Simulated XUV Photoelectron Spectra of THz-pumped Liquid Water
Caroline Arnold, Ludger Inhester, Sergio Carbajo, Ralph Welsch, Robin Santra
aa r X i v : . [ phy s i c s . c h e m - ph ] J a n The following article has been accepted for publication by Journal of Chemical Physics.After it is published, it will be found at https://doi.org/10.1063/1.5054272/ . Simulated XUV Photoelectron Spectra of THz-pumped Liquid Water
Caroline Arnold,
1, 2, 3, a) Ludger Inhester, Sergio Carbajo, Ralph Welsch, b) and RobinSantra
1, 2, 3 Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg,Germany Department of Physics, University of Hamburg, Jungiusstrasse 9, 20355 Hamburg,Germany The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149,22761 Hamburg, Germany Stanford University and SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025, USA
Highly intense, sub-picosecond terahertz (THz) pulses can be used to induce ultra-fast temperature jumps (T-jumps) in liquid water. A supercritical state of gas-likewater with liquid density is established, and the accompanying structural changesare expected to give rise to time-dependent chemical shifts. We investigate the pos-sibility of using extreme ultraviolet (XUV) photoelectron spectroscopy as a probefor ultrafast dynamics induced by sub-picosecond THz pulses of varying intensitiesand frequencies. To this end, we use ab initio methods to calculate photoionizationcross sections and photoelectron energies of (H O) clusters embedded in an aque-ous environment represented by point charges. The cluster geometries are sampledfrom ab initio molecular dynamics simulations modeling the THz-water interactions.We find that the peaks in the valence photoelectron spectrum are shifted by up to . after the pump pulse, and that they are broadened with respect to unheatedwater. The shifts can be connected to structural changes caused by the heating, butdue to saturation effects they are not sensitive enough to serve as a thermometer forT-jumped water. a) Electronic mail: [email protected] b) Electronic mail: [email protected] . INTRODUCTION Water is the main solvent on earth and the primary component of living organisms. Theultrafast processes that unfold in water on a femto- to picosecond time scale are thus of directrelevance to many biological and chemical processes, e.g., radiation damage and reactionkinetics . To investigate these ultrafast chemical reactions, one requires means to triggerthem in a controlled and abrupt way. It is therefore desirable to immediately transfer energyinto specific degrees of freedom that initiate the sought-after ultrafast processes. To this end,short pulses that directly target vibrational modes can be used. In the infrared (IR) rangeintramolecular modes are excited, while in the terahertz (THz) range the intermolecularlibrations (hindered rotations) and vibrations are pumped. Large amounts of energy can betransferred from ultrashort, high-intensity THz pulses to water through the efficient couplingof THz radiation to water molecules due to the large dipole moment of water. This resultsin an ultrafast increase in temperature known as a temperature jump (T-jump).T-jump experiments were originally introduced to measure rates of chemical reactionsin solutions on the timescale of microseconds . The advent of femtosecond lasers allowedto investigate the fundamental timescale of chemical dynamics . Using IR laser light inresonance with intramolecular O-H modes, a T-jump of few Kelvin on the timescale ofpicoseconds has been observed in liquid water through transient x-ray absorption . Similartechniques were used to resolve ultrafast changes in the hydrogen bond network . Excitingintermolecular modes in the THz range is of special interest, as they are tied directly to thehydrogen bond network that is assumed to play a role in the numerous water anomalies ,as well as the solvation dynamics . These processes can be investigated by 2D Raman-THz spectroscopy . However, these types of experiments are very hard to interpret ,and thus more direct approaches to investigate the structural dynamics and the role of thehydrogen-bond network in solvation dynamics of THz-pumped water are desirable.THz-induced T-jumps can also be used to vibrationally excite other inorganic or organicmolecules of interest that are solvated in liquid water . Here, the THz pulse does notdirectly couple to vibrational modes of the solvated molecule, but energy is redistributedthrough the excitation of solvent modes. This allows to trigger ultrafast molecular dynamicsin these molecules that are not accessible by current techniques in ultrafast, time-resolvedexperiments that typically trigger reactions by direct, electronic excitation with an ultrashort2ulse. This opens new possibilities to explore in the field of ultrafast chemistry.High-intensity THz pulses of a duration of less than a picosecond have recently been re-alized experimentally in both lab-based sources and as part of free-electron laser (FEL)beamlines . At FELs like, e.g., FLASH, split THz-XUV beamlines are available . AtFLASH, THz pulses are created by the same electron bunch as the XUV beam, producingaligned and synchronized pulses. This setup is ideally suited for pump-probe experiments,where a THz pulse triggers dynamics in liquid water that are then probed by XUV spec-troscopy. The short probe pulse duration of 50 to 100 fs enables the time-resolution ofultrafast processes. An even better time resolution is conceivable