**2.2. Kβ and valence-to-core RXES**

In comparison to other spectrometer solutions employed at synchrotron beamlines [5, 8] that use two-dimensional focusing, the dispersive-type spectrometer employs only one-dimen‐ sional focusing of X-rays. Dispersive-spectrometers are characterized by lower detection efficiency in comparison to, for example, spectrometers working in Johann geometry. On the other hand, the dispersive-spectrometer geometry allows for measurements of X-ray emission spectra in dispersive-mode, which enables detection of X-ray emission in a wide range of energies (few tens to few hundreds of eV) without any scanning elements during measure‐ ment. For the experiments requesting short acquisition times, the dispersive-spectrometer

are being developed, with different spectrometer geometries and arrangements depending

on particular needs and goals of experiments. In the present section we focus solely on

dispersive‐type spectrometer because of its particular parameters and operating

In comparison to other spectrometer solutions employed at synchrotron beamlines [5, 8] that

use two‐dimensional focusing, the dispersive‐type spectrometer employs only one‐

dimensional focusing of X‐rays. Dispersive‐spectrometers are characterized by lower

geometry. On the other hand, the dispersive‐spectrometer geometry allows for

measurements of X‐ray emission spectra in dispersive‐mode, which enables detection of X‐

ray emission in a wide range of energies (few tens to few hundreds of eV) without any

scanning elements during measurement. For the experiments requesting short acquisition

**Figure 1:** (Left) Schematic representation of von Hamos spectrometer geometry (from [4]).

There are two common geometries allowing for spectrometer setup in dispersive mode:

Johannson‐type [10] and von Hamos‐type [11]. Schematic representation of von Hamos

geometry is shown in Figure 1 (left) [4]. In such arrangement, the X‐ray fluorescence from

the sample is dispersed on cylindrically bent crystal. The dispersion axis and therefore

energy range covered by the setup is limited by the length of the crystal/detector along

(Right) Schematic view of the geometrical setup used in Johansson geometry (from [9]).

**Figure 1.** (Left) Schematic representation of von Hamos spectrometer geometry (Reprinted with permission from [4]. Copyright (2012), American Institute of Physics). (Right) Schematic view of the geometrical setup used in Johansson

There are two common geometries allowing for spectrometer setup in dispersive mode: Johannson-type [10] and von Hamos-type [11]. Schematic representation of von Hamos geometry is shown in Figure 1 (left) [4]. In such arrangement, the X-ray fluorescence from the sample is dispersed on cylindrically bent crystal. The dispersion axis and therefore energy range covered by the setup is limited by the length of the crystal/detector along dispersion axis. One-dimensional bending of the crystal aims at increasing the efficiency of the setup, as compared to flat crystal geometry, by focusing the diffracted X-rays onto the detector plane. The von Hamos setup provides good energy resolution being often below 1eV at relatively large Bragg angles. The Bragg angle domain is changed by linear displacement of the crystal and detector along dispersion axis, where the detector distance from the sample is always twice that of the crystal. Because of linear motions of the crystal/detector, the von Hamos spectrom‐ eter allows for flexible arrangements around the sample environment. Moreover, because of application of short curvature radiuses without loss on energy resolution, the spectrometer requires relatively small space for operation. Finally, the spectrometer geometry can be easily extended into multicrystal operation allowing for enhanced spectrometer efficiency or

In Johannson geometry, schematically shown in Figure 1 (right), the X-ray fluorescence from the sample is diffracted by cylindrically bent crystal; however, unlike in von Hamos geometry,

geometry (Reprinted with permission from [9]. Copyright (2012), American Institute of Physics)

times, the dispersive‐spectrometer geometry may be thus regarded as optimal solution.

detection efficiency in comparison to, for example, spectrometers working in Johann

5

geometry may be thus regarded as optimal solution.

6 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

measurements of multiple X-ray emission lines [12].

characteristics.

