Elucidation of the photoaquation reaction mechanism in ferrous hexacyanide using synchrotron x-rays with sub-pulse-duration sensitivity

A mechanistic understanding of chemical reactions involving solvated transition metal complexes is desirable due to the many biological and chemical roles these complexes play in nature and their promising use in a wide range of applications (e.g., photodynamic therapy,^1,2 solar light harvesting,³ and energy storage devices^4,5). This understanding can be challenging to obtain because of the complexity of these systems; there are multiple coupled degrees of freedom within the molecule (atomic position, spin, and electronic structure) as well as the influence of the solvent, which in some cases can alter the reaction dynamics quite substantially.⁶ Time-resolved x-ray spectroscopy, as a selective probe of the metal and its immediate surroundings, has proven to be a powerful tool for studying reaction dynamics of these systems and is undergoing rapid development.^7–9 When combined with hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations and spectroscopy calculations, detailed information about the structure, spectra, and mechanism of the reaction can be revealed.¹⁰ In this paper, we present a study of a reaction ubiquitous to transition metal systems, that of ligand substitution, using laser-pump, x-ray-probe, x-ray absorption spectroscopy (XAS), and QM/MM molecular dynamics simulations. The rates and mechanisms for ligand substitution reactions are not easily obtained a priori as they are dependent on several factors (e.g., ligand-ligand repulsion, ligand-metal electron donation, crystal field stabilization energy, and metal spin state). The mechanism for a particular reaction is usually constructed from several empirical observations (e.g., from NMR, flash photolysis, transient optical absorption, and EPR) and theoretical calculations. Photoinitiation of ligand substitution reactions is being harnessed for photopatterning of proteins,¹¹ photodynamic therapy^12–15 and photochemotherapy,^16,17 release of antimicrobial agents¹⁸ and neurochemicals,^19,20 light actuation of hydrogels,²¹ the construction of reconfigurable surfaces,²² and to power molecular machines.²³ High precision time-resolved x-ray spectroscopy is a new means of investigating these reactions and can potentially yield information valuable for the design of complexes for these applications. Additionally, studies of solvent substitution from photoexcited molecular complexes have long been recognized as valuable for understanding solvation dynamics,²⁴ and the application of x-ray spectroscopy and QM/MM modeling to this problem holds promise for providing new insights.

We focus on the case of photoaquation in the model system [Feⁱⁱ(CN)₆]⁴⁻ where excitation with light leads to exchange of a CN⁻ ligand with a H₂O from the solvent. Ground state [Feⁱⁱ(CN)₆]⁴⁻ is a highly stable complex with octahedral geometry. Its photoreactivity has long been a subject of study^25–28 but continues to be actively researched in disciplines as varied as, for instance, the prebiotic chemistry of early Earth²⁹ and environmental science.^30,31 In addition to its photoreactivity, it has been of interest due to the fact that it is a small, highly charged anion that therefore interacts strongly with polar solvents. Recent studies have investigated its hydration^32–35 and impact on the hydrogen bond network of water.^32,36–38 In addition, along with its redox partner [Feⁱⁱⁱ(CN)₆]³⁻, it exhibits interesting bonding characteristics and this has made them excellent model systems to explore with various x-ray spectroscopies.^10,39–48

The primary photoreactions of [Feⁱⁱ(CN)₆]⁴⁻ were established in 1970 by Shirom and Stein using flash photolysis and steady illumination experiments.^49,50 They determined that excitation with UV light can lead to two wavelength-dependent reactions: (1) photo-oxidation, producing hydrated electrons and [Feⁱⁱⁱ(CN)₆]³⁻, and (2) photoaquation, producing the aquated species [Feⁱⁱ(CN)₅H₂O]³⁻ and free CN⁻,

At wavelengths >313 nm, photoaquation is the sole reaction with a wavelength-independent quantum yield of 0.2.^49,51 At wavelengths <313 nm, both reactions occur with photo-oxidation dominating and exhibiting a quantum yield that increases with decreasing wavelength to a very high value of 0.9 at 228 nm. As the quantum yield for the oxidation reaction increases, the yield for the aquation reaction decreases.^49,51

Ultrafast studies aimed at understanding the mechanisms behind these reactions have been summarized in a recent review by Chergui.⁵² While there have been several femto- and picosecond-resolved studies of the photo-oxidation reaction, the photoaquation reaction has not been explored with ultrafast methods until very recently.^51–54 Reinhard et al. included a focus on the aquation reaction in studies employing transient x-ray absorption spectroscopy,⁵³ 2D UV spectroscopy, transient visible spectroscopy, and transient IR spectroscopy⁵¹ that probed the dynamics of laser excited [Feⁱⁱ(CN)₆]⁴⁻ and [Feⁱⁱⁱ(CN)₆]³⁻. Their UV and VIS spectroscopy results revealed three characteristic time scales for the aquation reaction, 0.5 ps, ∼4 ps, and ∼20 ps, as well as a long-time component that was assigned to the aquated photoproduct. These same time scales were also observed in their IR studies, and with the aid of calculated vibrational bands, obtained using DFT and an implicit solvent model, the time scales were assigned to the appearance or disappearance of particular species. Their findings led them to construct the following scenario for the photoaquation reaction: first, excitation to the ¹T_1g state rapidly converts to a triplet state on an ultrashort time scale and, due to the population of antibonding e_g orbitals in this triplet state, Fe–C axial bonds elongate; consequently, a CN⁻ ligand is released and the pentacoordinated species, in a triplet state and with square pyramidal (SP) geometry, is formed in ∼0.5 ps; partial in-cage (geminate) recombination of CN⁻ and ³SP [Feⁱⁱ(CN)₅]³⁻ occurs and the remaining ³SP [Feⁱⁱ(CN)₅]³⁻ structurally relaxes to the trigonal bipyramidal (TBP) geometry in 3–4 ps and over this time scale, water molecules compete with caged CN⁻ for bond formation with ³SP [Feⁱⁱ(CN)₅]³⁻; the majority of the aquation takes place on the relatively slow ∼20 ps time scale from the ³TBP pentacoordinated species.

