Linear and non-linear responses of solids with the ABINIT software : phonons, electric fields, and other perturbations

April 26, 2010 to April 30, 2010
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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  • Razvan Caracas (Ecole Normale Supérieure-Lyon, France)
  • Philippe Ghosez (University of Liege, Belgium)
  • Xavier Gonze (Catholic University of Louvain, Belgium)



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COMMUNICATION : The deadline for application is passed. The accepted applicants will be contacted by e-mail by March 5.


This ABINIT tutorial will present basic and advanced features of the ABINIT package, mainly to the community of young European students and postdocs interested in the fields of vibrational spectroscopies, thermodynamics, thermal properties, non-linear dynamical properties, etc. Applications will concern a wide variety of materials such as semiconductors, ferroelectrics and piezoelectrics, insulators, crystalline and disordered materials, nanostructures etc.

It will typically include two types of activities : (1) lectures on theory, algorithms and implementations in the morning sessions and (2) hands-on exercises in the afternoon sessions. The lectures and exercises will be synchronized in such a way as to have the practical applications of the morning classes investigated in detail with the developers support in the afternoons.

To make the tutorial attractive and highly beneficial to beginners and advanced students, we will deal with 2 groups in parallel during the first two days, giving a lectures on the PAW implementation to advanced students during the time beginners learn the basic of DFT and its implementation in ABINIT. Then, from the middle of the second day, all students will follow the same lecture as detailled in the detailed plan below.

The program will cover in five days the following topics:

- density functional theory (DFT) and density functional perturbation theory (DFTP) in both the standard planewave-pseudopotential and projector-augmented wavefunctions (PAW) formulations,
- phonon band structures and thermodynamical properties
- response functions and couplings with electric field, magnetic field, and strain
- response in finite electric field
- Raman and electro-optic responses
- electron-phonon coupling

For applications submitted before February 19, the candidate will be informed of the decision of acceptance/non-acceptance by March 5 (not by March 1st, like initially planned, sorry for this).


Plan of lectures


Day 1: 


- Lecture 1a (beginners) : Introduction to DFT, plane-waves, iterative methods

- Lecture 1b (advanced) : Introduction to the PAW approach

- Lecture 2a (beginners) : Introduction to DFT, plane-waves, iterative methods

- Lecture 2b (advanced) : Introduction to the PAW approach



- Hands-on 1a (beginners) : On-line basic lessons 1-3 (on H2 molecule and Silicon) 

- Hands-on 1b (advanced) : On-line lesson on PAW method 


Day 2: 


- Lecture 3a (beginners) : Practical DFT implementation within ABINIT

- Lecture 3b (advanced) : Generation of PAW potentials and basis

- Lecture 4 (all) : Polarization, Berry phase and calculations for finite electric fields



- Hands-on 2a (beginners) :  On-line basic lesson 4 (metals) + on-line lesson on polarization and finite electric fields

- Hands-on 2b (advanced) : On-line lesson on PAW atomic data files generation + on-line lesson on polarization and finite electric fields.


Day 3: 


- Lecture 5 (all) : Basics of density functional theory and linear responses to electric fields and atomic displacements.

- Lecture 6 (all) : Phonon dispersion curves, interatomic force constants and thermodynamic properties



- Hands-on 3 (all) : On-line lessons on response-function 1 and 2


Day 4: 


- Lecture 7 (all) : Elastic and piezoelectric responses

- Lecture 8 (all) : Static non-linear optical responses (Raman susceptibilities, non-linear optical susceptibilities, electro-optic tensor)



- Hands-on 4 (all) : On-line lessons on the elastic properties and on the static non-linear properties 


Day 5: 


- Lecture 9 (all) : Electron-phonon coupling 

- Lecture 10 (all) : Magnetic fields



- Hands-on 5 (all) : On-line lessons on the electron-phonon interaction


The ABINIT package

[1] X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, Ph. Ghosez, J.-Y. Raty, D.C. Allan, First-principles computation of material properties : the ABINIT software project. Computational Materials Science 25, 478-492 (2002)

[2] X. Gonze, G.-M. Rignanese, M. Verstraete, J.-M. Beuken, Y. Pouillon, R. Caracas, F. Jollet, M. Torrent, G. Zerah, M. Mikami, Ph. Ghosez, M. Veithen, V. Olevano, L. Reining, R. Godby, G. Onida, D. Hamann, D. C. Allan. A brief introduction to the ABINIT software package, Zeit. Kristallogr. 220, 558-562 (2005)

[3] X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Cote, T. Deutsch, L. Genovese, Ph. Ghosez, M. Giantomassi, S. Goedecker, D. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. Oliveira, T. Rangel, Y. Pouillon, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. Verstraete, G. Zerah, J. Zwanziger, ABINIT : first-principles approach to material and nanosystem properties. Computer Physics Communications 180, 2582-2615 (2009).

Linear and non-linear responses :

[4] S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).

[5] X. Gonze, First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm, Phys. Rev. B 55, 10337 (1997).

[6] X. Gonze and C. Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997).

[7] D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, Metric tensor formulation of strain in density-functional perturbation theory, Phys. Rev. B 71, 035117 (2005)

[8] M. Veithen, X. Gonze and Ph. Ghosez, Non-linear optical susceptibilities, Raman efficiencies and electrooptic tensors from first-principles density functional perturbation theory, Phys. Rev. B 71, 125107 (2005).


[9] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias and J.D. Joannopoulos, "Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients", Rev. Mod. Phys. 64, 1045 (1992)

[10] R. M. Martin, Electronic Structure. Basic Theory and Practical Methods (Cambridge, University Press, 2004) (see Ch. 1 to 13, and appendices L and M)