# ABINIT. List of features.

This file describes the major features of the ABINIT package.

##### Copyright (C) 1998-2009 ABINIT group (DCA,XG)
This file is distributed under the terms of the GNU General Public License, see ~abinit/COPYING or http://www.gnu.org/copyleft/gpl.txt .
For the initials of contributors, see ~abinit/doc/developers/contributors.txt .

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### Contents:

- 0. Related documentation.
- 1. Available physical properties.
  - 1.A. Total energy of an assembly of nuclei and electrons placed in a repeated cell.
  - 1.B. Derivatives of the total energy and eigenenergies.
  - 1.C. Excited states.
  - 1.D. Displacement of atoms, and changes of cell parameters.
  - 1.E. Analysis and graphical tools.
  - 1.F. Interfacing with other codes.
- 2. Speed and memory.
  - 2.A. Speed in the sequential version.
  - 2.B. Speed in the parallel version.
  - 2.C. Memory.
- 3. The user's point of view.
  - 3.A. The Web site.
  - 3.B. Portability.
  - 3.C. Running jobs, input and output files.
  - 3.D. Documentation.
  - 3.E. Generation of the k-points, geometries, and starting wavefunctions.
  - 3.F. Automatic determination of input parameters.
- 4. The programmer's point of view.

### 0. Related documentation

Besides the documentation available on the Web, there is a wealth of information inside the package itself, see the directory "doc". The reader might consult the latest version of the "doc/users/context.txt" file for the description of the ABINIT project and its history. The latest version of the "doc/developers/planning.txt" file will give an idea of possible future developments. The different versions of the "doc/release_notes/*html" files will allow to see the actual development of the project since version 1.5, released in August 1998.

### 1. Available physical properties

#### 1.A. Computation of the total energy of an assembly of nuclei and electrons placed in a repeated cell.

- 1.A.1. The computation can be done using plane waves and norm-conserving pseudopotentials, or, alternatively, so-called "Projector-Augmented Waves" (PAW method), with appropriate pseudoatomic data. Some computations can also be done using wavelets, see 1.A.14.
- 1.A.2. The total energy computation is done according to the Density Functional Theory. Most of the important local approximations (LDA) are available, including the Perdew-Zunger one. Two different local spin density (LSD) are available, including the Perdew Wang 92, and one due to M. Teter. The Perdew-Burke-Ernzerhof, the revPBE, the RPBE and the HCTH GGAs (spin unpolarized as well as polarized) are also available.
- 1.A.3. Self-consistent calculations will generate the DFT ground-state, with associated energy and density. Afterwards, a non-self-consistent calculation might generate eigenenergies at a large number of k-points, for band structures. The electronic Density-Of-States can be computed either within the tetrahedron method, or using a smearing technique.
- 1.A.4. The program admits many different types of pseudopotentials. There are two complete sets of pseudopotentials available for the whole periodic table, one of the Troullier-Martins type, one of the Goedecker type (this one include the spin-orbit coupling). Four codes are available to generate new pseudopotentials when needed. Two of them are able to generate pseudopotentials with a core hole, in order to compute core-level shifts. Two of them are able to generate GGA pseudopotentials. No ultra-soft pseudopotential can be used. Pseudopotentials can be mixed, to generate "alchemical" pseudoatoms.
- 1.A.5. Metallic as well as insulating systems can be treated. Schemes for determination of the occupation number include the Fermi broadening, the Gaussian broadening, the Gaussian-Hermite broadening, as well as the modifications proposed by Marzari. Finite temperatures can also be treated using a smearing scheme (Verstraete scheme).
- 1.A.6. The cell may be orthogonal or non-orthogonal. Any kind of symmetries and corresponding sets of k-point can be input, and taken into account in the computation.
- 1.A.7. The electronic system may be computed in the spin-unpolarized or spin-polarized case, with the possibility to impose occupation numbers of majority and minority spins, and the spins of the starting configuration. A specific option for efficient treatment of anti-ferromagnetism (Shubnikov groups) is available. The treatment of non-collinear magnetism is available, but only for the total energy (no forces, stresses, reponse-functions ...). The total magnetic moment of the unit cell can be constrained.
- 1.A.8. The total energy, forces, stresses, and electronic structure can be provided with the spin-orbit coupling included (the latter not for PAW).
- 1.A.9. A finite electric field can be imposed on insulators, using the proper Hamiltonian for periodic systems based on Berry's phase (not for PAW).
- 1.A.10. The decomposition of energy in its different component (local potential, XC, hartree ...) is provided.
- 1.A.11. Inner electronic eigenvalues can be computed thanks to the minimisation of the residual with respect to a target energy value.
- 1.A.12. The charge density of states close to the Fermi energy can be output, and provide a simple approach to STM image calculations (not for PAW).
- 1.A.13. The lifetime of positrons can be computed.
- 1.A.14. The use of wavelets (instead of plane waves) is also being implemented. At present, it works for the SCF cycles : one can get density, total energy and forces, in some basic cases (non-spin-polarisation, HGH or GTH pseudopotentials only).
- 1.A.15. The DFT+U approximation is also available (LDA+U, GGA+U), on the basis of PAW calculations.

