research papers
Advanced calculations of Xray spectroscopies with FEFF10 and Corvus
^{a}Department of Physics, University of Washington, Seattle, WA 98195, USA, and ^{b}Theory Institute for Materials and Energy Spectroscopies, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
^{*}Correspondence email: jjkas@uw.edu
The realspace Green's function code FEFF has been extensively developed and used for calculations of Xray and related spectra, including Xray absorption (XAS), Xray emission (XES), inelastic Xray scattering, and electron energyloss spectra. The code is particularly useful for the analysis and interpretation of the finestructure (EXAFS) and the nearedge structure (XANES) in materials throughout the periodic table. Nevertheless, many applications, such as nonequilibrium systems, and the analysis of ultrafast pump–probe experiments, require extensions of the code including finitetemperature and auxiliary calculations of structure and vibrational properties. To enable these extensions, we have developed in tandem a new version FEFF10 and new FEFFbased workflows for the Corvus workflow manager, which allow users to easily augment the capabilities of FEFF10 via auxiliary codes. This coupling facilitates simplified input and automated calculations of spectra based on advanced theoretical techniques. The approach is illustrated with examples of hightemperature behavior, vibrational properties, manybody excitations in superheavy materials, and fits of calculated spectra to experiment.
Keywords: spectroscopy; EXAFS; XAS; Green's functions; FEFF10; Corvus.
1. Introduction
The realspace Green's function (RSGF) code FEFF (Rehr & Albers, 2000; Rehr et al., 2009, 2010) has been extensively developed and is in wide use for calculations of Xray absorption (XAS) and a number of related spectroscopies (van Bokhoven & Lamberti, 2014). Owing to its versatility and broad applicability, FEFF has become a workhorse for simulations and analysis of extended Xray absorption finestructure (EXAFS). However, both the theory and experiment continue to increase in sophistication. For example, the advent of timedomain spectra at XFEL sources and increased resolution have enabled many novel experimental studies. Improved treatments of manybody effects, such as inelastic losses and thermal vibrations, have also been developed. As a consequence, extensions to the computational framework are desirable. At the same time, it is no longer efficient to include all of these extensions within a single monolithic code like FEFF9 and its predecessors. For many advanced or highquality calculations, input from auxiliary codes based on density functional theory (DFT), quantumchemistry, and Monte Carlo sampling methods are needed.
To address these issues, we have developed a hybrid computational approach based on a new version FEFF10 and the recently developed Corvus workflow tool (Story et al., 2019). Other automation schemes and workflow tools have been developed for similar purposes (Barrand et al., 2003; Larsen et al., 2017). Some have been developed specifically for workflows that are similar to those we discuss below, such as calculations of vibrational effects in (Dimakis et al., 2009). However, our Corvus workflow machinery is unique in that it is relatively general in terms of tools to create new workflows, but is tailored to focus on calculations of Xray and other excitedstate spectra.
The monolithic FEFF10 code implements several extensions, while Corvus enables workflows that link multiple codes seamlessly to facilitate advanced and custom applications. In Section 2 we describe the realspace Green's function approach implemented in FEFF10, and in Section 3 a brief summary of the Corvus workflow framework together with examples of advanced calculations that can be implemented with FEFF10 and Corvus. In particular, we discuss finitetemperature simulations, vibrational effects, inelastic losses and spectra of superheavy elements, full spectrum optical constants, and fitting of theoretical XANES spectra to experimental data. Finally, Section 4 summarizes the status of the Corvus/FEFF10 capabilities and possible improvements.
2. RSGF theory of Xray spectra
The RSGF theory of Xray spectra is now well established (Rehr & Albers, 2000) and has been automated and optimized in the several generations of FEFF. In contrast to traditional wavefunction approaches, the RSGF approach is based on a realspace treatment of the oneparticle Green's function. This strategy is advantageous, since it avoids calculations of and sums over eigenstates as in the traditional Fermi's golden rule approach. The approach also facilitates the inclusion of key manybody effects such as inelastic losses.
The theory can also be generalized straightforwardly to finite temperature (FT) (Tan et al., 2021). The implementation of the theory in FEFF is modular and designed to facilitate systematic improvements. Consequently, extensions described here utilize much of the code base in previous versions (Rehr & Albers, 2000; Rehr et al., 2009, 2010), and permit backward compatibility. Thus, we only summarize the basic elements of the theory here, and focus on the extensions included in FEFF10 and the Corvus interface with auxiliary codes in the next sections.
