## Final Report Summary - MSNANO (A Multiple-Scattering Computing Platform For (Nano) Materials)

The principal objectives of the MSNano network were (a) to develop lasting collaborations constructed on the basis of existing bilateral projects, and (b) to construct a common computing platform for the characterization of materials with spectroscopy techniques. This platform, which will continue its activity after the completion of the project, is designed as an interrelated set of advanced tools for the interpretation of spectroscopy techniques based in particular on synchrotron radiation (SR) and X-ray free electron laser (XFEL) facilities. The common feature between all the codes is that they rely on the same framework of multiple scattering (MS) theory. Among recent breakthroughs in MS, the possibility to treat within the same framework bound and extended states, general potentials without approximation, and new schemes to take into account electron correlation while keeping the physical transparency and the modularity of the method, is at the centre of our work. One consequence is that with the same theory, we can treat electrons on a wide range of kinetic energies (from negative values to about 100 keV), which is not the case with other frameworks such as standard electronic structure methods. Thanks to the adaptability of the MS formalism, we propose the user (experimentalists as well as theoreticians) a diversity of algorithms that can deal with the various ranges of energy. Another advantage of the MS approach is that we do not require any periodicity within MS, which makes it the best possible approach for nanostructures, without the need to build up a periodic supercell. All the scientists involved in this network have developed codes of their own to model spectroscopy techniques within the MS framework. Some of them are more involved in the description of electron correlation while others try to extend the theory to describe more and more spectroscopy techniques.

This platform is available to the public through a dedicated website.

Work within MSNano is decomposed into seven work packages:

WP1: Common data format of MS and interface with electronic structure codes

WP2: Microscopies and resonant spectroscopy techniques within multiple scattering

WP3: Full potential real space approach to SR and XFEL spectroscopy techniques

WP4: Surface and embedded systems, angular dependence of polarized spectra

WP5: High energy PES, phonons and QED effects on core and valence spectra

WP6: Electron correlation in spectroscopy techniques

WP7: Impact spectroscopy techniques within multiple scattering

Here is a short description for each work package of what has been done and what had not time to be done.

WP1: The first objective of this work package was to set up the website of the project. This was done at the very beginning of the network. The next deliverables were also done (all program packages compatible with all operating systems - OS): the MsSpec, SPR-KKR, MXAN, FPMS, MSGF and MCMS codes are now compatible with all OS. This WP has produced one of the cornerstones of this network: the ES2MS computer package. This package is the result of deliverable D1.3 and allows our codes to use a self-consistent potential calculated by the VASP package. VASP is probably the most widely used computer program to compute the electronic structure of a material. ES2MS allows all our codes to use such an accurate potential instead of computing it ourselves in a probably not as accurate way. The interface with Gaussian code, very much used to compute the electronic structure of molecules is also under completion. Finally, work to refine the MSNano website was interrupted by the death of the head of the WP1, as after his death his group was disbanded.

WP2: The core of WP2 was to implement into the MsSpec computer package new spectroscopies, namely EELS and REXS, and STM and BEEM , and to prepare the work to extend all spectroscopies to very high kinetic energies. There have been some deviations from the original plan: a year ago or so, two research engineers showed their interest in making contributions to the development of MsSpec: one of them to develop a new graphical interface and the other to embed the numerous parts of the package into Python scripts, and allow MsSpec to be driven by the ASE environment which is becoming sort of a standard in atomistic simulations (ASE is already used as a front-end by many electronic structure codes). Due to this, the incorporation of new spectroscopies into the package has been frozen, as some rewriting of some parts, common to all spectroscopies is needed. Therefore, the REXS code is ready but not incorporated yet, the subroutines of the EELS code, like those for partitioning are also ready. However, they will not be incorporated into the MsSpec package before the work on the GUI and the integration into ASE is finished, as all spectroscopies share numerous subroutines. This integration and the new GUI were not forecasted when the MSNano work started. On the theoretical side, a new multiple scattering framework based on the impact parameter representation has been derived. Its implementation, which is not part of the MSNano work, will not alter the whole structure of the MsSpec package. The formulation of the STM and BEEM has been carried out, although the subroutines have not been written yet. The reason is that these two microscopies are much more demanding from the computing time point of view because of the huge number of atoms involved. Therefore, before implementing them, we decided that it would be more important to test first MsSpec on GPUs (Graphical Processor Units) to see what gain of computing time we could obtain from using them instead of CPUs. The first tests on GPUs are encouraging, but optimizing MsSpec for GPUs might be necessary, which means rewriting some parts. This is why it seemed to us better to perform these tests prior to the writing of the subroutines as the optimization for GPUs might induce to write them in a completely different way.

