Valence-to-core x-ray emission spectroscopy (VtC XES) combines the sample flexibility and element specificity of hard x-rays with the chemical environment sensitivity of valence spectroscopy. We extend this technique to study geometric and electronic structural changes induced by photoexcitation in the femtosecond time domain via laser-pump, x-ray probe experiments using an x-ray free electron laser. The results of time-resolved VtC XES on a series of ferrous complexes [Fe(CN)2n(2, 2′-bipyridine)3−n]−2n+2, n = 1, 2, 3, are presented. Comparisons of spectra obtained from ground state density functional theory calculations reveal signatures of excited state bond length and oxidation state changes. An oxidation state change associated with a metal-to-ligand charge transfer state with a lifetime of less than 100 fs is observed, as well as bond length changes associated with metal-centered excited states with lifetimes of 13 ps and 250 ps.

Valence-to-core x-ray emission spectroscopy (VtC XES) is an emerging technique for studying inorganic 3d metal based molecular systems. In the VtC spectral region (Kβ″ and Kβ2,5), emission arises from radiative decay of valence electrons to the metal 1s core hole created by an x-ray absorption process. Such transitions gain dipole-allowed intensity via mixing of metal np character into the valence orbitals. Therefore, VtC XES is sensitive to bonding and the chemical environment of the absorbing atom but retains specificity to the absorbing atom. Static VtC XES studies have demonstrated the technique’s sensitivity to ligand environment, including protonation, as well as oxidation state and bond lengths.1–8 

Extending VtC XES to ultrafast time-resolved experiments holds promise as a tool to probe the local geometry, ligand environment, and oxidation state of transient species. The goal of understanding chemical reaction dynamics and mechanisms requires resolution on femtosecond and picosecond time scales and sensitivity to the geometric and electronic structure of transient species. VtC XES spectra are sensitive to both electronic and geometric structure and have proven straightforward to model: ground state density functional theory (DFT) calculations of single-electron transitions are found to agree well with experimental VtC data, in contrast to the many-electron approaches necessary to model Kβ1,3 transitions.3,5

Time-resolved XES in the 2p-1s (Kα) and 3p-1s (Kβ1,3) main line regions has already been used to uncover the spin state of short-lived intermediates and track the population of optically dark metal-centered states in a variety of molecules, including proteins.9–14 XES has the advantage of being element-specific, and working in the hard x-ray regime allows considerable flexibility in sample environments, including solids and liquids at variable temperatures and conditions. The VtC region’s sensitivity to the local structure and oxidation state, in conjunction with the simplicity of modeling the spectrum, makes it an attractive addition to transient Kα and Kβ1,3 XES experiments to concurrently monitor spin, geometric, and oxidation state changes. In terms of geometric sensitivity, other methods such as time-resolved x-ray solution scattering (XSS) and extended x-ray absorption fine structure (EXAFS) access geometric information directly; however, XSS is complex to interpret, and EXAFS requires scanning of the incident monochromatic photon energy, making this method less amenable to x-ray laser sources. In contrast to EXAFS, full XES spectra can be measured on a shot-by-shot basis using dispersive spectrometers15 and can be combined with XSS in a single experiment, providing complementary information and taking advantage of the total flux of the XFEL SASE pulses.

A major challenge in implementing time-resolved VtC XES is the very small signal magnitude, since the Kβ2,5 emission is 50–100 times less intense than the Kβ1,3 main line. Time-resolved VtC XES studies at the Advanced Photon Source light source observed transient species on the 100 ps time scale,16–18 taking advantage of the MHz repetition rate of the light source to obtain difference spectra at a high photon flux (>1015 ph/s).18,19 With the application of time-slicing methods, the time scales available at synchrotrons can be improved to tens of ps regime.20 In comparison, x-ray free-electron laser (XFEL) sources such as the Linac Coherent Light Source (LCLS) combine high photon flux (>1014 ph/s) with femtosecond time resolution. Thus, XFEL experiments could ideally be used to record a two-dimensional map of VtC changes with high resolution in both emission energy and time.

This study demonstrates femtosecond resolution VtC XES at the LCLS. We present energy-resolved difference spectra integrated over tens of picoseconds and femtosecond time-resolved difference spectra integrated over a few eV to provide information about geometric and electronic structure of transient species. The signal-to-noise of the data presented here precludes robust two-dimensional mapping of the VtC difference spectra. Pump–probe VtC XES was performed on a series of ferrous complexes: [Fe(CN)6]4−, [Fe(CN)4(bpy)]2− (bpy = 2, 2′-bipyridine), and [Fe(CN)2(bpy)2]. Our measurements focused on demonstrating the ability of VtC to characterize the properties of short-lived intermediates formed following ultrafast internal conversion, intersystem crossing, charge transfer, and ligand rearrangement. Experimental difference spectra were compared to theoretical spectra extracted from ground state DFT calculations of the expected species to demonstrate sensitivity to bond length expansion in the triplet excited state of [Fe(CN)4(bpy)]2− and the quintet excited state of [Fe(CN)2(bpy)2]. Time traces of a difference spectrum of [Fe(CN)4(bpy)]2− with ≈100 fs resolution show sensitivity to the Fe oxidation state that allows a short-lived charge-transfer state to be observed.

Optical laser pump/x-ray probe measurements on solution samples were carried out at the XCS hutch21 of the LCLS. The samples were delivered in a 50 µm round liquid jet in a helium environment. [Fe(CN)6]4− and [Fe(CN)4(bpy)]2− were dissolved in water at 50 mM and 33 mM concentrations, respectively, while [Fe(CN)2(bpy)2] was dissolved in methanol at 15 mM concentration to maintain an optical density (OD) of ≈0.5 at the pump wavelength in the jet. For [Fe(CN)4(bpy)]2− and [Fe(CN)2(bpy)2], the sample was pumped with 495 nm laser pulses generated from a Ti:sapphire laser and an optical parametric amplifier described elsewhere.22 The optical pulse duration was less than 70 fs. The optical pulse energy was 7 µJ (spot size 170 × 360 µm; 5 mJ/cm2) for all plotted datasets, except for the data shown in Fig. 1(b), where the pulse energy varied from 7 µJ to 17 µJ among averaged data runs. For [Fe(CN)6]4−, the sample was pumped with 266 nm light using the third harmonic of the same Ti:sapphire laser with a pulse energy of 13.5 µJ (spot size and fluence on the order of 100 × 100 µm; 100 mJ/cm2).