The method of resonant emission X-ray scattering (RXES) is recognized as one of the most sensitive measurement techniques that allows the detection of very small changes in the electronic structure of studied element [13]. The method is based on X-ray scattering process in which the core electron is excited to unoccupied electronic states above Fermi level, and simultaneous detection of X-ray emission accompanied by atomic decay from intermediate to final state. By the monitoring of X-ray intensity and X-ray emission shape analysis, the detailed information on the electronic structure may be retrieved.

As an example, in Figure 2 we show the Kβ-RXES plane for TiO2 anatase recorded around Ti K-absorption edge [18,21]. In the experiment, the incidence X-ray energy was tuned around 4968–4992eV range allowing probing by 1s electron the lowest unoccupied electronic states. Simultaneously, the Kβ and valence-to-core decay channels were measured by means of dispersive-type von Hamos spectrometer. The relatively large range of spectrometer crystal along dispersive axis, allowed to probe both Kβ and valence-to-core transition at once, so that only the incident beam energy had to be scanned to record the full RXES plane.

The measured RXES map exhibits several features depending on excitation and emission Xray energy. The first X-ray emission signal appears at incidence X-ray energy of around 4968 eV. This weak pre-edge feature corresponds to the 1s-3d-like excitation and extends up to the excitation energy of 4974eV. The s→d types of electron excitations are quadrupole transitions that are characterized by relatively small excitation probability as compared to dipole excita‐ tions, which are commonly examined by RXES. However, as shown with the help of theoretical calculations, because of the strong d→p hybridization in TiO2 compound, the 1s→3d excitation is characterized by a relatively high excitation probability. RXES measurements using transi‐ tions from higher electronic states (i.e., 3p→1s) proved to be extremely sensitive to determine the nature of the lowest unoccupied 3d states of Ti. With the excitation of an electron from a 1s shell to a 3d-localized state, excited electron interacts with the 3p electron, resulting in a shift of 3p→1s emission line by 1.8 eV to lower energies due to the electron–electron interaction effect. This effect can be seen in RXES plane in Figure J1 for lowest excitation energy of 4968eV. However, if the 3d excitation state is delocalized, the electron–electron interaction is negligible and shift of 3p→1s emission is thus not observed for pre-edge features at excitation energies above 4970eV. The Kβ and valence-to-core RXES measurements give unique opportunity to investigate simultaneously lowest unoccupied and highest occupied electronic states by X-ray absorption and X-ray emission spectral projections (see for details [18, 21]). We shall discuss shortly here the possibility of determining the absolute value of the energy band gap as well as possibility to employ RIXS measurements in cases where the commonly used optical methods are insufficient (i.e., in the case of "dark-samples" or samples containing so-called color-centers). The results obtained to date suggest that determination of the absolute band gap energy by Kβ-RIXS may be difficult due to interactions of the core excited electron with 3d valence electrons as well as because of the effects of core-hole shielding. Both processes can induce a small, but not negligible, change to the electron levels before Ti atom decays to its final state. However, the obtained Kβ-RIXS results based on comparison experimental RXES spectra of rutile and anatase TiO2 structures suggest that the relative change in the band gap energy can be determined and examined to a high precision.

Figure 2: Kβ-RXES plane of TiO2 anatase measured for Ti around K-absorption edge. The **Figure 2.** Kβ-RXES plane of TiO2 anatase measured for Ti around K-absorption edge. The main detected spectroscopic features are labeled on the RXES plane. On top, the nonresonant Kβ and valence-to-core X-ray emission spectrum is shown, which was recorded for incidence X-ray energies above K-shell ionization threshold. (From [18] - Reproduced by permission of The Royal Society of Chemistry)

2.3 Time-resolved RXES

for incidence X-ray energies above K-shell ionization threshold.

