Femtosecond photoexcitation dynamics inside a quantum solvent

The observation of chemical reactions on the time scale of the motion of electrons and nuclei has been made possible by lasers with ever shortened pulse lengths. Superfluid helium represents a special solvent that permits the synthesis of novel classes of molecules that have eluded dynamical studies so far. However, photoexcitation inside this quantum solvent triggers a pronounced response of the solvation shell, which is not well understood. Here, we present a mechanistic description of the solvent response to photoexcitation of indium (In) dopant atoms inside helium nanodroplets (HeN), obtained from femtosecond pump–probe spectroscopy and time-dependent density functional theory simulations. For the In–HeN system, part of the excited state electronic energy leads to expansion of the solvation shell within 600 fs, initiating a collective shell oscillation with a period of about 30 ps. These coupled electronic and nuclear dynamics will be superimposed on intrinsic photoinduced processes of molecular systems inside helium droplets.

Since the award of the 1999 Nobel Prize for Chemistry [1], various fundamental molecular processes have been investigated on their natural time scales, e.g.fragmentation via different pathways on the molecular potential energy surface [2], non-adiabatic electron-nuclear coupling [3], or electron dynamics initiated by ultrashort laser pulses [4].Superfluid helium nanodroplets (He N ) have been used as nanocryostats to isolate atoms or molecules at 0.4 K temperature, or to form new weakly bound aggregates [5,6].Their gentle influence on guest particles is demonstrated, for example, by electron spin resonance [7] or molecular rotation and alignment experiments [8,9].He droplets are an appealing spectrosopic tool because of their transparency for electromagnetic radiation up to the extreme ultraviolet energy regime [5].However, photoexcitation inside the droplet leads to dissipation of significant excess energy via coupling to collective modes of the surrounding helium, which is expected to be a fast process.Femtochemistry inside He N will allow real time tracking of photochemical reactions in novel systems, such as fragile agglomerates [10,11,12], or molecules in a microsolvation environment [13].This will, however, require a detailed knowledge about the response of the quantum fluid to the photoexcitation of a dopant atom or molecule.So far, only the ultrafast dynamics in pure helium droplets have been studied [14], and femtosecond measurements on doped helium droplets were restricted to the surface bound alkali metals [15,16] that can hardly couple to helium bubble modes.Since most foreign atoms and molecules reside inside the droplets and couple more strongly, we have concentrated on the electronic excitation of single atoms well inside the droplets.In this way, no other degrees of freedom such as rotation or vibration would interact and only the coupling of the electronic excitation with the modes of the surrounding helium should be detected.Previous spectroscopic studies in the frequency domain have shown blue-shifted excitation bands of dopants inside droplets compared to gas phase indicating that an excess energy is required to create a correspondingly larger helium bubble to accommodate the excited electron orbital [5].This excess energy must be released to the helium in form of a damped helium excitation mode.In our work, we follow the expansion of the helium bubble after the electronic excitation of the dopant in real time.After an expansion from 4.5 Å to 8.0 Å radius in 600 fs, an oscillation with a period of (28 ± 1) ps starts until the excited dopant atom leaves the droplet about 60 ps after the electronic excitation.As observable in our fs pump-probe measurements, we chose the photoelectrons released because they have been shown to exit the droplet rather ballistically without being significantly influenced by the helium environment [15,14,17].In spite of its importance for photochemical studies in superfluid helium droplets, this sequence of events has not previously been observed.

Results
We investigate photoexcitation dynamics of the In-He N system with a combination of time-resolved photoelectron spectroscopy (TRPES) and time-dependent density functional theory (TDDFT) simulation, as described in the following.A mechanistic description of the processes deduced from experiment and theory will be discussed in the final paragraph.

