ABSTRACT Charge transfer between molecules lies at the heart of many chemical processes. Here, we focus on the ultrafast electron dynamics associated with the formation of

charge-transfer-to-solvent (CTTS) states following X-ray absorption in aqueous solutions of Na+, Mg2+, and Al3+ ions. To explore the formation of such states in the aqueous phase, liquid-jet

photoemission spectroscopy is employed. Using the core-hole-clock method, based on Auger–Meitner (AM) decay upon 1_s_ excitation or ionization of the respective ions, upper limits are

estimated for the metal-atom electron delocalization times to the neighboring water molecules. These delocalization processes represent the first steps in the formation of hydrated

even above the ionization threshold, i.e., metal-ion electronic resonances associated with the CTTS state manifolds are formed. The three studied isoelectronic ions exhibit quantitative

differences in their electron energetics and delocalization times, which are linked to the character of the respective excited states. SIMILAR CONTENT BEING VIEWED BY OTHERS OBSERVATION OF A

TRANSIENT INTERMEDIATE IN THE ULTRAFAST RELAXATION DYNAMICS OF THE EXCESS ELECTRON IN STRONG-FIELD-IONIZED LIQUID WATER Article Open access 26 November 2022 A LOCALIZED VIEW ON MOLECULAR

DISSOCIATION VIA ELECTRON-ION PARTIAL COVARIANCE Article Open access 28 March 2022 FOLLOWING EXCITED-STATE CHEMICAL SHIFTS IN MOLECULAR ULTRAFAST X-RAY PHOTOELECTRON SPECTROSCOPY Article

Open access 11 January 2022 INTRODUCTION Charge-transfer processes between atoms and molecules lie at the heart of many fundamental processes, including photosynthesis. Electron-transfer

processes in an aqueous environment are of particular importance1. These reactions start with photoabsorption and threshold electron-ejection processes, leading to the population of

charge-transfer-to-solvent (CTTS) states. These states consist of a hydrated parent species with an excited electron, stabilized by solvent polarization2,3. In water, CTTS states are

short-lived, and the excited electron rapidly becomes solvated or, specifically in water, hydrated. The dynamics of the CTTS states of valence-excited hydrated anions have been extensively

studied on femtosecond (fs) to nanosecond (ns) timescales using time-resolved spectroscopy4,5,6,7,8,9 or, more recently, molecular dynamics (MD) simulations10,11. The picture that emerges

from these studies is a sequential ultrafast process, starting from initial photoexcitation and leading to the formation of hydrated electrons. First, a locally excited or “trapped” state

with a lifetime of 50–100 fs is formed. This first state subsequently relaxes to a more delocalized, second state, described as a “wet” or “pre-equilibrated” but not yet fully hydrated

electron. On a 100–400 fs timescale, solvent reorganization converts this second state into the equilibrated ground state of the hydrated electron7,8,9,10,12. Despite extensive study, it

has, however, not been possible to characterize the initial valence-excitation mechanism and associated electron delocalization process due to their exceptionally short timescales. As we

demonstrate here, this is, however, possible for core-level excitations, enabling quantification of the excitation energy dependence, energetics, and upper-limit attosecond timescales of the

initial steps in the electron delocalization for three exemplary, isoelectronic, monoatomic ions in aqueous solution. Recent advances in attosecond science bring the inherent timescales of

electron dynamics into focus13,14,15. A direct way of probing attosecond dynamics is to use attosecond-duration photon pulses. The implementation of extreme ultraviolet (EUV) attosecond

pulse trains and isolated attosecond pulses, typically produced by high harmonic generation, has enabled ultrafast electron dynamics—such as time delays in photoemission and charge migration

after prompt ionization of gases, liquids, and solids—to be probed directly, as recently reviewed in ref. 16. Attosecond soft X-ray pulses produced at free-electron lasers have also

recently been used to probe, e.g., electronic wave-packet dynamics associated with Auger–Meitner (AM) decay in NO molecules17 and valence ionization of liquid water in the first

attosecond-duration X-ray pump, attosecond-duration X-ray probe study on a condensed-phase system18. Attosecond dynamics have also been probed using indirect methods, relying on some other

dynamic process to act as an internal clock. For example, dissociative nuclear dynamics in H2 has been used to track sub-femtosecond autoionization dynamics19, and molecular orientation with

respect to a photon beam has been used to resolve the zeptosecond time delay between electron emission from the two centers of the hydrogen molecule20. In CO21 and NO22 molecules, the

attosecond Wigner time delay for photoionization has been reconstructed from the photoelectron angular emission distribution in the molecular frame. The core-hole-clock technique belongs to

the same group of indirect methods of probing attosecond electron dynamics; here, the lifetime of a core hole, typically produced via photonionization or photoexcitation, is used as an

internal temporal reference for ultrafast phenomena that occur in parallel with core-hole relaxation23,24,25,26. In the case of electron-transfer processes, the core-hole-clock technique is

based on the identification of separate contributions to AM electron spectra27 (see Fig. 1) and the derivation of dynamic timescales from energy-resolved experiments. The AM spectrum can be

compared in some ways to a photograph taken with a long exposure time, where motion can be observed even though the moving object is too fast to be sharply imaged. AM decay is an exponential