considering lab-basedprobe-pulse sources .Theoretical descriptions of the sub-picosecond, THz-induced T-jump in liquid waterhave been given employing both classical force fields and ab initio molecular dynamics(AIMD) . The maximum energy transfer is reached with pump pulse frequencies between14 and 17 THz, where rotations of water molecules are excited . Ultrafast T-jumps ofmore than within tens of femtoseconds are predicted within currently accessible THzintensity levels . The instantaneous temperature can be calculated directly from the molec-ular dynamics (MD) trajectories of THz-pumped water and was shown to be independent ofthe simulation box size . It can be connected to structural changes of the pumped water.Observing these structural changes in experiments with time resolution of less than 100 fscan be used to evaluate the efficiency of the THz-induced T-jump.Measuring ultrafast T-jumps experimentally is challenging. Generally, in ultrafast pump-probe experiments, structural changes may be probed employing two different strategies.First, by x-ray diffraction techniques the rearrangement of nuclear geometries can be directlyinvestigated. The structure factor, related by Fourier transform to the radial distributionfunction (RDF), is an indicator for the order maintained in a liquid. Especially in water,vanishing peaks in the RDF have been used as indicators of the rupture of hydrogen bondsin supercritical conditions . Second, changes in the molecular geometries have impact onthe electronic structure . The supercritical state of water that can be created by sub-picosecond THz pump pulses, where the T-jump occurs isochorically, will be accompaniedby changes in the valence electron levels that are susceptible to changes in the hydrogenbond network . In the context of IR-induced T-jumps in water, x-ray absorption hasbeen used as a probe . With photon energies close to the oxygen K-edge, low-lying unoc-3upied molecular orbitals are investigated. The complementary tool to study shifts in theoccupied outer and inner valence molecular orbitals is x-ray emission spectroscopy or XUVphotoelectron spectroscopy .In this manuscript, we will explore the potential of photoelectron spectroscopy as a probefor the structural changes induced by an ultrafast T-jump in liquid water following the ex-citation by high-intensity, sub-picosecond THz pulses of various peak intensities and fre-quencies. In Sec. II, we analyze the structural changes that are induced by sub-picosecond,high-intensity THz pulses based on AIMD trajectories . We then describe the theoreticalframework for the calculation of photoionization cross sections from liquid water in Sec. III.The simulated photoelectron spectrum of liquid water is discussed in Sec. IV A and charac-teristic changes in the photoelectron spectrum following a high-intensity THz pump pulseare investigated in Sec. IV B. Finally, in Sec. V we summarize our results and open upconnections to possible experiments. II. STRUCTURAL CHANGES INDUCED BY THZ-PUMPINGA.
Ab initio
Molecular Dynamics Trajectories
The analysis in this work is based on ab initio molecular dynamics (AIMD) trajectoriesof THz-pumped water that were the subject of previous work . The trajectories were gener-ated with the CP2K molecular dynamics package , employing the Perdew-Burker-Ernzerhof(PBE) functional together with the Geodecker-Teter-Hutter (GTH) pseudopotential, as wellas the TZV2P basis set. The non-empirical PBE functional was chosen by Mishra et al. as itreproduces electronic polarizability well. This property determines the coupling to the THzpump pulse, and a good description is thus imperative to study THz-induced T-jumps. Formore details, we refer to Refs. 21, 25. Nonetheless, please note that the PBE functional re-sults in water with liquid properties that deviate from bulk water at room temperature .Mishra et al. obtained ten different initial conditions by taking snapshots from an ab initio trajectory under NVT conditions, stabilized with the Nose-Hoover thermostat, a tempera-ture of 300 K and a fixed density of / cm . A total number of 128 water molecules wasused with periodic boundary conditions for a cubic box of
16 ˚A edge length. Mishra et al. sampled ten initial conditions with a time separation of 300 fs. Since the the PBE functional4nderestimates diffusion constants and prolongates equilibration times , this resulted in aslightly favored orientation of the water molecules in the initial trajectory snapshots with h cos ϑ i = 0 . . . . . , where ϑ is the angle between a molecular dipole and the THz fieldaxis. The variance of these angles was h cos ϑ i ≈ / across all initial conditions, whichcorresponds to the value expected with uniform sampling. The partially incomplete equi-libration may cause some short-time non-equilibrium dynamics. As the sub-picosecond,high-intensity THz pulse quickly drives the system far out of equilibrium, this will not affectthe main conclusions drawn in this work.For each pulse intensity and frequency given in Table I, these initial snapshots werepropagated for
500 fs including a THz pulse, and for an additional without any externalfield. The THz pump pulse was implemented by E ( t ) = ε ( t ) e z cos(2 πνt + ϕ ) , (1)where the Gaussian pulse envelope was ε ( t ) = A exp ( − t / σ ) , with a width of σ = τ FWHM / √ ln 2 , τ FWHM = 150 fs , carrier-envelope phase ϕ = π/ , and the central THzfrequency ν . The peak field amplitudes considered were A = 0 .