A key approximation in the RSGF formalism is the muffintin approximation, in which the scattering potential v(r) is partitioned into Voronoi cells and approximated as spherical within each cell centered at R, v(r) = . Then the Green's function can be solved exactly in terms of radial wavefunctions and spherical harmonics. The contribution to the from a given core level is then expressed compactly as
where M_{L} is the dipole matrix element between the corestate and a scatteringstate L〉 of angular momentum L at the absorbing atom site R = 0, and = are matrix elements of the densitymatrix spectral function at the absorbing atom R = 0, where for simplicity the site indices R and R′ have been suppressed. Finally, E_{c} and μ are the energy of the corelevel and the and f(E) is the Fermi function. The dipole matrix elements M_{L} couple the scattering (photoelectron) states to relativistic atomic states, calculated using an automated single configuration version of the multiconfigurational Dirac–Fock atomic code of Desclaux (Desclaux, 1973; Ankudinov et al., 1996), which we have recently extended to treat superheavy elements up to Z = 138 (Zhou et al., 2017). Next the Green's function G is separated into central atom and scattering parts G = G_{c} + G_{sc}, which are calculated separately. The central atom part can be represented in a basis of relativistic, spherically symmetric scattering states = . The scattering part can be expressed in terms of the free Green's function G_{0} and scattering Tmatrices at each site,
where the Tmatrix is diagonal in l and R, = , t_{l} = , δ_{l} are the scattering phase shifts (Rehr & Albers, 2000), and is G^{0} with the diagonal elements set to 0 to avoid scattering from the same atom consecutively. For the XANES region (where the maximum angular momentum l_{max} is typically about 4), the matrix inverse is easily calculated, i.e. by fullmultiplescattering (FMS). For the where l_{max} ≃ 20, inversion is computationally prohibitive, and it is more efficient to expand the matrix inverse in a rapidly converging geometric series, corresponding to the multiplescattering (MS) path expansion,
Here the successive terms represent single, double, and higherorder scattering processes, which are calculated using a separable approximation (Rehr & Albers, 2000). Conventionally the = is expressed in terms of a quasiatomic background from the central absorbing atom, and a scattering part = . Using the path expansion, the fine structure χ due to MS of the photoelectron by the environment can be expressed in terms of the equation, like that of Sayers, Stern & Lytle (Sayers et al., 1971),
It is important to note that the scattering amplitudes f_{eff}(k) (from which the FEFF code takes its name) include important curved wave corrections. The same representation applies to both single and MS contributions where f_{eff} is defined for a given path. The equation also includes path and temperaturedependent Debye–Waller factors due to fluctuations in the path lengths R.
Corrections for multielectronic excitations can be included in terms of a convolution over the corespectral function A_{c}(ω),
where ω′ is the (Campbell et al., 2002). Formally the core spectral function A_{c}(ω) = Σ_{n}S_{n}^{2}δ(ω − ε_{n}), where S_{n} = is an N − 1 electron manybody overlap integral between the state of the system upon photoabsorption and the eigenstates of the electron system in the presence of the corehole . This function characterizes the effects of inelastic losses and leads to an energydependent broadening of the Likewise, the net is also given by a convolution with the quasiparticle fine structure. For each MS path R, this convolution leads to an amplitude reduction factor which is roughly constant, and a negative phase shift Φ_{R}(ω), = Typically, S_{0}^{ 2} ≃ 0.9, consistent with the reduction observed in experiments (Campbell et al., 2002). Approximate calculations of the corespectral function A_{c}(ω) in equation (5) are also possible in FEFF, using an atomic approximation with the SFCONV card. However, more precise calculations require auxiliary calculations, as discussed in Section 3.2.
Much of the above discussion is a review of the theory of Xray spectra as implemented in the previous versions of FEFF; thus we briefly describe the extensions available in FEFF10 compared with what was available in FEFF9, although we note that some of the extensions are not wholly contained within the FEFF10 code, and are only (easily) available via the combination of FEFF10 and Corvus. Here we list the main extensions available within FEFF10 + Corvus, which would not be possible with FEFF9:
(i) Finitetemperature calculations of ab initio calculations utilizing Corvus as detailed in Section 3.1.
over very broad temperature ranges up to the warm dense matter (WDM) regime. This extension involves a number of changes, including the effects of temperature on the exchangecorrelation potential, selfconsistent densities, and Fermi distribution function. Additional lattice temperature effects can be included via Debye–Waller factors or(ii) Calculations of Xray spectra of superheavy elements up to Z = 138. This extension is based on our previous work which extends Dirac–Fock calculations of atomic properties (energies, densities, etc.) up to Z = 138 as detailed in Section 3.5.
(iii) Many other changes were added to enable workflows based on Corvus + FEFF10. For example, the extensions in FEFF10 are required to enable RIXS, opticalconstant workflows, and others using Corvus.
3. Corvus and FEFF10
FEFF10 has a variety of extended capabilities for calculations of electronic structure and spectra. However, for many advanced or highquality calculations, FEFF must be augmented with calculations of structure and other properties based on DFT, quantumchemistry, Monte Carlo sampling, etc. Examples include calculations of spectra based on DFT optimized structure, inclusion of vibrational effects through calculations of the dynamical matrix (Vila et al., 2007, 2018a,b) or simulations (Vila et al., 2008, 2012, 2017), or treatment of through realtime timedependent DFT (TDDFT). For these purposes, an intelligent workflow tool dubbed Corvus has been developed (Story et al., 2019). This tool replaces JFEFF, the Javabased GUI of FEFF9, which is difficult to maintain and extend. Instead, the combination of FEFF10 and Corvus facilitates many advanced calculations previously limited to expert users. In this section we briefly describe Corvus, and give details on the extensions to FEFF available within the FEFF10 code itself, as well as in combination with Corvus, which is now the preferred method for running FEFF10.