#### 1.B. Derivatives of the total energy and eigenenergies (incl. linear and non-linear DFPT responses)

- 1.B.1. Hellman-Feynman forces are computed from an analytical formula, and corresponds exactly to the limit of finite differences of energy for infinitesimally small atomic displacements when the ground-state calculation is at convergence. This feature is available for all the cases where the total energy can be computed (except non-collinear magnetism). A correction for non-converged cases allows to get accurate forces with less converged wavefunctions than without it. The decomposition of the forces in their different components can be provided.
- 1.B.2. Stress can also be computed. This feature is available for all the cases where the total energy can be computed, except non-collinear magnetism. The decomposition of the stresses in their different components can be provided. A smearing scheme applied to the kinetic energy allows to get smooth energy curves as a function of lattice parameters and angles. Alternatively, a facility for correcting the computed stress by the Pulay stress is provided.
- 1.B.3. The polarization can be computed within the Berry phase formulation. This feature is available for insulators, magnetic or non-magnetic, but not yet when spin-orbit splitting is present or for PAW. The localisation tensor can also be computed. Constrained-polarization calculations can be performed, following Na Sai et al, PRB 66, 104108 (2002).
- 1.B.4. For norm-conserving pseudopotentials, accurate responses to atomic displacements and homogeneous electric fields are available, and allows to compute the interatomic force constants, the Born effective charges, the dielectric constant, the phonon band structure. Symmetry characters of the phonons at Gamma are computed. Thermodynamical properties, like the free energy, the heat capacity or the entropy, can also be computed, in the quasi-harmonic approximation. The atomic temperature factors (Debye-Waller factors) are also available. Available for the GGAs (except the HCTH one), while for spin-orbit, only responses to atomic displacements are available.
- 1.B.5. For norm-conserving pseudopotentials, accurate responses to strain perturbations are available, and allow to compute, presently, the elastic constants ("rigid-ion" as well as "relaxed"), the piezoelectricity tensor, as well as the so-called "internal strains", change of forces to atoms due to a strain, or change of the stress due to an atomic displacement. (no treatment of spin-orbit coupling yet).
- 1.B.6. For norm-conserving pseudopotentials, approximate or accurate susceptibility matrix and dielectric matrix can be computed, thanks to a sum over states. (no treatment of spin-polarized cases or spin-orbit coupling yet)
- 1.B.7. For norm-conserving pseudopotentials, derivatives of the electronic eigenenergies with respect to the wavevector can be computed analytically.
- 1.B.8. For norm-conserving pseudopotentials, optical conductivity can be computed, thanks to the Kubo-Greenwood formula. (no treatment of spin-polarized cases or spin-orbit coupling yet)
- 1.B.9. For norm-conserving pseudopotentials, the band-by-band decomposition of the Born effective charges, and the localisation tensor is available. (no treatment of spin-polarized cases or spin-orbit coupling yet)
- 1.B.10. For norm-conserving pseudopotentials, selected non-linear response coefficients can be computed thanks to the 2n+1 theorem of perturbation theory. At present : - the electro-optic coefficients - the Raman cross sections (no treatment of spin-polarized cases or spin-orbit coupling yet)
- 1.B.11. For norm-conserving pseudopotentials, electron-phonon matrix elements are available directly from the output of a linear-response phonon calculation. They can be analyzed to give e.g. the phonon linewidth or superconducting temperature. (no treatment of spin-polarized cases or spin-orbit coupling yet), or the thermal conductivity (phonon transport, limited by electron-phonon collisions), and the electrical conductivity (electron transport, limited by electron-phonon collisions)
- 1.B.12. For norm-conserving pseudopotentials, the computation of responses with respect to atomic displacement is possible when a finite electric field is present. This feature is available for insulators, non-magnetic, no spin-orbit coupling. Computation of other linear or non-linear responses within an electric field is not yet possible.