FIG. 1.

Measured and calculated VtC spectra for the three complexes. [(a)–(c)] Experimental laser-off (black) and laser-on (red) averaged spectra. Difference signals (red, with shaded error bars) have been multiplied by 2. [(d)–(f)] Calculated spectra and difference signals for relevant states. Difference signals have been multiplied by 0.5.

FIG. 1.

Measured and calculated VtC spectra for the three complexes. [(a)–(c)] Experimental laser-off (black) and laser-on (red) averaged spectra. Difference signals (red, with shaded error bars) have been multiplied by 2. [(d)–(f)] Calculated spectra and difference signals for relevant states. Difference signals have been multiplied by 0.5.

Close modal

The sample was probed with pink x-ray pulses centered at 9450 eV ([Fe(CN)4(bpy)]2− and [Fe(CN)2(bpy)2]) or 8000 eV ([Fe(CN)6]4−) with a spectral width ΔE/E of 1 × 10−3, a pulse duration of 50 fs, and 120 Hz repetition rate.21 The x-ray pulse energy on the sample was ∼0.75 mJ/pulse. The incident x-rays were focused by compound refractive beryllium lenses with a ∼4 m focal length to a round beam size of 20 × 20 µm. The full Fe Kβ XES spectra (from 7025 eV to 7115 eV) were collected using a four-crystal von Hamos spectrometer15 in a shot-by-shot mode. Four cylindrically bent Ge(620) crystal analyzers with a 250 mm bending radius were used. The crystal analyzers are 110 × 25 mm, and the spectrometer collects a total solid angle of ≈1.4% of the sphere. The energy resolution is estimated to be 0.6 eV, including major geometrical contributions and the intrinsic energy resolution of the crystal analyzer (Darwin width and broadening associated with stress induced in the lattice planes when the analyzer is bent). The spectrum was collected on an ePix100 detector.23 A helium bag was used between the sample, crystals, and detector to minimize attenuation of the fluorescence and to reduce background from diffuse scattered radiation. The spectrometer was calibrated to the spectrum of a reference sample ([Fe(CN)6]4− in water, 350 mM concentration).

The time delay between the laser pump and x-ray probe pulses was scanned continuously with an encoded delay stage.24 A spectrally encoding timing tool25 was used to measure the x-ray arrival time relative to the optical pump pulse by probing the x-ray induced change in the refractive index of a thin crystal [Si3N4 for all datasets except the data shown in Fig. 1(b), which contain data taken with both Si3N4 and Ce:YAG timing tools] with chirped white-light pulses derived from the optical laser. Sorting the single shot XES spectra by the measured probe arrival time eliminates the majority of the pump–probe time delay jitter and leads to a time resolution of ≈100 fs.

Every seventh x-ray shot was taken without the optical laser, and these were averaged to form a laser-off spectrum. The laser-on spectra were binned by time delay. Background scatter was removed from the spectrum by subtracting an average signal from regions of the area detector on either side of the spectrum. All averaged, background-subtracted spectra were normalized to the area under the Kβ1,3 main line (7025–7092 eV) to allow intensity changes to be reliably measured. Examples of pre-normalization laser-off and laser-on spectra are shown in the supplementary material. For the calculation of the area under the VtC spectrum, the signal due to the tail of the Kβ1,3 main line was removed by subtracting a single pseudo-Voigt lineshape (variable-weighted sum of Gaussian and Lorentzian functions) fitted to the Kβ1,3 main line, as shown in the supplementary material. In all cases, about 10% of x-ray shots were removed from the analysis due to very low counts on one or more detectors. Therefore, the laser-off spectra (one-seventh of x-ray shots) represent the statistics possible from an x-ray flux of ∼ 1 × 1013 photons/s. The spectra shown in Fig. 1 are the result of 50 min ([Fe(CN)6]4−), 260 min ([Fe(CN)4(bpy)]2−), and 100 min ([Fe(CN)2(bpy)2]) integration times, corresponding to doses ranging from 1016 to 1017 x-ray photons for the laser-off spectra. The data used to calculate VtC difference areas for [Fe(CN)4(bpy)]2− and [Fe(CN)2(bpy)2] in Table I were integrated for 80 min and 40 min, respectively. The data shown in Fig. 4 is the result of 80 min of integration time.

TABLE I.

Ratio of excited-state area AES to ground-state area AGS under calculated and experimental VtC spectra, integrated from 7095 eV to 7115 eV. Experimental values have been scaled to unity excitation fraction as described in the text.

