^{1,2,a)}, V.-T. Pham

^{1}, R. M. van der Veen

^{1}, D. Grolimund

^{2}, R. Abela

^{2}, M. Chergui

^{1,b)}and C. Bressler

^{1,2}

### Abstract

We present a novel analysis of time-resolved extended x-rayabsorption fine structure (EXAFS)spectra based on the fitting of the experimental transients obtained from optical pump/x-ray probe experiments. We apply it to the analysis of picosecond EXAFS data on aqueous , which undergoes a light induced conversion from its low-spin (LS) ground state to the short-lived excited high-spin (HS) state. A series of EXAFSspectra were simulated for a collection of possible HS structures from which the ground state fit spectrum was subtracted to generate transient difference absorption (TA) spectra. These are then compared with the experimental TA spectrum using a least-squares statistical analysis to derive the structural change. This approach reduces the number of required parameters by cancellation in the differences. It also delivers a unique solution for both the fractional population and the extracted excited state structure. We thus obtain a value of the Fe–N bond elongation in the HS state with subpicometer precision .

This work was funded by the Swiss National Science Foundation via Contract Nos. 620–066145, 200021–107956, PP002–110464, 200020–116023, 200021–105239, and 200020-116533.

I. INTRODUCTION

II. TIME-RESOLVED EXTENDED X-RAY ABSORPTION FINE STRUCTURE SPECTROSCOPY

III. DATA TREATMENT AND STRUCTURAL SIMULATIONS

IV. STATISTICAL ANALYSIS OF THE EXPERIMENT

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Extended X-ray absorption fine structure spectroscopy
- 73.0
- Excited states
- 36.0
- X-ray absorption near edge structure
- 24.0
- Chemical bonds
- 18.0
- X-ray absorption spectra
- 15.0

## Figures

(a) Sketch of the effect of shell fitting by moving an entire coordination shell. Here, the Fe–N distance in . Such a treatment distorts the structure of the bpy ligands. (b) This can be avoided by locking the bpy structure and moving each ligand by a certain distance along their trigonal axis implying a consequent change in the N–Fe–N angle.

(a) Sketch of the effect of shell fitting by moving an entire coordination shell. Here, the Fe–N distance in . Such a treatment distorts the structure of the bpy ligands. (b) This can be avoided by locking the bpy structure and moving each ligand by a certain distance along their trigonal axis implying a consequent change in the N–Fe–N angle.

(a) XAS of aqueous and (b) transient XAS at 50 ps time delay after laser excitation.

(a) XAS of aqueous and (b) transient XAS at 50 ps time delay after laser excitation.

GS EXAFS of together with its fit to Eq. (1) delivering the reactant EXAFS spectrum , whose parameters are kept constant for the calculation of the excited state EXAFS spectra for several structures with the Fe–N distance set to by moving each bpy ligand symmetrically by along their associated trigonal axis.

GS EXAFS of together with its fit to Eq. (1) delivering the reactant EXAFS spectrum , whose parameters are kept constant for the calculation of the excited state EXAFS spectra for several structures with the Fe–N distance set to by moving each bpy ligand symmetrically by along their associated trigonal axis.

Sketch of the procedure to generate transient EXAFS spectra shown for two structures: (a) geometrical representation of the input structures used for calculating the EXAFS; (b) -weighed EXAFS spectra calculated from (a) as a function of the photoelectron wave vector ; (c) back-transformed EXAFS spectra to energy space (and removing the weighing) so that the GS EXAFS coincides with the GS calculation; (d) for two different structures, the transient spectrum is calculated and shown for comparison with the actual transient data (not yet scaled according to the fractional population).

Sketch of the procedure to generate transient EXAFS spectra shown for two structures: (a) geometrical representation of the input structures used for calculating the EXAFS; (b) -weighed EXAFS spectra calculated from (a) as a function of the photoelectron wave vector ; (c) back-transformed EXAFS spectra to energy space (and removing the weighing) so that the GS EXAFS coincides with the GS calculation; (d) for two different structures, the transient spectrum is calculated and shown for comparison with the actual transient data (not yet scaled according to the fractional population).

Square residuals between the experimental data and transient simulations [Eq. (11)] for the excited state structure by moving the entire bpy ligands in steps of 0.005 Å in the range from 0.15–0.23 Å. The curves serve as a guide to the eyes and connect the values for a fixed -value (varied in steps of 1% from 12%–28%). The transient spectra (and the square residuals shown here) have been calculated for four different values of the chemical shift : (a) 0 eV, (b) −0.6 eV, (c) −1.2 eV, and (d) −2.5 eV. The values were obtained by restricting the data to the range of the LS photoelectron wave vector .

Square residuals between the experimental data and transient simulations [Eq. (11)] for the excited state structure by moving the entire bpy ligands in steps of 0.005 Å in the range from 0.15–0.23 Å. The curves serve as a guide to the eyes and connect the values for a fixed -value (varied in steps of 1% from 12%–28%). The transient spectra (and the square residuals shown here) have been calculated for four different values of the chemical shift : (a) 0 eV, (b) −0.6 eV, (c) −1.2 eV, and (d) −2.5 eV. The values were obtained by restricting the data to the range of the LS photoelectron wave vector .