274 V / ˚A , correspondingto a peak pulse intensity of I = 1 × W / cm , and A = 0 .
614 V / ˚A , corresponding to I = 5 × W / cm , respectively.The THz pump pulse excites intermolecular modes and transfers a large amount of energyto bulk water within less than a picosecond. Prior analysis of the trajectories revealed thatthe induced T-jump is maximal for
16 THz . The T-jump scales with intensity obeyinga power law, ∆ ¯ T ( I ) ∝ I β ν , where a nonlinear regime could be found for ν <
19 THz( β ν ≈ . ... . , separated from a saturation regime at higher THz frequencies ( β ν < .The large amount of energy deposited through the pump pulse led to problems with energyconservation in some of the AIMD trajectories. Therefore, for the high intensity considered,these trajectories had to be excluded from the analysis, reducing the available numberof trajectories as summarized in Table I. The trajectories were generated under isochoricconditions, as the bulk water does not expand considerably during the first 1.2 ps followingthe THz pump pulse . Therefore, all structural changes that can be extracted from thetrajectories are related to the excitation of intra- and intermolecular modes.5 able I. Number of trajectories from different initial conditions, considered for different values ofthe THz pump pulse intensity I and central frequency ν . I [W / cm ] ν [THz] Trajectories × , , , × , × × , t = 250 fs : T-jump values ∆ T repeated fromMishra et al. and remaining fraction f HB of hydrogen bonds. I [W / cm ] ν [THz] ∆ T [K] f HB × ×
19 212 0.44 ×
30 128 0.78 × ×
19 1193 0.06 ×
30 558 0.19
B. Transformation to Super-Critical State by THz pump
From the AIMD trajectories, the radial distribution function (RDF) of heated water afterthe pulse ( t = 250 fs , where t = 0 fs refers to the maximum of the pump pulse envelope) iscalculated for different pump pulse frequencies, see Fig. 1. At I = 1 × W / cm (Fig. 1a),the change in structure is dependent on the pump pulse frequency: at the frequencies thatwere shown to be most efficient at transferring energy to the water molecules, i.e., 16 and 19THz , the RDF is evened out more than at 7 and 30 THz, which indicates more structuralchanges are induced. At I = 5 × W / cm (Fig. 1b), the loss of order in the liquid is muchmore apparent. The RDF evens out, and the bulk water approaches a supercritical state ofliquid density but gas-phase-like lack of order, regardless of the pump pulse frequency. Notethat the employed PBE functional overestimates the degree of initial structural correlations6 igure 1. Radial distribution function (RDF) for oxygen pairs for a THz pulse intensity of (a) × W / cm and (b) × W / cm , and frequencies of 7, 16, 19, and 30 THz, re-spectively. The RDF is calculated from trajectory snapshots directly after the end of the pumppulse,
250 fs after the pulse maximum, with 128 molecules employing periodic boundary conditionsand averaged over up to ten trajectories, cf. Table I. The RDF of unheated water, i.e., t = −
250 fs ,is shown as a black solid line. compared to neutron diffraction data .We evaluate additional quantities at t = 250 fs directly from the AIMD trajectories, seeTable II. The fraction of hydrogen bonds remaining after the pulse is given. A hydrogen bondis here defined geometrically between two molecules where the oxygen-oxygen distance isless then d OO = 3 . , and the angle between the covalently bound hydrogen and the acceptoroxygen is less then α = 20 ◦ . For the lower I = 1 × W / cm , the remaining fraction ofhydrogen bonds is frequency-dependent. With the stronger I = 5 × W / cm , the numberof hydrogen bonds is depleted strongly regardless of the frequency. Both the structuralchanges seen from the RDF as well as the depletion of hydrogen bonds are frequency-dependent only for the lower intensity. When taking into account the T-jumps (repeatedfrom Ref. 21 in Table II), we note that, though the T-jump at the higher intensity and7 igure 2. Distribution of various intra- and intermolecular distances and angles across trajectories,obtained after the THz pulse ( t = 250 fs) : For I = 1 × W / cm and ν =
7, 19, and 30 THz,the distributions of (a) the distance between neighboring oxygen atoms d OO , (b) the covalent bondlength d OH , and (c) the intramolecular angle α H O are displayed. The corresponding distributionsfor I = 5 × W / cm are shown in panels (d) – (f ) . For all quantities, the initial distributionobtained from unheated water ( t = −
250 fs) is included (solid black line) . See Table S1 in the SMfor the values of the mean and width of the displayed distributions.