TRPES
The feasibility of ultrafast experiments inside He N ultimately depends on the availability of an ex-perimental observable that is available with sufficiently low distortion by the intermediate helium.
Ion detection, as used on the droplet surface, is not possible because ions are captured inside the droplet due to their attractive potential [15].Photoelectron (PE) detection, in contrast, has been successfully used for pure and doped He N [17,15,14].TRPES is a well established method for ultrafast gas-phase studies and is primarily sensitive to the electronic structure of a system [18,19].
As depicted in figure 1a, after photoexcitation by a pump pulse the evolution of the excited state is probed by time-delayed photoionization and the PE kinetic energy (red arrows) is measured.
When applied inside a He N , photoexcitation induces an abrupt disturbance of the quantum fluid solvation shell due to expansion of the valence electron wave function.Because the energies of the electronic states depend on the structure of the He environment, the transient response of the quantum solvent can be sensed with TRPES (see figure 1a).
Figure 2 shows the time-dependent evolution of the PE signal within the first picosecond after around 0.32 eV, which is about 0.02 eV above the gas-phase peak that appears at around 0.30 eV (solid line in figure 2).The remaining shift represents the reduced ionization potential of In atoms in the He environment due to polarization effects [17].
In figure 3 the PE kinetic energy up to 100 ps is shown (blue crosses).After a steep decrease representing the tail of the initial peak shift shown in figure 2, the peak position slowly decreases to reach a constant value at about 60 ps with a temporary increase at (28 ± 1) ps.

TDDFT
To obtain further insight into the ultrafast dynamics, photoexcitation of the In-He N system is simulated with TDDFT using the BCN-TLS-He-DFT computing package [8], which has been successfully applied to reproduce the dynamics of He N loaded with various different atomic species [21].
In the present case, an extraordinary amount of excess energy of several hundred meV is coupled into the system in the photoexcitation process.We therefore carefully tested the simulations for convergence by variation of the simulation parameters (see supplementary note 3 and supplementary figures 3 and 4).
Figure 1b shows He density distributions for selected times after photoexcitation and the corre-sponding bubble expansion over time is plotted in figure 4a.Inside the droplet the energies of the In excited state (5s 2 6s) and its ionic state (5s 2 ) deviate from the bare atom values by the interaction energies E HeN-In* and E HeN-In + , respectively.These interaction energies, plotted in figure 4b, are calculated by integrating the respective pair potentials over the He density.While E HeN-In* (green curve) is positive and decreases with time (for larger bubbles), E HeN-In + (red curve) is negative and increases.This behavior can be expected from the repulsive and attractive character of the excited and ionic state pair potentials, respectively (supplementary figure 2).The simulated PE peak shift with respect to the free atom, as plotted in figure 4c, is calculated as the difference of the two interaction energies (E HeN-In* -E HeN-In + ) and compared to the measured transient peak shift in figures 2a and 4c, revealing good agreement.Below 200 fs the experimental peak shifts are slightly lower than the simulated ones, which we ascribe to a distortion of the PE peaks due to a cross correlation signal caused by overlap of pump and probe pulses in this temporal region (c.f., figure 2b).
Next, we compare the steady decrease of the excited state electronic energy (green curve in figure 4b) to the kinetic energy of the helium atoms (dashed line in figure 4b), and find that the two curves show almost exactly complementary trends.
Finally, the simulated PE peak position for an In atom, that is photoexcited at a distance of 20 Å from the droplet center, is shown in figure 3 (orange line).The simulated curve shows the same overall decrease as the experimental values (blue crosses), although with a more pronounced temporal increase at 22 ps.