Briefly, Corvus is a Pythonbased workflow framework which consists of several layers of code. First, a set of general workflow tools and an internal system dictionary that holds a description of all of the scientific properties of the physical system at hand provides the capability to easily develop, or automatically generate workflows. Second, external software facing `handlers' translate between the format of the internal system dictionary and specific external scientific software packages. In addition, these handlers provide a layer of automation in terms of smart, input derived default parameters, as well as error catching capabilities. Because the handlers translate all input and output to a standard Corvus format, and automate many of the codespecific parameters associated with specific external software packages, the input is relatively simple, allowing the user to focus mostly on the physical system at hand.
In addition to the Python workflow framework, we have developed several Corvus web interfaces. The first serves as a demonstration of the capabilities of FEFF10 and Corvus, and allows anyone to try a few simple calculations. It is hosted on the local TIMES cluster at SLAC (https://timesfeff.stanford.edu). The second interface provides a portal to the National Energy Research Scientific Computing Center (NERSC). This allows users to easily set up, run, and monitor calculations using Corvus and a variety of underlying scientific software (https://portal.nersc.gov/project/m2757/corvusFront.html).
3.1. Electronic and lattice temperature effects
With the combination of FEFF10 and Corvus, it is possible to treat spectra at finite temperature, including electronic and lattice temperature effects. While the electronic temperature effects are built into FEFF10, the treatment of finite temperature (FT) lattice effects generally requires auxiliary calculations. The combination of FEFF10 and Corvus allows for the simulation of a broad range of temperatures from zero to the WDM regime. In addition, this allows for simulations of nonequilibrium states of matter, such as those produced during pump–probe and shock experiments. Here we briefly summarize the treatment of FT effects, which are discussed in more detail elsewhere (Tan et al., 2021).
One of the new options in the FEFF10 code is the inclusion of an FT generalization of the RSGF algorithms. The effects of temperature on the electronic system require extensions of several parts of the theory (Tan et al., 2018). First, the selfconsistent field (SCF) calculations have been updated to include Fermi–Dirac occupations by integration in the complex plane, and summing over the appropriate Matsubara poles. Second, the exchange correlation potential in the SCF has been updated to include explicit temperature dependence (Karasiev et al., 2014, 2016). Third, Fermi–Dirac statistics are included. At low temperatures the effects of temperature on the electronic system cause the to shift following the Sommerfeld expansion, while the edge broadens and lowers due to the Fermi–Dirac statistics. At higher temperatures, however, the electronic structure changes, and the shift in the and shape of the can deviate from the Sommerfeld approximations. Finally, a temperaturedependent selfenergy can be important at very high T. These observations can be explained by noting that at low temperatures compared with the Fermi temperature T << T_{F} (which is typically of order 10^{4} K), the exchangecorrelation potential and selfenergy are weakly temperature dependent. Thus a zerotemperature approximation is often adequate for electronic structure, although vibrational effects become substantial for T of order of the Debye temperature θ_{D} (which is typically 10^{2}–10^{3} K). However, in the WDM regime T ≃ T_{F}, explicit temperature dependence is necessary, as the exchangecorrelation potential changes from exchange to correlationdominated behavior in the WDM (Kas et al., 2019).
The primary effect of the electronic temperature is due to the inclusion of Fermi factors for the occupied and unoccupied levels in the calculations of the μ(T) which is determined selfconsistently in the FT SCF loop. This is illustrated in Fig. 1 for several temperatures. The figure also shows a complementary reduction in the above the edge.
Notably, these effects shift the edge with increasing temperature as determined by theIt is essential to treat lattice vibrations in order to describe FT effects on the T ≃ θ_{D} and high energies E − E_{0} above ∼40 eV, the spectrum is strongly damped by lattice vibrations even at zero temperature through zeropoint motion. At low temperatures and high energies, these effects can be treated via Debye–Waller factors, which damp the fine structure by an exponential factor where σ^{2} is the (pathdependent) meansquare relative displacement (MSRD) along the path in question. There are several methods for approximating the MSRD, including the use of a correlated Debye or Einstein model, where the Debye temperature θ_{D} of the material can either be treated as a fitting parameter or estimated roughly from tabulated elasticity parameters (Anderson, 1963). This method is illustrated in Fig. 1(b). For more complex systems where the correlated Debye model is not applicable, a more accurate and widely applicable method based on the DFT calculation of the dynamical matrix can be used (Vila et al., 2007). This method computes the MSRD for a given scattering path R from Debye integrals over the phonon (PDOS) ρ_{R}(ω) projected onto that path (Poiarkova & Rehr, 1999a,b; Krappe & Rossner, 2002),
accurately. The various regimes can be treated with different approximations, split by low or high energy, and low or high temperature. At low temperatureswhere μ_{R} is the for the path and β = 1/k_{B}T. In the DMDW module of FEFF10, the PDOS is calculated using a continued fraction representation of the phonon Green's function generated with the iterative Lanczos algorithm (Deuflhard & Hohmann, 1995),
where is the Lanczos seed for a massweighted normal displacement of the atoms along the path, and D is the dynamical matrix of force constants,
Here u_{jlα} is the α = {x, y, z} Cartesian displacement from the equilibrium position of atom j in l, M_{j} is its mass, and E is the energy of the Thus, the only quantity required to obtain ab initio MSRDs is the dynamical matrix which, however, cannot be computed directly in FEFF. This approach has been applied to study and crystallographic MSRDs of simple systems (Vila et al., 2007), but can also be used for more complex materials with negative (Vila et al., 2018a,b). To streamline the generation of D, we have developed Corvus handlers to a variety of codes [e.g. ABINIT (Gonze et al., 2016), NWChem (Valiev et al., 2010)] that can be used to automatically generate MSRDs, crystallographic Debye–Waller factors, vibrational free energies and phonon densities of states. Corvus has the advantage that the complicated process of interfacing the computation of the dynamical matrix to the computation of any of those quantities is done automatically. For example, Fig. 2 shows a typical Corvus input for the computation of the phonon DOS of GaAs.
