# Workshops

## State of the art, developments and perspectives of electronic structure calculations in the frame of the Projector Augmented-Wave (PAW) method.

### Organisers

- François Jollet
*(CEA-DIF, Bruyères le Châtel, France)* - Natalie Holzwarth
*(Wake Forest University, USA)* - Peter E. Bloechl
*(Clausthal University of Technology, Germany)* - Jens Jørgen Mortensen
*(Technical University of Denmark, Denmark)*

### Description

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Since the pioneer work of Hohenberg and Kohn, the Density Functional Theory (DFT) has proved to be an efficient framework to calculate the electronic properties of many materials [1]. Its practical use is made possible thanks to the Local Density Approximation (LDA) in which the exchange and correlation energy is calculated in each point as the exchange and correlation energy of an homogeneous electron gas. More sophisticated approximations, like the Generalized Gradient Approximation (GGA) have been developed to make DFT accurate enough to be used for example in chemistry. Two important approaches for computing thermodynamic properties are the augmented wave methods and the planewave pseudopotential methods:

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the first one is based on a partition of space in two regions: a spherical one around the atomic positions, in which a local basis is chosen to describe the great variation of wavefunctions in the neighbouring of nuclei (a spherical harmonics basis for instance), and an interstitial region in which another basis is chosen (plane waves for instance) and connected to the first local basis. These types of approaches are called all electron methods because they take explicitly into account all the electron of the system [2] ( Full Potential Linear Muffin Tin Orbitals - FP-LMTO- method, Augmented Spherical Waves ASW method, Full potential Linear Augmented Plane Waves FLAPW method). These methods are very accurate but they have the drawback that the local basis depends by definition on the atomic positions and are therefore not well suited to dynamical calculations.

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The second one uses a plane wave basis to develop the electronic wavefunctions [3]. As such a basis is not well suited to wavefunctions that vary too much in space, like core electrons wavefunctions, only valence electrons are taken into account. The interactions between valence electrons on one part, and core electron + nucleus on the other part, are then taken into account through an atomic pseudopotential. The plane wave pseudopotential approach is very powerful for which concerns dynamical calculations, but only valence electron are taken into account and only pseudo-wavefunctions (and therefore, pseudo energies) can be calculated.

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In 1994, Peter Blöchl introduced the Projector Augmented-Wave (PAW) method [4], that is an extension of augmented wave methods and the pseudopotential approach, which combines their traditions into a unified electronic structure method. Indeed, the PAW method is an all electron method, in the sense that energies, electronic densities and wavefunctions that are accessed are all electron quantities, although the electronic minimisation is done thanks to auxiliary functions that are developed on a plane wave basis. The PAW method has many advantages:

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<LI>all electron quantities can be accessed.</LI>

<LI>the auxiliary plane wave basis can be made as soft as ultrasoft plane wave basis.</LI>

<LI>the accuracy of the calculation can be easily controlled and compared to all electron calculations.</LI>

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This explains why the PAW method tends to become the reference method for electronic structure calculations. Indeed, several new implementations have been developed in the literature [5-8]. Moreover, the application field of the PAW method has been extended to the calculation of NMR chemical shifts [9], electric-field gradient calculations [10], LDA+U calculations [11], and GW calculations [12]. Other ones are under development, like the linear response functions. All these developments have led to a great number of publications in the solid state physics field as well as in the physical chemistry one.

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