Area ratio AES/AGS
MoleculeSpin mult.ExperimentalCalculated
[Fe(CN)4(bpy)]2− 0.7 ± 0.1 0.76 
 … 0.50 
[Fe(CN)2(bpy)2… 0.78 
 0.6 ± 0.1 0.58 
Area ratio AES/AGS
MoleculeSpin mult.ExperimentalCalculated
[Fe(CN)4(bpy)]2− 0.7 ± 0.1 0.76 
 … 0.50 
[Fe(CN)2(bpy)2… 0.78 
 0.6 ± 0.1 0.58 

Density functional theory calculations were carried out with the ORCA 4.1.2 package.26 Geometries in various spin states were optimized using the B3LYP functional and def2-TZVP27 basis set using the DFT-D3 approach with Becke–Johnson damping.28,29 The B3LYP functional has been shown to match metal–ligand bond lengths from crystal structures for these complexes with errors of less than 3%.30 The effect of the solvent (water for [Fe(CN)6]4− and [Fe(CN)4(bpy)]2−; methanol for [Fe(CN)2(bpy)2]) was simulated using the conductor-like polarizable continuum model (CPCM).31 

X-ray emission spectra were calculated using the one-electron approach described by Lee et al.,3 wherein ground state DFT calculations are used to determine the energetics of the occupied valence orbitals that participate in VtC transitions. Only electric dipole transitions were included in the spectrum. The B3LYP functional and def2-TZVP basis set were used, except for the Fe atom, which used the CP(PPP) basis set with a special integration accuracy of 7, as used in several studies for VtC calculations of ferrous complexes.3,5,16,17 Scalar relativistic effects were included via the zero-order regular approximation (ZORA),32,33 and the solvent was again modeled using the CPCM method. An input file for the XES calculation is shown in the supplementary material. The calculated transitions were broadened by a 3 eV FWHM Gaussian function and shifted by 23 eV to match the experiment, as described in the supplementary material.

The time-resolved VtC spectra of the three complexes are summarized in Fig. 1. Panels (a)–(c) show laser-on, laser-off, and difference (multiplied by a factor of 2) spectra for each complex. Panels (d)–(f) show the calculated spectra of relevant species and their difference spectra multiplied by a factor of 0.5.

Aqueous [Fe(CN)6]4− was excited with 266 nm light into the charge-transfer-to-solvent (CTTS) band. There are two major deactivation pathways: (1) photo-oxidation resulting in the oxidized species in a doublet state with a nanosecond lifetime34 and (2) photoaquation following internal conversion and loss of a cyano ligand.35 Flash photolysis measurements estimated the quantum yield of photo-oxidation at 266 nm to be ≈0.5,34 while the quantum yield of photoaquation was found to be below 0.2 via 2D UV spectroscopy in the range of 255–315 nm.35,36 Optical transient absorption (TA) measurements have demonstrated that photo-oxidation and dissociation are complete within the first few hundreds of fs.36,37 The lifetime of the penta-coordinated species resulting from dissociation, prior to coordinating a water molecule, has been measured via time-resolved x-ray absorption near-edge structure (XANES) to be 19 ps.20 On the 10–50 ps time scale shown in Fig. 1, 50% of initially excited molecules are photo-oxidized and 20% have dissociated, with aquation taking place over this time period. Photo-oxidation, therefore, represents >70% of the photoproduct, with penta-coordinate and aquated species representing the minority decay channels. This work focuses, in part, on the impact photo-oxidation has on the VtC XES spectra. An in-depth investigation of the multiple species present will be given in an upcoming publication. The VtC difference spectrum, integrated from 10 ps to 60 ps [Fig. 1(a)], resembles a shift to higher energy, consistent with the blueshift associated with oxidation in the calculated spectra (d) and with previous studies of ferrous and ferric hexacyanide.3,16,38

Aqueous [Fe(CN)4(bpy)]2− was excited with 495 nm light into a bpy-localized metal-to-ligand charge transfer (MLCT) state.11 Previous ultrafast XES and visible transient absorption (TA) experiments have determined the excited state dynamics of the molecule in water, with the MLCT state relaxing within 100 fs into a metal-centered triplet (3MC) state with a lifetime of 13 ps.11 The difference signal due to the 3MC state is visible in the transient VtC, integrated from 1 ps to 9 ps [Fig. 1(b)], and is in good agreement with the calculated difference spectrum (e).

[Fe(CN)2(bpy)2] in methanol was also excited with 495 nm light into a bpy-localized MLCT state.39 Previous Kβ1,3 XES measurements39 have determined that the MLCT state decays sequentially to a 3MC state, with time constant 120 fs, and then to a metal-centered quintet state (5MC), with time constant 60 fs. The final quintet state has a lifetime of 256 ps. The difference spectrum integrated from 1 ps to 50 ps [Fig. 1(c)] matches the expected signature of the quintet state from calculation (f), but signal-to-noise does not allow isolation of the short-lived triplet difference spectrum on the sub-ps time scale.

Photoexcitation of iron complexes leads to multiple changes in the electronic and nuclear structure including charge distribution and oxidation state, spin distribution and total spin moment, and metal–ligand bond lengths, angles, and coordination symmetry. Here, we demonstrate via calculated difference spectra and their comparison to the transient data that ultrafast VtC XES is primarily sensitive to metal–ligand bond lengths and the oxidation state of the iron center. The spectra are found to be only indirectly sensitive to the iron spin moment through the correlation of metal–ligand bond length and spin moment, which results from the occupation of antibonding orbitals in high-spin states.

Figure 2(a) shows the relationship between the total area of the simulated VtC spectrum and metal–ligand bond lengths of the optimized structures. The calculated spectrum for each Fe complex was integrated between 7095 eV and 7115 eV and plotted against the average distance between the iron center and the coordinating ligand atoms (nitrogens of bipyridine ligands or carbons of cyano ligands) in the DFT-optimized geometries. The metal–ligand distance affects the mixing between ligand orbitals and metal np orbitals, for which transitions to the Fe 1s core hole are dipole allowed. A decrease in integrated signal intensity as a function of bond length is observed, especially among structural variants of the same complex. Square pyramidal 3[Fe(CN)5]3− lies below the trend for Fe(CN)6 species. We assign this effect to the loss of a ligand, which decreases the total orbital overlap. When areas are normalized to the number of coordinating atoms, the penta-coordinated species aligns with the trend (see Fig. S4 of the supplementary material).

FIG. 2.