Our work extends on these studies. We use synchrotron x-rays to probe the photoaquation reaction, measuring x-ray absorption near edge spectra (XANES) at the Fe K-edge, which have direct sensitivity to the electronic and geometric structure surrounding the absorbing Fe atom. To overcome the long temporal duration of the x-ray pulses (80 ps FWHM), we use a “time-slicing” scheme^55–57 where we use a short-duration laser pulse (10 ps FWHM) to pump at variable time delays that span across the time profile of the x-ray probe pulse. By operating at a MHz pump-probe repetition rate, we are able to take full advantage of the high flux and stability of synchrotron radiation to achieve a set of high-signal-to-noise, time-resolved x-ray spectra that allow us to extract the XANES spectrum of the intermediate pentacoordinated species and determine its lifetime to be 19 (±5) ps. Additionally, analysis of the data is suggestive of a 1.5 (±0.6) ps formation time for the pentacoordinated intermediate. QM/MM molecular dynamics simulations and XANES calculations confirm our experimental findings, elucidate the aquation mechanism, and explain the origin of the relatively long lifetime for this intermediate.

XAS measurements were done at beamline 7-ID-D at the Advanced Photon Source⁵⁸ using the MHz-repetition-rate pump-probe, liquid-jet endstation developed there.⁵⁹ The synchrotron ran in the standard 24-bunch operating mode, producing x-ray pulses with 80 ps duration (FWHM) at a 6.52 MHz repetition rate. The x-ray energy was calibrated using an Fe foil to a precision of ∼0.25 eV. The x-ray flux at the sample was measured with an ion chamber to be ≈2 × 10¹² photons/s. The laser (355 nm and 266 nm wavelengths, 10 ps pulse duration, Duetto, Time Bandwidth/Lumentum) was synchronized to the storage ring and operated at 1.3 MHz so that laser pulses overlapped every 5th x-ray pulse. At this repetition rate, the x-ray pulses overlapped with the laser are from each of the 24 electron bunches circulating the ring, allowing us to use an ungated ion chamber measurement as an incident x-ray flux monitor for the pump-probe measurements. The laser pulse fluence on the sample was ≈35 mJ/cm² for both 355 nm and 266 nm. The sample was circulated by a high-performance liquid chromatography (HPLC) pump through a 130 μm diameter quartz nozzle that produced a cylindrical liquid jet. The flow rate was set to 25 ml/min to ensure a jet speed of ∼25 m/s to fully refresh the sample volume between laser shots. Refreshment of the sample was critical since the lifetime of the photoaquated species is longer than the laser repetition period. The x-rays were focused onto the jet to a spot size of 5 μm (H) × 3 μm (V) FWHM using Kirkpatrick-Baez mirrors. The laser beam crossed the x-ray beam with a small (5°) angle and was spatially overlapped with the x-rays at the jet position using a 50 μm diameter pinhole. Temporal overlap between laser and x-rays was achieved using a metal–semiconductor–metal (MSM) detector (Hamamatsu) to ∼10 ps precision, and then spatial and temporal overlap was optimized using a [Fe(bpy)₃]²⁺ reference sample in acetonitrile, which is known to have a prompt response.⁶⁰ 

XAS spectra were collected in fluorescence mode using an avalanche photodiode (APD) detector (Oxford Instruments) positioned at 90° relative to the incident x-ray beam. The detector was operated in analog mode to detect multiple fluorescence photons per shot. The APD signal was input to a MHz digital boxcar average (UHFLI, Zurich Instruments) to provide average signals for the x-ray pulses just preceding the laser-overlapped pulses (OFF) and the x-ray pulses overlapped with laser pulses (ON). The difference spectra were constructed by subtracting OFF from ON.

The accumulation times for the “time-sliced” datasets were 11.5 h for the XANES spectra and 4 h for the delay curves. To minimize the impact of systematic errors, the accumulation was broken up into short scans, 12 min each for the XANES and 7 min each for the delay curves, each cycling through the selected delays (for XANES) or energies (for the delay curves). The scans for each delay (XANES) or energy (delay curves) were then averaged. The number of averaged scans depended on the signal strength at a given delay (or energy), ranging from a minimum of 2 to a maximum of 28 for the XANES and a minimum of 4 to a maximum of 8 for the delay curves.