#### 1.C. Excited states.

(Note : at present, for norm-conserving pseudopotentials only)

- 1.C.1. Computation of ionisation energies (N -> N-1 electrons) and affinities (N -> N+1 electrons) in the GW approximation. Three plasmon pole models are available, but that calculation can also be done by a full integration over frequencies. ABINIT is able to treat insulators as well as metals, but should be improved to treat polymers or clusters. In the GW implementation, it is possible to disable the full computation, and actually do an Hartree-Fock, screened exchange or COHSEX calculation. Self-consistency is implemented at a very primitive level. The Faleev method, see PRL 93, 126406 (2004), is implemented. Available for the non-spin-polarized as well as spin-polarized case, but not yet for spinor wavefunctions.
- 1.C.2. Excited states of atoms and molecules can be computed within TDDFT (Casida approach). Oscillator strengths are available. In the non-spin-polarized case, spin-singlet as well as spin-triplet excitations are computed. Spin-polarized case is also available.
- 1.C.3. Frequency-dependent linear optical response is available, for all components of the tensor (xx,yy,zz,xy,yz,zx), real as well as imaginary part. This property is computed within the very simple "sum-over-state" approximation (i.e. without local field corrections). See the "optics" utility, for norm-conserving pseudopotentials.
- 1.C.4. Frequency-dependent non-linear optical response is available, for all components of the tensor (xxx,yyy,zzz,xyz ... ), real as well as imaginary part. This property is computed within the very simple "sum-over-state" approximation (i.e. without local field corrections). See the "optics" utility, for norm-conserving pseudopotentials.
- 1.C.5. Frequency-dependent electronic conductivity, the thermal conductivity, and the thermopower (electron transport, high temperature, Kubo-Greenwood formalism) real as well as imaginary part. This property is computed within the very simple "sum-over-state" approximation (i.e. without local field corrections). See the "conducti" utility, for norm-conserving pseudopotentials, as well as PAW.

#### 1.D. Displacement of atoms, and changes of cell parameters.

- 1.D.1. Different algorithms (Broyden; modified Broyden; Verlet with sudden stop of atoms) allows to find the equilibrium configuration of the nuclei, for which the forces vanish. The cell parameters can also be optimized concurently with the atomic positions. Specified lattice parameters, or angles, or atomic positions, can be kept fixed if needed.
- 1.D.2. Two molecular dynamics algorithm (Numerov or Verlet) allow to perform simulations in real (simulated) time. The displacement of atoms may be computed according to Newton's law, or by adding a friction force to it. Nose-Hoover thermostat is available with Verlet algorithm. Langevin dynamics is also available.
- 1.D.3. The code can provide an automatic analysis of bond lengths and angles, and the atomic coordinates in a format suitable for vizualisation with XMOL.