19 THz is about twice the T-jump at 7 and 30 THz, the structural changes are comparable.We conclude that there is a saturation regime of structural changes with respect to theenergy transferred by the THz pump pulse, and that it has been reached with the higherintensity.Overall, the THz pump pulse deposits a large amount of energy in the water, giving riseto a larger variability in structural arrangements of the water molecules. Comparing theunpumped and pumped water, the widths of distributions for different intra- and intermolec-ular distances and angles are increased. This is shown in Fig. 2 for the distance between8eighboring oxygen atoms, the covalent bond length, and the intramolecular bending an-gle at lower intensity, I = 1 × W / cm , panel (a)–(c) , as well as at higher intensity, I = 5 × W / cm , panel (d)–(f ) . Moreover, small shifts in the means of these distributionscan be observed. Both the broadening and the shifts increase with intensity. The valuesof the mean and width of these distributions can be found in Table S1 of the supplementalmaterial (SM). Figure 3. Schematic description of XUV photoelectron spectroscopy as a probe for chemical shifts.XUV photons with energy ¯ hω XUV create photoelectrons (PE) with kinetic energies given by thedifference of the photon energy and the molecular orbital energy. Ultrafast structural changesinduce chemical shifts . From time t (left) to t (right), the molecular orbitals are shifted inenergy, which is directly reflected in the photoelectron spectrum. Structural changes in water can induce chemical shifts of valence electrons, that then alterthe photoelectron spectrum , see Fig. 3. In the following we investigate the photoelectronspectrum of T-jumped liquid water excited by THz pump pulses of varying intensities andfrequencies and analyze changes in the valence photoelectron spectrum as an experimentalsignature of structural changes. 9 II. CALCULATION OF PHOTOELECTRON SPECTRA OF LIQUIDWATER
The valence orbitals of water can be probed using XUV photons . We consider a probepulse of ω XUV = 60 eV photon energy, and calculate both photoionization cross sections andphotoelectron energies. We do not account for attenuation of the ejected photoelectrons inbulk water and note that, generally, photoelectrons probe the surface of liquids as attenua-tion lengths are on the order of few nanometers . A. Xmolecule
Photoionization Cross Sections
The photoionization cross sections of THz-pumped water are calculated using an extendedversion of the
Xmolecule toolkit . The outgoing photoelectron is described by atomiccontinuum wave functions, and its energy is obtained by Koopmans’ theorem as ε = ω XUV + ε a , where ε a is the Hartree-Fock (HF) energy of the ionized molecular orbital (MO). MOs arerepresented in Xmolecule as linear combinations of atomic orbitals (LCAO) . Followingthe approximations of Ref. 48, the photoionization cross section for linearly polarized XUVlight from MO φ a , averaged over the orientation of the molecules, is given by σ a ( ω XUV ) = 4 π αω XUV atoms X A X lm X d = x,y,z " X µ onA C µa | h χ µ | d | χ εlm i | +2 X µ<ν onA C µa C νa h χ µ | d | χ εlm i h χ ν | d | χ εlm i , (2)where α is the fine-structure constant, χ µ a basis function in a minimal atomic orbital basisset, and χ εlm the wave function of the outgoing photoelectron with angular quantum numbers l, m and energy ε . The transition dipole matrix elements h χ µ | d | χ εlm i are obtained fromtabulated values from an atomic electronic structure calculation performed with Xatom .Further details are given in previous work . For calculations with the larger basis set, aprojection of the MOs expanded in the larger basis set onto the minimal basis set is performedto obtain an LCAO description of the MOs with minimal basis functions. Accordingly, thecorresponding LCAO coefficients for the minimal basis set are given by C ( m ) = S − · O · C ( l ) , (3)10here C ( l ) is the matrix of orbital coefficients in the larger basis set, C ( m ) are the orbitalcoefficients in the minimal basis set, O is the overlap matrix between the different basis sets,and S − the inverse of the overlap matrix of the minimal basis set. B. Embedded Water Clusters