9

main detected spectroscopic features are labeled on the RXES plane. On top, the

nonresonant Kβ and valence-to-core X-ray emission spectrum is shown, which was recorded

The use of X-ray spectroscopic methods for measuring a high time resolution data is limited

by several technical factors. RXES measurements, employing two-dimensional focusing

crystals, requires scanning of both incidence and emission X-ray energy. Therefore, the

RXES method, despite the exceptional sensitivity of the measurement, could be applied only

in experiments in which the sample was kept in a steady-state chemical equilibrium. The

use of dispersive-type spectrometer for RXES spectroscopy significantly reduces the

measurement time due to the dispersive type of detection of X-rays emitted from the

sample. In such experimental configuration, the measurement time is determined only by

the speed of the scanning incidence X-ray beam energy, which at present synchrotrons may

be in the order of a several seconds [42, 43]. The acquisition time is an important aspect in

the study of irreversible processes in which repeating the experiment at the same chemical

## **2.3. Time-resolved RXES**

1s shell to a 3d-localized state, excited electron interacts with the 3p electron, resulting in a shift of 3p→1s emission line by 1.8 eV to lower energies due to the electron–electron interaction effect. This effect can be seen in RXES plane in Figure J1 for lowest excitation energy of 4968eV. However, if the 3d excitation state is delocalized, the electron–electron interaction is negligible and shift of 3p→1s emission is thus not observed for pre-edge features at excitation energies above 4970eV. The Kβ and valence-to-core RXES measurements give unique opportunity to investigate simultaneously lowest unoccupied and highest occupied electronic states by X-ray absorption and X-ray emission spectral projections (see for details [18, 21]). We shall discuss shortly here the possibility of determining the absolute value of the energy band gap as well as possibility to employ RIXS measurements in cases where the commonly used optical methods are insufficient (i.e., in the case of "dark-samples" or samples containing so-called color-centers). The results obtained to date suggest that determination of the absolute band gap energy by Kβ-RIXS may be difficult due to interactions of the core excited electron with 3d valence electrons as well as because of the effects of core-hole shielding. Both processes can induce a small, but not negligible, change to the electron levels before Ti atom decays to its final state. However, the obtained Kβ-RIXS results based on comparison experimental RXES spectra of rutile and anatase TiO2 structures suggest that the relative change in the band gap

9

nonresonant Kβ and valence-to-core X-ray emission spectrum is shown, which was recorded

The use of X-ray spectroscopic methods for measuring a high time resolution data is limited

by several technical factors. RXES measurements, employing two-dimensional focusing

crystals, requires scanning of both incidence and emission X-ray energy. Therefore, the

RXES method, despite the exceptional sensitivity of the measurement, could be applied only

in experiments in which the sample was kept in a steady-state chemical equilibrium. The

use of dispersive-type spectrometer for RXES spectroscopy significantly reduces the

measurement time due to the dispersive type of detection of X-rays emitted from the

sample. In such experimental configuration, the measurement time is determined only by

the speed of the scanning incidence X-ray beam energy, which at present synchrotrons may

be in the order of a several seconds [42, 43]. The acquisition time is an important aspect in

the study of irreversible processes in which repeating the experiment at the same chemical

for incidence X-ray energies above K-shell ionization threshold.

**Figure 2.** Kβ-RXES plane of TiO2 anatase measured for Ti around K-absorption edge. The main detected spectroscopic features are labeled on the RXES plane. On top, the nonresonant Kβ and valence-to-core X-ray emission spectrum is shown, which was recorded for incidence X-ray energies above K-shell ionization threshold. (From [18] - Reproduced

energy can be determined and examined to a high precision.