This input simplifies the complex series of steps required to generate the dynamical matrix in ABINIT and converts it to the input that DMDW uses. Figure 3 presents the total phonon computed with this workflow, showing that overall agreement with experiment is qualitatively correct. More importantly, the moments of the distribution and their associated mean frequencies (Table 1) are in excellent agreement with experiment, thus ensuring the accuracy of the Debye integrals described above.

The methods described above rely on the quasiharmonic approximation. At higher temperatures, however, the distribution of path lengths becomes nonharmonic, and is not well described by standard Debye–Waller factors. In addition, at low energies (in the nearedge region) the use of for magnesium oxide (MgO) with Monte Carlo sampling. These methods have been implemented within Corvus, and can be run with a single simplified input file.
Debye–Waller factors does not capture the effects of symmetry breaking, even at low temperatures. For these situations it is preferable to treat disorder using an ensemble average, with structural snapshots taken from or vibrational Monte Carlo sampling. This method is illustrated in Fig. 43.2. Multielectron excitations
Inelastic losses in corelevel Xray spectra arise from manybody excitations, leading to broadening and damping as well as satellite peaks in Xray photoemission (XPS) and Xray absorption (XAS) spectra. While calculations of these effects pose a formidable challenge, there has been significant progress. In particular, the development of cumulant Green's function methods and the quasiboson approximation permit approximate calculations of these effects. Here we summarize the main results. Formally the inelastic losses can be partitioned into intrinsic, extrinsic and interference terms. The intrinsic losses arise from excitations due to the sudden creation of the corehole, and can be represented in terms of the corehole Green's function G_{c} [see Kas et al. (2016), equation (13)]. Calculations of G_{c}(t) in the timedomain are facilitated by the cumulant expansion, using the Langreth form (Kas et al., 2016). The calculations can be carried out using realtime TDDFT. The extrinsic losses are obtained from the GW approximation of the photoelectron selfenergy and the interference terms are approximated. These effects are included in the spectra using a convolution with an energydependent particle–hole spectral function.
The quasiparticle μ_{qp}(ω) is calculated using FEFF10 as described in Section 2 with an appropriate approximation for the FT selfenergy. An approximation for manybody including the effects of intrinsic excitations is given by a convolution with the core spectral function A_{c}(ω) as in equation (5). More generally, a more complete calculation is given by a convolution with the particle–hole spectral function, which includes excitations caused by the corehole (intrinsic excitations), those caused by the photoelectron (extrinsic excitations), as well as interference between them (Kas et al., 2015). We have found that several simple approximations are useful: (i) Use of the intrinsic spectral function alone is a fast approximation that is quite good in many cases over the range of energies that includes the near edge, especially in insulators (Woicik et al., 2020a,b). This is included in FEFF10; (ii) A simple model for the interference and extrinsic can be used for metals, with a single free parameter describing the interference amplitude (Kas et al., 2016); (iii) The entire quasiboson (intrinsic, extrinsic, and interference) can be modeled from the intrinsic spectrum alone, as the shape of the extrinsic is, to a good approximation, the same as that of the intrinsic (Zhou et al., 2015).
Here we focus on a straightforward extension to the atomic approximation in FEFF10 for the corehole spectral function. This is based on the cumulant expansion approximation for the corehole Green's function given by an exponential expression in time,
where ε_{c} is the corelevel quasiparticle energy, and C(t) is the cumulant, which encapsulates all manybody excitations. The spectral function is given by the Fourier transform of the Green's function, A_{c}(ω) = −(1/π)Im G_{c}(ω). Within linear response, the cumulant is related to the density fluctuations caused by the sudden appearance of the corehole,
In the above, δρ(t) is the density induced by the sudden appearance of the corehole at time t = 0, v_{c}(r) is the corehole potential, which we approximate as a Coulomb potential centered on the absorbing atom, and β(ω) can be interpreted as the quasiboson We calculate the response to the corehole within realtime TDDFT using the RTSIESTA code (Takimoto et al., 2007; Vila et al., 2010; Kas et al., 2015).
