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

(registrations on the CECAM web site)

Organisers

· Razvan Caracas (CNRS-ENS Lyon)
· Philippe Ghosez (University of Liege)
· Xavier Gonze (Universite Catholique de Louvain)

Supports

CECAM

Description

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 lecture 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

Plan of lectures

Day 1:

Morning
- 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
Afternoon
- 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:

Morning
- 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 infinite electric fields
Afternoon
- 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:

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

Day 4:

Morning
- Lecture 7 (all) : Elastic and piezoelectric responses
- Lecture 8 (all) : Static non-linear optical responses (Raman susceptibilities, non-linear
optical susceptibilities, electro-optic tensor)
Afternoon
- Hands-on 4 (all) : On-line lessons on the elastic properties and on the static non-linear
properties

Day 5:

Morning
- Lecture 9 (all) : Electron-phonon coupling
- Lecture 10 (all) : Linear response to magnetic fields
Afternoon
- Hands-on 5 (all) : On-line lessons on the electron-phonon interaction

References

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, in press.
Linear and non-linear responses :
[4] S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from densityfunctional
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).
Background:
[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)
CECAM - Centre Européen de Calcul Atomique et Moléculaire
Station 13, Bat. PPH, 1015 Lausanne, Switzerland