8 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

2.3 Time-resolved RXES

by permission of The Royal Society of Chemistry)

The use of X-ray spectroscopic methods for measuring a high time resolution data is limited by several technical factors. RXES measurements, employing two-dimensional focusing crystals, requires scanning of both incidence and emission X-ray energy. Therefore, the RXES method, despite the exceptional sensitivity of the measurement, could be applied only in experiments in which the sample was kept in a steady-state chemical equilibrium. The use of dispersive-type spectrometer for RXES spectroscopy significantly reduces the measurement time due to the dispersive type of detection of X-rays emitted from the sample. In such experimental configuration, the measurement time is determined only by the speed of the scanning incidence X-ray beam energy, which at present synchrotrons may be in the order of a several seconds [42, 43]. The acquisition time is an important aspect in the study of irreversible processes in which repeating the experiment at the same chemical conditions is very difficult or sometimes even impossible, for example, because of the small amount of available sample.

**Figure 3.** a) Scheme showing RXES process in gold. b) Experimental setup employed for in situ RXES spectroscopy. c) Series of RXES planes measured during the experiment (time-resolved RXES) together with schematic description of data analysis using genetic algorithm. (Reprinted with permission from [43] Copyright (2014) American Chemical So‐ ciety)

Figure 2: Kβ-RXES plane of TiO2 anatase measured for Ti around K-absorption edge. The main detected spectroscopic features are labeled on the RXES plane. On top, the As an example, we briefly discuss the aspect of time resolution in RIXS measurements by employing dispersive spectrometer to study the local electronic structure of Au in the tem‐ perature-programmed reduction (TPR) of Au2O3 gold oxide. During the measurements, the gold oxide Au2O3 was maintained under H2 atmosphere and at the same time heated contin‐ uously at a rate of about 5OC per minute in the range from 20OC to 300OC. Schematic description of the experimental setup is shown in Figure 3, together with evolution of experimental timeresolved RXES spectra. RXES experiment, employing excitation from 2p3/2 to 5d and following decay transition from 3d3/2 to 2p3/2 final state, showed a change in electronic valence configu‐ ration of Au from 5d8 6s0 to 5d106s1 , corresponding to gold oxide Au2O3 reduction to the metallic form Au0 at temperatures above 150OC. However, as stressed in [43], thanks to obtained time resolution of RXES acquisition, the transitional forms of Au in the configuration of 5d106s0 and corresponding to the formation of gold (I) oxide (i.e., Au2O) were registered. The result was surprising, because the Au2O compound is unstable and is quickly reducing to a form of Au0 . On the basis of RIXS measurements and by using analysis based on genetic algorithm, it was possible to determine the structure of 5d electronic states, as well as to determine the Au2O crystallographic structure. The experimental results were examined with density functional theory (DFT) calculations, confirming the two-stage reduction process of Au2O3. The applica‐ tion of the RXES technique with high temporal resolution has been the key to obtain the described results. The time-resolved RXES enabled for the first time to investigate the structure of the unstable gold (I) oxide.

## **2.4. High energy resolution off-resonant spectroscopy**

In many synchrotron studies of chemical processes the experiments are artificially slowed down in order to obtain good quality experimental data. The time limit, of the order of several seconds, drawn by the need of scanning the incident X-ray energy, was still a major constraint to study the electronic state of matter under working conditions as well as main restriction in ability to follow individual reaction steps. The idea for solving these technical problems was the application of off-resonant X-ray scattering, a process of photon–atom interaction for excitation energies being set below an absorption threshold [14]. The concept of using offresonant X-ray scattering process dates back to 1982, when based on the Kramers-Heisenberg theory, J. Tulkki and T. Åberg developed simplified differential equations describing the interaction of photons with the atom [15]. In this theoretical study they found that for the incidence X-ray beam energy tuned below the absorption edge of an atom, the shape of the Xray emission spectrum (XES) is proportional to the density of unoccupied electronic states, i.e., equivalent to X-ray absorption. However, the potential and possibilities of determining the electronic structure from the X-ray emission spectra at off-resonant conditions has not been extensively studied due to its very low cross section.