process described by a time profile \({{{{\rm{e}}}}}^{-t/{\tau }_{1s}}\), where _τ_1_s_ is the lifetime of the 1_s_ core hole and _t_ is the time since 1_s_ electron excitation. If no other

process competes with the AM decay, the AM spectrum contains only spectator lines in the energetic region where normal AM signals are expected (the related participator lines occur at

higher kinetic energies), see the upper part of panel (b) in Fig. 1. If charge transfer occurs on the same timescale as AM decay, the AM spectrum contains contributions from both normal and

spectator AM decay; see the middle section of panel (b) in Fig. 1. Previous core-hole-clock studies have experimentally revealed charge-transfer times ranging from 9 fs for weakly coupled N2

physisorbed on graphite23, over 320 as for S chemisorbed on ruthenium26, and down to tens of attoseconds for Xe adsorbed on metal surfaces28. In the context of liquid water and aqueous

solutions, processes such as delocalization of electrons excited into CTTS states have been shown to occur on the timescale of 2_p_ core-hole lifetimes for Cl− ions (≈6 fs)29,30. The

core-hole-clock concept has also, for example, been used to show that the timescale for electron hopping from water, core-excited at the post-edge region into unoccupied delocalized

orbitals, is <500 as31, while cations significantly slow down this delocalization to the few-femtosecond timescale32. For hydrated cations, the core-hole-clock method has been used to

determine a few tens to few hundreds of femtoseconds timescales of 2_p_ core-level intermolecular Coulombic decay (ICD, a special type of non-local autoionization decay33) for Na+, Mg2+, and

Al3+34 as well as K+ and Ca2+35. Based on line-shape analyses of core-level photoelectron spectra, even faster intermolecular Coster–Kronig-like processes have been reported for 2_s_

core-level ICD in hydrated Na+, Mg2+, and Al3+ ions, with inferred lifetimes of 3.1, 1.5, and 0.98 fs, respectively36. More recently, the corehole-clock method was used to quantify the

delocalization dynamics following excitation or ionization of aqueous-phase K+ and Cl−37. Given the chemical selectivity afforded by core-level spectroscopy and the possibility to probe

electron dynamics on few- and even sub-femtosecond timescales, the core-hole-clock technique is expected to remain a powerful tool for the investigation of even complex, biologically

relevant systems. The potential of this method will correspondingly continue to be explored, despite emerging opportunities for time-resolved pump-probe experiments with attosecond X-ray

pulses, and may well serve as a calibration method for the latter. Furthermore, currently, the application of attosecond X-ray pulses to aqueous-phase photoemission spectroscopy is hampered

by the low pulse repetition rates of the available light sources, forcing the use of overly high pulse intensities and leading to significant and difficult-to-quantify space-charge effects.

In this paper, we investigate the first steps of charge separation associated with CTTS formation, which take place on the sub-femtosecond timescale. We do this by exploring the

X-ray-induced electron dynamics that occur following excitation or ionization of the 1_s_ electron of the hydrated Na+, Mg2+, and Al3+ ions (all with isoelectronic neon-like 1_s_22_s_22_p_6

electronic configurations). With increasing ionic charge across this sample series, the ion–water distance decreases, and the interaction changes from pure ion–dipole to a combination of

ion–dipole and dative covalent bonding36. By selectively exciting or ionizing the 1_s_ electron from the solvated metal ions, we use the core-hole-clock method in a similar way to that

described in ref. 37, determining the delocalization timescales of the initially localized excited-state electronic wave packets into states that are predominantly delocalized over the

surrounding water molecules. The experimental findings are accompanied by ab initio calculations that describe the character and energetics of the initial CTTS states and the final states of

the AM decay. Comparison between the hydrated Na+, Mg2+, and Al3+ ion results reveals how an increasing ionic charge, and consequently a more organized hydration shell, influences the time

it takes for the excited electron to delocalize from the ion to the water environment. These results correspondingly provide insights into how the attosecond electron dynamics related to the

first steps of charge separation change with increasing electronic coupling, specifically in going from a system dominated by ion–dipole bonding towards a system with appreciable

coordination bonding. RESULTS AND DISCUSSIONS X-RAY ABSORPTION We start with a brief overview of the studied processes from a time-dependent perspective. Upon the interaction of a photon

with a 1_s_ electron, an excited-state electronic wave packet is formed. This wave packet is initially localized in the proximity of the excited atom and is of _p_ symmetry within the dipole

approximation. For isolated atoms, the wave packet gradually transforms into one of the _n__p_ atomic states, if permitted by the energy resonance condition. The situation is, however,

different for the hydrated ions. The initial electronic wave packet scatters from neighboring water molecules, forming complicated wave packets, which gradually evolve into CTTS states. The

system still resides in a continuum of doubly ionized and charge-separated, hydrated electron states, and the excited-state eigenstates are not fully formed during the finite lifetime of the

1_s_ core-hole states. The absorption process is expected to take place on a sub-femtosecond timescale, which is close to the 1_s_ core-hole lifetimes of the studied ions, as further

discussed below. The non-stationary evolution of the electronic wave packet of the core-hole state is probed by the AM decay, which provides a snapshot of the degree of wave-packet