Least-squares results as a function of for the calculations shown in Fig. 5 ( not shown in Fig. 5) for two different ranges: (solid circles) and . (a) Least-squares values (with their associated fractional population indicated in percent) and (b) the corresponding Fe–N bond distance. The error bars represent a 95% confidence level. A chemical shift of approximately −1.2 eV can be derived from this analysis, corresponding to a bond elongation of for the HS species.

Least-squares results as a function of for the calculations shown in Fig. 5 ( not shown in Fig. 5) for two different ranges: (solid circles) and . (a) Least-squares values (with their associated fractional population indicated in percent) and (b) the corresponding Fe–N bond distance. The error bars represent a 95% confidence level. A chemical shift of approximately −1.2 eV can be derived from this analysis, corresponding to a bond elongation of for the HS species.

Least-squares analysis results as a function of for a constant fractional population of 15% (down triangles), 17% (solid circles), 19% (up triangles), and 22% (open squares). (a) Least-squares values and (b) Fe–N bond elongation. (Error bars have been removed for visibility.)

Least-squares analysis results as a function of for a constant fractional population of 15% (down triangles), 17% (solid circles), 19% (up triangles), and 22% (open squares). (a) Least-squares values and (b) Fe–N bond elongation. (Error bars have been removed for visibility.)

Experimental transient absorption spectrum and the least-squares transient simulation (with ). The different ranges used for the statistical analysis are indicated by the horizontal bars in the graph. The feature near in the simulated transient is an artifact due to the utilized Fourier window for generating the excited state models and was thus excluded from the statistical analysis.

Experimental transient absorption spectrum and the least-squares transient simulation (with ). The different ranges used for the statistical analysis are indicated by the horizontal bars in the graph. The feature near in the simulated transient is an artifact due to the utilized Fourier window for generating the excited state models and was thus excluded from the statistical analysis.

Analysis of the Fe–N distance on the fractional population of the HS state population in the present analysis for using the derived value of (a) and using the previously published value of (b) in Ref. 13. Both data ranges used for the analysis are displayed (large blue error bars: , up triangles; small red error bars: , down triangles). All treatments show very similar results within uncertainty with the smallest uncertainty occurring at .

Analysis of the Fe–N distance on the fractional population of the HS state population in the present analysis for using the derived value of (a) and using the previously published value of (b) in Ref. 13. Both data ranges used for the analysis are displayed (large blue error bars: , up triangles; small red error bars: , down triangles). All treatments show very similar results within uncertainty with the smallest uncertainty occurring at .

Comparison between the transient XAS signal of aqueous recorded at 7126 eV (open circles with error bars) and the optical femtosecond transient absorption signal (solid circles) together with their fit functions. Both experiments were performed under (nearly) identical laser conditions and have been rescaled and reflect the actual (optical) and convoluted (XAS) fractional population due to the much larger x-ray pulse width. Both populations decay nonradiatively into the GS with a lifetime of 0.6 ns. The dashed Gaussian-shaped line illustrates the x-ray pulse width at the used time delay (50 ps).

Comparison between the transient XAS signal of aqueous recorded at 7126 eV (open circles with error bars) and the optical femtosecond transient absorption signal (solid circles) together with their fit functions. Both experiments were performed under (nearly) identical laser conditions and have been rescaled and reflect the actual (optical) and convoluted (XAS) fractional population due to the much larger x-ray pulse width. Both populations decay nonradiatively into the GS with a lifetime of 0.6 ns. The dashed Gaussian-shaped line illustrates the x-ray pulse width at the used time delay (50 ps).

Fe–N bond elongation determined from different procedures: [(a) and (b)] applying 95% and 90% confidence level from the present analysis, (c) using previously published values and , [(d) and (e)] reproduced from MXAN fits, and (f) from an EXAFS fit of the extracted HS spectrum. [(d)–(f)] Taken from Ref. 13. (For details see text.)

Fe–N bond elongation determined from different procedures: [(a) and (b)] applying 95% and 90% confidence level from the present analysis, (c) using previously published values and , [(d) and (e)] reproduced from MXAN fits, and (f) from an EXAFS fit of the extracted HS spectrum. [(d)–(f)] Taken from Ref. 13. (For details see text.)

## Tables

Structural parameters (Fe–N bond distance and N–Fe–N bond angle ) of the LS state of in and their changes in going from the LS to the HS state along with the chemical shift and the photoexcitation yield derived from the present EXAFS analysis (uncertainties are given in brackets). The present parameters correct those previously published.

Structural parameters (Fe–N bond distance and N–Fe–N bond angle ) of the LS state of in and their changes in going from the LS to the HS state along with the chemical shift and the photoexcitation yield derived from the present EXAFS analysis (uncertainties are given in brackets). The present parameters correct those previously published.

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