Few-femtosecond passage of conical intersections in the benzene cation

Abstract

Observing the crucial first few femtoseconds of photochemical reactions requires tools typically not available in the femtochemistry toolkit. Such dynamics are now within reach with the instruments provided by attosecond science. Here, we apply experimental and theoretical methods to assess the ultrafast nonadiabatic vibronic processes in a prototypical complex system-the excited benzene cation. We use few-femtosecond duration extreme ultraviolet and visible/near-infrared laser pulses to prepare and probe excited cationic states and observe two relaxation timescales of 11 ± 3 fs and 110 ± 20 fs. These are interpreted in terms of population transfer via two sequential conical intersections. The experimental results are quantitatively compared with state-of-the-art multi-configuration time-dependent Hartree calculations showing convincing agreement in the timescales. By characterising one of the fastest internal conversion processes studied to date, we enter an extreme regime of ultrafast molecular dynamics, paving the way to tracking and controlling purely electronic dynamics in complex molecules.

Fig. 1

Schematic of the studied dynamics. Schematic overview of the lowest eight electronic component states of the benzene cation, depicted as potential energy V in eV as a function of a dimensionless effective nuclear coordinate Q _eff (see also Supplementary Note 1). Ionisation by the XUV pulse can simultaneously populate all of the cationic states that are shown (violet arrows). Of these cationic states, only the $\tilde{D}$-state and the $\tilde{E}$-state can be excited beyond the threshold for C₄H${}_3^{+}$ formation by a two-photon process (orange arrows). The dashed green and light blue curves are a cartoon drawing of the time-evolution of a cation originally transferred to the ${\tilde{E}}^2{B}_{2u}$ and to the ${\tilde{D}}^2{E}_{1u}$ state, respectively. Internal conversion processes via the conical intersections indicated in the figure lead to population of the ${\tilde{B}}^2{E}_{2g}$ state. The potential energy surfaces are reproduced from ref.

Fig. 2

XUV and mass spectrum. a Spectrally filtered XUV spectrum (solid black line), as used in the experiment, shown alongside partial photoelectron cross sections for the first five cationic states of benzene (taken from ref. ). b The mass spectrum acquired for time-overlapped XUV pump and VIS/NIR probe pulses (Δt = 0 fs, red line) exhibits the appearance of C₄H${}_2^{+}$ and C₄H${}_3^{+}$, which are not observed in an XUV-only (black line) measurement

Fig. 3

Time-resolved experimental data. Experimentally measured C₄H${}_3^{+}$ fragment yield as a function of the XUV-VIS/NIR delay (red dots). The bold black line is a biexponential fit to the data, the dashed lines represent the contributions from the two timescales. The inset displays a long range pump-probe scan of C₄H${}_3^{+}$

Fig. 4

Comparison of theory and experiment. Time-dependent ‘yields’ (blue lines), obtained by summing the populations of the $Ẽ$ and $\tilde{D}$ states from MCTDH calculations (see main text). The curves are derived from separate wavepacket calculations for an initial pure excitation in the $Ẽ$ and in the $\tilde{D}$ state, respectively. The solid (dashed) line represent the result obtained for adiabatic (diabatic) electronic populations. The inset displays the yield for the adiabatic state calculation, convoluted with the Gaussian instrument response function, for direct comparison to the experiment (red points, cf. Fig. 3)