(de)localization, thereby reflecting the electron dynamics. Panel (a) of Fig. 2 shows the integrated KLL electron PEY-XAS (the spectra are based on the 2D maps presented below, where the

integrated kinetic-energy ranges were 982.5–986.5 eV for Na+, 1173–1178 eV for Mg2+, and 1378–1382 eV for Al3+), which approximate the true 1_s_ XAS. Below the 1_s_ ionization threshold,

marked by dotted lines in Fig. 2, the X-ray absorption is dominated by electronic transitions into unoccupied orbitals. Photoabsorption is much more probable above the 1_s_ ionization

thresholds (1076.7, 1309.9, and 1567.7 eV for the hydrated Na+, Mg2+, and Al3+ cations, respectively36). For an isolated atom, the main resonant transitions are 1_s_ → _n__p_, _n_ ≥ 3, with

the relative transition strengths decreasing with _n_. The unoccupied orbitals of the hydrated metal cations are, however, affected by the surrounding water, and the atomic notation is not

fully adequate in the case of the CTTS states. In spite of this, in the text, we use the _n__p_ term to describe the virtual orbitals with a significant contribution from the metal-cation

_n__p_ orbital. We now focus on the character of the core-excited CTTS states from the perspective of electronic-structure theory. Simulated XAS are presented in Fig. 2 panels (b)–(d), which

were performed at the SRC2-R2 level with a cc-pCVTZ basis set on the cation, a cc-pVTZ basis set on the water molecules, in a polarizable continuum. The SRC2-R2 spectra agree well with the

results obtained at the CVS-EOM-EE-CCSD level and within the RT-TDDFT level, see Supplementary Fig. 3 in the SI. The spectra calculated for a randomly selected structure of the

\({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{6}]}^{n+}\) cluster are shown in panel (b) of Fig. 2. The weight of the localized character is calculated as (1−_C__T_) and projected as a

color bar onto the oscillator strength (gray bar). The respective unoccupied NTOs are shown as insets in Fig. 2 panel (b). As can be seen from the figure, the spectra below the 1_s_

ionization threshold correspond to the transitions from the metal-cation 1_s_ orbitals to the unoccupied orbitals with partially localized _n__p_ and partially delocalized character. The

character of the unoccupied orbitals differs for each cation. The Na+ hydration shell is loose and allows the electron density to be accommodated in the space between the cation and the

closest water molecules. The shape of the orbital resembles that of the _n__p_ state of an atom. This can be seen in most of the transitions, the local contributions (violet bars) to the

excited states are relatively high for all excited states, see Fig. 2 panel (b). For Al3+, the water hydration shell is tight and organized (a “cage” is formed by the surrounding water

molecules), and the resulting confined space cannot fully accommodate the diffuse _n__p_ state in the same way as observed for Na+. Consequently, the electron density is partially localized

near the excited cation and largely scattered over the neighboring water molecules. The local contributions (orange bars) to the excited states are negligible below the 1_s_ ionization

thresholds and are approximately half of the total intensity above the ionization threshold, see Fig. 2 panel (b). The character of the excited states for the Mg2+ cation is between those of

the Na+ and Al3+ ions. A similar picture can be derived from the _σ_e parameter, the root-mean-square size of the excited electron with respect to the hole localized on the metal center,

depicted in Supplementary Fig. 1 in the SI. In the case of the smaller clusters, for Na+, a significant number of the excited states with a non-zero oscillator strength are very diffuse

(high value of _σ_e), while for Al3+, the _σ_e value is much smaller, which means that the excited electron is closer to the metal center. The differences between individual cations in terms

of _σ__e_ are much smaller for the larger cluster size \({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{18}]}^{n+}\) because the excited-state wave functions are also scattered over the

second hydration shell. The XAS spectra calculated for a set of 50 structures for the \({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{6}]}^{n+}\) clusters are shown in Fig. 2 panel (c)

and for \({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{18}]}^{n+}\) clusters, which also include the second solvation shell, in Fig. 2 panel (d). The filled area shows the contributions

of the local excited states to the overall spectrum. As can be seen from the spectra, the local character is most pronounced for the Na+ cation (the filled area corresponds to 56% of the

total area for \({[{{{\rm{Na}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{6}]}^{+}\)) and relatively weak for the Mg2+ and Al3+ cations for clusters including the first solvation shell (the filled

areas correspond to 31% for [Mg(H2O)6]2+ and 36% for [Al(H2O)6]3+, respectively). When the second solvation shell is additionally included, Fig. 2 panel (d), the local contributions to the

excited states are smaller for all three cations (24% for [Na(H2O)18]+, 14% for [Mg(H2O)18]2+, and 15% for [Al(H2O)18]3+). The highest local contributions are again observed for Na+. It is

clear from the analysis of Fig. 2 that the cation charge and structural flexibility/rigidity of the environment shape the character of the CTTS states, which we use as a proxy of the

electronic wave packet. The hydration environment likely similarly controls the actual outgoing electronic wave packet produced following excitation above the 1_s_ ionization threshold.