#### 1.E. Analysis and graphical tools.

- 1.E.1. A post-processor, called "cut3d", is available to analyse density, potential and wavefunction files. It is able to change the format of these files, to extract the data on a 2D plane, or along a 1D line. It can perform the Hirshfeld computation of atomic charges. It can analyse the charge contained in an atomic sphere, and determine the angular momentum projected charge (l=0 to 4) contained in that sphere. (only available for norm-conserving pseudopotentials)
- 1.E.2. Another post-processor, called "aim", is available to perform the Bader "Atom-In-Molecule" analysis of the density. (only available for norm-conserving pseudopotentials)
- 1.E.3. A special part in the tutorial (see later) indicates how to generate properly formatted data for the visualisation of :
  - the band structure (visualisation thanks to XMGR)
  - total energies vs different parameters (also using XMGR)
  - the charge density (3D isosurfaces)
  (the cut3d postprocessor must be used, followed by matlab) The cut3d postprocessor also allows to prepare 2D charge density plots.
- 1.E.4. The post-processor band2eps allows to draw phonon dispersion curves automatically, in a file written in Encapsulated PostScript (eps). Moreover, a color code allows to emphasize the contribution of individual atoms to the corresponding eigenvector (at most three types of atoms).
- 1.E.5. Utilities to view the structures and make the band structure are available (StructureViewer, BandStructureMaker).

#### 1.F. Interfacing with other codes.

- 1.F.1. ABINIT is interfaced with WanT (see http://www.wannier-transport.org). WanT, as a postprocessor of ABINIT results, allows to compute maximally localized Wannier functions, as well as transport properties through nanostructures.
- 1.F.2. ABINIT is interfaced with CASINO, a code for Quantum Monte Carlo calculation of the properties of solids and molecules.
- 1.F.3. XML pseudopotentials can be used, these being common with the SIESTA code.
- 1.F.4. The _WFK functions can be used as starting basis by the TDDFT, GW and/or Bethe-Salpether softwares EXC, SELF and DP code, see http://www.abinit.org/community/?text=links .
- 1.F.5. ABINIT can produce and read files following the Nanoquanta/ETSF file format (http://www.etsf.eu/fileformats)

### 2. Speed and memory.

#### 2.A. Speed in the sequential version.

- 2.A.1. Depending on the number of atoms, there are two regimes in the code : at low number of atoms and electrons, the CPU time is dominated by Fast Fourier Transforms with an average scaling O(N^2 log N) where N is some number characteristics of the size of the system (atoms, electrons); at large number of atoms and electrons, the CPU time is dominated by non-local operator aplication and orthogonalisation, with an average scaling O(N^3).
- 2.A.2. The complex-to-complex Fast Fourier Transform routine for application of the Hamiltonian has been highly optimized, and take into account the fact that the wavefunction do not fill the reciprocal space FFT box. Library FFTs are also available, but they are found to be slower than the present FFT routine, developed starting from a routine provided by S. Goedecker. A real-to-complex FFT is used for treating potential and densities of the ground state, since they are real. For selected k-points, invariant under time-reversal symmetry, ( (0 0 0), (1/2 0 0), (0 1/2 0), (0 0 1/2), (1/2 1/2 0) ... (1/2 1/2 1/2) ), the number of planewave explicitly treated is divided by two. A real-to-complex FFT is used then.
- 2.A.3. The non-local potential is applied in reciprocal space. It has been optimized carefully, although there is still some speed-up to be coded when the k-point is invariant under time-reversal. The orthogonalisation procedure can be done twice per loop or only once.
- 2.A.4. At the level of the generation of electronic eigenfunctions, an efficient band-by-band preconditioned conjugate-gradient algorithm is used, in its non-self-consistent version. An alternative algorithm "lobpcg" is also available.
- 2.A.5. At the level of the self-consistency loop, an efficient potential-based preconditioned conjugate-gradient algorithm is used. Simple mixing is also available, as well as the Anderson algorithm. Preconditioning of this algorithm is achieved through a model dielectric function, or through an approximate dielectric matrix.