Conclusions
The transient shift in the pump-probe PE spectrum of the In-He N system within the first ps (fig- ure 2) has to be related to solvation shell dynamics, as no internal degrees of freedom are available for relaxation of the In atom in its lowest electronically excited state.The energy of the excited valence electron in the In*-He N system is a very sensitive probe for the temporal evolution of the He environment because of strong Pauli repulsion with the surrounding helium [22].TRPES measures the transient PE kinetic energy, which additionally depends on a temporal shift of the ionic state energy (E HeN-In + , figure 4b).Therefore, we use TDDFT modeling of the photoexcitation process in order to distinguish these two contributions.Previously, TDDFT simulations could only be compared to time-dependent experiments at the weakly-interacting droplet surface [16].
In the interior, the dopant-He interaction is much stronger, with the consequence that significantly more excess energy (270 meV ≈ 2200 cm −1 in our case) is coupled into the system during photoexcitation, challenging the accuracy of the TDDFT approach.The reproduction of the observed transient PE peakshift by TDDFT (figures 2a and 4c), without using any experimental input for the simulation, demonstrates that a simulation of photoexcitation dynamics is possible even in the case of significant excess energy.
By combining experiment and theory we obtain the following mechanistic picture of the coupled, ultrafast electronic and nuclear relaxation process: Photoexcitation increases the radial expansion of the valence electron wave function, thereby pushing the surrounding He away (see supplementary video 1).The spherical He bubble containing the excited In atom almost doubles its radius from 4.5 Å to 8.0 Å within 600 fs after excitation (figures 1b and 4a).This process can also be explained with the corresponding potential energy surfaces (figure 1a): Because the equilibrium bubble radius of the excited electronic state is larger than that of the ground state, photoexcitation causes enlargement of the solvation shell.This nuclear relaxation can be followed as transient PE peak shift because the potential energies of the excited state and the ionic state depend on the distance of neighboring He atoms to the In dopant.From an energetic viewpoint, the bubble expansion is accompanied by the conversion of electronic energy into kinetic energy of the He atoms, as illustrated by the mirror-imaged progression of the two corresponding curves (excited state interaction energy E HeN-In* and kinetic energy of the He atoms E kin, He ) in figure 4b.
The impulsive stimulation of the He solvation layer initiates a collective oscillation of the He bubble, the first contraction of which is observed as increase of the PE kinetic energy in figure 3 at (28 ± 1) ps, induced by the temporally increased He density in the vicinity of the In atom.The repulsive character of the excited state In-He pair potential (see supplementary note 2 and supple-mentary figure 2) leads to ejection of the In atom from the droplet on a time scale of about 60 ps (see supplementary video 2).Consequently, the PE kinetic energy decreases to the free-atom value within this time span (see figure 3) and only one bubble oscillation can be observed.While the TDDFT simulation assumes a fixed starting location of the In atom, the experimentally observed ensemble comprises a distribution of In atoms within the droplet.As a consequence, the timing of the first bubble contraction will appear smeared out in the experimental data.Nevertheless, the observation of the collective oscillation in superfluid He provides insight into the hydrodynamics of the bubble in real time [23].
In conclusion, our experiments prove that ultrafast, coupled electronic and nuclear dynamics of particles located inside superfluid He nanodroplets can be observed and simulated.As a proof of concept, our results pave the way to use helium droplets as a novel sample preparation technique for ultrafast studies on previously inaccessible tailor-made or fragile molecular systems.
support by Miriam Meyer and acknowledge financial support by the Austrian Science Fund (FWF) under Grant P29369-N36, as well as support from NAWI Graz.

Helium droplet generation and In atom pickup
Helium droplets with an average size of about 4000 atoms are generated by supersonic expansion of high purity (99.9999 %) helium gas through a cooled nozzle (5 µm diameter, 18 K temperature, 40 bar stagnation pressure) into high vacuum.The expansion in combination with evaporative cooling results in droplet temperatures of about 0.4 K, which is well below the superfluid phase transition of helium.The He N are doped with In atoms inside a pickup region, where indium is resistively heated.Pickup conditions are optimized for single atom pickup and for an acceptable signal-to-noise ratio.After passing a differential pumping stage to increase the vacuum quality, the doped droplets enter the measurement chamber, where the He N beam is crossed at right angle by the femtosecond laser pulses inside the extraction region of a time-of-flight spectrometer.

