  
RXES
XAS
XES

Abstract
We review a theory of resonant xray emission spectroscopy (RXES) based on a realspace multiple scattering Green’s function formalism.
The RXES signal is conveniently calculated as a convolution of an effective xray absorption spectrum (XAS) with the xray emission spectrum (XES).
We provide a comparison of our calculated results to those of experiment for anatase TiO2.


HERFD
RSMS

Introduction
Resonant xray emission spectroscopy (RXES) is a powerful probe of both electronic structure and manybody excitations.
In addition, high resolution fluorescence detection (HERFD) xray absorption (XAS), as well as valence level RXES contains important information on charge transfer, oxidation state, and material structural properties.
However, the interpretation of RXES is complicated by the presence of strong manybody and solidstate effects. Here we review a theory of RXES based on realspace multiple multiple scattering (RSMS) Green’s function techniques1,2.
The RXES signal is given as a convolution of an effective xray absorption signal with the xray emission spectrum (XES), with manybody excitations treated via a further convolution with an effective spectral function.
The theory is implemented as an extension of the computationally efficient realspace multiple scattering code FEFF9, which is well known for its use in XAS and XES,
but is now also able to calculate a variety of other quantities such as NRIXS, EELS, and Compton scattering. As an illustrative example, we compare our theoretical results with experimental data for anatase TiO2.

1 J. J. Rehr and R. C. Albers, Rev. Mod. Phys. 72, 621–654 (2000).
2 J. J. Kas, J. J. Rehr, J. A. Soininen, and P. Glatzel, Phys. Rev. B 83, 235114 (2011).


Theory
Within our approximation of the KramersHeisenberg formula3, we give the RXES as a convolution of an effective XAS signal with the XES signal2, i.e.,
where Ω is the frequency of the incoming xray, ω is the frequency of the outgoing xray, Eb is the edge energy in the intermediate state, and Γb is the intermediate state core hole lifetime broadening.
The effective XAS signal is given in terms of an energy dependent transition operator which replaces the dipole operator in the normal XAS formula,
where c stands for the final state core hole, gc is the final state Green’s function, and the transition operator is given by
Finally, Δν is the difference between the intermediate and final state core hole potentials.
In the limit Δν = 0, Eq. (2) reduces to the normal formula for the XAS,
and becomes very similar to previous calculations which give the RXES signal as a convolution of the occupied and unoccupied angular momentum projected densities of states4,5,
albeit with the effects of the matrix elements included.

3 H. A. Kramers and W. Heisenberg, Z. Phys. 31, 681 (1925).
4 J. JimenezMier, J. van Ek, D. L. Ederer, T. A. Callcott, J. J. Jia, J. Carlisle, L. Terminello, A. Asfaw, and R. C. Perera, Phys. Rev. B 59, 2649 (1999).
5 P. Glatzel, J. Singh, K. O. Kvashnina, and J. A. van Bokhoven, J. Am. Chem. Soc. 132, 2555 (2010).

FEFF9

Implementation in FEFF9
We have implemented our theory as an extension the FEFF9 RSMS code6.
FEFF9 has been used extensively in calculations of electronic structure, EXAFS, XANES, and other related excited state spectroscopies, and is an efficient method which is not restricted to any particular symmetries,
and can thus treat a large class of materials, including periodic, amorphous, molecular, and nanomaterials. In addition, the code is capable of treating a variety of manybody effects including photoelectron selfenergy effects,
vibrational (DebyeWaller) effects, and corehole interactions.

6 John J. Rehr, Joshua J. Kas, Micah P. Prange, Adam P. Sorini, Yoshinari Takimoto, Fernando Vila, Comptes Rendus Physique 10 548559 (2009).


Results and Discussion
As an illustrative example, Fig. 1 shows the Ti Kα (top), Kβ (middle), and Kvalence (bottom) RXES of anatase TiO2.
The plot gives the RXES signal as a function of the incident energy of the photons (xaxis) and the energy loss, or difference between the incident and outgoing photon energies (yaxis).
These axes are related to the intermediate and final electronic states of the system respectively. The progression from deep core hole in the final state (Kα) to a valence hole in the final state (Kvalence) can provide valuable information on corehole interactions.
In this case one sees the preedge quadrupole peak moving upwards along the energy loss axis as the difference in corehole potentials becomes larger.
The interpretation is that the localized dstates associated with the preedge peak are strongly effected by the core hole, while the itinerant states associated with the rest of the spectrum are not.




Fig. 1: Ti Kα (top), Kβ (middle), and Kvalence (bottom) RXES of anatase TiO2.
Note the changing position of the preedge peak as a function of the depth of the final state core hole.


Summary
We have developed a realspace multiple scattering approach to RXES, and implemented it as an extension of the FEFF9 code.
The qualitative agreement of our results for anatase TiO2 show that the method incorporates corehole interaction in both the intermediate and final states of the RXES process,
and takes solid state effects into account via a reasonable first principles fashion.
In addition to the the results shown above, the method has been used to investigate a variety of other systems including adsorption on small Pt nanoparticles interacting with adsorbates7,
catalytically important Mo oxide standards8, and actinide and lanthanide based systems9.
The theory provides a useful method to interpret RXES in a variety of materials.

7 Matthew W. Small et al, Submitted to Angewandte Communications.
8 Rowena Thomas et al, Submitted to J. Phys. Chem. B.
9 T Vitova et al 2013 J. Phys.: Conf. Ser. 430 012117.


Acknowledgement
This work was supported by DOE BES Grant No. DEFG0397ER45623 and was facilitated
by the DOE Computational Materials and Chemical Sciences Network (J.J.K. and J.J.R.). J.A.S. gratefully acknowledges the ﬁnancial support from the Eemil Aaltonen foundation and Magnus Ehrnrooth foundation.
The ESRF is acknowledged for providing beam time and technical support (P.G.).