Aqueous solutions were prepared by dissolving high purity K₄[Fe(CN)₆]·3H₂O and K₃[Fe(CN)₆], purchased from Sigma-Aldrich, in distilled water. The concentration was 50 mM. To prevent contamination of spectra from accumulating irreversible photoproducts, a large sample volume of 1 l was used that was periodically replaced with a fresh volume.

All calculations were performed with the NWChem computational chemistry package.⁶¹ Hybrid QM/MM molecular dynamics (MD) simulations⁶² were first performed on the [Feⁱⁱ(CN)₆]⁴⁻ complex solvated in water. A single anion was placed in a cubic box and solvated with 4182 water molecules from a previously equilibrated bulk water “template” system having a density of 1 g/cm³ (water density at the standard temperature-pressure). The resulting box size was 49.98 Å × 49.98 Å × 49.98 Å. Four K⁺ cations were randomly placed (approximately 15 Å away from the anion) to provide an overall neutral charge for the entire solvated system. The K⁺ counter ions were allowed to move freely. The transition metal complex was treated quantum mechanically (QM), while the rest of the system (the water bath) was treated at the molecular mechanics (MM) level. This simple partitioning avoids the need for reassignment of QM and MM atoms during the molecular dynamics simulations, which is challenging when solvent exchange is possible between the subsystems. The water molecules and potassium cations, which comprise the MM region, were treated with the SPC/E water model⁶³ and the SPC/E-specific K+ force-field of Joung and Cheatham,⁶⁴ respectively. The QM region was described at the DFT level of theory with the global hybrid PBE0⁶⁵ (25% Hartree-Fock exchange) exchange-correlation functional. The 6-311G^** basis set^66,67 was used for the C and N atoms, and the Stuttgart basis set/relativistic small-core effective core potential (ECP)⁶⁸ was assigned to the Fe atom. Lennard-Jones parameters were assigned to the atoms of the complex for the nonbonding van der Waals interaction with the water molecules. Specifically, SPC/E-compatible GAFF (generalized AMBER forcefield)⁶⁹ Lennard-Jones parameters were used for the C (“c1”) and N (“n1”) atoms, and the Lennard-Jones “feo” parameters of CLAYFF⁷⁰ were used for the tight octahedral environment of the Fe atom.

The entire system was annealed through a series of freeze and thaw cycles of the complex and solvent until the energy change was less than 0.0001 hartrees. Five freeze and thaw cycles were used for both solution systems. Following this initial annealing phase, the complex was held fixed, and dynamics were performed on the solvent only for 100 ps with a 2 ps time step. Following the second annealing phase, QM/MM molecular dynamics were performed on the entire complex and solvent system at 298.15 K (NVT) for 20 ps after a 1 ps equilibration with a time step of 0.25 fs. For the SPC/E water model, the SHAKE algorithm⁷¹ was used to keep the water molecules rigid (constraining the bond lengths and bond angle). The QM region was allowed to move freely in the MM bath (i.e., the SHAKE method was not applied).

The photoaquation reaction was performed in steps. We started with the CN⁻ ligand dissociation as the first step. We then studied the pentacoordinated species, [Feⁱⁱ(CN)₅]³⁻, as the QM region in the triplet state and three K⁺ counterions in the MM solvent bath. The system was further optimized and equilibrated, and dynamics were run for ∼15 ps using the same protocol described earlier. For the aquated species, we started with a pentacoordinated configuration, where a water molecule was close to the vicinity of the Fe center. The QM region was redefined to include the pentacoordinated species and the close water molecules. The system was again further optimized and equilibrated, and dynamics were run in both the triplet and singlet spin states. The triplet spin state MD run of the aquated system resulted in a fragmentation of the complex after ∼1 ps, returning to the pentacoordinated species. The singlet spin state MD was stable throughout for ∼20 ps.

Representative cluster models, showing the different phases of the reaction, were extracted from the dynamics for the XANES calculations. Five clusters for each reaction species were constructed by taking the Fe center as well as a 4 Å-thick shell of explicit water molecules surrounding the complex. The conductorlike screening model (COSMO) was used to model the bulk solvent (ε = 78.4) beyond the explicit water molecules in the cluster models. These calculations were performed using the TDDFT-based^72,73 restricted excitation window approach including multipole contributions to the oscillator strengths as implemented in NWChem.⁷⁴ The Sapporo TZP-2012⁷⁵ and 6-311G^** all-electron basis sets were used for the Fe atom and the light atoms, respectively, and the PBE0 exchange-correlation functional. We found that this functional was sufficiently accurate to describe the spectra over a broad energy range (IR, UV/vis, and x-ray) for [Feⁱⁱ(CN)₆]⁴⁻ and [Feⁱⁱⁱ(CN)₆]³⁻ model systems¹⁰ and our earlier studies on the solvated mixed valence Fe(ii)Ru(iii) dimer complex.⁷⁶ All calculations (QM/MM and spectroscopy) were performed with the complexes treated as low spin species because of the strong ligand field-splitting of the dominant CN⁻ ligands.

The choice of DFT and TDDFT levels of theory was motivated by the sizes and ensembles of the explicitly solvated clusters considered in this work. Both theories offer the best compromise between accuracy and computational performance for large systems. Even though higher order correlated wavefunction-based approaches are more accurate, these methods quickly become prohibitively expensive computationally for large systems without symmetry.