(a) Area under the simulated VtC spectrum from 7095 eV to 7115 eV as a function of Fe–ligand bond lengths for all species, shown in Fig. 1, as well as 3[Fe(CN)6]4−. States of the same spin group together in both area and bond length. (b) Area integrated from 7110 eV to 7113 eV as a function of iron oxidation state. The blueshift associated with oxidation moves intensity to this region of the spectrum.

FIG. 2.

(a) Area under the simulated VtC spectrum from 7095 eV to 7115 eV as a function of Fe–ligand bond lengths for all species, shown in Fig. 1, as well as 3[Fe(CN)6]4−. States of the same spin group together in both area and bond length. (b) Area integrated from 7110 eV to 7113 eV as a function of iron oxidation state. The blueshift associated with oxidation moves intensity to this region of the spectrum.

Close modal

Static VtC measurements of Mn and Fe complexes have found an exponential relationship between the area of the Kβ″ region of the VtC spectrum and metal–ligand bond length,1,5 and Lee et al. found an exponential relationship between the total VtC area and metal–ligand bond length for an Fe(III) D4h complex.3 These studies investigated large ranges of bond lengths, which varied by more than 0.5 Å, in contrast to our case, where the bond lengths vary by less than 0.25 Å based on DFT calculations; the exponential relationship between the calculated VtC area and artificially varied bond lengths in this narrow range is shown in Fig. S5 of the supplementary material.

To demonstrate that the trend of decreasing VtC area is primarily due to bond length changes and not to the population of different metal 3d orbitals in the high-spin state, additional DFT calculations were carried out with low spin electronic configurations on fixed high-spin geometries. This isolates the effects of geometry and spin. Figure 3(a) shows the calculated spectra of [Fe(CN)2(bpy)2] in singlet, triplet, and quintet geometries. The spin state is fixed to both the native value (solid lines) and singlet value (dashed lines). Different spin states on the same geometry (solid vs dashed lines) yield small changes in the ratio between peaks and overall shifts of less than 0.2 eV. The effect of spin state on the integrated area is shown in Fig. 3(b) (solid vs open circles). The dominant effect is demonstrated to be geometric, with relatively small area changes associated with the spin state.

FIG. 3.

(a) Calculated VtC spectra of [Fe(CN)2(bpy)2], with ground state (black), triplet (red), and quintet (blue) geometries calculated in native (solid) and singlet (dashed) electronic configuration. (b) Integrated area under the curves in (a) as a function of average Fe–ligand bond length, with native (solid) and singlet (open) electronic configurations. Change in spin configuration results in minimal change in area and shifts of <0.2 eV.

FIG. 3.

(a) Calculated VtC spectra of [Fe(CN)2(bpy)2], with ground state (black), triplet (red), and quintet (blue) geometries calculated in native (solid) and singlet (dashed) electronic configuration. (b) Integrated area under the curves in (a) as a function of average Fe–ligand bond length, with native (solid) and singlet (open) electronic configurations. Change in spin configuration results in minimal change in area and shifts of <0.2 eV.

Close modal

The appearance of new transitions on the high energy side of the spectrum due to population of new orbitals in the high-spin state, as observed by March et al.17 in [Fe(terpy)2]2+, is dependent on the symmetry of the molecule. From the DFT calculations, for the octahedral [Fe(CN)6]4−, population of new 3d orbitals in the triplet state is not observed in the spectrum, as the iron p and d orbitals do not mix in this symmetry. In [Fe(CN)4(bpy)]2−, which has C2v symmetry in the ground state, p/d mixing causes a new transition at 7111.2 eV, resulting from population of an orbital of primarily Fe d character, to appear in the triplet state. This transition does not appear in the calculated spectrum of the triplet geometry with singlet spin (these spectra are shown in Fig. S6 of the supplementary material). However, this marker of the spin state is of low intensity and does not appreciably affect the total VtC area. In [Fe(CN)2(bpy)2], which has C2 symmetry in the ground state, no new transitions appear on the high energy shoulder in the high-spin state. This is due to the lowered symmetry, which causes enough mixing of p and d orbitals that there are no longer any energetically well-separated orbitals of primarily Fe d character.

The sensitivity of the total VtC area to orbital overlap can be used to correlate experimental data to changes in metal-ligand bond length in the excited state. To formulate a quantity that is directly comparable between calculation and experiment, an area ratio is defined as the ratio between the total area in the excited state AES and the total area in the ground state AGS. Table I reports the areas of calculated spectra for triplet and quintet [Fe(CN)4(bpy)]2− and [Fe(CN)2(bpy)2], divided by the area of the ground-state calculation for each complex.

Comparable area ratios were extracted from experimental data by obtaining a difference area ΔA and a ground state area AGS and scaling the difference area to represent 100% population in the excited state. The experimental area ratio is given by

AESAGS=11αΔAAGS,
(1)

where α represents the fractional population in the excited state during the time delays integrated to calculate ΔA. ΔA was obtained by integrating the difference spectrum from 7095 to 7115 eV. AGS was obtained from the ground-state VtC spectrum, background-subtracted as described in Sec. II, integrated over energy from 7095 eV to 7115 eV. Using the known excitation fraction, which is extracted from the Kβ1,3 XES data by comparison to model spectra,11 and the known decay times of the 3MC state of [Fe(CN)4(bpy)]2− and 5MC state of [Fe(CN)2(bpy)2], the excited state population α was calculated for each molecule. For [Fe(CN)4(bpy)]2−, the signal was integrated from 1 ps to 9 ps and divided by a factor of α = 0.20, accounting for the initial total excited fraction of 0.26, an ionization yield of 5%, and 13 ps lifetime of the 3MC state, all obtained from the analysis of Kβ1,3 XES. For [Fe(CN)2(bpy)2], the signal was integrated from 1 ps to 60 ps, giving α = 0.38 (initial excitation fraction 0.42; lifetime of 256 ps). The resulting area ratios are reported in Table I.