This approach has been developed as a workflow in Corvus. The workflow consists of first calculating the realtime response to the sudden appearance of the corehole using a modified version of the RTSIESTA code (Kas et al., 2015). This calculated realtime response is then used in the cumulant expansion approach to obtain the corehole spectral function. Finally, manybody excitation effects are added to the quasiparticle via convolution with the corehole spectral function. Within Corvus, we have implemented a workflow that allows the user to request the manybody Starting from a (CIF), and a small amount of additional information provided by the user (Fig. 5), Corvus then produces input for RTSIESTA and FEFF using Pymatgen (https://pymatgen.org; Ong et al., 2013), runs RTSIESTA to obtain the corehole response, and calculates the manybody corehole spectral function. FEFF is then used to calculate the quasiparticle and, finally, Corvus produces the manybody spectrum by convolving the resulting with the cumulant spectral function. Results of this workflow for the M_{45}edge XANES of CeO_{2} are shown in Fig. 6, along with the experimental electron energyloss spectra (EELS) data (Song et al., 2014) and the single particle calculation (without manybody convolution). Note the appearance of the satellite peaks at ∼890 eV and 910 eV in the manybody calculation, in reasonable agreement with those in the experiment. The discrepancy in the M_{4}/M_{5} ratio between the calculated and experimental results reflects the lack of any treatment of the mixing of the M_{45} holes in the theory. There are various methods for treating this, including multiplet methods, TDDFT, or the solution of the Bethe–Salpeter equation. However, we leave the treatment of these effects to the future.
3.3. Analysis of Xray spectra
We have also implemented a method for analysis of XANES, LMFIT library (Newville et al., 2014). The user requests a fit as the target property, and provides basic information, including the target of the fit (XANES, or XPS). Free parameters along with their initial values are also defined in the input (Fig. 7). At present, only a few key free parameters are available for use within Corvus. These include parameters for edge alignment, adjustment, broadening, overall coordinate expansion, and rigid movement of clusters of atoms (rigid movement of a ligand system, for example) along a bond.
or similar spectra using nonlinear leastsquares fitting routines provided by theFigure 8 shows results of a fit to the experimental of [LMn(acac)N]BPh_{4} (Smolentsev et al., 2009), along with the [LMn(acac)N]^{+} ion used in the calculations. The main physical parameters used in the fit were the bond length of the apical nitrogen, and an overall expansion of the molecule. The most important physical parameter is the bond length of the apical nitrogen, which is found to be 1.52 ± 0.02 Å, in good agreement with experimental data (1.518 ± 0.004) (Niemann et al., 1996).
3.4. Optical constants from UVVIS to Xray
Optical constants are important for materials design as they describe the frequencydependent interaction between light and matter (dielectric constant), or charged particles and matter (energyloss function). Here we briefly describe the use of FEFF10 and Corvus to produce optical constants over a wide range of energies from the the UVVIS to Xray regimes. The optical constants can all be obtained from the imaginary part of the ε_{2}(ω). In particular, the real part of the can be found via a Kramers–Kronig transform,
From the complex dielectric function, various other optical constants are obtained, such as the complex index of refraction n + iκ, μ, reflectivity R, and energyloss spectrum L,
The imaginary part of the dielectric function can be split into contributions from the valence electrons , and contributions from the core electrons . The core contributions can be calculated using the standard methods implemented within FEFF, as described elsewhere and in Section 2 (Prange et al., 2009; Kas et al., 2021). Corvus facilitates these calculations by setting up the correct energy grids, calculating all edges in the system, including the nearedge and extended regimes, and summing to obtain the complete contribution from all corelevels. The valence contribution is more difficult to obtain, but an approximate method is given by a convolution of the lowenergy edges with the appropriate angular momentum projected densities of states and can give quite reasonable results. However, in some cases, especially when strong excitonic behavior is expected, such as in Si, the Bethe–Salpeter equation must be solved in order to obtain good results (Lawler et al., 2008). For such cases we suggest the use of the OCEAN code, which combines DFT with the NIST Bethe–Salpeter equation solver (Vinson et al., 2011).
3.5. Superheavy elements up to Z = 138
Recent experimental and theoretical work has focused on the formation of compounds including superheavy elements (Eichler et al., 2016; Oleynichenko et al., 2018; Iliaš & Pershina, 2017; Even et al., 2014; Hammou et al., 2019). For example, a Seaborgium molecule (Z = 106) Sg(CO)_{6} has been detected in the gas phase. Since the lifetime of such molecules is only on the order of seconds, experimental methods of investigating their chemical and structural properties must be fast. is a particularly good candidate, given its ultrashort probe time, element specificity, and ability to probe shortrange order (Fig. 9). As noted above, FEFF10 now includes the capability to treat systems with superheavy elements up to Z = 138 (Zhou et al., 2017), based on an automated single configuration version of the multiconfigurational Dirac–Fock atomic code (Desclaux, 1973; Ankudinov et al., 1996). These calculations can be carried out, for example, with a FEFFonly Corvus workflow, or with more elaborate calculations as desired.
3.6. Other developments
Together with the workflows described above, we have developed several other workflows that simplify calculations based on FEFF10. These include, for example, sums over edges (e.g. L_{23} or M_{45}) and configurational averaging, i.e. averaging of spectra over the unique sites in a crystal, and calculations of resonant inelastic Xray scattering (RIXS).