IDENTIFICATION OF THE DECAY CHANNELS AND AM-TYPE PROCESSES The next step is to study the decay channels following the X-ray absorption process. For that, we inspect the 2D photoemission data

maps shown in Fig. 3 and follow the evolution of the resonant excitation and subsequent ionization of the 1_s_ electron with increasing photon energy. In the 2D maps shown in Fig. 3, the

1_s_−1 ionization energies are marked by horizontal, dotted lines (the 1_s_ ionization energies are detailed in the SI of ref. 36). To interpret the possible decay channels, we employed ab

initio calculations. The calculated energies corresponding to various electronic states are collected in Supplementry Table 1 and are shown in Supplementary Fig. 4 in the SI for Na+, Mg2+,

and Al3+ ions embedded in both water cluster sizes. Experimental energy values, as inferred from the 2D maps at the 1_s_ ionization thresholds, are also presented in the Supplementry Table 1

in the SI. The best agreement with the experimental values is achieved when larger clusters are used for the MOM calculations; in the case of highly charged species in aqueous solutions,

the long-range polarization of the environment is particularly important36,38. Based on the calculations, we assign the most intense feature in the 2D maps for all three ions to the KLL AM

decay of the 1_s_−1 core-ionized states to produce 1D 2_p_−2 two-hole (2_h_) final states. This feature occurs at constant kinetic energy, corresponding to vertical spectral lines in each of

the 2D maps shown in Fig. 3, specifically at 984.6, 1175.6, and 1380.9 eV kinetic energy for the hydrated Na+, Mg2+, and Al3+ ions, respectively. All three 2D maps additionally show

parallel but fainter constant-kinetic-energy signals at slightly lower kinetic energies (980, 1171, and 1376 eV for the hydrated Na+, Mg2+, and Al3+ ions, respectively) corresponding to the

transitions to another 2_p_−2 multiplet, 1S. In addition to the constant-kinetic-energy features associated with the KLL AM decay most importantly, a dispersive feature is also present for

all three sample ions. A similar feature was observed in a previous study of aqueous-phase K+ and Cl−37. The kinetic energy of the dispersive feature is linearly dependent on the photon

energy, meaning that the feature is characterized by a constant ionization energy (88.0, 131.3, and 183.4 eV for the Na+, Mg2+, and Al3+ ions, respectively). Based on the calculations, see

below, we assign this dispersive feature to the 2_p_−23_p_ final states after AM decay. These two-hole-one-electron (2_h_1_e_) states can be formed as shake-up satellite states to the main

2_p_−1 states (ionization energies of 35.4, 55.6, and 80.4 eV for the Na+, Mg2+, and Al3+ ions, respectively36) and by spectator resonant AM decay from the 1_s_ core-excited states, as

depicted in Fig. 4. Additionally, as seen in Fig. 3, all three cations exhibit a parallel, low-intensity, constant-ionization-energy feature, which we assign to the 2_p_−23_s_ (2_h_1_e_)

final states after AM decay (spectator decay, also see Supplementary Table 1 in the SI). As can be seen from Fig. 3, the KLL AM decay from the 1_s_−1 to the 2_p_−2 final states dominates

both below and above the 1_s_ ionization limit. The 2_p_−23_p_ final states after spectator AM decay exhibit resonant enhancement even above the 1_s_ ionization threshold. This can be

understood in terms of the wave-packet evolution, see Fig. 4. After X-ray photon absorption, the electronic wave packet evolves into charge-separated states and, at the same time, decays via

AM processes. Following near-resonant excitation, we can identify two associated main types of final states after AM decay: (i) the localized 2_p_−23_p_ (2_h_1_e_) final states after

spectator AM decay and (ii) the delocalized 2_p_−2 (2_h_) final states after electron delocalization and normal AM decay (see Fig. 4). Spectator AM decay to the 2_p_−23_p_ final states

requires that the excited electron has a sufficient degree of localized metal _n__p_ character. As the excited-state wave packet evolves from mostly localized metal _n__p_ character to the

states delocalized over several water molecules, spectator AM decay to the 2_p_−23_p_ final states mainly occurs for early-time AM decays. During the core-hole lifetime, the wave packet can

evolve into states in which most of the electron density is on the surrounding water molecules, i.e., we observe electron delocalization from the cation to hydrating water molecules (see

Fig. 4). Such later-time AM decays are not influenced by the excited electron, which is sufficiently delocalized and screened not to affect the local energetics of the metal ion, resulting

in normal AM decay to the 2_p_−2 final states. These 2_p_−2 final states appear to be locally identical to the 2_p_−2 final states that are predominantly populated following non-resonant

excitation well above the 1_s_ ionization threshold, in which the ionized electronic wave packet is also delocalized from the metal ion and screened. The “electron delocalization” can be

interpreted to represent the first step of charge separation and evolution from a localized excitation to a hydrated electron. Such competition between resonant AM decay and delocalization

of the excited electron has also been observed in ref. 37. ELECTRON DELOCALIZATION DYNAMICS The intensity ratio between the 2_p_−23_p_ and the 2_p_−2 final states depends on the relative

timescale of the electronic wave-packet evolution and the 1_s_ core-hole lifetime. The 1_s_ core-hole lifetime can be derived using _τ_1_s_ = _ℏ_/_Γ_1_s_, where _Γ_1_s_ is the total decay

width of that state. Based on ref. 39, experimental _Γ_1_s_ parameters of 0.28 ± 0.03, 0.43 ± 0.12, and 0.44 ± 0.04 eV can be derived for metallic Na, Mg, and Al, respectively (where the Na

value is associated with a single X-ray photoemission study and the Mg and Al values correspond to the averages and standard deviations of all of the tabulated experimental