**Figure 4.** Schematic representation and energy level drawing for an off-resonant scattering process (left). On right we plot HEROS-XES for the 3d5/2-2p3/2 transition of a Pt foil recorded at excitation energy of 11537eV. The reconstructed HEROS-XAS spectrum using Kramers-Heisenberg formalism is also plotted and compared to conventional total fluo‐ rescence yield XAS. (Adapted from [61] - Reproduced by permission of The Royal Society of Chemistry)

Correspondence of off-resonant scattering and X-ray absorption processes can be derived starting with simplified cross-section formulas describing photon–atom interaction in vicinity of ionization threshold. Within the Kramers-Heisenberg approach, the differential cross sections for resonant X-ray scattering can be expressed as follows [15] (Eq. 1):

resolved RXES spectra. RXES experiment, employing excitation from 2p3/2 to 5d and following decay transition from 3d3/2 to 2p3/2 final state, showed a change in electronic valence configu‐

resolution of RXES acquisition, the transitional forms of Au in the configuration of 5d106s0

corresponding to the formation of gold (I) oxide (i.e., Au2O) were registered. The result was surprising, because the Au2O compound is unstable and is quickly reducing to a form of Au0

On the basis of RIXS measurements and by using analysis based on genetic algorithm, it was possible to determine the structure of 5d electronic states, as well as to determine the Au2O crystallographic structure. The experimental results were examined with density functional theory (DFT) calculations, confirming the two-stage reduction process of Au2O3. The applica‐ tion of the RXES technique with high temporal resolution has been the key to obtain the described results. The time-resolved RXES enabled for the first time to investigate the structure

In many synchrotron studies of chemical processes the experiments are artificially slowed down in order to obtain good quality experimental data. The time limit, of the order of several seconds, drawn by the need of scanning the incident X-ray energy, was still a major constraint to study the electronic state of matter under working conditions as well as main restriction in ability to follow individual reaction steps. The idea for solving these technical problems was the application of off-resonant X-ray scattering, a process of photon–atom interaction for excitation energies being set below an absorption threshold [14]. The concept of using offresonant X-ray scattering process dates back to 1982, when based on the Kramers-Heisenberg theory, J. Tulkki and T. Åberg developed simplified differential equations describing the interaction of photons with the atom [15]. In this theoretical study they found that for the incidence X-ray beam energy tuned below the absorption edge of an atom, the shape of the Xray emission spectrum (XES) is proportional to the density of unoccupied electronic states, i.e., equivalent to X-ray absorption. However, the potential and possibilities of determining the electronic structure from the X-ray emission spectra at off-resonant conditions has not been

**Figure 4.** Schematic representation and energy level drawing for an off-resonant scattering process (left). On right we plot HEROS-XES for the 3d5/2-2p3/2 transition of a Pt foil recorded at excitation energy of 11537eV. The reconstructed HEROS-XAS spectrum using Kramers-Heisenberg formalism is also plotted and compared to conventional total fluo‐

rescence yield XAS. (Adapted from [61] - Reproduced by permission of The Royal Society of Chemistry)

at temperatures above 150OC. However, as stressed in [43], thanks to obtained time

, corresponding to gold oxide Au2O3 reduction to the metallic

and

.

ration of Au from 5d8

of the unstable gold (I) oxide.

form Au0

6s0

to 5d106s1

10 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

**2.4. High energy resolution off-resonant spectroscopy**

extensively studied due to its very low cross section.