The measured Fe K-edge XANES of ground state [Feⁱⁱ(CN)₆]⁴⁻ is shown in Fig. 1. We also show, for comparison, the ground state spectrum of [Feⁱⁱⁱ(CN)₆]³⁻. The features present in these spectra have been studied in depth previously.¹⁰ We mention some to highlight the sensitivity of the XANES region of the absorption spectrum to the electronic structure near the absorbing Fe ion and to the geometrical arrangement of neighboring atoms. Both complexes have very similar geometry, O_h symmetry with Fe–C distances of 1.92 Å ([Feⁱⁱ(CN)₆]⁴⁻) and 1.93 Å ([Feⁱⁱⁱ(CN)₆]³⁻).^10,42 Above the ionization threshold at about 7.125 keV, there are large modulations that are due to multiple scattering resonances as the liberated photoelectron passes through the rigid CN⁻ ligands.^42,77 The [Feⁱⁱⁱ(CN)₆]³⁻ edge position is blue shifted relative to [Feⁱⁱ(CN)₆]⁴⁻, reflecting the lower charge density at the iron center. In the pre-edge region, shown in the inset of Fig. 1, the [Feⁱⁱⁱ(CN)₆]³⁻ spectrum exhibits an additional pre-edge resonance, reflecting its different Fe 3d orbital occupancy. The pre-edge region is discussed in more detail in Sec. IV A 4.

Our experimental investigations began by establishing the spectrum of the aquated photoproduct, [Feⁱⁱ(CN)₅H₂O]³⁻, so we describe the spectral signatures of this photoproduced species first. To initiate the photoaquation reaction, we pumped the ground state [Feⁱⁱ(CN)₆]⁴⁻ sample with 355 nm light. At this wavelength, the photon energy is insufficient to induce the photo-oxidation reaction. The changes we observe in the spectrum after pumping are small (<1%) because of the low extinction coefficient at this wavelength (300 M⁻¹ cm⁻¹),⁵¹ small quantum yield (≈0.2),^49,51 and the need to keep the laser fluence low to avoid multiphoton processes. Yet, the changes are easily seen in the difference between laser-pumped and unpumped spectra, shown in Fig. 2(b). Two pump-probe delays are plotted, 215 ps and 153 ns, and they are found to be identical, indicating that the species present in the pumped spectrum is long lived. We determined its lifetime to be >1 μs, which was the longest delay we could probe with the setup used for this experiment. We estimated that this species comprised 1.3% of the laser-pumped signal (the remainder being ground state [Feⁱⁱ(CN)₆]⁴⁻), and with this value reconstructed the absorption spectrum for the photoproduct, shown in Fig. 2(a). The estimation for the excited state fraction is based on the measurement of the transmission through the sample using an optical probe pulse that was synchronized with the x-ray probe pulse. Details on this measurement are found in the supplementary material. Comparing the reconstructed spectrum to the ground state spectrum, one can see that the edge is red shifted and that there is a reduction in the amplitude of the modulations above the edge. Additionally, the pre-edge peak at 7.113 keV is greatly enhanced in amplitude and red shifted compared to the 7.114 keV ground state peak and there is a smaller increase in intensity at the 7.1165 keV peak. The changes are consistent with what is expected for the photoaquated species, [Feⁱⁱ(CN)₅H₂O]³⁻. The loss of the strongly bonding (π acceptor) CN⁻ results in more electron density at the Fe center, causing the edge shift, and a reduction in modulation depth above the edge is expected since there is one less CN⁻ from which to scatter. The replacement of a CN⁻ with H₂O distorts the O_h symmetry of the ground state species allowing the contribution of dipole transitions to the pre-edge peak.⁷⁸ Further discussion of the pre-edge peak is found in Sec. IV A 4. Our spectrum for the [Feⁱⁱ(CN)₅H₂O]³⁻ species agrees well with that presented by Reinhard et al.⁵³ 

As further confirmation of our assignment, we found this difference signal to also be present after 266 nm excitation. At this pump wavelength, photo-oxidation is the dominant reaction while photoaquation occurs as a minor channel.^49,51 Therefore, we expect the difference signal to be primarily due to the photo-oxidation photoproduct, [Feⁱⁱⁱ(CN)₆]³⁻, and to have a small contribution from photoaquated [Feⁱⁱ(CN)₅H₂O]³⁻. The ground state spectra of [Feⁱⁱ(CN)₆]⁴⁻ and [Feⁱⁱⁱ(CN)₆]³⁻ are shown in Fig. 3(a) alongside the reconstructed [Feⁱⁱ(CN)₅H₂O]³⁻ spectrum from Fig. 2. Laser-pumped minus ground-state difference spectra at three different pump-probe delays are shown in Figs. 3(b)–3(d). For each pump-probe delay, it can be seen that the difference signal is indeed composed of [Feⁱⁱⁱ(CN)₆]³⁻ and what we have assigned as [Feⁱⁱ(CN)₅H₂O]³⁻. In each panel, the blue curve overlaid with the black difference spectrum is the difference between [Feⁱⁱⁱ(CN)₆]³⁻ and [Feⁱⁱ(CN)₆]⁴⁻ scaled to match the transient signal strength. Shifted down by 0.03, for easy of visibility, is the component that remains after subtracting the scaled [Feⁱⁱⁱ(CN)₆]³⁻ signal from the difference signal. Overlaid on this residual is the difference signal we recorded at 355 nm (Fig. 2), scaled to match the residual signal intensity. The match of spectral features is very good, and the scaling is what is expected considering the quantum yields reported by Shirom and Stein⁴⁹ for the oxidation reaction (ϕ = 0.52 at 266 nm) and Emschwiller and Legros²⁵ for the photoaquation reaction (ϕ = 0.14 at 254 nm and ϕ = 0.31 at 366 nm). The [Feⁱⁱⁱ(CN)₆]³⁻ population decays on the nanosecond time scale as the hydrated electron recombines with [Feⁱⁱⁱ(CN)₆]³⁻ to form [Feⁱⁱ(CN)₆]⁴⁻.⁷⁹ The [Feⁱⁱ(CN)₅H₂O]³⁻ population remains fairly constant at 2%. There seems to be a slight increase to 2.4% at 30 ns delay, which may indicate a secondary process resulting in [Feⁱⁱ(CN)₅H₂O]³⁻ formation that is concurrent with hydrated electron recombination, but this is not further investigated in this work.