WP3: This work package consists in developments in the code MXAN that has been developed essentially by the INFN partner with some external help. MXAN is basically a multiple scattering code that fits an X-ray absorption calculation to an experimental spectrum. So far, it was based on the so-called muffin-tin approximation where the potential of the cluster describing the material is composed of a superposition of spherical atomic potentials with a constant interstitial potential used as the energy reference. There are however many cases now where this approximation is not sufficient. A new version based on a full potential description has been developed and tested. Then, a new subroutine to incorporate a treatment of thermal disorder into the calculation of the t-matrices has been implemeted and tested. The last deliverable has been abandoned because it has become obsolete due to the availability of the ES2MS package. Indeed, using this interface package in order to use a VASP potential in MXAN is much better that trying to compute the selfconsistent potential into MXAN.

WP4: This work package invoved developments within the Munich SPR-KKR program package. An important extension of the SPR-KKR program package was the implementation of the full potential (FP) mode. This work could be completed for most program modules. Further tests in particular for embedded clusters are still necessary and are done recently together with the FZUAVCR partner. The SPR-KKR program package uses the layer KKR formalism already in the context of angle-resolved photo emission. The extension of the layer KKR program module to deal also with ground state properties had to be postponed because of lack of manpower. Because of manpower problems the use of the U-matrix formalism to deal with static lattice relaxations has also been postponed. On the other hand, it could be firmly established as an indispensable tool to deal with thermal lattice displacements within the alloy analogy model based on the CPA. A similar scheme was suggested by the colleagues at INFN and mutual exchange of experience was most fruitful. By now the scheme of the LMU group is successfully used in the context of photo emission

and X-ray absorption as well as electric transport and Gilbert damping. The spectroscopy module of the SPR-KKR program package was extended in various directions. The inclusion of thermal lattice vibrations by means of the alloy analogy model was already mentioned. This approach was exploited recently to account also for thermal spin fluctuations. This scheme was first tested quantitatively for electric transport and then transferred to deal with photo emission and X-ray absorption as well.

WP5: This work package was centered on the necessity to provide a sound theoretical basis to X-ray Absorption and photoemission spectroscopies by using the Keldysh Green's function approach. This has been done within the framework of the relativistic and non relativistic Quantum Electrodynamics (QED) theory. More precisely, work in WP5 has focused on a precise description of a certain number of effects that are not described properly within the standard theory of multiple scattering, such as radiation field screening, core-hole moving, recoil effects in the high kinetic energy range, phonon effects on X-ray Absorption and photoemission spectra, and plasmon loss peaks. An accurate treatment of phonon and plasmons effects based an a quasiboson approach has been derived. A relativistic XMCD code based on relativistic quantum electrodynamics (QED) theory has been developed. This approach can handle many-body effects in XMCD analyses using real space full multiple scattering theory. This code allows us to calculate angular dependence ; in particular we can calculate the XMCD spectra where the incident X-ray propagation vector K is perpendicular to the magnetization direction B ( transverse XMCD). This type of XMCD can only be observed in the case of low symmetry atomic arrangements around an X-ray absorbing atom. If it has Cn axis around B, we cannot observe the transverse XMCD. A spin-polarized XPD code based on the same theoretical framework has also been developed. The 4-dimensional Dirac Green’s function is expanded in terms of full non-relativistic two-dimensional Green’s functions using Gestzesy expansion, which enables us to use well-defined Debye-Waller factors and optical potentials developed within the framework of nonrelativistic theory. This code allows us to calculate spherical K, L1 and also nonspherical core L23 excitations. We can calculate spin-polarized XPD spectra caused by Fano effects, the Daimon effects caused by circularly polarized X-rays and also XPD from magnetic systems influenced by spin dependent exchange scatterings.