Although the statistical uncertainty is large in these datasets, the area ratios are consistent with the spectral changes predicted by DFT. In future time-resolved experiments with sufficient signal-to-noise to extract difference spectra at many time points, this method could potentially be used to follow structural dynamics such as vibrations.

While the area under the VtC spectrum depends primarily on metal–ligand orbital overlap, the position of the spectrum in energy is sensitive to the oxidation state of the iron center. A blueshift is associated with increased oxidation state, which is more pronounced than the shifts observed in the Kβ1,3 region.3 A center-of-mass shift of 1.3 eV and 1.4 eV is observed in the calculated VtC spectra [Figs. 1(d) and 1(e)] for oxidized [Fe(CN)6]4− and the 3MLCT state of [Fe(CN)4(bpy)]2−, respectively. This shift moves intensity into the high energy shoulder of the spectrum (7110–7113 eV), as quantified in Fig. 2(b) for the calculated spectra. The two calculated states where the iron center is oxidized have more than five times the intensity in this region than any of the hexa-coordinated Fe(II) states. Therefore, the integrated area of the high-energy shoulder of the spectrum has the potential to be used to track the local oxidation state of the metal in these complexes.

While there are also energetic shifts associated with metal–ligand bond length and symmetry changes,8 their effects on the difference intensity in this energy range are comparatively small. The center-of-mass of the triplet state spectra are shifted 0.3–0.4 eV relative to the singlet, and the quintet state spectra are shifted by 1.1–1.2 eV. Because the intensity of the spectrum for high-spin states is considerably smaller, due to loss of overlap between metal and ligand orbitals, even the relatively large shift associated with quintet states does not affect the integrated intensity of the high-energy shoulder to the extent that oxidation state changes do. This allows even large bond length changes to be separated from oxidation state changes. However, the symmetry change associated with the loss of a ligand between [Fe(CN)6]4− and 3[Fe(CN)5]3− also has a large effect in this area of the spectrum, indicating that for reactions with both oxidation state changes and coordination changes, more subtle analysis is necessary.

Figure 4 shows experimental time traces of the difference signal for [Fe(CN)4(bpy)]2− integrated in two regions. The first region (7103–7110 eV, red) tracks the overall overlap of metal and ligand orbitals as the molecule expands. The second region (7110–7113 eV, green) tracks the oxidation state of the iron as the molecule is excited into the MLCT state and then quickly decays into the 3MC state. Overlaid on the plot (dashed lines) is the signal expected from the calculated spectra and the lifetimes of the MLCT (90 fs) and 3MC (13 ps) states from Kβ1,3 XES.11 Good agreement between the expected and observed signal demonstrates that the time-resolved VtC can be used to differentiate charge transfer and metal–ligand bond length changes occurring simultaneously.

FIG. 4.

Time traces of integrated difference intensity in 7103–7110 eV (red) and 7110–7113 eV (green) regions of [Fe(CN)4(bpy)]2− data. Dashed lines represent the expected signal from kinetics extracted from Kβ1,3 XES fits and VtC spectra from DFT calculations.

FIG. 4.

Time traces of integrated difference intensity in 7103–7110 eV (red) and 7110–7113 eV (green) regions of [Fe(CN)4(bpy)]2− data. Dashed lines represent the expected signal from kinetics extracted from Kβ1,3 XES fits and VtC spectra from DFT calculations.

Close modal

Femtosecond time-resolved VtC XES measurements of three Fe-centered complexes are presented, which demonstrate the geometric and oxidation state sensitivity of this method on ultrafast time scales. Calculations indicate that the VtC spectrum is primarily sensitive to geometry and only indirectly sensitive to the spin state via correlation between the spin state and metal–ligand bond lengths. Direct spin sensitivity can instead be achieved with ultrafast Kβ1,3 XES, making VtC and Kβ1,3 XES complementary approaches to acquiring a more complete characterization of electronic and nuclear excited state dynamics in 3d transition metal complexes. Leveraging the whole Kβ XES spectrum for combined spin, oxidation and geometric information on transient species could be an important method for the field of ultrafast photochemistry, where electronic and nuclear changes dictate excited state reactivity. Kβ1,3 and VtC XES data can be collected concurrently with x-ray solution scattering (XSS), which is also sensitive to structure. The local metal–ligand bond length information available in VtC XES could be used to constrain interpretation of global structural information given by XSS. The low emission cross section for VtC XES remains a challenge, but combining high-throughput spectrometers such as the one used here and the increased repetition rates of superconducting accelerator based x-ray lasers such as European XFEL, LCLS-II, and LCLS-II-HE will greatly increase the average x-ray flux and enable robust difference spectra to be measured rapidly, providing the opportunity to track charge distribution and structural dynamics with femtosecond resolution transient VtC XES.

See the supplementary material for additional figures and DFT calculation details.

This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Some of the computing for this project was performed on the Sherlock cluster. We thank Stanford University and the Stanford Research Computing Center for providing computational resources and support that contributed to these research results. K.L. was supported by a Melvin and Joan Lane Stanford Graduate Fellowship and a Stanford Physics Department fellowship. A.G. acknowledges the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Catalysis Science Program to the SUNCAT Center for Interface Science and Catalysis.