X-ray-spectroscopy data). Although these _Γ_ values are expected to vary somewhat with electronic charge state and chemical environment, they are generally found to be consistent with

independent-particle-model computations39 and our aqueous-phase Na+, Mg2+, and Al3+ 1_s_ data, as exemplified in Fig. S5. Based on the experimental values collected in ref. 39, the

aqueous-phase metal 1_s_ core-hole lifetimes can be inferred as _τ_1_s_ values of \(2.3{5}_{-0.23}^{+0.28}\) fs, \(1.5{4}_{-0.33}^{+0.57}\) fs, and \(1.5{1}_{-0.13}^{+0.15}\) fs for the Na,

Mg, and Al 1_s_−1 states, respectively. For a selected set of photon energies spanning the 1_s_ resonant excitation to post-ionization regimes, the AM spectra were fitted, and the integrated

intensities of the peaks corresponding to the 2_p_−2 and 2_p_−23_p_ final states were determined. Note that there are two contributions to the 2_p_−23_p_ final states: direct, off-resonant

photoemission and resonant spectator photoemission. As we are not interested in the direct, off-resonant photoemission contribution, the intensity corresponding to this feature was

subtracted from the integrated intensity. Using the intensities obtained in this way, the timescale of electron delocalization was determined as _τ_delocalization, which is calculated as

\({\tau }_{1s}\times {I}_{2{p}^{-2}3p}/{I}_{2{p}^{-2}}\), where \({I}_{2{p}^{-2}3p}\) is the integrated intensity of the peak corresponding to 2_p_−23_p_ and \({I}_{2{p}^{-2}}\) is that of

2_p_−2. Fig. 5 shows the correspondingly obtained _τ_delocalization as a function of the photon energy for the three ions, together with the associated standard deviations of the determined

values (shaded areas), as determined by propagating the uncertainty in the reference _Γ_1_s_ values for the different aqueous-phase cations. As shown in Fig. 5, for Na+, _τ_delocalization is

estimated to be  ≈150 as at the 1_s_ threshold, decreasing to  ≈0 at 4.5 eV above the threshold; for Mg2+, _τ_delocalization is  ≈200 as at the 1_s_ threshold, decreasing to a value of

about 20 as 4 eV above the threshold. In the case of the Al3+ ion, _τ_delocalization is longer than for Na+ and Mg2+, decreasing from about 350 as at the 1_s_ threshold to about 100 as 3 eV

above the threshold. Comparing the results for the three ions, we see that _τ_delocalization is similar for Na+ and Mg2+, and slightly longer for Al3+ across almost the entire photon-energy

range, except for at the lowest photon energies. There are likely both structural and energetic reasons for this observation. First, both the ion–water distance and the spatial extent of the

excited states decrease from Na+ over Mg2+ to Al3+36. This is supported by the picture provided by the ab initio calculations in Fig. 2 and Supplementary Fig. 1 in the SI. Another important

observation in the present study is that _τ_delocalization decreases with increasing photon energy for all three ions. This is consistent with a higher degree of delocalization with

increasing energy of the formed CTTS states. Yet, remarkably, the electron seems to reside in the vicinity of the cations even above the ionization limit. This points to the possible

existence of long-living electron resonances in water under these conditions. Furthermore, it suggests that the core-excited state is a resonantly occupied state, weakly coupled to the

surrounding bulk water via tunneling through an energy barrier40,41. In addition, we note that the electron delocalization into the bulk water requires empty states in water for the excited

electron to transfer into. The XAS spectra in Fig. 2 represent the excitation of the 1_s_ electron into unoccupied electronic states formed by the unoccupied water valence levels in the

liquid bulk (see refs. 42,43,44,45,46). The calculated band structures42,43,44,45,46 show a steep increase in the density of states with increasing energy, and the observed decrease of

electron delocalization timescales with increasing photon energy is qualitatively consistent with an increased number of water states available for the excited electron to be transferred to.

This enables rapid delocalization of the excited electron to unoccupied states in bulk liquid water, eventually leading to the formation of pre-hydrated and then hydrated electrons. Another

perspective on these ultrafast processes is provided by the _Z_ + 1, or equivalent core, approximation. In this approach, the effect of the 1_s_ core hole on the outer electrons is

considered to be like that of an extra proton in the nucleus. This means that the valence electronic structure of an element _Z_ with a core hole will be like that of an element _Z_ + 1. In

this case, this means that the core-excited states of Na+, Mg2+, and Al3+ ions will temporarily resemble the ground states of Mg+, Al2+, and Si3+ ions, respectively. While Si does not form

monoatomic ions in water, Mg and Al do. However, Mg+ and Al2+ are not stable ions in water and would rapidly give up electrons to form Mg2+ and Al3+. For these two cations, the _Z_ + 1

approximation provides a qualitative understanding of our observation of electron delocalization dynamics after core excitation. CONCLUSIONS Ultrafast electron dynamics connected to

core-level excitation and associated formation of the CTTS states of the isoelectronic Na+, Mg2+, and Al3+ ions in water have been investigated using a combination of X-ray absorption

spectroscopy, AM spectroscopy, and ab initio calculations. Due to the short core-hole lifetime of about 2 fs, the AM spectra reflect the ultrafast dynamics of the system. The 1_s_ excitation

of the metal ion produces electronic wave packets partially localized on the ionized atom, which gradually evolve towards states with electron density delocalized over the surrounding water

molecules. This “electron delocalization" represents the first step of charge separation in the evolution from a localized excitation to a hydrated electron. In the AM spectra, final

states after AM decay of 2_p_−23_p_ and 2_p_−2 character are identified, and both types are observed both below and above the 1_s_ ionization threshold. As no qualitatively different

behavior is observed below and above the 1_s_ threshold, it is inferred that the slow outgoing photoelectron wave resides in the vicinity of the core-ionized ion for a sufficient amount of

time that the 2_p_−23_p_ final states can be formed. The relative intensity of the 2_p_−23_p_ and 2_p_−2 final states reflects the wave-packet evolution from more localized _n__p_ states to

delocalized states, with most of the electron density localized on the water molecules. Using the core-hole-clock method, we see that the delocalization timescales decrease from  ≈150 as for

