, respectively—the case of low-energy photoelectron dynamics (ε = 50 meV) is discussed in Supplementary Information section 2.3 and illustrated in Supplementary Fig. 5. Including the HOMO excited states of Fig. 3a in the dynamical calculations yields the time-resolved MP-PECD shown in Fig. 3b,d. The calculations are started at t = 10 fs to ensure no temporal overlap between the pump and probe pulses. The computed asymmetry presents clear modulations as a function of the pump–probe delay. The power spectra of the MP-PECD signals, obtained by Fourier analysis, are compared with their experimental counterparts in Fig. 3c,e. An excellent agreement is found at ε = 250 meV, at which the oscillatory pattern of the MP-PECD is traced back to the pump-induced coherent superposition of 3d and 4p Rydberg states respectively located at E_3d = 8.834 eV and E_4p = 9.120 eV in Fig. 3a. This coherent superposition leads to quantum beatings with approximately 15 fs period, associated with an energy difference between the states of about 300 meV, which survive long after the pump pulse vanishes. We note that the most stable geometries of methyl lactate do not have any vibrational mode in the vicinity of 2,200 cm⁻¹ (about 15 fs)³². Similarly, the coherent superposition of 4p and 4d,f Rydberg states results in the oscillatory feature of the MP-PECD signal at ε = 500 meV. A small mismatch of about 60 meV is observed between the experimental and theoretical power spectra in Fig. 3e. This mismatch is on the order of the error made in quantum chemistry computations of excited-state energies. Overall, Fig. 3b,d unmistakably demonstrates that the electronic coherence of the intermediate Rydberg states, as identified in Fig. 3a, modulates the molecular chiroptical response.

a, Two-photon absorption (TPA) cross-sections for the excited states originating from almost pure HOMO excitation. The cross-sections have been convoluted with the UV-pump intensity squared. The blue and green curves correspond to the spectral probe intensity (I_1-NIR), down-shifted in energy to elicit the transient Rydberg states leading to photoelectrons with energies ε = 250 meV and ε = 500 meV through ionization by one photon centred at frequency ω = 1.75 eV. b, Calculated MP-PECD for photoelectrons with ε = 250 meV (green) compared with the experiment (blue). The calculations start at t = 10 fs, corresponding to the end of the pump–probe overlap region (yellow area). c, Corresponding power spectra from a Fourier analysis. The frequency axis is shown for beatings of excited states with an energy spacing between 150 meV (27.6 fs period) and 500 meV (8.3 fs period). The main peak from the computed MP-PECD evolution is at 291 meV (14.2 fs). The power spectrum of the experimental data, evaluated up to t = 35 fs, at which the oscillations are damped, shows a peak frequency at 280 meV (14.8 fs). d, Calculated MP-PECD for photoelectrons with ε = 500 meV (green) compared with the experiment (blue). e, Corresponding power spectra with a central component at 269 meV (15.4 fs) for the computed curve. The power spectrum of the experimental data is shown, with a central frequency at about 329 meV (12.6 fs). a.u., arbitrary units; FFT, fast Fourier transform.

Source Data

In our fixed-nuclei description, the electronic coherences leading to oscillatory MP-PECD do not vanish and even lead to an overestimation of the MP-PECD amplitude at all delays t. By contrast, the oscillations observed in the experimental MP-PECD (Fig. 2c–e) are damped over time, which coincides with the approximately 40 fs lifetime encoded in the time-dependent photoelectron yield (Extended Data Fig. 5). Describing the coupled electron and nuclear dynamics in an energy range in which tens of electronic states lie is beyond state-of-the-art theoretical approaches. Therefore, we alternatively performed ab initio molecular dynamics calculations on the ground state of cationic methyl lactate to which all the HOMO Rydberg states involved in the pump–probe dynamics correlate following ionization (see Supplementary Information section 3 and associated Supplementary Figs. 6–8). These calculations suggest that the most probable source of decoherence in this investigation is non-adiabatic transitions.

The oscillations of the chiroptical response for ε = 250 meV mainly result from the coherent superposition of two states, the 3d and 4p Rydberg states. We now investigate in more detail the role of these states in the chiroptical response. For a single molecular orientation \(\widehat{{\bf{R}}}\), the excited electron wave packet reads, at time t after the pump pulse vanishes, \(\Phi \left(\widehat{{\bf{R}}},{\bf{r}},t\right)=\sum _{j={\rm{3d,4p}}}{A}_{j}(\widehat{{\bf{R}}}){\Psi }_{j}\left({\bf{r}}\right)\exp (-{\rm{i}}{E}_{j}t/\hbar )\), in which \({A}_{j}(\widehat{{\bf{R}}})\) are the real two-photon transition amplitudes associated with the excited states \({\Psi }_{j}\left({\bf{r}}\right)\). The associated electron density can be partitioned as