1.
U.
Bergmann
,
C.
Horne
,
T.
Collins
,
J.
Workman
, and
S.
Cramer
, “
Chemical dependence of interatomic X-ray transition energies and intensities—A study of Mn Kβ″ and Kβ2,5 spectra
,”
Chem. Phys. Lett.
302
,
119
124
(
1999
).
2.
P.
Glatzel
and
U.
Bergmann
, “
High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes: Electronic and structural information
,”
Coord. Chem. Rev.
249
,
65
95
(
2005
).
3.
N.
Lee
,
T.
Petrenko
,
U.
Bergmann
,
F.
Neese
, and
S.
DeBeer
, “
Probing valence orbital composition with iron Kβ X-ray emission spectroscopy
,”
J. Am. Chem. Soc.
132
,
9715
9727
(
2010
).
4.
C. J.
Pollock
and
S.
DeBeer
, “
Valence-to-core X-ray emission spectroscopy: A sensitive probe of the nature of a bound ligand
,”
J. Am. Chem. Soc.
133
,
5594
5601
(
2011
).
5.
P.
Chandrasekaran
,
K. P.
Chiang
,
D.
Nordlund
,
U.
Bergmann
,
P. L.
Holland
, and
S.
DeBeer
, “
Sensitivity of X-ray core spectroscopy to changes in metal ligation: A systematic study of low-coordinate, high-spin ferrous complexes
,”
Inorg. Chem.
52
,
6286
6298
(
2013
).
6.
M. U.
Delgado-Jaime
,
S.
Debeer
, and
M.
Bauer
, “
Valence-to-core X-ray emission spectroscopy of iron-carbonyl complexes: Implications for the examination of catalytic intermediates
,”
Chem. - Eur. J.
19
,
15888
15897
(
2013
).
7.
E.
Gallo
and
P.
Glatzel
, “
Valence to core X-ray emission spectroscopy
,”
Adv. Mater.
26
,
7730
7746
(
2014
).
8.
C. J.
Pollock
and
S.
DeBeer
, “
Insights into the geometric and electronic structure of transition metal centers from valence-to-core X-ray emission spectroscopy
,”
Acc. Chem. Res.
48
,
2967
2975
(
2015
).
9.
W.
Zhang
,
R.
Alonso-Mori
,
U.
Bergmann
,
C.
Bressler
,
M.
Chollet
,
A.
Galler
,
W.
Gawelda
,
R. G.
Hadt
,
R. W.
Hartsock
,
T.
Kroll
,
K. S.
Kjær
,
K.
Kubiček
,
H. T.
Lemke
,
H. W.
Liang
,
D. A.
Meyer
,
M. M.
Nielsen
,
C.
Purser
,
J. S.
Robinson
,
E. I.
Solomon
,
Z.
Sun
,
D.
Sokaras
,
T. B.
van Driel
,
G.
Vankó
,
T.-C.
Weng
,
D.
Zhu
, and
K. J.
Gaffney
, “
Tracking excited-state charge and spin dynamics in iron coordination complexes
,”
Nature
509
,
345
348
(
2014
).
10.
J.
Kern
,
R.
Tran
,
J.
Hattne
,
R. J.
Gildea
,
N.
Echols
,
B.
Lassalle-Kaiser
,
A.
Lampe
,
G.
Han
,
S.
Gul
,
R. W.
Grosse-Kunstleve
,
P. H.
Zwart
,
P. D.
Adams
,
N. K.
Sauter
,
V. K.
Yachandra
,
J.
Yano
,
R.
Alonso-Mori
,
D.
Milathianaki
,
A. R.
Fry
,
A.
Miahnahri
,
D. W.
Schafer
,
M.
Messerschmidt
,
M. M.
Seibert
,
J. E.
Koglin
,
W. E.
White
,
M. J.
Bogan
,
G. J.
Williams
,
S.
Boutet
,
U.
Bergmann
,
C.
Glockner
,
J.
Hellmich
,
D.
DiFiore
,
A.
Zouni
,
H.
Laksmono
,
R. G.
Sierra
,
S.
Koroidov
,
J.
Messinger
,
D.
Sokaras
,
T.-C.
Weng
,
J.
Sellberg
,
M. J.
Latimer
, and
P.
Glatzel
, “
Simultaneous femtosecond x-ray spectroscopy and diffraction of photosystem II at room temperature
,”
Science
340
,
491
495
(
2013
).
11.
K. S.
Kjær
,
K.
Kunnus
,
T. C. B.
Harlang
,
T. B.
Van Driel
,
K.
Ledbetter
,
R. W.
Hartsock
,
M. E.
Reinhard
,
S.
Koroidov
,
L.
Li
,
M. G.
Laursen
,
E.
Biasin
,
F. B.
Hansen
,
P.
Vester
,
M.
Christensen
,
K.
Haldrup
,
M. M.
Nielsen
,
P.
Chabera
,
Y.
Liu
,
H.
Tatsuno
,
C.
Timm
,
J.
Uhlig
,
V.
Sundstöm
,
Z.
Németh
,
D. S.
Szemes
,
É.
Bajnóczi
,
G.
Vankó
,
R.
Alonso-Mori
,
J. M.
Glownia
,
S.
Nelson
,
M.
Sikorski
,
D.
Sokaras
,
H. T.
Lemke
,
S. E.
Canton
,
K.
Wärnmark
,
P.
Persson
,
A. A.
Cordones
, and
K. J.
Gaffney
, “
Solvent control of charge transfer excited state relaxation pathways in [Fe(2,2′-bipyridine)(CN)4]2−
,”
Phys. Chem. Chem. Phys.
20
,
4238
(
2018
).
12.
W.
Zhang
,
K. S.
Kjær
,
R.
Alonso-Mori
,
U.
Bergmann
,
M.
Chollet
,
L. A.
Fredin
,
R. G.
Hadt
,
R. W.
Hartsock
,
T.
Harlang
,
T.
Kroll
,
K.
Kubiček
,
H. T.
Lemke
,
H. W.
Liang
,
Y.
Liu
,
M. M.
Nielsen
,
P.
Persson
,
J. S.
Robinson
,
E. I.
Solomon
,
Z.
Sun
,
D.
Sokaras
,
T. B.
van Driel
,
T.-C.
Weng
,
D.
Zhu
,
K.
Wärnmark
,
V.
Sundström
, and
K. J.
Gaffney