Upon very close inspection of Fig. 3(b), one can see that the agreement between the 355 nm [Feⁱⁱ(CN)₅H₂O]³⁻ difference signal and the 50 ps residual component is not as good as the agreement with residuals at longer delays. This is more easily seen in Fig. 4(a) where the 266 nm, 50 ps, and 2 ns residual components are plotted together with the 355 nm [Feⁱⁱ(CN)₅H₂O]³⁻ difference signal. The most prominent differences are seen in the pre-edge region, shown in the inset of Fig. 4(a). In the 50 ps difference spectrum, the 7.113 keV peak is reduced in intensity and slightly shifted to the red and there is more intensity around the small 7.1165 keV peak. We observe similar differences after 355 nm excitation. Comparing a 55 ps delay to 215 ps, shown in Fig. 4(b), we find that again the 7.113 keV peak is reduced and shifted and there is more intensity around the 7.1165 keV peak. These changes are consistent with what would be expected from the presence of a pentacoordinated intermediate species in the aquation reaction. As described by Westre et al.,⁷⁸ the pre-edge peak for an Fe²⁺ octahedral complex will shift to lower energy as it undergoes weak field distortion, or elongation of a ligand-metal bond to the extreme case where one is left with a square pyramidal geometry.

Because [Feⁱⁱ(CN)₆]⁴⁻ likely undergoes secondary photochemical reactions where absorption of additional photons after the primary reaction leads to other products, we verified that the small changes we were observing were not due to the absorption of multiple photons. We repeated the 355 nm measurement at a 2 times higher laser pump power. While additional features, presumably due to multiphoton processes, did appear in the higher power difference spectra, the difference between the long delay (215 ps) and short delay (50 ps) difference spectra looks the same as the difference of difference spectra at low laser power. As seen in Fig. 4(c), when scaling the high power curve by the ratio of laser powers it is found to fall exactly on the low power curve. This demonstrates that the changes we observe at ≈50 ps delays are linearly dependent on the laser power and, therefore, due to a single photon absorption process.

The temporal width of the x-ray probe pulses is 80 ps FWHM, so pump-probe delays <80 ps reflect times that are within the x-ray temporal profile. The measured difference signal at these short delays is a sum of contributions from the aquated photoproduct and the presumed pentacoordinated product and this sum is convolved with the x-ray probe temporal profile (and the 10 ps FWHM pump laser profile). In order to isolate the pentacoordinated difference spectrum and determine its time dependence, we collected a set of XANES scans at 10 different time delays spanning the x-ray probe temporal profile and a set of pump-probe delay scans at 8 energies strategically selected to have different sensitivities to the aquated and pentacoordinated species. The XANES spectra are shown in Fig. 5 and the delay scans in Fig. 6.

We carried out a singular value decomposition (SVD) analysis of the 10 XANES difference curves and determined that the spectra are composed of two components. The details of this analysis are found in the supplementary material. The spectra at long delays (>100 ps) are consistent with the transient signal of the aquated product shown in Fig. 2 indicating that the pentacoordinated species has fully decayed at these times. Therefore, we could fix this spectral shape as the aquated species associated difference spectrum. To construct the species associated spectrum for the pentacoordinated product, we used the time evolution of the signal obtained from the kinetic fitting model for the delay scans (see Sec. IV B 1). These two components add to reconstruct the measured difference spectra as shown in Fig. 5.

Armed with the difference spectrum of the [Feⁱⁱ(CN)₅]³⁻ species, we set out to reconstruct its absorption spectrum. In order to do this, the fraction of [Feⁱⁱ(CN)₅]³⁻ comprising the measured difference signal at a given time delay must be known. We estimate the fraction by assuming all the pentacoordinated molecules decay to aquated molecules and all the aquated molecules are produced from the pentacoordinated molecules, neglecting the possibility of decay by recombination with CN⁻ and neglecting the possibility of an aquated product formation that does not go through the pentacoordinated species. We calibrated our kinetic model functions (see Sec. IV B 1) to the established fraction for the photoaquated species at long time delays. The plot showing this calibration is presented in the supplementary material. Then, using the XANES difference spectrum at a delay where the amplitude of the pentacoordinated contribution is comparable to that of the aquated, and the calibrated fraction, we reconstructed the [Feⁱⁱ(CN)₅]³⁻ spectrum. This is shown in Fig. 7 along with the spectra of [Feⁱⁱ(CN)₆]⁴⁻ and [Feⁱⁱ(CN)₅H₂O]³⁻. The changes observed in the [Feⁱⁱ(CN)₅]³⁻ spectrum are similar to those observed comparing [Feⁱⁱ(CN)₅H₂O]³⁻ to [Feⁱⁱ(CN)₆]⁴⁻, but more pronounced, with larger pre-edge intensity enhancement, larger red-shift of the edge, and further reduction of the above-edge modulations.