4. Summary and conclusions
We have developed FEFF10, a new version of the RSGF code FEFF, together with Corvus, an efficient workflow tool to enable advanced calculations of Xray spectra by combining FEFF10 with auxiliary codes. This hybrid approach permits a number of extensions and features including finitetemperature with auxiliary calculations of structure and vibrational properties. The approach is generally applicable to systems throughout the periodic table, temperatures up to the WDM regime, and nonequilibrium systems including simulations of timeresolved pump–probe experiments. The code utilizes an improved Dirac–Fock code with the capability of treating superheavy elements up to Z = 138. We have also described the augmentation of FEFF10 with auxiliary codes through automated workflows implemented within the Pythonbased Corvus workflow manager. This coupling facilitates automated advanced calculations. The calculations have been compared with both experiment and other theoretical methods, and generally give good results. Many extensions and applications are possible.
Funding information
The development of FEFF10 and Corvus software was carried out within the Theory Institute for Materials and Energy Spectroscopies (TIMES) at SLAC, and is supported by the US DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DEAC0276SF00515. The development of the finitetemperature extension in FEFF10 was supported by the DOE Office of Science BES Grant DEFG0297ER45623, with computational support from NERSC, a DOE Office of Science User Facility, under Contract No. DEAC0205CH11231.
References
Anderson, O. L. (1963). J. Phys. Chem. Solids, 24, 909–917. CrossRef CAS Web of Science Google Scholar
Ankudinov, A., Zabinsky, S. & Rehr, J. (1996). Comput. Phys. Commun. 98, 359–364. CrossRef CAS Web of Science Google Scholar
Barrand, G., Binko, P., Chwajol, G., Dönszelmann, M., Hoschek, W., Johnson, T., Medernach, E., Moneta, L., Moscicki, J., Papadopoulos, I., Pfeiffer, A., Sang, M., Serbo, V. & Turri, M. (2003). AIDA–abstract interfaces for data analysis. http://aida.freehep.org/. Google Scholar
Blakemore, J. (1982). J. Appl. Phys. 53, R123–R181. CrossRef CAS Web of Science Google Scholar
Bokhoven, J. A. van & Lamberti, C. (2014). Editors. XAS and XES; Theory and Applications. New York: Wiley. Google Scholar
Campbell, L., Hedin, L., Rehr, J. J. & Bardyszewski, W. (2002). Phys. Rev. B, 65, 064107. Web of Science CrossRef Google Scholar
Desclaux, J. (1973). At. Data Nucl. Data Tables, 12, 311–406. CrossRef CAS Google Scholar
Deuflhard, P. & Hohmann, A. (1995). Numerical Analysis. Berlin: de Gruyter. Google Scholar
Dimakis, N., Mion, T. & Bunker, G. (2009). J. Phys. Conf. Ser. 190, 012011. CrossRef Google Scholar
Eichler, R., Asai, M., Brand, H., Chiera, N., Di Nitto, A., Dressler, R., Düllmann, C., Even, J., Fangli, F., Goetz, M., Haba, H., Hartmann, W., Jäger, E., Kaji, D., Kanaya, J., Kaneya, Y., Khuyagbaatar, J., Kindler, B., Komori, Y., Kraus, B., Kratz, J., Krier, J., Kudou, Y., Kurz, N., Miyashita, S., Morimoto, K., Morita, K., Murakami, M., Nagame, Y., Ooe, K., Piguet, D., Sato, N., Sato, T., Steiner, J., Steinegger, P., Sumita, T., Takeyama, M., Tanaka, K., Tomitsuka, T., Toyoshima, A., Tsukada, K., Türler, A., Usoltsev, I., Wakabayashi, Y., Wang, Y., Wiehl, N., Wittwer, Y., Yakushev, A., Yamaki, S., Yano, S., Yamaki, S. & Qin, Z. (2016). EPJ Web Conf. 131, 07005. Google Scholar
Even, J., Yakushev, A., Düllmann, Ch. E., Haba, H., Asai, M., Sato, T. K., Brand, H., Di Nitto, A., Eichler, R., Fan, F. L., Hartmann, W., Huang, M., Jäger, E., Kaji, D., Kanaya, J., Kaneya, Y., Khuyagbaatar, J., Kindler, B., Kratz, J. V., Krier, J., Kudou, Y., Kurz, N., Lommel, B., Miyashita, S., Morimoto, K., Morita, K., Murakami, M., Nagame, Y., Nitsche, H., Ooe, K., Qin, Z., Schädel, M., Steiner, J., Sumita, T., Takeyama, M., Tanaka, K., Toyoshima, A., Tsukada, K., Türler, A., Usoltsev, I., Wakabayashi, Y., Wang, Y., Wiehl, N. & Yamaki, S. (2014). Science, 345, 1491–1493. Web of Science CrossRef CAS PubMed Google Scholar