, “
Manipulating charge transfer excited state relaxation and spin crossover in iron coordination complexes with ligand substitution
,”
Chem. Sci.
8
,
515
523
(
2017
).
13.
S. E.
Canton
,
K. S.
Kjær
,
G.
Vankó
,
T. B.
van Driel
,
S.-i.
Adachi
,
A.
Bordage
,
C.
Bressler
,
P.
Chabera
,
M.
Christensen
,
A. O.
Dohn
,
A.
Galler
,
W.
Gawelda
,
D.
Gosztola
,
K.
Haldrup
,
T.
Harlang
,
Y.
Liu
,
K. B.
Møller
,
Z.
Németh
,
S.
Nozawa
,
M.
Pápai
,
T.
Sato
,
T.
Sato
,
K.
Suarez-Alcantara
,
T.
Togashi
,
K.
Tono
,
J.
Uhlig
,
D. A.
Vithanage
,
K.
Wärnmark
,
M.
Yabashi
,
J.
Zhang
,
V.
Sundström
, and
M. M.
Nielsen
, “
Visualizing the non-equilibrium dynamics of photoinduced intramolecular electron transfer with femtosecond X-ray pulses
,”
Nat. Commun.
6
,
6359
(
2015
).
14.
M. W.
Mara
,
R. G.
Hadt
,
M. E.
Reinhard
,
T.
Kroll
,
H.
Lim
,
R. W.
Hartsock
,
R.
Alonso-mori
,
M.
Chollet
,
J. M.
Glownia
,
S.
Nelson
,
D.
Sokaras
,
K.
Kunnus
,
K. O.
Hodgson
,
B.
Hedman
,
U.
Bergmann
,
K. J.
Gaffney
, and
E. I.
Solomon
, “
Metalloprotein entatic control of ligand-metal bonds quantified by ultrafast x-ray spectroscopy
,”
Science
356
,
1276
1280
(
2017
).
15.
R.
Alonso-mori
,
J.
Kern
,
D.
Sokaras
,
T.-c.
Weng
,
D.
Nordlund
,
R.
Tran
,
P.
Montanez
,
J.
Delor
, and
V. K.
Yachandra
, “
A multi-crystal wavelength dispersive x-ray spectrometer
,”
Rev. Sci. Instrum.
83
,
073114
(
2012
).
16.
A. M.
March
,
T. A.
Assefa
,
C.
Bressler
,
G.
Doumy
,
A.
Galler
,
W.
Gawelda
,
E. P.
Kanter
,
Z.
Németh
,
M.
Pápai
,
S. H.
Southworth
,
L.
Young
, and
G.
Vankó
, “
Feasibility of valence-to-core X-ray emission spectroscopy for tracking transient species
,”
J. Phys. Chem. C
119
,
14571
14578
(
2015
).
17.
A. M.
March
,
T. A.
Assefa
,
C.
Boemer
,
C.
Bressler
,
A.
Britz
,
M.
Diez
,
G.
Doumy
,
A.
Galler
,
M.
Harder
,
D.
Khakhulin
,
Z.
Németh
,
M.
Pápai
,
S.
Schulz
,
S. H.
Southworth
,
H.
Yavaş
,
L.
Young
,
W.
Gawelda
, and
G.
Vankó
, “
Probing transient valence orbital changes with picosecond valence-to-core X-ray emission spectroscopy
,”
J. Phys. Chem. C
121
,
2620
2626
(
2017
).
18.
M.-F.
Tu
,
G.
Doumy
,
A. A.
Haddad
,
A. M.
March
,
L.
Assoufid
,
Y.
Kumagai
,
D.
Walko
,
Z.
Liu
,
B.
Shi
,
L.
Young
, and
C.
Bostedt
, “
Micro-focused MHz pink beam for time-resolved X-ray emission spectroscopy
,”
J. Synchrotron Radiat.
26
,
1956
(
2019
).
19.
A. M.
March
,
A.
Stickrath
,
G.
Doumy
,
E. P.
Kanter
,
B.
Krässig
,
S. H.
Southworth
,
K.
Attenkofer
,
C. A.
Kurtz
,
L. X.
Chen
, and
L.
Young
, “
Development of high-repetition-rate laser pump/x-ray probe methodologies for synchrotron facilities
,”
Rev. Sci. Instrum.
82
,
073110
(
2011
).
20.
A. M.
March
,
G.
Doumy
,
A.
Andersen
,
A.
Al Haddad
,
Y.
Kumagai
,
M. F.
Tu
,
J.
Bang
,
C.
Bostedt
,
J.
Uhlig
,
D. R.
Nascimento
,
T. A.
Assefa
,
Z.
Németh
,
G.
Vankó
,
W.
Gawelda
,
N.
Govind
, and
L.
Young
, “
Elucidation of the photoaquation reaction mechanism in ferrous hexacyanide using synchrotron x-rays with sub-pulse-duration sensitivity
,”
J. Chem. Phys.
151
,
144306
(
2019
).
21.
R.
Alonso-Mori
,
C.
Caronna
,
M.
Chollet
,
R.
Curtis
,
D. S.
Damiani
,
J.
Defever
,
Y.
Feng
,
D. L.
Flath
,
J. M.
Glownia
,
S.
Lee
,
H. T.
Lemke
,
S.
Nelson
,
E.
Bong
,
M.
Sikorski
,
S.
Song
,
V.
Srinivasan
,
D.
Stefanescu
,
D.
Zhu
, and
A.
Robert
, “
The X-ray correlation spectroscopy instrument at the Linac coherent light source
,”
J. Synchrotron Radiat.
22
,
508
513
(
2015
).
22.
M. P.
Minitti
,
J. S.
Robinson
,
R. N.
Coffee
,
S.
Edstrom
,
S.
Gilevich
,
J. M.
Glownia
,
E.
Granados
,
P.
Hering
,
M. C.
Hoffmann
,
A.
Miahnahri
,
D.
Milathianaki
,
W.
Polzin
,
D.
Ratner
,
F.
Tavella
,
S.
Vetter
,
M.
Welch
,
W. E.
White
, and
A. R.
Fry
, “
Optical laser systems at the Linac coherent light source
,”
J. Synchrotron Radiat.
22
,
526
531
(
2015
).
23.
G.
Blaj
,
P.
Caragiulo
,
G.
Carini
,
S.
Carron
,
A.
Dragone
,
D.
Freytag
