The first use of density functional theory (DFT) for the calculation of X-ray absorption spectra (similar to EELS) was done by Müller et al. using a linearized augmented plane waves method in the late 70s .
Even though the electronic structure information is available in the low-loss EEL spectrum (see page4360), the interpretation is difficult because there is no direct relationship between the EELS and the density of states (DOS). Therefore, in contrast to ELNES, low-loss EELS has been much less widely used to measure and understand electronic structure. Recently, low-loss EEL spectra have been calculated using density-functional theory (DFT) based on WIEN2k codes. [2 - 3]
Band structure (BS) methods used in EELS modeling are applied in reciprocal space based on density functional theory (DFT) [4 - 5]. BS methods were originally developed to derive the electron density. The advantage of BS methods is that based on ELNES and low loss spectra, many physical properties can be derived from the same calculation. Those properties can be band structure diagrams, density of states, elastic constants, optical properties, electron densities, etc. The drawback of BS methods is that they yield only ground states properties, and thus the calculation of excited states properties is not guaranteed to work. However, the calculation of ELNES and of low loss spectra with DFT works very well .
Among the various codes available for DFT calculations, two codes are commercially available and can be used to model ELNES: i) Pseudopotential code CASTEP, which was developed in University of Cambridge [7 - 8] (www.accelrys.com/cerius2/castep.html) and ii) WIEN2k which was developed at the Vienna University of Technology [9 - 10] (www.wien2k.at.).
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 Pickard, C.J., Payne, M.C., 1997. Ab initio EELS: beyond the fingerprint. In: Electron Microscopy and Analysis Group Conference EMAG97. IOP Publishing Ltd, pp. 179–182.
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 Hébert-Souche, C., Louf, P.-H., Blaha, P., Nelhiebel, M., Luitz, J., Schattschneider, P., Schwarz, K., Jouffrey, B., 2000. The orientation dependent simulation of ELNES. Ultramicroscopy 83 (1–2), 9–16.