The XANES calculations, using the procedure outlined in Sec. III, are shown in Fig. 8. All calculations were performed with the complexes treated as low spin species because of the strong ligand field-splitting of the CN⁻ ligands. The calculated spectra have been blue shifted by 144.0 eV. The orbital characteristics of the various transitions for the different species are given in the supplementary material.

For the [Feⁱⁱ(CN)₆]⁴⁻ and [Feⁱⁱⁱ(CN)₆]³⁻ reference complexes, the calculations capture the key pre-edge quadrupole transitions as well as the t_2g-e_g splitting ∼3.7 eV (expt: ∼3.4 eV) in [Feⁱⁱⁱ(CN)₆]³⁻. We also refer the reader to the recent study of Ross and co-workers¹⁰ for a comprehensive study of the reference complexes.

For the photoaquation mechanism, as discussed in Sec. IV B 2, our QM/MM MD simulations predict two transient pentacoordinated structures, trigonal bipyramidal (TBP) and square pyramidal (SP) that are interconvertible. From our spectroscopy calculations [Fig. 8(b)], we predict that the experimental XANES signal arises from a mixture of both structures. For the TBP structure, there are two dipole dominated transitions of similar intensities separated by ∼0.29 eV. Both features involve transitions to the Fe 3d orbitals which are mixed with N p orbitals of the CN⁻ ligands and Fe 4p orbitals. For the SP structure, we also find two dipole dominant transitions separated by ∼1.07 eV and the lower transition at ∼7.111 keV is approximately three times weaker than the stronger feature at ∼7.112 keV. The orbital characteristics of the transitions are similar to the TBP species. The further red-shifting of ∼2.5 eV with respect to the ground state [Feⁱⁱ(CN)₆]⁴⁻ is also captured in good agreement with the experiment.

For the aquated species, the calculated spectra capture the intense pre-edge feature ∼7.113 keV. The replacement of a CN⁻ with H₂O distorts the O_h symmetry. This results in transitions with dipole characteristics due to mixing of the Fe 3d orbitals with the unoccupied p orbitals of the C and N atoms of the CN⁻ ligands (see the supplementary material). The red-shifting of the main pre-edge feature at ∼1.5 eV with respect to the [Feⁱⁱ(CN)₆]⁴⁻ ground state reference is also captured and compares well with the experiment.

To gain insight into the mechanism behind this reaction, we can turn to the time dependence of the different species and analysis of the set of delay scans taken at different energies. These data are shown in Fig. 6. It is evident at first glance that there is a long-lived component (dominating in the 7.113 keV scan for example) and a short lived component (easily seen in the 7.1295 keV scan), consistent with the findings from the XANES analysis. To extract the time dependence of these components, we carried out a global least-squares fit using a fit function composed of the temporal dependence of the concentrations of the two species convolved with the instrument response function (IRF). The time dependence of the concentrations was derived from a simple kinetic model that assumes that dissociation of the CN⁻ ligand from the [Feⁱⁱ(CN)₆]⁴⁻ excited state occurs with time constant τ₁ and the aquated species is formed from the pentacoorinated species with time constant τ₂,

The IRF is dominated by the x-ray temporal profile but contains contributions from the laser profile and x-ray/laser temporal jitter. Details of the IRF and parameterization of the fit function are included in the supplementary material. The best least-squares global fit to the delay scans is shown in Fig. 6 along with the individual temporal profiles for the aquated and pentacoordinated species. From the global fit, we find that the lifetime of the pentacoordinated species is τ₂ = 21.1 (±1.6) ps and that it appears with a time constant τ₁ = 1.148 (±0.005) ps. We are not sensitive to the initial excited [Feⁱⁱ(CN)₆]⁴⁻ species likely because its lifetime is too short to produce the appreciable signal over the long probe pulse duration. Extraction of such a short appearance time, relative to the long 80 ps probe pulses, needs to be considered suggestive rather than a definitive measure and should be verified using shorter duration x-ray probe pulses available at an x-ray free electron laser (XFEL) facility. We found that if we assume we do not have sensitivity to the growth time for [Feⁱⁱ(CN)₅]³⁻ and fix τ₁ to a very small value in our fit, making it instantaneously produced on our probed time scale, we get a good fit of the data with χ²/ν = 1.013 and a value for τ₂ = 22.7 (±1.5) ps. Allowing τ₁ as a free parameter in the fit yields a slightly better fit with χ²/ν = 0.982. Given this and the fact that the growth time is on par with that reported by Reinhard et al.⁵¹ and also with the results of our MD simulation, we are inclined to believe that it may be meaningful. More details of this analysis are included in the supplementary material.

