=================================================================================
The first use of density functional theory (DFT) for the calculation of Xray absorption spectra (similar to EELS) was done by Müller et al. using a linearized augmented plane waves method in the late 70s [1].
Even though the electronic structure information is available in the lowloss 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, lowloss EELS has been much less widely used to measure and understand electronic structure. Recently, lowloss EEL spectra have been calculated using densityfunctional 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 [6].
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.).
[1] Müller, J.E., Jepsen, O., 1978. Systematic structure in the Kedge photoabsorption
spectra of the 4d transition metals: theory. Phys. Rev. Lett. 40 (11), 720 
722.
[2] V. J. Keast, Ab initio calculations of plasmons and interband transitions in the lowloss electron energyloss spectrum, Journal of Electron Spectroscopy and Related Phenomena 143 (2005) 97–104.
[3] K. Schwarz, P. Blaha, G.K.H. Madsen, Comput. Phys. Commun. 147 (2002) 71.
[4] Hohenberg, P., Kohn, W., 1964. Inhomogeneous electron gas. Phys. Rev. 136 (3B), B864–B871.
[5] Kohn, W., Sham, L.J., 1965. Selfconsistent equations including exchange and correlation effects. Phys. Rev. 140 (4A), A1133–A1138.
[6] Rez, P., Bruley, J., Brohan, P., Payne, M., Garvie, L.A.J., 1995. Review of
methods for calculating near edge structure. Ultramicroscopy 59, 159–167.
[7] Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A., Joannopoulos, J.D., 1992. Iterative minimization techniques for ab initio totalenergy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64 (4), 1045  1097.
[8] 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.
[9] Blaha, P., Schwarz, K., Sorantin, P., 1990. Fullpotential, linearized augmented plane wave programs for crystalline systems. Comput. Phys. Commun. 59, 399–415.
[10] HébertSouche, 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.
