This document gives an overview of the features implemented in the ABINIT package, grouped in different topics, for the beginner as well as more experienced user.

It might answer the question "How to ... with ABINIT ?", to some extent.

It also gives a synthetic view on the needed settings.

- 1. Foreword
- 2. ABINIT specifications for static DFT calculations
- 2.1. Settings for atoms : cell, atoms, atomic positions, and symmetries
- 2.2. Physical settings for electrons : XC functionals, atomic/pseudo potentials, metal/insulator, spin, Coulomb interaction ...
- 2.3. Numerical settings for electrons : basis set, planewaves and real space sampling, Brillouin zone sampling, ...
- 2.4. SCF algorithms, tuning and stopping criteria
- 2.5. Added electric/magnetic field, other artificial constraints/modifications, and related properties ...
- 3. Global control parameters : flow, parallelism, output files, output content, timing and memory control, ...
- 4. Molecular dynamics, geometry optimization, transition paths
- 5. Correlated electrons
- 6. Adiabatic response properties (phonons, low-frequency dielectric, Raman, elasticity, temperature dependence ...)
- 7. Excited state calculations, and frequency-dependent electronic and optical properties
- 8. Electronic properties and analysis tools (DOS, STM, Wannier, band plotting and interpolating...)
- 9. Other physical properties (e.g. positron)
- 10. Analysis/postprocessing tools
- 11. Miscellaneous topics

Documenting the features of a large scientific code is a complex task. The present list of features refers to different "topics". Each topic has a dedicated page, which should be quick to read, unlike the lessons of the tutorial, each of which is usually at least one hour work. Many of the topics make the link between a physical property or quantity (including bibliographical references for the theory, and sometimes pointing to published work using this feature) and the way it is to be computed with ABINIT (e.g. corresponding input variable, example input files, and possibly tutorial(s)).

This "topic"-based approach might be used by the beginner to get a broad overview of the capabilities of ABINIT as well as to the more expert user to quickly find the way to compute some existing quantity, or to remember which input variable is useful or mandatory for the calculation of a given property. Some topics are rather "input"-oriented (e.g. how to specify the atomic geometry, the occupation numbers, etc), other are more "property"-oriented (e.g. how to compute the elastic constants, the temperature-dependence of the electronic structure, etc), other are related to proper/better usage of the code.

Care is taken not to duplicate existing more complete documentation in ABINIT, but to point to it if appropriate.
Not all the ABINIT documentation is covered by the Web-accessible documents, there are still a few unlinked documents
in the subdirectories of ~abinit/doc (work is in progress to make it all available).
Discussions on the ABINIT forum might also allow to get information.

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The topic Building an input file briefly explains the content of an ABINIT input file.
The following topics go more into the details, however restricting to **static DFT calculations**, without
doing anything fancy with the exchange-correlation functionals. Going beyond these is left
for other sections (Sec. 3 and beyond). In particular, for any accurate electronic properties, e.g.
correct band structure, optical response, or for strongly correlated electrons, please go beyond the present sec. 2.
Also, topics related to global control parameters, that apply, generally speaking, to all types of calculations
are explained later.

- Unit cell
- Types of atoms and alchemy
- Crystalline structure and symmetries
- Smart symmetrizer
- Atom manipulator (advanced topic)

- Overview of available exchange and correlation functionals
- Hybrid functionals
- Van der Waals functionals
- Correlation energy within RPA
- Pseudopotentials and PAW atomic datasets
- Bands and occupation numbers for metals and insulators
- Spin-polarised systems and spin-orbit coupling
- Coulomb interaction and charged cells

- Planewaves and real space sampling
- PAW special settings
- Wavelets in ABINIT
- Wavevector sampling (k point grid)

- SCF algorithms
- SCF control, tolerances and stopping criteria
- Forces and stresses
- Tuning the speed of the calculation
- Recursion methods and orbital free calculations (not in production)

- Electric polarization and finite electric field
- External magnetic field
- Constrained atomic magnetic moment
- Electric field gradients
- Artificial modifications of the system