$$\frac{d\sigma\left(o\_1\right)}{d o\_2} = 2\pi r\_0^2 \int \frac{\left(o\_l - o\_{l'}\right)g\_{jl}\left(o\_l - o\right)dg\_i}{d o\_1} \frac{d\alpha}{\left(o\_{l'} + o - o\_1\right)^2 + \frac{\Gamma\_l^2}{4\hbar^2}} \frac{\frac{\Gamma\_{<}}{2\hbar}}{\left(o\_1 - o\_{l'} - o - o\_2\right) + \frac{\Gamma\_{>}^2}{4\hbar^2}} d\alpha$$

where r0 <sup>2</sup> is the classical electron radius. The energies of the initial and final states are repre‐ sented by ℏω<sup>i</sup> and ℏω<sup>f</sup> , whereas ℏω1 and ℏω2 are the incoming and outgoing photon energies, respectively. The initial and final state broadenings are given by Γ<sup>i</sup> and Γ<sup>f</sup> . The gfi stands for the oscillator strength of the X-ray transition from the final to initial vacancy state, and the dgi /dω represents the oscillator strength distribution for electron excitation.

The second term in Eq. 1 ensures the energy conservation given by ω=ω1-ω<sup>f</sup> -ω2 and accounts for the final state broadening (Γ<sup>f</sup> ). By neglecting the final state width, the second term of Eq. 1 can be replaced by the Dirac delta function (Eq. 2):

$$\frac{d\sigma\left(\alpha\_1\right)}{d\alpha\_2} = 2\pi r\_0^2 \int \frac{\alpha\_2}{\alpha\_1} \frac{\left(\alpha\_i - \alpha\_f\right)g\_{jl}\left(\alpha\_l - \alpha\right)d g\_i / d\alpha}{\left(\alpha\_i + \alpha - \alpha\_1\right)^2 + \Gamma\_i^2 / 4\hbar^2} \delta\left(\alpha\_1 - \alpha\_f - \alpha - \alpha\_2\right)d\alpha$$

For the off-resonant excitations the oscillator strength distribution (dgi /dω) is directly propor‐ tional to the X-ray absorption spectrum (XAS). Therefore, the shape of the X-ray emission spectrum (XES), which is proportional to the differential cross sections, can be described as follows (Eq. 3):

$$XES\left(E\_2\right) = \int \frac{E\_2}{E\_1} \frac{\left(E\_i - E\_f\right)\left(E\_i - E\right)XAS\left(E\right)}{\left(E\_i + E - E\_1\right)^2 + \Gamma\_i^2 / 4} \delta\left(E\_1 - E\_f - E - E\_2\right) dE$$

the above equation the constants were omitted and frequencies replaced by E according to ω=E/ ℏ. By keeping E1-Ef -E- E2=0, Eq. 3 can be represented analytically for XAS(E) solution (Eq. 4):

$$XAS\left(E\right) = \frac{E\_1}{E\_2} \frac{\left(E\_i - E\_f - E\_2\right)^2 + \Gamma\_i^2 / 4}{\left(E\_i - E\_f\right)\left(E\_i - E\_f + E\_1 - E\_2\right)} XES\left(E\_2\right)$$

This simplified formula provides the XAS(E) function that can be analytically solved for any measured XES(E2). We should note that Eq. 4 is valid only at condition where E1<<Ei , i.e., the measured off-resonant spectrum is free of any resonant features. Typically, the detuning of excitation energy should be as large as 5 x Γ<sup>i</sup> . The final state broadening (Γ<sup>f</sup> ), the incoming beam energy distribution, and the resolution of the X-ray spectrometer are not considered in this equation. Therefore, the derived HEROS-XAS curves will be broadened by these three contributions.