Na+,  ≈200 as for Mg2+, and  ≈350 as for Al3+ below the 1_s_ ionization threshold to  ≈20 as for Na+,  ≈20 as for Mg2+, and  ≈100 as for Al3+ above the threshold. It is remarkable that no

discontinuity in the decrease of _τ_delocalization is observed at the 1_s_ ionization energies. The 2_p_−23_p_ (2_h_1_e_) states are, in fact, also enhanced in intensity for the photon

energies exceeding the 1_s_ ionization threshold. At these photon energies, the electron is no longer bound, but it is quite slow and possibly temporarily trapped by scattering in the local

potential, as observed for molecular shape resonances47. We speculate that this may lead to electron recapture after the AM decay, explaining the enhanced intensity just above the 1_s_

threshold. The picture provided by the ab initio simulations is not complete, yet it reveals an important insight into the differences between the hydration patterns and

electron-delocalization-to-solvent feasibility of the respective ions. Full ab initio dynamics, taking into account the gradual formation of the initial wave packets and simultaneous AM

decay on the femtosecond timescale in a condensed environment, is beyond state-of-the-art computational capabilities. Consequently, the present systems can serve as convenient test beds for

the further development of quantum dynamics calculations of complex hydrated systems. Recently, theoretical progress has been obtained for related phenomena connecting the simultaneous

appearance of photoionized and autoionized electrons, such as Fano resonances19,48,49. The present results on X-ray-induced electron delocalization provide insight into the ultrafast

dynamics of the first step of charge separation in aqueous solutions and into the process of going from a localized excitation to a hydrated electron. The electron delocalization can be seen

as an example of an intermolecular electron-transfer process, which is a fundamental step in many chemical processes. With the advent of attosecond X-ray pulse sources, such as

free-electron lasers (FELs), it is becoming possible to study the dynamics of these and other types of X-ray-induced processes through direct X-ray pump–X-ray probe measurements. Our results

thus provide a glimpse of one of the complex phenomena that ultrafast science is now starting to probe, although the application of attosecond photoemission pump-probe schemes to the

aqueous phase using FELs remains technically challenging. METHODS EXPERIMENTAL SETUP The AM electron spectra for the hydrated Na+, Mg2+, and Al3+ ions were measured across the metal-atom

1_s_ ionization energies (IEs) at the P04 beamline of the synchrotron facility PETRA III (DESY, Hamburg, Germany),50 using the _EASI_ liquid-microjet photoemission spectroscopy setup51. A

similar Mg2+ spectrum was recorded at the HIPPIE beamline of MAX IV (Lund, Sweden)52 (see Supplementary Fig. 5 in the SI). The present analysis is based on the spectra recorded at P04. The

P04 beamline provides circularly polarized X-rays with energies between 250–3000 eV and an on-target flux of  ≈1012 photons/s (at a resolving power of 10,000). Here, the beamline was

operated with a 1200 lines/mm grating and a 100 μm exit-slit width, offering photon-energy resolutions between 210 and 380 meV at photon energies between 1050 and 1600 eV. A general

description of the _EASI_ experimental setup is given in ref. 51. With an 800  μm entrance slit into our hemispherical electron analyzer and 100 eV (Na+ and Mg2+ samples) or 200 eV (Al3+

sample) pass energies implemented in these measurements, analyzer energy resolutions of  ≈200 and  ≈400 meV were respectively achieved. This led to estimated total experimental energy

resolutions of  ≈290,  ≈360, and  ≈560 meV in the Na+, Mg2+, and Al3+ experiments, respectively. The sample solutions were horizontally injected into the sample vacuum chamber using an HPLC

pump (0.8 ml/min flow rate) and a fused silica nozzle (inner diameter of 28 μm). This resulted in a free-flowing, cylindrical liquid microjet and a  ≈10−4 mbar average pressure in the

interaction chamber. The generated liquid microjet was irradiated by the focused synchrotron radiation (≈180 × 40 μm2, horizontal × vertical, spot size) 1–2 mm downstream from the tip of the

jet nozzle. The kinetic energies of the emitted electrons were measured using a differentially pumped hemispherical electron analyzer, mounted at a 130° angle with respect to the X-ray beam