Time-resolved photoelectron spectroscopy
A commercial Ti:sapphire femtosecond laser system (Coherent Vitara oscillator, Legend Elite Duo amplifier) delivers 25 fs laser pulses with 800 nm central wavelength and 4 mJ pulse energy at a repetition rate of 3 kHz.The pulses are split into a pump and a probe path with variable time delay.Pump pulses are frequency up-converted by an optical parametric amplifier (Coherent OPerA Solo) that tunes the wavelength to 376 nm (6 nm full width at half maximum, FWHM).Probe pulses are frequency doubled to 405 nm (3 nm FWHM) with a 1 mm thick BBO crystal and guided over a delay stage.Dichroic mirrors are used in both beam paths to remove undesired wavelengths from the upconversion process.Pump and probe pulses are focused into the extraction region of the linear time-of-flight spectrometer, where they overlap in space and time at the intersection region with the He N beam.A magnetic bottle configuration [1] ensures high electron detection efficiency and a small positive repeller voltage of a few hundred meV increases the electron kinetic energy resolution.The measurement chamber is operated at a base pressure of 10 −10 mbar.
The intensities of the pump and probe pulses are optimized to obtain a maximum pump-probe signal with respect to pump-only and probe-only backgrounds.The pump wavelength for In excitation to the lowest excited state (5s 2 6s) is chosen to be 376 nm in order to optimize the monomer to dimer ratio (see supplementary note 1 and supplementary figure 1), which is blue-shifted by 270 meV with respect to the gas-phase excitation wavelength at 410 nm [2].This amount of excess energy is coupled into the In-He N system at photoexcitation.The pump-probe cross correlation is estimated with 150 fs.

Time-dependent helium density functional theory
In the last years the approach of TDDFT for the bosonic system of helium has been successfully applied to describe the dynamical interaction of surface-and centre-located species with the helium quantum fluid, providing important insight into effects like superfluidity on the microscopic level [3], desorption dynamics [4], or collision processes [5,6].Details on the application and formalism of static and dynamic HeDFT are given elsewhere [9] and the computing package of the BCN-TLS group is available to the public as open source [8].Here only the basic concepts that affect the presented results are given: Both static and dynamic computations are based on the diatomic In-He potential energy surfaces.These pair potentials were calculated with high level ab initio methods for the ground, excited and ionic state (see supplementary note 2 and supplementary figure 2).The simulations are performed for a He 4000 droplet with the In impurity located in the centre by using a He-functional that includes the solid term [7].We use a three dimensional Cartesian box of 96 Å length with a discrete grid size of 320 pt (0.3 Å spacing) and time steps of 0.1 fs to simulate the bubble expansion dynamics within the first ps and a grid size of 256 pt (0.375 Å spacing) and time steps of 1 fs for the bubble oscillation dynamics up to 100 ps.For the bubble oscillation dynamics the starting position was chosen to be at 20 Å distance to the centre, in order to obtain a similar ejection behavior as in the experiment (whereas the bubble expansion in the first picosecond is a purely local effect and doesn't depend on the dopant location).
With the statically optimized ground state He density, a dynamical evolution is triggered by re-placing the ground state pair potential with the excited state pair potential.This instantaneous perturbation drives the system and TDDFT allows to follow the resulting dynamics in real time [9].
Photoelectron spectra are simulated by integrating the pair potential energies E He-In over the whole droplet density for both the excited state and for the ionic state.The difference between the interaction energies directly compares to the difference in ionization energy of the immersed impurity and therefore to the shift in PE energy.
Since a huge amount of energy is deposited into the system in the excitation process, the simulations were tested for numerical uncertainties by variation of different parameters (grid size, time step and cutoff energy), as presented in supplementary note 3 and supplementary figures 3-4.erence configuration interaction (MRCI) [8,9] is applied.The active space of the MRCI approach consists of three valence electrons, the core orbitals are optimized in the MCSCF calculation and kept doubly occupied.The curves are basis set-extrapolated by applying additional calculations with the aug-cc-pVQZ and aug-cc-pVTZ basis set families and the three-point extrapolation formula by Wilson and Dunning [10].By using the Breit-Pauli operator, the spin-orbit splitting is calculated.
figure 8d), but still remains in the 10 −9 eV range.
Another important parameter is the cutoff-energy for the different pair potentials, that has to be chosen high enough in order to avoid unphysical He density cumulations and energetic instabilities.
The cutoff-energies for the ground state, the excited state and the ionic state potential are chosen with 2150 cm −1 , 1008 cm −1 and 5560 cm −1 , respectively.As the excited state cutoff-energy has the lowest value, different energies around 1008 cm −1 were tested with the result that the influence on the excited state interaction energy was below 10 −10 eV (not shown).