By combining the aspects of off-resonant scattering, high energy and dispersion-type of detection to the measurements of unoccupied electronic states a high energy resolution offresonant spectroscopy has been established. The proposed method does not require any scanning optical elements during the measurement, and therefore allows for X-ray spectro‐ scopy measurements at timescales unattainable to XAS or RXES techniques [61, 64, 65, 16]. Figure 4 demonstrates the principle of HEROS. The Lα1 X-ray emission (3d5/2 - 2p3/2 transition) of a Pt foil was recorded at a fixed incident X-ray beam energy tuned below the L3 absorption edge. The off-resonant X-ray emission was recorded by means of von Hamos spectrometer that allowed to cover over 60eV energy range at fixed optical arrangement. The corresponding HEROS-XAS spectrum was reconstructed using the measured X-ray emission spectrum and Eqs. 1–4. The HEROS-XAS spectrum (open circles) is compared to the X-ray absorption spectrum (filled orange area) that was recorded by means of total fluorescence yield (TFY). We should stress here, that the derived HEROS-XAS spectrum exhibited more detailed informa‐ tion than the conventional XAS spectrum, due to the removal of the initial state broadening. The result implies that the HEROS-XES exhibits the same information as high-energy resolu‐ tion XAS. Moreover, the HEROS experiment is performed at a fixed optical arrangement, meaning acquisition time resolution is simply controlled by experimental efficiency, not by the speed of scanning the incident energy axis. Finally, as recently demonstrated, the HEROS spectra are free of self-absorption effects [63]. Self-absorption belongs to one of the phenomena disturbing the absorption measurements [17] and leads to a modification of the shape of the measured absorption spectrum, visible in particular in the case of samples having high concentrations of the studied element. There are several methods, both computational and experimental, that allow minimizing the effects of self-absorption in the experimental spectra, but until now there was no spectroscopic method allowing direct measurement of the XAS spectra that does not contain the effect of self-absorption. No effect of self-absorption in the HEROS measurement is explained by a fixed experimental geometry (i.e., no scanning optical elements during measurements), allowing for the acquisition of spectra at fixed both incident beam and emission energies. Therefore, the HEROS method could be used not only for measurements requiring a high time resolution, but also in the experiments, where the exact knowledge of the electronic structure is essential for the chemical speciation or theoretical calculations.

## **3. Case studies**

### **3.1. Materials' characterization**

Photocatalytic properties are intimately related to the electronic structure of the employed semiconductors. They determine materials' optical properties and to a large extent surface reactivity. RXES measurements can determine the electronic structure of conduction band (XAS) and valence band (v2c-XES). To demonstrate RXES abilities, we determined the electronic structure of N-doped TiO2 [18]. TiO2 is the most used photocatalyst, and N-doping is often used to change its band gap in order for the material to absorb in the visible range.

energy distribution, and the resolution of the X-ray spectrometer are not considered in this equation. Therefore, the derived HEROS-XAS curves will be broadened by these three

By combining the aspects of off-resonant scattering, high energy and dispersion-type of detection to the measurements of unoccupied electronic states a high energy resolution offresonant spectroscopy has been established. The proposed method does not require any scanning optical elements during the measurement, and therefore allows for X-ray spectro‐ scopy measurements at timescales unattainable to XAS or RXES techniques [61, 64, 65, 16]. Figure 4 demonstrates the principle of HEROS. The Lα1 X-ray emission (3d5/2 - 2p3/2 transition) of a Pt foil was recorded at a fixed incident X-ray beam energy tuned below the L3 absorption edge. The off-resonant X-ray emission was recorded by means of von Hamos spectrometer that allowed to cover over 60eV energy range at fixed optical arrangement. The corresponding HEROS-XAS spectrum was reconstructed using the measured X-ray emission spectrum and Eqs. 1–4. The HEROS-XAS spectrum (open circles) is compared to the X-ray absorption spectrum (filled orange area) that was recorded by means of total fluorescence yield (TFY). We should stress here, that the derived HEROS-XAS spectrum exhibited more detailed informa‐ tion than the conventional XAS spectrum, due to the removal of the initial state broadening. The result implies that the HEROS-XES exhibits the same information as high-energy resolu‐ tion XAS. Moreover, the HEROS experiment is performed at a fixed optical arrangement, meaning acquisition time resolution is simply controlled by experimental efficiency, not by the speed of scanning the incident energy axis. Finally, as recently demonstrated, the HEROS spectra are free of self-absorption effects [63]. Self-absorption belongs to one of the phenomena disturbing the absorption measurements [17] and leads to a modification of the shape of the measured absorption spectrum, visible in particular in the case of samples having high concentrations of the studied element. There are several methods, both computational and experimental, that allow minimizing the effects of self-absorption in the experimental spectra, but until now there was no spectroscopic method allowing direct measurement of the XAS spectra that does not contain the effect of self-absorption. No effect of self-absorption in the HEROS measurement is explained by a fixed experimental geometry (i.e., no scanning optical elements during measurements), allowing for the acquisition of spectra at fixed both incident beam and emission energies. Therefore, the HEROS method could be used not only for measurements requiring a high time resolution, but also in the experiments, where the exact knowledge of the electronic structure is essential for the chemical speciation or theoretical