(back-scattering geometry51), which is close to the magic angle. The distance between the ionization locus and the 800-μm entrance orifice of the electron analyzer was less than 0.5 mm,

which results in a  ≈±20° acceptance angle, with the exact value depending on analyzer operation mode51. The aqueous solutions of 2 M AlCl3, 1 M MgCl2, and 1 M NaCl were prepared by

respectively dissolving commercially purchased AlCl3, MgCl2, and NaCl (Sigma–Aldrich with purity >98%) salts in MilliQ water (18.2 MΩ/cm). For each sample, the electron spectra were

measured as a function of the photon energy across the 1_s_ ionization thresholds of the cations. These series of photoemission spectra are presented as two-dimensional (2D) maps of photon

energy versus electron kinetic energy, with the intensity of the emitted electrons encoded in a color scale. This is a common presentation (see Fig. 3 of the present work), which provides a

convenient visualization of evolving resonant spectral features53,54. Single photoemission (i.e., AM) spectra, recorded at a given photon energy, then correspond to a horizontal cut through

a given map of the type shown in Fig. 3. Signal integration in the horizontal direction, within the kinetic-energy range of the AM peaks, yields the respective partial-electron-yield X-ray

absorption spectra as a function of photon energy, PEY-XAS. The individual electron spectra were fitted using the Spectrum Analysis by Curve Fitting (SPANCF)55 macro package for Igor Pro

(Wavemetrics, Inc., Lake Oswego, USA). The main KLL AM peaks have a high-kinetic-energy tail arising from post-collision interaction (PCI) between the photoelectron and the AM electron.

Thus, PCI profiles were used to fit the AM peaks, while Voigt profiles were used to fit the 2_p_−23_p_ peaks. The integrated intensities and peak positions of the aforementioned peaks were

obtained from these fits. An exemplary fit for the case of the \({{{{\rm{Al}}}}}_{({\rm {aq}})}^{3+}\) spectrum recorded at a photon energy of 1569.9 eV is shown in Supplementary Fig. 7, and

the obtained energies and intensities for all analyzed cases are listed in Supplementary Table 2. The photon energies and the electron kinetic energies were calibrated using peaks of known

ionization energy in combination with the first- and second-order light from the beamline, as described in detail in ref. 36. Photoemission spectra recorded at fixed photon energies above

the respective 1_s_ thresholds were analyzed in our previous works refs. 36,56 to reveal signatures of non-local solute autoionization channels, which occur at higher or lower kinetic

energies than the data reported in this work. THEORETICAL METHODS The simultaneous ultrafast processes interrogated here were divided into individual steps. The initial configurational space

was sampled by classical molecular dynamics (MD) simulations. The simulation box for NaCl and MgCl2 solutions contained 160 molecules of salts and an appropriate number of water molecules

(8753 water molecules for NaCl and 8810 for MgCl2). For AlCl3, the simulation box contained 267 aluminum cations, 801 chloride anions, and 8472 water molecules. The total length of each

simulation was 200 ns, the time step for the propagation was set to 2 fs, and 3D periodic boundary conditions were employed. The simulation temperature was set to 300 K and was controlled by

a velocity-rescale thermostat with time coupling set to 0.5 ps (0.1 ps for AlCl3). The pressure of the system was set to 1 bar, which was controlled by the Parrinello–Rahman barostat with a

coupling constant of 1 ps (2 ps for AlCl3). The van der Waals interactions were truncated at 1.5 nm (1.2 nm for AlCl3); the long-range electrostatic interactions were calculated by the

particle mesh Ewald method. The details of the force field are described in great detail in ref. 36. The simulations were performed for 2 M AlCl3, 1 M MgCl2, and 1 M NaCl solutions to match

the experimental conditions. For further calculations, we selected 200 or 50 geometries for two cluster sizes: [M(H2O)6]_n_+ and larger

\({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{18}]}^{n+}\), where _n_ = 1, 2, 3 for M = Na, Mg, Al, respectively. The smaller cluster size represents the first hydration shell around

the solvated cation, and the larger cluster includes the hydration shell up to the second layer. X-RAY ABSORPTION The X-ray absorption spectra (XAS) were calculated at the

equation-of-motion-coupled-cluster level with a core-valence separation scheme (CVS-EOM-EE-CCSD) and the time-dependent density functional theory (TDDFT) level with a restricted orbital

space. Both methods can only provide stationary states of the studied systems, ignoring the coupling to the continuum, and can only provide proxies of the true XAS spectra. The spectra at

the CVS-EOM-EE-CCSD level were constructed for an ensemble of 50 geometries of [M(H2O)6]_n_+ in the gas phase. The calculations of the core-excited states require relatively large basis

sets, preferentially with triple-_ζ_ quality. In the case of CVS-EOM-EE-CCSD, a combined basis set—the uncontracted cc-pCVTZ on the metal cation and the smaller cc-pVDZ on the water

molecules—was used. The TDDFT calculations were performed for both cluster sizes, including the first and also the second solvation shells, for an ensemble of 50 structures of [M(H2O)6]_n_+

and \({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{18}]}^{n+}\), each. The SRC2-R2 functional, specifically tailored to core excitations57, with the cc-pVTZ basis set on water and the

cc-pCVTZ basis set on the metal cation, was employed throughout the simulations. The spectra were broadened by 0.28 eV for Na+, 0.43 eV for Mg2+, and 0.44 eV for Al3+ to reflect the

core-hole lifetime broadening39. XAS spectra were also simulated within the real-time time-dependent functional theory approach (RT-TDDFT) with the SRC2-R2 functional58 and the combined

cc-pVTZ and cc-pCVTZ basis sets59. The non-equilibrium solvation model, as implemented in Q-Chem 6.060, was used for all TDDFT XAS calculations. Some properties of the excited states in the