WP6: This work package was devoted to the various implementations of correlation within the different computer packages developed by the MSNano network. The last year of the project was mainly devoted to last task (6.3) and to dissemination. The multichannel density matrix approach was formulated previously in collaboration between INFN, Chiba, CNRS and FZUAVCR nodes [C. R. Natoli, P. Krüger, K. Hatada, K. Hayakawa, D. Sebilleau and O. Sipr, J. Phys.: Condens. Matter 24, 365501 (2012)]. In the reporting period, implementation of this scheme into the MSGFCC code of the SFedU node has been continued during secondments between the INFN and SFedU nodes. Considerable progress has been achieved including the calculation of Coulomb integrals for arbitrary spin-orbitals. Details are given in the separate report on deliverable D6.3. However, complete implementation of the density matrix approach into the MSGFCC code turned out to be a huge effort and is not finished yet. Therefore we have, in parallel, followed a much simpler way to tackle the same physical problem, that is correlation effects in X-ray absorption beyond the particle-hole picture. Namely we have extended crystal field multiplet calculations by computing all parameter from a first principles multiple scattering code. This approach gave good results for iron phthalocyanine.

WP7: The objectives of WP7 were to develop a MS description of (e,2e/3e) spectroscopies and to incorporate the calculation of their cross-section within the MsSpec package. These spectroscopies are impact spectroscopies involving one incoming electron and two or three outgoing electrons. They are very popular in atomic physics, but no sound extension to condensed matter physics had been done so far to our knowledge. We have developed a MS theory of (e,2e/3e). We also have designed a benchmark for the atomic case. The subroutines necessary to implement this description into the computer package MsSpec are ready. They have not been incorporated yet, as detailed in WP2, because of the development of a new GUI for MsSpec and its integration within the ASE environment, we have frozen any new extension until the new structure of the package is ready. This new GUI and integration into ASE were not into the development plans of MsSpec when the MSNano network started, but it came onto the agenda because two research engineers proposed to join the development team. These two new tools (GUI and ASE integration) will make MsSpec much easier to use and are therefore very important. Of course, an (e,2e) code could be assembled very quickly if necessary, but to the risk that its structure would need to be rewritten once the GUI and ASE integration are completed. An important by-product of this WP which was not anticipated when starting MSNano, is that when deriving the formalism for (e,2e), we have realized that (e,2e) and EELS (WP2) are strongly connected, the latter being in fact the angular average of the former when summing over the second electron. This important result will provide us with a tool to test the two codes in parallel and assess easily their correctness.

This platform is available to the public through a dedicated website.

Work within MSNano is decomposed into seven work packages:

WP1: Common data format of MS and interface with electronic structure codes

WP2: Microscopies and resonant spectroscopy techniques within multiple scattering

WP3: Full potential real space approach to SR and XFEL spectroscopy techniques

WP4: Surface and embedded systems, angular dependence of polarized spectra

WP5: High energy PES, phonons and QED effects on core and valence spectra

WP6: Electron correlation in spectroscopy techniques

WP7: Impact spectroscopy techniques within multiple scattering

Here is a short description for each work package of what has been done and what had not time to be done.

WP1: The first objective of this work package was to set up the website of the project. This was done at the very beginning of the network. The next deliverables were also done (all program packages compatible with all operating systems - OS): the MsSpec, SPR-KKR, MXAN, FPMS, MSGF and MCMS codes are now compatible with all OS. This WP has produced one of the cornerstones of this network: the ES2MS computer package. This package is the result of deliverable D1.3 and allows our codes to use a self-consistent potential calculated by the VASP package. VASP is probably the most widely used computer program to compute the electronic structure of a material. ES2MS allows all our codes to use such an accurate potential instead of computing it ourselves in a probably not as accurate way. The interface with Gaussian code, very much used to compute the electronic structure of molecules is also under completion. Finally, work to refine the MSNano website was interrupted by the death of the head of the WP1, as after his death his group was disbanded.