in which \({\rho }_{{\rm{incoh}}}\left(\widehat{{\bf{R}}},{\bf{r}}\right)={A}_{{\rm{3d}}}^{2}\left(\widehat{{\bf{R}}}\right){\Psi }_{{\rm{3d}}}^{2}\left({\bf{r}}\right)+{A}_{{\rm{4p}}}^{2}\left(\widehat{{\bf{R}}}\right){\Psi }_{{\rm{4p}}}^{2}\left({\bf{r}}\right)\) and \({\rho }_{{\rm{cross}}}(\widehat{{\bf{R}}},{\bf{r}})\,=\,\)\({2A}_{{\rm{3d}}}(\widehat{{\bf{R}}}){A}_{{\rm{4p}}}(\widehat{{\bf{R}}}){\Psi }_{{\rm{3d}}}({\bf{r}}){\Psi }_{{\rm{4p}}}({\bf{r}})\). Figure 4a shows, for one selected orientation \(\widehat{{\bf{R}}}\), the coherent part \(\rho \left(\widehat{{\bf{R}}},{\bf{r}},t\right)-{\rho }_{{\rm{incoh}}}\left(\widehat{{\bf{R}}},{\bf{r}}\right)\) of the electron density, oscillating back and forth along the molecular structure with a period T = 2πħ/(E_4p − E_3d) of 14.4 fs. Ionization of the 3d and the 4p state superposition leads, after averaging over the orientations \(\widehat{{\bf{R}}}\), to the total photoelectron yield, which can be decomposed similarly to equation (1):

a, Temporal evolution of the coherent part of the electron density over one period of the quantum beating (see equation (1)). b, Photoelectron yield as a function of the pump–probe delay, oscillating in phase with the variation of the electron density shown in a, as expected from equations (1) and (2). c, MP-PECD as a function of the pump–probe delay according to equation (3). d, Snapshots of the electronic current induced by the pump pulse, on a Rydberg sphere of 10 a.u. radius surrounding the molecule for two distinct orientations \({\widehat{{\bf{R}}}}_{i}\). Propensity rules enhance ionization for orientation \({\widehat{{\bf{R}}}}_{1}\), for which the current co-rotates with the circularly polarized probe field (red arrow). e, Active orientation of the produced cations along the light-propagation axis \(\widehat{{\bf{z}}}\) as a function of time according to equation (6). f, Resulting FBFA along \(\widehat{{\bf{z}}}\) in the reactive fragmentation of methyl lactate cations (see equation (7)). The insets illustrate the preferential directions of emission of CO₂CH₃ and CH₃CHOH⁺ fragments. a.u., arbitrary units.

Source Data

The computed yield is presented in Fig. 4b for ε = 250 meV, showing how the coherent state superposition leading to \({b}_{{0}_{{\rm{cross}}}}^{(\pm 1)}\left(\varepsilon \right)\cos \left[\left({E}_{{\rm{4p}}}-{E}_{{\rm{3d}}}\right)t/\hbar \right]\) modulates the incoherent sum \({b}_{{0}_{{\rm{incoh}}}}^{(\pm 1)}\left(\varepsilon \right)\) of individual ionization cross-sections. The unnormalized MP-PECD can in turn be written as:

in which the extra phase Δϕ arises from the interference of the state-selective continuum partial wave amplitudes building the asymmetry of the photoelectron yield (see Supplementary Information). As usual, this interference is washed out at the level of the total photoelectron yield^30,33. The temporal evolution of the unnormalized two-state MP-PECD is shown in Fig. 4c, from which we extract the time delay Δt = 1.8 fs associated with Δϕ = 0.79 rad. The MP-PECD reverses sign within one period of the oscillation because the asymmetries of single 3d-mediated and 4p-mediated pathways, contributing to the incoherent MP-PECD around which the coherent part oscillates, verify |MP-PECD_cross(ε)| > |MP-PECD_incoh(ε)|. A similar behaviour is observed at lower kinetic energy in the measurement reported in Fig. 2c. Notably, the MP-PECD depends not only on the transient bound resonances—as evidenced in Figs. 2c–e and 3a,b,d—but also on the dichroism encoded by ionization with circularly polarized light. In this respect, we note that a photoexcitation electron circular dichroism (PXECD) configuration³⁴, in which molecules are photoexcited by a circularly polarized pump pulse and subsequently ionized with a linearly polarized probe, would reduce the degrees of freedom to only the transient bound resonances.

The electron dynamics uncovered in this work underlies yet another consequence on the molecular response of photoexcited chiral systems: the coherent superposition of excited states induced by the pump allows to selectively filter—within a few femtoseconds—specific molecular orientations through enantiosensitive photoionization¹⁰. An electron moving within the coherent state superposition creates an electronic current³⁵ \({\bf{J}}(\widehat{{\bf{R}}},{\bf{r}},t)=\frac{\hbar }{m}{\mathfrak{I}}[{\Phi }^{* }(\widehat{{\bf{R}}},{\bf{r}},t){\boldsymbol{\nabla }}\Phi (\widehat{{\bf{R}}},{\bf{r}},t)]\), which reduces to

when expanding Φ on the (real) 3d and 4p bound eigenstates. The chirality of the molecule induces a curl in the generated electron current, whose rotation direction reverses periodically. Rotating electron currents are known to influence the ionization probability by circularly polarized light: the propensity rules³⁶ establish that one-photon ionization is enhanced when the electrons rotate in the same direction as the electric field. Therefore, the molecules oriented such that their electronic current rotates in the same plane and direction as the ionizing laser pulse are preferentially ionized; see Fig. 4d. Consequently, the produced molecular cations are selectively oriented along the probe polarization rotation axis, corresponding to the light-propagation axis \(\widehat{{\bf{z}}}\).