,
G.
Haller
,
P.
Hart
,
J.
Hasi
,
R.
Herbst
,
S.
Herrmann
,
C.
Kenney
,
B.
Markovic
,
K.
Nishimura
,
S.
Osier
,
J.
Pines
,
B.
Reese
,
J.
Segal
,
A.
Tomada
, and
M.
Weaver
, “
X-ray detectors at the Linac coherent light source
,”
J. Synchrotron Radiat.
22
,
577
583
(
2015
).
24.
J. M.
Glownia
,
K.
Gumerlock
,
H. T.
Lemke
,
T.
Sato
,
D.
Zhu
, and
M.
Chollet
, “
Pump–probe experimental methodology at the Linac coherent light source
,”
J. Synchrotron Radiat.
26
,
685
691
(
2019
).
25.
M.
Harmand
,
R.
Coffee
,
M.
Bionta
,
M.
Chollet
,
D.
French
,
D.
Zhu
,
D. M.
Fritz
,
H.
Lemke
,
N.
Medvedev
,
B.
Ziaja
,
S.
Toleikis
, and
M.
Cammarata
, “
Achieving few-femtosecond time-sorting at hard X-ray free-electron lasers
,”
Nat. Photonics
7
,
215
218
(
2013
).
26.
F.
Neese
, “
Software update: The ORCA program system, version 4.0
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
,
e1327
(
2018
).
27.
F.
Weigend
and
R.
Ahlrichs
, “
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
,”
Phys. Chem. Chem. Phys.
7
,
3297
3305
(
2005
).
28.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
, “
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu
,”
J. Chem. Phys.
132
,
154104
(
2010
).
29.
S.
Grimme
,
S.
Ehrlich
, and
L.
Goergik
, “
Effect of the damping function in dispersion corrected density functional theory
,”
J. Comput. Chem.
32
,
1456
(
2011
).
30.
D. N.
Bowman
and
E.
Jakubikova
, “
Low-spin versus high-spin ground state in pseudo-octahedral iron complexes
,”
Inorg. Chem.
51
,
6011
6019
(
2012
).
31.
V.
Barone
and
M.
Cossi
, “
Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model
,”
J. Phys. Chem. A
102
,
1995
(
1998
).
32.
C.
van Wüllen
, “
Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations
,”
J. Chem. Phys.
109
,
392
399
(
1998
).
33.
E. V.
Lenthe
,
P. E. S.
Wormer
, and
A. V. D.
Avoird
, “
Density functional calculations of molecular hyperfine interactions in the zero order regular approximation for relativistic effects
,”
J. Chem. Phys.
108
,
4783
4796
(
1998
).
34.
M.
Shirom
and
G.
Stein
, “
Excited state chemistry of the ferrocyanide ion in aqueous solution. I. Formation of the hydrated electron
,”
J. Chem. Phys.
55
,
3372
3378
(
1971
).
35.
M.
Shirom
and
G.
Stein
, “
Excited state chemistry of the ferrocyanide ion in aqueous solution. II. Photoaquation
,”
J. Chem. Phys.
55
,
3379
3382
(
1971
).
36.
M.
Reinhard
,
G.
Aubo
,
N. A.
Besley
,
I. P.
Clark
,
G. M.
Greetham
,
M. W. D.
Hanson-heine
,
R.
Horvath
,
T. S.
Murphy
,
T. J.
Penfold
,
M.
Towrie
,
M. W.
George
, and
M.
Chergui
, “
Photoaquation mechanism of hexacyanoferrate(II) ions: Ultrafast 2D UV and transient visible and IR spectroscopies
,”
J. Am. Chem. Soc.
139
,
7335
7347
(
2017
).
37.
S.
Pommeret
,
R.
Naskrecki
,
P.
Van Der Meulen
,
M.
Ménard
,
G.
Vigneron
, and
T.
Gustavsson
, “
Ultrafast events in the electron photodetachment from the hexacyanoferrate(II) complex in solution
,”
Chem. Phys. Lett.
288
,
833
840
(
1998
).
38.
M.
Ross
,
A.
Andersen
,
Z. W.
Fox
,
Y.
Zhang
,
K.
Hong
,
J. H.
Lee
,
A.
Cordones
,
A. M.
March
,
G.
Doumy
,
S. H.
Southworth
,
M. A.
Marcus
,
R. W.
Schoenlein
,
S.
Mukamel
,
N.
Govind
, and
M.
Khalil
, “
Comprehensive experimental and computational spectroscopic study of hexacyanoferrate complexes in water: From infrared to X-ray wavelengths
,”
J. Phys. Chem. B
122
,
5075
5086
(
2018
).
39.
K. S.
Kjær
,
W.
Zhang
,
R.
Alonso-mori
,
U.
Bergmann
,
M.
Chollet
,
R. G.
Hadt
,
W.
Hartsock
,
T.
Harlang
,
T.
Kroll
,
K.
Kubiček
,
H. T.
Lemke
,
H. W.
Liang
,
Y.
Liu
,
M. M.
Nielsen
,
J. S.
Robinson
,
E. I.
Solomon
,
D.
Sokaras
,
T. B. V.
Driel
,
D.
Zhu
,
P.
Persson
,
K.
Wärnmark
,
V.
Sundström
, and
K. J.
Gaffney
, “
Ligand manipulation of charge transfer excited state relaxation and spin crossover in [Fe(2,2′-bipyridine)2(CN)2]
,”
Struct. Dyn.
4
,
044030
(
2017
).

Supplementary Material