WP2: The core of WP2 was to implement into the MsSpec computer package new spectroscopies, namely EELS and REXS, and STM and BEEM , and to prepare the work to extend all spectroscopies to very high kinetic energies. There have been some deviations from the original plan: a year ago or so, two research engineers showed their interest in making contributions to the development of MsSpec: one of them to develop a new graphical interface and the other to embed the numerous parts of the package into Python scripts, and allow MsSpec to be driven by the ASE environment which is becoming sort of a standard in atomistic simulations (ASE is already used as a front-end by many electronic structure codes). Due to this, the incorporation of new spectroscopies into the package has been frozen, as some rewriting of some parts, common to all spectroscopies is needed. Therefore, the REXS code is ready but not incorporated yet, the subroutines of the EELS code, like those for partitioning are also ready. However, they will not be incorporated into the MsSpec package before the work on the GUI and the integration into ASE is finished, as all spectroscopies share numerous subroutines. This integration and the new GUI were not forecasted when the MSNano work started. On the theoretical side, a new multiple scattering framework based on the impact parameter representation has been derived. Its implementation, which is not part of the MSNano work, will not alter the whole structure of the MsSpec package. The formulation of the STM and BEEM has been carried out, although the subroutines have not been written yet. The reason is that these two microscopies are much more demanding from the computing time point of view because of the huge number of atoms involved. Therefore, before implementing them, we decided that it would be more important to test first MsSpec on GPUs (Graphical Processor Units) to see what gain of computing time we could obtain from using them instead of CPUs. The first tests on GPUs are encouraging, but optimizing MsSpec for GPUs might be necessary, which means rewriting some parts. This is why it seemed to us better to perform these tests prior to the writing of the subroutines as the optimization for GPUs might induce to write them in a completely different way.

WP3: This work package consists in developments in the code MXAN that has been developed essentially by the INFN partner with some external help. MXAN is basically a multiple scattering code that fits an X-ray absorption calculation to an experimental spectrum. So far, it was based on the so-called muffin-tin approximation where the potential of the cluster describing the material is composed of a superposition of spherical atomic potentials with a constant interstitial potential used as the energy reference. There are however many cases now where this approximation is not sufficient. A new version based on a full potential description has been developed and tested. Then, a new subroutine to incorporate a treatment of thermal disorder into the calculation of the t-matrices has been implemeted and tested. The last deliverable has been abandoned because it has become obsolete due to the availability of the ES2MS package. Indeed, using this interface package in order to use a VASP potential in MXAN is much better that trying to compute the selfconsistent potential into MXAN.

WP4: This work package invoved developments within the Munich SPR-KKR program package. An important extension of the SPR-KKR program package was the implementation of the full potential (FP) mode. This work could be completed for most program modules. Further tests in particular for embedded clusters are still necessary and are done recently together with the FZUAVCR partner. The SPR-KKR program package uses the layer KKR formalism already in the context of angle-resolved photo emission. The extension of the layer KKR program module to deal also with ground state properties had to be postponed because of lack of manpower. Because of manpower problems the use of the U-matrix formalism to deal with static lattice relaxations has also been postponed. On the other hand, it could be firmly established as an indispensable tool to deal with thermal lattice displacements within the alloy analogy model based on the CPA. A similar scheme was suggested by the colleagues at INFN and mutual exchange of experience was most fruitful. By now the scheme of the LMU group is successfully used in the context of photo emission

and X-ray absorption as well as electric transport and Gilbert damping. The spectroscopy module of the SPR-KKR program package was extended in various directions. The inclusion of thermal lattice vibrations by means of the alloy analogy model was already mentioned. This approach was exploited recently to account also for thermal spin fluctuations. This scheme was first tested quantitatively for electric transport and then transferred to deal with photo emission and X-ray absorption as well.