As the investigation of liquid water requires sampling of many water cluster geometries,an efficient electronic structure method is imperative. The calculations are done at the HFlevel of theory employing the 6-31G basis set on water clusters containing 20 water molecules,which are embedded in point charges that model the surrounding water molecules. Froma given trajectory snapshot, we select a (H O) water cluster around a central moleculecorresponding to roughly two solvation shells around the central water molecule ( r ≈ . .At this cluster size, spectral features are converged with our electronic structure method,see Fig. S14 of the SM. For water molecules beyond the second solvation shell, it is sufficientto consider their charge distribution rather than include them in the quantum electronicstructure calculation . Thus, 108 surrounding molecules are substituted with point chargesof q O = − . at the oxygen positions and q H = +0 . at each of the hydrogen positions,according to the charge values of the SPC 3-site water model . To sample different wa-ter geometries, photoelectron spectra are averaged from 43 (H O) clusters per trajectorysnapshot. The dependence of photoelectron spectra on different water geometries is shownin Fig. S15 of the SM. The calculated spectral transitions are convolved with Gaussians of . bandwidth to account for further broadening effects. IV. PHOTOELECTRON SPECTROSCOPY OF THZ-PUMPED WATERA. Photoelectron Spectrum of Unheated Water
The simulated photoelectron spectrum of liquid water before the action of the THz pulseis shown in Fig. 4. The photoelectron spectrum obtained from the clusters in vacuum iscompared to the spectrum from embedded clusters. From higher to lower binding energies,the arising peaks are labeled with the molecular orbitals of a single H O . Their extensionalong the binding energy axis, as obtained from Hartree-Fock electronic structure calcula-tions, is 42 to 30 eV (2 a ) , 24 to 19 eV (1 b ) , 19 to 14 eV (3 a ) , and 14 to 9 eV (1 b ) . The11 igure 4. Photoelectron spectrum of unheated liquid water from (H O) water clusters in vacuum (yellow dashed line) , averaged over 43 geometries from ten trajectory snapshots, and the sameclusters embedded in 108 additional water molecules modeled as point charges ( q O = − . , q H =+0 . (velvet solid line) . Experimental data is included for comparison (black dotted line) , shiftedby 2 eV towards lower binding energies and rescaled to the outer-valence peak height obtained fromembedded (H O) clusters. The arising peaks are labeled with the molecular orbitals of a single H O for later reference. Their extension along the binding energy axis, as obtained from Hartree-Fock electronic structure calculations, is 42 to 30 eV (2 a ) , 24 to 19 eV (1 b ) , 19 to 14 eV (3 a ) , and14 to 9 eV (1 b ) . low-lying a orbital is formed mostly from the oxygen s orbital and is beyond the energy ofXUV photons. The embedding leads to a more compact photoelectron spectrum, as surfaceeffects are diminished. For comparison, an experimental XUV photoelectron spectrum ofliquid water is included . Most of the relevant spectral features, peak positions, widths,and relative heights, are well reproduced within our theory. The gap between the outer-and inner-valence peaks is overestimated due to the lack of relaxation mechanisms in theemployed electronic structure model. While the b peak is clearly discernible, the a and b peak are less separated than seen in experimental data. This is consistent with elec-tronic structure calculations on gas phase H O , that show the gap between these peaks tobe 1.43 eV, underestimating the experimental gap of 2.24 eV . In the following, we concen-trate on relative changes in the photoelectron spectrum induced by THz-pumping, and thesystematic errors introduced by the electronic structure method mostly cancel.12 . Photoelectron Spectrum of T-jumped Water Figure 5. Time evolution of the photoelectron spectrum for incident XUV photon energy
60 eV , THzpump pulse parameters I = 5 × W / cm , ν = 19 THz , and ∆ τ FWHM = 150 fs . Here, spectra from43 geometries of (H O) from seven trajectory snapshots, embedded in an additional 108 moleculesthat are modeled as point charges, were averaged. (a) Time evolution of the photoelectron spectrumto , convolved in time with the expected XUV pulse duration of
50 fs for comparison withfuture experimental data. (b)
Photoelectron spectra for distinct time steps, where t = 0 fs refersto the maximum of the THz pulse envelope. The initial photoelectron spectrum of the unheatedwater is shown as the shaded area. (c) Difference spectra for distinct time steps with respected tothe photoelectron spectrum of unheated water at t = −