#### 2.B. Speed in the parallel version.

- 2.B.1. For ground-state calculations, the code has been parallelized on the k-points, on the spins, on the bands, and on the FFT grid and plane wave coefficients. For the k-point and spin parallelisations (using MPI), the communication load is generally very small. This allows it to be used on a cluster of workstations. However, the number of nodes that can be used in parallel might be small, and depends strongly on the physics of the problem. A combined FFT / band parallelisation is available, and has shown very large speed up on powerful computers with a large number of processors and high-speed interconnect. It cannot be used concurrently with the k point and spin parallelisation though.
- 2.B.2. For response calculations, the code has been parallelized on k-points, spins, and bands (MPI), as well as on the FFT grid and plane wave coefficients (OpenMP). For the k-points, spins and bands parallelisation, the communication load is rather small also, and, unlike for the GS calculations, the number of nodes that can be used in parallel will be large, nearly independently of the physics of the problem. The FFT grid parallelisation (using OpenMP) works only for SMP machines, and is still to be optimized.
- 2.B.3. GW calculations are parallelized over k-points. They are also parallelized over bands, but the two parallelisation cannot be used currently at present.
- 2.B.4. A careful study of the speed-up should still be done, in both the GS and RF cases.

#### 2.C. Memory.

- 2.C.1. The requirements of the different conjugate gradient algorithms on memory are relatively low, especially when the number of atoms is large. Optionally, it is even possible to use disk space to save memory, at the expense of computing time. In particular, when the number of k points is large, they can be stored in memory one at a time. Phase factors in the application of the non-local operator can also be recomputed at each application, in order to save memory. For k-points that are invariant under time-reversal symmetry, the storage required for wavefunctions is half the storage for other k-point.

### 3. The user's point of view.

#### 3.A. The Web site.

- 3.A.1. A Web site can be accessed. The complete sources (and all the tests) of the ABINIT package are available there. Executables for many different platforms are also available, in specific packages that also include the 'Infos' directory are also available. Installation notes, current features of ABINIT, the tutorial, on-line help can be vizualized directly from the web.
- 3.A.2. Also available from the Web site :
  - the pseudopotentials
  - some utilities (including cut3d, a density analyser)
  - five mailing lists (one for "official announcements", one for the developpers, one for the developers using the GNU Arch repository, one "forum mailing list" , one for the advisory committee)
  - the ABINIT bibliography database, that contains references of papers in which ABINIT or one of its predecessors have been used
  - the FAQ (frequently asked questions) database
  - ... (many more infos)

#### 3.B. Portability.

- 3.B.1. The ABINIT package has been installed successfully on the following different platforms :
  - PC/Linux based on PPro, PII, PIII, PIV processors, with pghpf compiler, Intel compiler, fujitsu compiler, NAG compiler, g95 compiler and gfort compiler.
  - PC under Windows
  - ItaniumII
  - HP/SPP1600, HP/S-class, HP/N-class based on the HP 7200, 8000 and 8500 processors
  - Compaq/DEC alpha workstations under OSF, based on EV56, EV6, EV67 or EV68
  - Compaq/DEC alpha workstations under Linux, based on EV56
  - IBM RS6000 based on Power 2, 3+, 4 and 5 processors
  - SGI Origin 2000 and O2
  - CRAY T3E
  - FUJITSU VPP-700
  - Sun ultrasparc II
  - NEC
  - HITACHI SR8000
  - Mac OS X
- 3.B.2. In particular, the parallel version is available on clusters of Intel/Linux, DEC or IBM workstations, as well as on CRAY T3E, SGI Origin 2000, HP/SPP1600, HP/S-class, HP/N-class, FUJITSU VPP-700 machines, HITACHI SR8000, IBM 44P, Sun ultrasparc.
- 3.B.3. Installation is made thanks to the autotools (autoconf and automake) as well as different scripts. All machine-dependent parameters are grouped in one single short file for each machine. The parallel and sequential version of the code, as well as the different versions for the different machines, are prepared on-the-fly, so that there is only one unique source code.
- 3.B.4. Binaries for different machines can be managed in the same main directory, as they might be placed automatically in different sub-directories.