WP5: This work package was centered on the necessity to provide a sound theoretical basis to X-ray Absorption and photoemission spectroscopies by using the Keldysh Green's function approach. This has been done within the framework of the relativistic and non relativistic Quantum Electrodynamics (QED) theory. More precisely, work in WP5 has focused on a precise description of a certain number of effects that are not described properly within the standard theory of multiple scattering, such as radiation field screening, core-hole moving, recoil effects in the high kinetic energy range, phonon effects on X-ray Absorption and photoemission spectra, and plasmon loss peaks. An accurate treatment of phonon and plasmons effects based an a quasiboson approach has been derived. A relativistic XMCD code based on relativistic quantum electrodynamics (QED) theory has been developed. This approach can handle many-body effects in XMCD analyses using real space full multiple scattering theory. This code allows us to calculate angular dependence ; in particular we can calculate the XMCD spectra where the incident X-ray propagation vector K is perpendicular to the magnetization direction B ( transverse XMCD). This type of XMCD can only be observed in the case of low symmetry atomic arrangements around an X-ray absorbing atom. If it has Cn axis around B, we cannot observe the transverse XMCD. A spin-polarized XPD code based on the same theoretical framework has also been developed. The 4-dimensional Dirac Green’s function is expanded in terms of full non-relativistic two-dimensional Green’s functions using Gestzesy expansion, which enables us to use well-defined Debye-Waller factors and optical potentials developed within the framework of nonrelativistic theory. This code allows us to calculate spherical K, L1 and also nonspherical core L23 excitations. We can calculate spin-polarized XPD spectra caused by Fano effects, the Daimon effects caused by circularly polarized X-rays and also XPD from magnetic systems influenced by spin dependent exchange scatterings.

WP6: This work package was devoted to the various implementations of correlation within the different computer packages developed by the MSNano network. The last year of the project was mainly devoted to last task (6.3) and to dissemination. The multichannel density matrix approach was formulated previously in collaboration between INFN, Chiba, CNRS and FZUAVCR nodes [C. R. Natoli, P. Krüger, K. Hatada, K. Hayakawa, D. Sebilleau and O. Sipr, J. Phys.: Condens. Matter 24, 365501 (2012)]. In the reporting period, implementation of this scheme into the MSGFCC code of the SFedU node has been continued during secondments between the INFN and SFedU nodes. Considerable progress has been achieved including the calculation of Coulomb integrals for arbitrary spin-orbitals. Details are given in the separate report on deliverable D6.3. However, complete implementation of the density matrix approach into the MSGFCC code turned out to be a huge effort and is not finished yet. Therefore we have, in parallel, followed a much simpler way to tackle the same physical problem, that is correlation effects in X-ray absorption beyond the particle-hole picture. Namely we have extended crystal field multiplet calculations by computing all parameter from a first principles multiple scattering code. This approach gave good results for iron phthalocyanine.

WP7: The objectives of WP7 were to develop a MS description of (e,2e/3e) spectroscopies and to incorporate the calculation of their cross-section within the MsSpec package. These spectroscopies are impact spectroscopies involving one incoming electron and two or three outgoing electrons. They are very popular in atomic physics, but no sound extension to condensed matter physics had been done so far to our knowledge. We have developed a MS theory of (e,2e/3e). We also have designed a benchmark for the atomic case. The subroutines necessary to implement this description into the computer package MsSpec are ready. They have not been incorporated yet, as detailed in WP2, because of the development of a new GUI for MsSpec and its integration within the ASE environment, we have frozen any new extension until the new structure of the package is ready. This new GUI and integration into ASE were not into the development plans of MsSpec when the MSNano network started, but it came onto the agenda because two research engineers proposed to join the development team. These two new tools (GUI and ASE integration) will make MsSpec much easier to use and are therefore very important. Of course, an (e,2e) code could be assembled very quickly if necessary, but to the risk that its structure would need to be rewritten once the GUI and ASE integration are completed. An important by-product of this WP which was not anticipated when starting MSNano, is that when deriving the formalism for (e,2e), we have realized that (e,2e) and EELS (WP2) are strongly connected, the latter being in fact the angular average of the former when summing over the second electron. This important result will provide us with a tool to test the two codes in parallel and assess easily their correctness.