250 fs . We now calculate relative changes induced through THz-pumping in the photoelectronspectra with respect to the initial spectrum shown in Fig. 4. This allows us to quantifythe impact of sub-picosecond THz-induced T-jumps on photoelectron spectra of bulk wa-ter. We focus on pulse parameters that induce a strong T-jump of about , i.e., I = 5 × W / cm and ν = 19 THz . Figure 5 shows the time evolution of the photo-electron spectrum of embedded (H O) clusters, averaged over 43 water cluster geometriesper trajectory snapshot. Changes in the photoelectron spectrum are highlighted by com-13 igure 6. Time evolution of the means (a) and widths (b) of the peaks in the photoelectronspectrum induced by the same pulse as in Fig. 5. The change of peak means and the relativechange in peak widths is plotted, with the initial values at t = −
250 fs indicated in the respectivepanels. The THz pump pulse intensity is included as the shaded grey area. From top to bottom,the peaks shown correspond to a , b , a , and b , cf. Fig. 4. paring the photoelectron spectrum along the trajectories with the initial, unperturbed one(Fig. 5b, shaded grey area), and by including the difference spectrum with respect to theinitial photoelectron spectrum (Fig. 5c).To quantify these changes, we identify the peaks labeled by the MOs of a single H O at14he intervals described above (cf. Fig. 4). For each interval, we calculate the mean and widthas the first cumulant and square root of the second cumulant of the spectrum, respectively.The resulting changes in the photoelectron spectra are shown in Fig. 6. The inner-valenceshell a peak, as well as the b peak, shift towards higher binding energies by up to ∆ µ ( t ) = µ ( t ) − µ ( t ) ≈ . . These two peaks are formed by MOs with strong bindingcharacter and are thus affected by the heating of intramolecular degrees of freedom. The a peak, formed by MOs that contribute to OH-bonding shifts slightly to lower bindingenergies by about 0.1 eV. Finally, the b peak, characterized by MOs from the oxygen lonepairs, stays unaffected. The relative increases in peak widths, ∆ σ ( t ) = ( σ ( t ) − σ ( t )) /σ ( t ) ,amount to about . for the a and . for the b peak. The a peak is constant in width,and the b peak again extends slightly by . . Taken together, the three outer-valencepeaks are broadened. After the pulse has ended at t = 250 fs , the centers and widths ofthe peaks in the photoelectron spectrum only show small changes around the then-achievedvalues. The details of the transient changes occuring during the THz pulse are discussed inthe SM.The temporal variations in the photoelectron spectra indicate changes in the chemicalenvironment and are associated with the transformation from liquid bulk water to super-critical water-like structures, i.e., gas with liquid density. Intramolecular vibrations areincreasingly heated , and hydrogen bonds are broken. The sampled water cluster geome-tries show greater variation in intra- and intermolecular degrees of freedom than in theunheated water, which explains the increasing peak widths. The non-uniform initial orien-tation of molecular dipole moments (cf. Sec. II A) is not expected to affect these conclusions,as the deposition of large amounts of energy through the THz pulse will quickly decreaseany artificial local order. From the analysis of trajectories with different THz frequencies,we observe that the changes in photoelectron spectrum peak centers that remain after thepulse ( t = 250 fs) are not frequency-dependent within the statistical error (see Fig. S1 inthe SM). However, the T-jump at I = 5 × W / cm was found to be about
720 K for and
560 K for
30 THz , respectively . This indicates that the energy transferred bythe high-intensity pulse exceeds a saturation threshold, in the sense that the changes in thephotoelectron spectra do not reflect the amount of the T-jump.For a lower pump pulse intensity of I = 1 × W / cm , the changes in peak positions arequalitatively the same, but now with a maximum variation of only . . A full analysis of15 igure 7. Time evolution of the a peak in the photoelectron spectrum induced by a THz pulse of I = 1 × W / cm and ν =
7, 19, and 30 THz. The changes during the pulse duration are omittedfor clarity. the photoelectron spectrum at lower intensity can be found in Fig. S2 of the supplementalmaterial (SM). Here, we focus on the a peak, that was most affected by the heating process.In Fig. 7, the time evolution of this peak position is shown for I = 1 × W / cm and pumppulse frequencies of 7, 19, and 30 THz. The frequency dependence that was discussed inSec. II B is visible, since pumping with ν = 19 THz induces up to twice the change comparedto pumping with ν = 7 ,
