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## Density Functional Theory and Transmission Electron Microscopy

#### CECAM-HQ-EPFL, Lausanne, Switzerland

#### Organisers

The Density Functional Theory and Transmission Electron Microscopy workshop aims at bringing together and strengthening links between two communities, computational materials science based on density-functional theory (DFT) and experimental nanoscience investigated by transmission electron microscopy (TEM). Recent advances in parallel computing on an all-electron basis on the one side and aberration-corrected TEM have made those approaches nowadays’ key techniques to assess novel material properties with high spatial and spectroscopic resolution. DFT and TEM yield complementary evidence on nanoscale structures, though, as they highlight different aspects of the investigated material: Experiment elucidates structural and electronic properties of realistic materials and theory provides an understanding of the basic interactions, which drive structural, electronic, magnetic and optical properties based on models. DFT and TEM can be combined in different manner. Indirectly, e.g. by comparing the result of High resolution TEM for the analysis of interface with calculations predicting the most stable configuration. Or directly, by comparing experimental and computed EELS spectra, or by using DFT to calculate electron densities and therefore predicting more accurately convergent beam diffraction patterns.Considering the numerical and technical achievements of the recent years in DFT and TEM such direct and quantitative comparison of modeled and measured data on realistic materials has come into reach. Yet, there is a lot more to gain for our understanding of fundamental physical and materials-related properties by carrying out DFT and TEM investigations not in parallel, but together – both in application and method development.

The workshop bases on an initiative that started five years ago at the DFTEM 2006 meeting in Vienna. There, the state of the art in both fields was reviewed - the broad variety of measurement techniques in the electron microscope and the different flavors of density-functional theory were presented by experts in the respective fields. Links between the two techniques emerged from collaborations between scientists from the two communities, mostly based on the material under study. Such collaborative effort has been continued and prominent results from existing or newly established joint research will be presented at the workshop. The goal here is to head for a quantitative basis of such co-operations. Furthermore, first attempts on the joint method development have matured since and progress in the field will be discussed along with the need for further activities. This extension of DFT +TEM approaches beyond the qualitative comparison of theoretical and experimental results is still the big challenge which drives the research on the topic. Finally, new developments in both fields shall be reviewed as a basis for triggering an interdisciplinary method development.

"Density Functional Theory and Transmission Electron Microscopy" will provide a platform for people in the respective fields to establish and strengthen DFT+TEM collaborations. It will give interdisciplinary incentives on all levels of scientific endeavor, including basic tutorial-type lectures for young investigators who just enter the field, advanced shorter presentations on more specific topics and ample space for the discussions necessary for two communities to learn really understanding each other.

Transmission Electron Microscopy (TEM) and Density Functional Theory (DFT) both allow for a detailed study of the structural and electronic properties of materials on a local scale. Cutting edge applications of both approaches address advanced materials with complex nanoscopic couplings of structural, electronic, magnetic and optical degrees of freedom, whose versatility promises both a deeper understanding of physical interactions on the nanoscale [1] and a broad range of applications. Recent examples for the up to now few joint DFT and TEM efforts on such materials cover polarization domains in multiferroic oxides, quantitatively investigated by DFT and by high-resolution TEM and TEM-holography [2, 3], magnetization dynamics in nanostructures covered by a DFT extension to dynamic spin systems [4] and imaged by Lorentz microscopy [5] or magnetic dichroism recently implemented in DFT codes [6, 7] and observed by advanced chiral TEM measurements [6]. Other examples evidence recent and rapid developments of either DFT or TEM. Modern theories of electrical polarization and orbital magnetization [8], for instance, have yet to see their quantitative counterparts in TEM science, whereas in-situ TEM transport observations of metals in carbon nanotubes [9] or carbon chain engineering [10] require further advances in DFT-based molecular dynamics. The workshop aims at bringing these initiatives together and head for a joint method development.

DFT: By design, DFT yields details of the ground-state electron density on the level of chemical bonding [11]. In an all-electron formulation, implemented for instance in the full-potential linearized augmented plane-wave (FLAPW) framework, DFT also yields the total interaction energy of electrons and nuclei in the system [12]. That, in turn, allows calculating forces on the nuclei, which can be employed to optimize geometries with atomic resolution and to calculate the vibrational spectra of molecules and phonons in solids by a perturbative formulation [13]. In a single-particle approximation electron binding energies and the symmetries of the corresponding states result as eigenvalues and eigenvectors of a set of coupled differential equations [14]. Though, in principle, obtained from a purely mathematical procedure such eigenenergies have successfully been correlated with measured electron spectroscopic data on the electronic structure by Janak in analogy with Koopmans’ theorem [15, 16]. Extensions by linear response theory also allow investigating the interaction with external electric fields [17] and to thus determine dielectric properties and piezoelectric constants of modern materials [18, 19]. Further investigations focus on the calculation of accurate core excitation energies, especially with a focus on molecules [20].

TEM: It is known as an evidence since the beginning of electron microscopy that many of the observations that can be made are related to either the crystal structure (nature and position of the nucleus in the lattice, e.g. high resolution TEM, High resolution STEM), to the electronic structure of the material like the fine structure of the ionization edges or the low losses (Electron energy loss spectroscopy, EELS), or both (intensities in diffraction and convergent beam diffraction). Nowadays state of the art transmission electron microscopes can provide atomic positions with picometer precision [21]; a result which is in line with what is obtained from DFT. EELS combined with TEM yields information on the electronic excitations (on a local scale) within a material with an energy resolution of 0.1 eV [22]. The low loss part of the spectrum gives information on the plasmon energy and the optical bandgap (e.g. [23]), whereas the core loss spectrum corresponds to the excitation of core electrons (e.g. [24]). Powerful software (EELSMODEL) has been developed to quantify EELS spectra using a model-based approach which leads to a dramatic increase in accuracy and precision [25].

Although DFT is not entirely appropriate to calculate the electronic excitations it is often used as a first approximation and a starting point for more elaborate calculations e.g. those based on many-body techniques like the GW-approach for the calculation of the bandgap and the calculation of the energy loss spectra through a solution of the Bethe-Salpeter equations [26].

DFTEM: Firsts attempt to interpret spectroscopic data with the support of DFT date back into the 70ies for perfect bulk crystals such as the 4d metals [27]. Later on more complicated structures like special grain boundaries with small cells could be analysed structurally as well as electronically by DFT and TEM [28]. Other pioneering combined studies involved DFT and TEM diffraction data [29] or EELS [30]. In the past 10 years, the increasing computing power and code developments have made the calculation of relatively complicated structures possible. An additional step forward to the use of DFT by a non-specialized team is the fact that many DFT code packages nowadays provide a user-friendly interface which has also contributed to their use in the TEM community [31]. Nevertheless, many of the current relevant problems in TEM relate to very complicated structures, requiring e.g. the refinement of cell parameters and atom positions in huge cells including interfaces or even complete nanostructures like filled nanotubes [32]. Beyond extremely powerful computers such applications place a strong need for further improvements of the DFT codes.

## References

**Belgium**

Dirk Lamoen (University of Antwerp) - Organiser

**Germany**

Sibylle Gemming (Helmholtz-Zentrum Dresden-Rossendorf) - Organiser & speaker

Thomas Gemming (IFW Dresden, Leibniz Institute for Solid State and Materials Research Dresden) - Organiser & speaker

**Switzerland**

Cecile Hebert (Swiss Federal Institute of Technology Lausanne (EPFL)) - Organiser & speaker

Robin Schaeublin (Swiss Federal Institute of Technology Lausanne (EPFL)) - Organiser