An additional uncertainty in our analysis is the precise form of the IRF. The IRF was not measured in our experimental setup during the beamtime in which the data were collected, so the exact form might differ from that we assume. We studied the impact of this on the fitting results by varying the parameters in the IRF function and observing the effect on the extracted time constants. We found that the results were robust and we derived error bars for the time constants from these results. Based on this, we report the growth time for the [Feⁱⁱ(CN)₅]³⁻ species to be 1.5 (±0.6) ps and the lifetime as 19 (±5) ps.

To understand the origin of these time constants and elucidate the photoaquation mechanism, we carried out QM/MM simulations as described in Sec. III. We did not simulate the initial relaxation dynamics to the lowest triplet state following photoexcitation. We started with the CN⁻ ligand dissociation as the first step,

This was started with the equilibrated [Feⁱⁱ(CN)₆]⁴⁻ complex, and the dynamics was performed on the triplet state. Our simulations show that dissociation takes place in ∼1.3 ps consistent with the experiment.

In the second step, the pentacoordinated species, [Feⁱⁱ(CN)₅]³⁻, dynamics was run in the triplet state and three K⁺ counterions in the MM solvent bath. This was further optimized and equilibrated, and dynamics were run for ∼15 ps using the same protocol described earlier. The dynamics simulations show two possible structures, square pyramidal (SP) and trigonal bipyramidal (TBP) that transform into each other over a time scale of ∼3 ps. This suggests a very small activation barrier and a mixed population of transient pentacoordinated species. We did not perform a detailed simulation of the kinetics as this would require a very large number of molecular dynamics runs,

For the aquated species, simulations were started with a pentacoordinated configuration, where a water molecule was close to the vicinity of the Fe center. The QM region was redefined to include the pentacoordinated species and the close water molecules. This was again further optimized and equilibrated, and dynamics were run in both the triplet and singlet spin states. Dynamics on the triplet spin state of the aquated system resulted in a fragmentation of the complex after ∼1 ps, returning to the pentacoordinated species. The singlet spin state MD was stable throughout for ∼20 ps resulting in the octahedrally coordinated aquated species,

The fact that we experimentally observe the pentacoordinated intermediate confirms that aquation occurs through a dissociative mechanism, where the H₂O attaches after the CN⁻ has left, but the question remains whether aquation can also occur before the CN⁻ ligand fully dissociates. Our experimental data cannot distinguish this, but our simulations suggest that this is unlikely. Our simulations indicate that the CN⁻ dissociation from the triplet [Feⁱⁱ(CN)₆]⁴⁻ state takes place in ∼1.3 ps. For the system to bypass the pentacoordinated species, a water molecule will have to almost simultaneously replace the leaving CN⁻ ligand. However, steric effects will not favor this. In addition, once the water molecule is near the pentacoordinated complex, it takes another ∼1.0 ps for the singlet spin state aquated complex to stabilize. This suggests, at least in water, that the aquated complex cannot form immediately after dissociation. We have also calculated the Q5 Steinhardt order parameter⁹¹ (see the supplementary material) around the Fe center to monitor the trigonal bypyramidal (TBP) vs square pyramidal (SP) characteristics of the [Feⁱⁱ(CN)₅]³⁻ complex. Based on this analysis, for every ∼3 ps of oscillation between the SP and TBP, the pentacoordinated structure resides in the SP for ∼500 fs and as TBP otherwise. This suggests that there is just a small window when the aquation can occur and provides an explanation for the long 20 ps it takes for the overall reaction. It is possible that disrupting the hydrogen bonding network in water around the complex may speed up the reaction by lowering the lifetime of the pentacoordinated species. This could be studied by introducing a “hydrogen bond disrupting” component to the solvent.

Our study builds upon and helps elucidate the photoaquation reaction mechanism proposed by Reinhard et al. As in their studies, we assume ligand dissociation begins from the triplet state of [Feⁱⁱ(CN)₆]⁴⁻. We find dissociation, and appearance of the pentacoordinated species, to occur in 1.5 ps, which is not dissimilar from the ∼0.5 ps dissociation time reported by Reinhard et al. from their UV/VIS and IR studies. Their calculations show the trigonal bipyramidal species as the lowest energy species and based on this; they assign spectral changes observed on the ∼3–4 ps time scale to the relaxation of the square pyramidal species to the trigonal species and then propose that aquation occurs on the 20 ps time scale from the TBP species. Our results, however, suggest a more dynamic situation, where the energies of the square pyramidal and trigonal bipyramidal species are close enough so that the solvent environment causes the two to interconvert on a ∼3 ps time scale. Aquation can occur when there is room for a water molecule to move in close, as in the square pyramidal geometry, and when the spin changes from triplet to singlet. The solvent plays a critical role in the process, not just in that a solvent molecule bonds to form the aquated complex, but also in perturbing the energies of the intermediate species.