Figure 1 :
Figure 1: Temporal evolution of the In-HeN system after photoexcitation.(a) Sketch of the In-HeN potential energy surfaces as function of the bubble radius for In in its ground [5s 2 5p ( 2 P 1/2 ), blue], lowest excited [5s 2 6s ( 2 S 1/2 ), green] and ionic ground state [5s 2 ( 1 S0), red].The purple arrow indicates pump excitation at 376 nm, blue arrows indicate probe ionization at 405 nm for characteristic delay times and red arrows correspond to the PE kinetic energy, as measured by TRPES.(b) Helium density distributions of a He4000 droplet with an In atom located in the centre for selected times after photoexcitation, as calculated with TDDFT.

Figure 2 :
Figure 2: Time-resolved PE spectra of single In atoms solvated inside HeN with an average size of 4000 He atoms per droplet.(a) PE kinetic energy spectrum as function of the pump-probe time delay ∆t, together with the simulated dynamics (dashed line) and the gas-phase PE energy (solid line).Around time-zero the PE signal is increased due to temporal overlap of the pump and probe pulses.(b) Selected spectra for different pump-probe time delays, which resemble horizontal cuts through the 2D plot in (a).

Figure 3 :
Figure 3: Transient PE peak position within 100 ps after photoexcitation, measured with TRPES (blue crosses) and simulated with TDDFT (orange line).The experimental peak position is obtained by Gaussian fits to the corresponding PE energy spectra.The start position for the TDDFT simulation was 20 Å from the droplet center in order to obtain a similar ejection behavior as the experiment.

Figure 4 :
Figure 4: Photoexcitation dynamics of the In-He4000 system simulated with TDDFT.(a) Bubble radius as a function of time, determined as position of the corresponding He distribution at which the density has dropped to 50% of the bulk value.Times for which the calculated He density is shown in figure 1b are indicated.(b) Interaction energy E He N -In* of the 5s 2 6s excited state (green curve) and interaction energy E He N -In + of the 5s 2 ionic state (red curve).Additionally, the kinetic energy of the He atoms, E kin, He , is plotted as dashed line.(c) Simulated PE peak shift induced by the He environment (orange line), obtained as E He N -In* -E He N -In + (indicated by the shaded area in (b)), which is also shown in figure 2a.For comparison to the measured shift of the PE peak position over time, the recorded electron spectra at all time delays (c.f., figure2b) are fitted with Gaussian functions and the line positions are indicated here by blue crosses.

Figure 5 :
Figure 5: Excitation spectrum of the indium monomer (In) and the indium dimer (In2), both solvated inside HeN.The spectra are measured in a pump-probe experiment with 200 ps time delay and photoion detection at the In monomer mass (115 amu) and the In dimer mass (230 amu), respectively.The pumpprobe delay time is sufficiently long that both monomers and dimers are ejected from the droplet and ionized in the gas phase.The spectra were recorded at a higher In pickup temperature as the presented experiments in order to obtain a stronger dimer signal.Additionally, the gas phase In transition (green, solid line) and the applied excitation wavelength (black, dashed line) are indicated.

Figure 6 :
Figure 6: Indium-Helium interaction pair potentials used for the DFT and TDDFT simulations.Ground state (blue), first excited state (green) and ionic state (red).