complex environment can be better understood in terms of a two-body exciton wave function, which describes the correlated motion of the hole and electron quasiparticles61,62. Specifically,

we focused on decomposing the excited states into local contributions (localized on the metal cation) and charge-transfer contributions (localized on the water molecules). For this purpose,

the so-called charge transfer variable, CT, was calculated. This collective variable quantifies the total weight of configurations for which the initial and final orbitals are situated on

different fragments, e.g., localized on the surrounding water molecules. The definition of the variables and a detailed discussion can be found in Supplementary Note 1 in the SI. The

analysis of the excited-state wave functions was performed by means of natural transition orbitals (NTOs) and exciton analysis63 using the TheoDORE code64 and the wave function analysis

library (libwfa)61,62, to directly analyze the one-particle transition density matrix and to compute the exciton and electron sizes and the charge transfer numbers. Charge transfer numbers

are based on population analysis and describe the weight of the transitions in which the electron density is transferred from one fragment to another, in the current case, from the metal ion

to water molecule(s). ENERGETICS OF THE FINAL STATES AFTER AM DECAY In the solvent, the final states after AM decay can be conveniently described by the maximum-overlap method (MOM)65. The

tailored short-range functionals exhibit larger errors for the MOM calculations58,66. Therefore, the _ω_B97X-D functional was selected with the cc-pVTZ basis set on all atoms. The

implementation of the MOM method provides only triplet-state energies for doubly ionized states; the energy differences between states of various multiplicities were evaluated at the

multireference configuration interaction (MRCI) level with an aug-cc-pVTZ basis set. SOLVENT EFFECTS The non-equilibrium solvation model was used for the description of the final states

after AM decay via the MOM. The permittivity of the solution was adjusted for 1 and 2 M concentrations36. All calculations were performed in Q-Chem 6.060. DATA AVAILABILITY The data

generated in this study have been deposited in the Zenodo database under accession code DOI: 10.5281/zenodo.10600582. All data needed to evaluate the conclusions in the paper are present in

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_J. Chem. Phys._ 158, 094111 (2023). Article  ADS  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association

HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III and we would like to thank Moritz Hoesch and his team for assistance in using beamline

P04. Beamtime was allocated for proposal I-20190339. We acknowledge Jens Buck, Florian Diekmann, Matthias Kalläne, and Sebastian Rohlf from Christian-Albrechts-Universität zu Kiel for

providing us with software to scan the photon energy via our SCIENTA spectrometer software. We thank Sebastian Malerz for participating in some of the measurements. We acknowledge Andrey

Shavorskiy and his team, as well as the MAX IV Laboratory, for time on the beamline HIPPIE under proposal 20180386. Research conducted at MAX IV, a Swedish national user facility, is

supported by the Swedish Research Council under contract 2018-07152, the Swedish Governmental Agency for Innovation Systems under contract 2018-04969, and Formas under contract 2019-02496.

B.W. and U.H. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No.

883759-AQUACHIRAL. P.S. and E.M. thank the Czech Science Foundation for the support via project number 23-07066S. F.T. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG,

German Research Foundation)—Project 509471550, Emmy Noether Program. F.T. and B.W. acknowledge support by the MaxWater initiative of the Max-Planck-Gesellschaft. C.C. acknowledges the

Swedish Research Council (project 2018-00740) and the Helmholtz Association through the Center of Free-Electron Laser Science at DESY. O.B. acknowledges funding from the Swedish Research

Council (VR) for the project VR 2023-04346. FUNDING Open access funding provided by Uppsala University. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Physical Chemistry,

University of Chemistry and Technology, Prague, Technická 5, 166 28, Prague, Czech Republic E. Muchová & P. Slavíček * Department of Physics and Astronomy, Uppsala University, Box 516,

SE-751 20, Uppsala, Sweden G. Gopakumar, I. Unger, E. Chatzigeorgiou, C. Caleman & O. Björneholm * Center for Free-Electron Laser Science, DESY, Notkestr. 85, 22607, Hamburg, Germany I.

Unger & C. Caleman * MAX IV Laboratory, Lund University, Box 118, SE-22100, Lund, Sweden G. Öhrwall * Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48 91192, Gif-sur-Yvette

Cedex, Paris, France D. Céolin * Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195, Berlin, Germany F. Trinter, U. Hergenhahn & B. Winter * Institute for Electronic

Structure Dynamics, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109, Berlin, Germany I. Wilkinson Authors * E. Muchová View author publications You can also search for this

author inPubMed Google Scholar * G. Gopakumar View author publications You can also search for this author inPubMed Google Scholar * I. Unger View author publications You can also search for

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author publications You can also search for this author inPubMed Google Scholar * C. Caleman View author publications You can also search for this author inPubMed Google Scholar * O.

Björneholm View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS G.G., I.U., G.Ö., and O.B. conceived the experiments. G.G., I.U., G.Ö., D.C.,

F.T., I.W., E.C., U.H., B.W., C.C., and O.B. planned, prepared, carried out the experiments, and discussed the data. E.M. performed the theoretical calculations. E.M. and P.S. interpreted

theoretical data. G.G., U.H., and G.Ö. analyzed the data. G.G., E.M., and O.B. wrote the manuscript with feedback from all authors. CORRESPONDING AUTHORS Correspondence to E. Muchová or O.

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