This study also highlights the high sensitivity that can be achieved using synchrotron x-rays in time-resolved spectroscopy studies. The combination of high flux and stability that is unique to synchrotrons can be fully utilized when operating at MHz pump-probe repetition rates and, as we have shown, leads to high statistics data that can reveal small signals. The “time-slicing” method can detect intermediates that live only 10’s of picoseconds, making beamtime at an XFEL using femtosecond x-ray pulses not required for studies of their properties. The method bridges the gap between the femtosecond temporal regime explored at XFELs, and the temporal regime >100 ps that is typically considered the domain of synchrotrons. Borrowing from “time-sliced” measurements in the optical regime, like time-correlated single photon counting, the shortest-lived species that can be detected are those that live for about 1/10 the duration of the probe pulse.⁸⁰ Therefore, we would expect to be able to detect 8 ps-lived species using the present APS x-rays and 20 ps-lived species after the upcoming APS upgrade that will provide higher brightness x-rays but elongate them from 80 ps to ∼200 ps. As transition metal complexes commonly exhibit dynamics on these time scales, the method promises to provide new insight into the photophysical and photochemical behavior of these systems.

The photoaquation reaction mechanism described here relies upon the assumption that ligand dissociation begins from the triplet state of [Feⁱⁱ(CN)₆]⁴⁻. Given that the initial photoexcitation is to a singlet state, it is of interest to explore the ultrafast dynamics that occur during the initial singlet to triplet spin change. Measurement of the spectrum of the x-ray fluorescence resulting from transitions from Fe 3p orbitals to the 1s core hole [Kβ x-ray emission spectroscopy (XES)] could be an informative means of experimentally investigating this. Kβ XES has been shown to be sensitive to spin state due to the exchange interaction between the unpaired 3d electrons and the 3p core hole final state of the emission process⁸¹ and has been used at XFELS^6,82–84 and synchrotrons,^85–89 to track the time dynamics of spin. Verification of the triplet spin state of the pentacoordinated intermediate can be carried out at a synchrotron by measuring “time-sliced” Kβ XES. While the signal strength is prohibitively small to carry out this measurement using monochromatic synchrotron x-rays, newly developed MHz pump-probe capabilities at the APS that use broadbandwidth, “pink beam” x-rays increase the x-ray flux by >600⁹⁰ and will make “time-sliced” XES feasible.

We have carried out an investigation of the photoaquation reaction in [Feⁱⁱ(CN)₆]⁴⁻ using time-resolved x-ray absorption spectroscopy and QM/MM MD simulations. Our XAS measurements identified the presence of a pentacoordinated intermediate with appearance time 1.5 (±0.6) ps and decay time 19 (±5) ps. The MD simulations show a dissociation time for the CN⁻ ligand from the initially excited ³[Feⁱⁱ(CN)₆]⁴⁻ that is consistent with the experimental findings. Additionally, simulations show that the square pyramidal and trigonal bipyramidal geometries for the pentacoordinated intermediate species are interconvertible and transform from one to the other over a time scale of ∼3 ps. Comparison of measured spectra for the pentacoordinated intermediate with the simulated spectra shows that the measured spectra are likely composed of a mixture of square pyramidal and trigonal bipyramidal species. The role of the solvent is quite important in this reaction, and further analysis of the MD simulation results could help show the details of its influence. The model for the reaction assumes a triplet state for the initial precursor to dissociation and for the pentacoordinated intermediates, but this has not yet been experimentally verified. Measurement of the Kβ XES spectrum would be a definitive means of verifying this assumption. Additionally, the predicted fluxional pentacoordinated state from our dynamics simulations and the initial very fast dynamics after photoexcitation, including the change from singlet to triplet states, has not been explored experimentally and could be undertaken using ultrashort x-ray pulses available at XFELs. Preliminary work has already been carried out at the Spring-8 Angstrom compact free electron laser (SACLA).⁵⁴ 

See the supplementary material for I: details on the determination of the excitation fraction; II: details on the singular value decomposition of the time-resolved XANES spectra; III: orbital information on the key pre-edge transitions of the different reaction species; IV: details on the determination of the instrument response function; V: details on the kinetic fits; and VI: details on the order parameter calculation.

We thank Michael Borland and the Diagnostics Group in the Accelerator Systems Division at the APS for sharing the streak camera data with us. This material is based upon the work supported by the U.S. Department of Energy, Office of Science, Basic Energy Science, Chemical Sciences, Geosciences and Biosciences Division under Contract Nos. DE-AC02-06CH11357 and KC030103172684. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by the Argonne National Laboratory. Argonne is a U.S. Department of Energy Laboratory managed by the University of Chicago Argonne, LLC, under Contract No. DE-AC02-06CH11357. Computational work was performed using EMSL, a DOE Office of Science User Facility sponsored by the Office of Biological and Environmental Research and located at the Pacific Northwest National Laboratory (PNNL). The PNNL is operated by the Battelle Memorial Institute for the United States Department of Energy under DOE Contract No. DE-AC05-76RL1830. The research also benefited from resources provided by the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Work by J.U. was supported by the Tryggers Science Foundation. Work by Z.N. and G.V. was financed by the “Lendület” (Momentum) Program of the Hungarian Academy of Sciences (Grant No. LP2013-59), the Government of Hungary and the European Regional Development Fund under Grant No. VEKOP-2.3.2-16-2017-00015, and the National Research, Development and Innovation Fund (Grant No. NKFIH FK 124460). W.G. acknowledges financial support from European XFEL and partial financial support from the National Science Centre (NCN) in Poland under SONATA BIS 6 Grant No. 2016/22/E/ST4/00543.