To quantify the degree of orientation of the photoionized molecules, we select a unitary vector \({\widehat{{\bf{e}}}}_{{\rm{mol}}}\) fixed to the internal C–C bond of the methyl lactate cation, as illustrated in the inset of Fig. 4e, and calculate its averaged value over the probe-filtered molecular orientations in the laboratory frame as¹⁰

in which \({\widehat{{\bf{e}}}}_{{\rm{lab}}}(\widehat{{\bf{R}}})\) is the \({\widehat{{\bf{e}}}}_{{\rm{mol}}}\) vector passively rotated in the laboratory frame and \({W}^{(\pm 1)}(\widehat{{\bf{R}}},\varepsilon ,t)\) is the ionization rate associated to helicity h = ±1 and photoelectrons of energy ε. Notably, the averaged orientation of the cations depends on ε because the ε dependence of the underlying photoionization yield is not the same for all orientations \(\widehat{{\bf{R}}}\). The x and y components of \({\left\langle {\widehat{{\bf{e}}}}_{{\rm{lab}}}\right\rangle }_{\widehat{{\bf{R}}}}^{\left(\pm 1\right)}(\varepsilon ,t)\) are found to be zero and only the z component survives the averaging¹⁰ (see Supplementary Fig. 9), leading to

in which θ_ion is the angle between the internal C–C bond and the probe propagation \(\widehat{{\bf{z}}}\) axis (see inset of Fig. 4e). \({\left\langle {\cos \theta }_{{\rm{ion}}}\right\rangle }_{{\rm{cross}}}^{\left(\pm 1\right)}(\varepsilon )\) involves chiral-sensitive products of 3d and 4p excitation and ionization amplitudes. The temporal evolution of \({\left\langle {\cos \theta }_{{\rm{ion}}}\right\rangle }_{\widehat{{\bf{R}}}}^{(+1)}\) is illustrated in Fig. 4e for ε = 250 meV. When \({\langle {\cos \theta }_{{\rm{ion}}}\rangle }_{\widehat{{\bf{R}}}}^{(+1)}(\varepsilon ,t) < 0\), the CO₂CH₃ moiety of the methyl lactate cations preferentially points forward with respect to \(\widehat{{\bf{z}}}\), whereas instead it points backward when \({\left\langle {\cos \theta }_{{\rm{ion}}}\right\rangle }_{\widehat{{\bf{R}}}}^{\left(+1\right)}(\varepsilon ,t) > 0\). Such asymmetry could be detected by resolving the direction of fragmentation of the molecular cations (see Supplementary Information section 4.2 and associated Supplementary Figs. 10 and 11). Indeed, the relative numbers of molecules pointing forward and backward at time t, \({N}_{+}^{\left(\pm 1\right)}(\varepsilon ,t)\) and \({N}_{-}^{\left(\pm 1\right)}(\varepsilon ,t)\), respectively, can be linked to \({\left\langle {\cos \theta }_{{\rm{ion}}}\right\rangle }_{\widehat{{\bf{R}}}}^{\left(\pm 1\right)}(\varepsilon ,t)\) (see Methods). This ultrafast filtering of molecular orientation affects the subsequent reactive dynamics of methyl lactate cations, with prompt photoionization dictating the subsequent dissociation along the selected molecular orientation. A forward/backward fragment asymmetry (FBFA) thus naturally arises, which we define as

The FBFA is shown in Fig. 4f for h = +1 and ε = 250 meV, reaching absolute values of about 30%, whereas its temporal evolution is dictated by the behaviour of the underlying electron current \({\bf{J}}\left(\widehat{{\bf{R}}},{\bf{r}},t\right)\). Similarly to the MP-PECD, the FBFA switches sign for h = −1 or when the other enantiomeric form of methyl lactate molecules is considered. Because the FBFA is created by the electron current, it vanishes in the case of incoherent population of excited states (see Supplementary Information section 4). This shows that the chiral electronic coherence directly observed in our experiment through TR-PECD is crucial to achieve control over enantioselective dynamics of the nuclei.

We have taken an important step forward by resolving the coherent chiral electronic dynamics of a chiral molecule in the first instants following prompt excitation by an achiral few-femtosecond UV pulse. The results showcase that TR-PECD can provide insights on the role of the primary electron dynamics in the light-induced chiral response of complex molecules. Beyond its impact on the chiroptical properties of the system, the chiral currents generated in our experiment can be exploited for photochemical control, as exemplified by our calculations on enantiosensitive charge-directed reactivity leading to oriented fragmentation. From a broader perspective, our results contribute to the fundamental understanding of electronic chirality at the molecular level and its impact on primary enantiosensitive interactions.