Gonze, X., Jollet, F., Abreu Araujo, F., Adams, D., Amadon, B., Applencourt, T., Audouze, C., Beuken, J.M., Bieder, J., Bokhanchuk, A., Bousquet, E., Bruneval, F., Caliste, D., Côté, M., Dahm, F., Da Pieve, F., Delaveau, M., Di Gennaro, M., Dorado, B., Espejo, C., Geneste, G., Genovese, L., Gerossier, A., Giantomassi, M., Gillet, Y., Hamann, D. R., He, L., Jomard, G., Laflamme Janssen, J., Le Roux, S., Levitt, A., Lherbier, A., Liu, F., Lukačević, I., Martin, A., Martins, C., Oliveira, M. J. T., Poncé, S., Pouillon, Y., Rangel, T., Rignanese, G., Romero, A. H., Rousseau, B., Rubel, O., Shukri, A. A., Stankovski, M., Torrent, M., Van Setten, M. J., Van Troeye, B., Verstraete, M. J., Waroquiers, D., Wiktor, J., Xu, B., Zhou, A. & Zwanziger, J. W. (2016). Comput. Phys. Commun. 205, 106–131. Web of Science CrossRef CAS Google Scholar
Hammou, N., Zaoui, A. & Ferhat, M. (2019). Mater. Res. Expr. 6, 115922. Web of Science CrossRef Google Scholar
Hjorth Larsen, A., Jørgen Mortensen, J., Blomqvist, J., Castelli, I. E., Christensen, R., Dułak, M., Friis, J., Groves, M. N., Hammer, B., Hargus, C., Hermes, E. D., Jennings, P. C., Bjerre Jensen, P., Kermode, J., Kitchin, J. R., Leonhard Kolsbjerg, E., Kubal, J., Kaasbjerg, K., Lysgaard, S., Bergmann Maronsson, J., Maxson, T., Olsen, T., Pastewka, L., Peterson, A., Rostgaard, C., Schiøtz, J., Schütt, O., Strange, M., Thygesen, K. S., Vegge, T., Vilhelmsen, L., Walter, M., Zeng, Z. & Jacobsen, K. W. (2017). J. Phys. Condens. Matter, 29, 273002. Web of Science CrossRef PubMed Google Scholar
Iliaš, M. & Pershina, V. (2017). Inorg. Chem. 56, 1638–1645. Web of Science PubMed Google Scholar
Jourdain, N., Recoules, V., Lecherbourg, L., Renaudin, P. & Dorchies, F. (2020). Phys. Rev. B, 101, 125127. Web of Science CrossRef Google Scholar
Karasiev, V. V., Calderín, L. & Trickey, S. B. (2016). Phys. Rev. E, 93, 063207. Web of Science CrossRef PubMed Google Scholar
Karasiev, V. V., Sjostrom, T., Dufty, J. & Trickey, S. B. (2014). Phys. Rev. Lett. 112, 076403. Web of Science CrossRef PubMed Google Scholar
Kas, J. J., Blanton, T. D. & Rehr, J. J. (2019). Phys. Rev. B, 100, 195144. Web of Science CrossRef Google Scholar
Kas, J. J., Rehr, J. J. & Curtis, J. B. (2016). Phys. Rev. B, 94, 035156. Web of Science CrossRef Google Scholar
Kas, J. J., Vila, F. D., Pemmaraju, C. D., Prange, M. P., Persson, K. & Rehr, J. J. (2021). arXiv: 2108.10981 [condmat.mtrlsci]. (Submitted to Comput. Mater. Sci.) Google Scholar
Kas, J. J., Vila, F. D., Rehr, J. J. & Chambers, S. A. (2015). Phys. Rev. B, 91, 121112. Web of Science CrossRef Google Scholar
Krappe, H. J. & Rossner, H. H. (2002). Phys. Rev. B, 66, 184303. Web of Science CrossRef Google Scholar
Lawler, H. M., Rehr, J. J., Vila, F., Dalosto, S. D., Shirley, E. L. & Levine, Z. H. (2008). Phys. Rev. B, 78, 205108. Web of Science CrossRef Google Scholar
Nemausat, R., Cabaret, D., Gervais, C., Brouder, C., Trcera, N., Bordage, A., Errea, I. & Mauri, F. (2015). Phys. Rev. B, 92, 144310. Web of Science CrossRef Google Scholar
Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. (2014). LMFIT: NonLinear LeastSquare Minimization and CurveFitting for Python, https://dx.doi.org/10.5281/zenodo.11813. Google Scholar
Niemann, A., Bossek, U., Haselhorst, G., Wieghardt, K. & Nuber, B. (1996). Inorg. Chem. 35, 906–915. CSD CrossRef PubMed CAS Web of Science Google Scholar
Oleynichenko, A., Zaitsevskii, A., Romanov, S., Skripnikov, L. V. & Titov, A. V. (2018). Chem. Phys. Lett. 695, 63–68. Web of Science CrossRef CAS Google Scholar
Ong, S. P., Richards, W. D., Jain, A., Hautier, G., Kocher, M., Cholia, S., Gunter, D., Chevrier, V. L., Persson, K. A. & Ceder, G. (2013). Comput. Mater. Sci. 68, 314–319. Web of Science CrossRef CAS Google Scholar