30 THz . The corresponding T-jumps are about
210 K for 19 THz,
80 K for 7 THz, and
130 K for 30 THz, see Table II. They are thus well below the that could be achieved by high-intensity THz pulses.
V. OUTLOOK AND CONCLUSION
We investigated the possibility of detecting ultrafast THz-induced T-jumps in liquid wa-ter by employing XUV photoelectron spectroscopy. The structural changes induced bysub-picosecond, high-intensity THz pulses of various frequencies were analyzed by calculat-ing RDFs, building on AIMD trajectories that were the subject of previous work . Wefound that, for a lower intensity, the loss of order is frequency-dependent. It is highest atthe frequencies that are associated with the largest energy transfer. At higher intensity, asupercritical phase of liquid density but gas-phase disorder is formed regardless of the fre-quency. We showed the impact of the induced disorder in nuclear geometry on the electronicstructure by simulating XUV photoelectron spectra. We found that for high pump-pulse16ntensity, the peak centers shift by up to 0.4 eV, and the peak widths are broadened.This work relies on the only AIMD trajectories of THz-pumped, T-jumped liquid waterthat are currently available at the high intensity and different frequencies we are inter-ested in. Due to the large number of pump pulse intensities and frequencies considered inRef. 21, the simulation protocol was restricted. The PBE functional was chosen based onthe good description of electronic polarizability , however this resulted in overly struc-tured water and subpar equilibration in the generation of initial configurations. Thedeficiencies could be overcome by using alternative density functionals or by scaling to ahigher initial temperature . However, such improvement is beyond the scope of this work.The large amount of energy transferred by the THz pulse is expected to overcome anydeficient initial equilibration. The electronic structure calculations were performed at theHartree-Fock level of electronic structure theory, since the time-dependent investigation ofXUV photoelectron spectra of liquid water called for an efficient electronic structure method.Since we focus on relative changes of the photoelectron spectra, the systematic errors in theelectronic structure calculations are expected to mostly cancel.During the temporal overlap of the THz pump and the XUV probe pulse, the photoelec-trons generated by the probe pulse are distorted by the laser field of the pump pulse. Thisleads to changes in the photoelectron spectrum known as THz streaking . The streakingeffect can approximately be calculated analytically and is widely employed as a per-shotanalysis tool for femtosecond pulses, as it allows inferring time-domain properties of thepulse by identifying them with changes in the photoelectron spectrum. Investigating theTHz streaking effects in connection with XUV photoelectron spectroscopy of THz-pumpedwater is left for future work.Regarding future experiments, we note that the reported changes in the photoelec-tron spectrum are small and close to the spectral resolution currently obtained with goodmonochromators . Photoelectron spectroscopy of liquid-phase systems poses additionaltechnical and instrumentation challenges, but has been demonstrated . Since the overallchanges in the photoelectron spectrum do not reflect the frequency-dependency of the T-jump at high THz pulse intensity, photoelectron spectroscopy on its own should not be seenas a thermometer for ultrafast heating of liquid water. It provides an interesting comple-mentary diagnostics tool in combination with x-ray diffraction studies and shows how theelectronic system adapts to the structural changes induced by the pump pulse.17 UPPLEMENTARY MATERIAL
Changes in photoelectron spectra induced by pump pulses with I = 5 × W / cm , ν = I = 1 × W / cm , ν = 19 THz ; Transient changes during the pump pulse;Analysis of transient and final geometrical changes and hydrogen-bond breaking; Electronicstructure method. ACKNOWLEDGMENTS
We thank Pankaj Kumar Mishra for fruitful discussions. This work has been supportedby the excellence cluster
The Hamburg Centre for Ultrafast Imaging - Structure, Dynamicsand Control of Matter at the Atomic Scale of the Deutsche Forschungsgemeinschaft.
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