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- Multi-dataset calculations
- Parallelism and ABINIT
- Printing files
- Tuning the output content in different files
- Time and memory control

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- Geometry optimization
- Molecular dynamics
- Transition path searches: NEB and string method
- Geometry constraints
- Path-integral molecular dynamics (PIMD)
- Learn-on-the-flight (LOTF) (not in production)

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When correlated electrons are to be considered (in most cases, when **d and f orbitals** plpay an active role),
it is necessary to go beyond the standard DFT framework.
ABINIT enables the following possibilities:

- Hybrid functionals
- DFT+U approximation
- Dynamical Mean Field Theory (DMFT)
- Calculation of the effective Coulomb interaction

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Many properties can be obtained in the approximation that the electrons **stay in their ground state** (adiabatic responses).
The poweful Density-Functional Perturbation Theory (DFPT) framework allows ABINIT to address directly all such properties
in the case that are connected to derivatives of the total energy with respect to some perturbation.
This includes all dynamical effects due to phonons and their coupling,
thus also temperature-dependent properties due to phonons.

- Generalities about DFPT
- Wavevectors for phonons (q-points)
- Vibrational and dielectric properties (phonon frequencies and modes, IR and Raman spectra, Born effective charges)
- Phonon bands and DOS, interatomic force constants, sound velocity
- Temperature dependent properties (free energy, entropy, specific heat, atomic temperature factors, thermal expansion)
- Elasticity and piezoelectricity
- Raman intensities and electro-optic properties
- Electron-phonon interaction
- Phonon linewidth due to the electron-phonon interaction
- Electronic transport properties from electron-phonon interaction (resistivity, superconductivity, thermal)
- Temperature dependence of the electronic structure from electron-phonon interaction
- Constrained polarization geometry optimization (advanced topic)

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Excited-state calculations and frequency-dependent properties (for frequencies that are non-negligible with respect to the electronic gap), can be addressed by a variety of methodologies, usually trading accuracy for speed. At the lowest level, one encounters the independent-particle approximation, building upon some previously obtained band structure (e.g. Kohn-Sham band structure from DFT). For charged excitations, allowing to obtain a quasiparticle band structure without the well-known DFT band gap problem, one has to resort to (costly) GW calculations. For neutral excitations (i.e. optical), the (costly) Bethe-Salpeter approach is the most accurate formalism presently available. TDDFT and Δ-SCF calculations are cheaper but will work well for molecules and for isolated defects in a solid, not for e.g. correcting the band gap.

- Linear and non-linear optical properties in the independent-particle approximation
- Definition of frequency meshes for Many-body perturbation theory
- Frequency-dependent susceptibility matrix, and related dielectric matrix and screened Coulomb interaction
- Electronic self-energy
- GW calculations for accurate band structure, including self-consistency
- Bethe-Salpeter calculations for accurate optical properties
- TDDFT calculations
- DeltaSCF calculations
- Random electronic stopping power
- GW- Lanczos-Sternheimer method (not in production)

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Many properties are directly deduced from the knowledge of the electronic wavefunctions, eigenenergies, density, potential, etc. Some necessitates additional tuning parameters or are linked to postprocessing tools and are described in the following topics. Some others are actually activated through a single printing parameter, such as the Electron Localization Function (ELF - see prtelf). See the list of "printing" input variables in topic_printing.

- Electronic band structure and related topics
- Electronic DOS and related topics
- Effective mass calculations
- Unfolding supercell band structures
- Manipulating the density and potentials
- Scanning Tunneling Microscopy map
- Wannier functions
- Bader Atom-In-Molecule analysis

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- Abipy - ABINIT swiss knife
- Abinit Post-Processor Application (APPA), for molecular-dynamics trajectory analysis
- Band2eps for phonon dispersion curves

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- Verification of the implementation
- Portability and non-regression tests
- Git, gitlab and github for the ABINIT project
- Miscellaneous for developers

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