Poiarkova, A. V. & Rehr, J. J. (1999a). Phys. Rev. B, 59, 948–957. Web of Science CrossRef CAS Google Scholar
Poiarkova, A. V. & Rehr, J. J. (1999b). J. Synchrotron Rad. 6, 313–314. Web of Science CrossRef CAS IUCr Journals Google Scholar
Prange, M. P., Rehr, J. J., Rivas, G., Kas, J. J. & Lawson, J. W. (2009). Phys. Rev. B, 80, 155110. Web of Science CrossRef Google Scholar
Rehr, J. J. & Albers, R. C. (2000). Rev. Mod. Phys. 72, 621–654. Web of Science CrossRef CAS Google Scholar
Rehr, J. J., Kas, J. J., Prange, M. P., Sorini, A. P., Takimoto, Y. & Vila, F. (2009). C. R. Phys. 10, 548–559. Web of Science CrossRef CAS Google Scholar
Rehr, J. J., Kas, J. J., Vila, F. D., Prange, M. P. & Jorissen, K. (2010). Phys. Chem. Chem. Phys. 12, 5503–5513. Web of Science CrossRef CAS PubMed Google Scholar
Sayers, D. E., Stern, E. A. & Lytle, F. W. (1971). Phys. Rev. Lett. 27, 1204–1207. CrossRef CAS Web of Science Google Scholar
Smolentsev, G., Soldatov, A. V., Messinger, J., Merz, K., Weyhermüller, T., Bergmann, U., Pushkar, Y., Yano, J., Yachandra, V. K. & Glatzel, P. (2009). J. Am. Chem. Soc. 131, 13161–13167. Web of Science CrossRef PubMed CAS Google Scholar
Song, K., Schmid, H., Srot, V., Gilardi, E., Gregori, G., Du, K., Maier, J. & van Aken, P. A. (2014). APL Mater. 2, 032104. Google Scholar
Story, S. M., Vila, F. D., Kas, J. J., Raniga, K. B., Pemmaraju, C. D. & Rehr, J. J. (2019). J. Synchrotron Rad. 26, 1694–1704. Web of Science CrossRef CAS IUCr Journals Google Scholar
Takimoto, Y., Vila, F. D. & Rehr, J. J. (2007). J. Chem. Phys. 127, 154114. Web of Science CrossRef PubMed Google Scholar
Tan, T. S., Kas, J. J. & Rehr, J. J. (2018). Phys. Rev. B, 98, 115125. Web of Science CrossRef Google Scholar
Tan, T. S., Kas, J. J. & Rehr, J. J. (2021). Phys. Rev. B, 104, 035144. Web of Science CrossRef Google Scholar
Valiev, M., Bylaska, E., Govind, N., Kowalski, K., Straatsma, T., Van Dam, H. J. J., Wang, D., Nieplocha, J., Apra, E., Windus, T. & de Jong, W. (2010). Comput. Phys. Commun. 181, 1477–1489. Web of Science CrossRef CAS Google Scholar
Vila, F. D., Hayashi, S. T. & Rehr, J. J. (2018a). Front. Chem. 6, 296. Web of Science CrossRef PubMed Google Scholar
Vila, F. D., Lindahl, V. E. & Rehr, J. J. (2012). Phys. Rev. B, 85, 024303. Web of Science CrossRef Google Scholar
Vila, F. D., Rehr, J. J., Kas, J. J., Nuzzo, R. G. & Frenkel, A. I. (2008). Phys. Rev. B, 78, 121404. Web of Science CrossRef Google Scholar
Vila, F. D., Rehr, J. J., Nuzzo, R. G. & Frenkel, A. I. (2017). J. Phys. Chem. Lett. 8, 3284–3288. Web of Science CrossRef CAS PubMed Google Scholar
Vila, F. D., Rehr, J. J., Rossner, H. H. & Krappe, H. J. (2007). Phys. Rev. B, 76, 014301. Web of Science CrossRef Google Scholar
Vila, F. D., Spencer, J. W., Kas, J. J., Rehr, J. J. & Bridges, F. (2018b). Front. Chem. 6, 356. Web of Science CrossRef PubMed Google Scholar
Vila, F. D., Strubbe, D. A., Takimoto, Y., Andrade, X., Rubio, A., Louie, S. G. & Rehr, J. J. (2010). J. Chem. Phys. 133, 034111. Web of Science CrossRef PubMed Google Scholar
Vinson, J., Rehr, J. J., Kas, J. & Shirley, E. (2011). Phys. Rev. B, 83, 115106. Web of Science CrossRef Google Scholar
Woicik, J. C., Weiland, C., Jaye, C., Fischer, D. A., Rumaiz, A. K., Shirley, E. L., Kas, J. J. & Rehr, J. J. (2020a). Phys. Rev. B, 101, 245119. Web of Science CrossRef Google Scholar
Woicik, J. C., Weiland, C., Rumaiz, A. K., Brumbach, M. T., Ablett, J. M., Shirley, E. L., Kas, J. J. & Rehr, J. J. (2020b). Phys. Rev. B, 101, 245105. Web of Science CrossRef Google Scholar
Zhou, J., Kas, J., Sponza, L., Reshetnyak, I., Guzzo, M., Giorgetti, C., Gatti, M., Sottile, F., Rehr, J. & Reining, L. (2015). J. Chem. Phys. 143, 184109. Web of Science CrossRef PubMed Google Scholar
Zhou, Z., Kas, J., Rehr, J. & Ermler, W. (2017). At. Data Nucl. Data Tables, 114, 262–280. Web of Science CrossRef CAS Google Scholar
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