Photocatalytic properties are intimately related to the electronic structure of the employed semiconductors. They determine materials' optical properties and to a large extent surface reactivity. RXES measurements can determine the electronic structure of conduction band

contributions.

12 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

calculations.

**3. Case studies**

**3.1. Materials' characterization**

In the case of photocatalysts, and more specifically on N-doped TiO2, the fundamental aspects for a high-performing material are: decent overlap between N and O orbitals (synergy effect), and dense and wide orbital levels in the conduction band (charge mobility). The first aspect defines how well-mixed the doped system is, a key parameter toward achieving the desired synergetic effect and visible light absorption. In the worst case scenario, the resultant material is composed of a solid solution of two different materials, namely, TiO2 and TiN. The second aspect refers to charge mobility, which in the case of TiO2 like any other semiconductor occurs via charge particles carriers trapping and detrapping mechanism [19]. Therefore, charge mobility depends on the number of available orbital levels (sub-bands) in the conduction and valence band and spacing between them.

**Figure 5.** Schematic representation of combined theory and experimental approach for the design of improved doped semiconductors. (Reproduced from elsewhere [18] with permission)

By combining RXES measured at Ti K-edge and FEFF calculations [20], we were able to determine the electronic structure of conduction band (XAS) and valence band (valence-tocore X-ray emission spectroscopy (v2c-XES). Figure 5 represents schematically the procedure to attain information about semiconductor electronic structure.

Figure 6 shows the effect of substitutional N-doping of TiO2. Starting with pristine TiO2, the XAS (conduction band) is constituted primarily of Ti-d empty states. The two peaks in the spectrum relates to the octahedral crystal field separation of the d-orbitals. The lowest energy peak is associated to the t2g orbitals and the highest to eg orbitals. The valence band (v2c-XES) is composed of O-2p and occupied Ti-d states. The valence edge is composed entirely of oxygen orbitals. However, the states are well-hybridized, thus one cannot state that electrons excited from valence edge are from oxygen. Rather, one can state that they were located in the oxygen orbitals at the time of the excitation.

**Figure 6.** Electronic band structure of TiO2 and TiN. (*Top*) Valence and conduction band electronic states extracted from measured RIXS plane. (*Below*) Calculated Ti, O, and N DOS for TiO2, TiN, and TiO2-xNx, where x amounts to 2% N-dopant level. (Reproduced from elsewhere [18] with permission)

The addition of N led to a shift of the valence edge to higher energy, i.e., reduction of semi‐ conductor band gap. The shift is due to the appearance of N-2p orbitals that are strongly hybridized with O-2p orbitals. However, too much N-doping results in the formation of TiN and consequent coloring in the sample, but according to the electronics of the materials, TiN could not work as a sensitizer. Plus, it is known that TiN has no catalytic activity and thus might decrease activity by blocking and/or reducing surface sites.

By confirming RXES measurements with FEFF calculations, we derived an elegant and costeffective strategy for the rational design of novel materials used in the conversion of solar energy into chemical bonds. Together, one is able to map the material electronic structure with high precision, requiring a very limited amount of sample (experimental work) or none (theory). The technique can be applied to other materials in all the forms they are normally found, namely nanopowders, and thin-films forms [21].