#### 3.C. Running jobs, input and output files.

- 3.C.1. The input variables are gathered in one unique file, read by a text processing facility build in the code. Many defaults values are provided, so that the input file can be kept rather short.
- 3.C.2. Many different stopping criteria allow the user to target the accuracy he or she wants to obtain.
- 3.C.3. The outputs are provided to one main file and one auxiliary file, as well as different specialized files (for density, potential, wavefunctions, ...) . The main file is shorter than the auxiliary file, and well formatted, while all important results are gathered there. It can be used for archival purposes. The auxiliary (log) file will contain all exception messages.
- 3.C.4. Exception handling is provided through four different types of messages : COMMENT, WARNING, BUG and ERROR. In each case, the accurate meaning of the exception is described, as well as the eventual action to be taken by the user.
- 3.C.5. Statistics of foreseen memory and disk usage is printed at the beginning of the run. Statistics of CPU time usage is printed at the end of the run.
- 3.C.6. There is a facility to stop the run in a clean way at any time. The user may specify a cpu time limit, after which the job must end smoothly.
- 3.C.7. A status file, updated very frequently, gives an on-the-fly report of progress of the current run.
- 3.C.8. The code can handle multiple datasets contained in the input file, where generic input variables valid for all datasets can be defined. These calculations for different dataset can be chained, so that in one run, many complex tasks can be accomplished. This allows easy convergence studies.
- 3.C.9. The code can start the current run from a wavefunction input file generated in a previous run. This allows to cut down the number of iteration to self-consistency, or to perform other tasks. This can be done even if the previous job had different computational parameters, like different k points, different energy cut-off, spin-unpolarized or spin-polarized wavefunctions, scalr or spinor wavefunctions ... Of course, the restart from wildly different parameters will not save a lot of CPU time.
- 3.C.10. ABINIT can produce CML (Chemical Markup Language) output files. It can also read the CML files it produced.

#### 3.D. Documentation.

- 3.D.1. A new_user_guide and a few rather detailed help files (abinis_help, respfn_help, anaddb_help, mrgddb_help, newsp_help, aim_help ... ) are available on-line.
- 3.D.2. A tutorial with more than 15 lessons is available on-line. It starts with the computation of different properties of the H2 molecule, describes convergence studies, then focuses on bulk Silicon, bulk Al and Al surface. It describes the use of response-function features, the GW calculation of band structures, the PAW methodology, computation of spin-dependent properties, analysis tools, the phonon band structure, linear and non-linear optics, electro-optic effects, electron-phonon coupling, phonon linewidths due to electron-phonon interaction, Raman scattering efficiencies, piezoelectricity, the computation of elastic constants, parallelism, the source code, etc ...
- 3.D.3. Many test cases are provided, and can help the user in setting up a run.
- 3.D.4. An ABINIT bibliography database, that contains references of papers in which ABINIT or one of its predecessors is available on the Web site.

#### 3.E. Generation of the k-points, geometries, and starting wavefunctions.

- 3.E.1. The code can automatically generate symmetries from the primitive cell and the position of atoms. In this case, it identifies automatically the Bravais lattice, point group and space group. Alternatively, it can start from the symmetries and generate the atomic positions from the irreducible set. Also, a database of the 230 spatial groups of symmetry is built inside ABINIT.
- 3.E.2. Anti-ferromagnetic symmetry operations, and associated magnetic space groups (Shubnikov groups) can be treated with the same facility as usual space groups, including a database of the 1191 Shubnikov groups.
- 3.E.3. A geometry builder is available inside the code. It can take one (or two) group of atoms, rotate it, translate it and repeat it, then create vacancies.
- 3.E.4. The generation of special k point sets (Monkhorst-Pack sets) and band structure k points can also be done directly inside ABINIT. A list of interesting k point sets, can be generated automatically, including a measure of their accuracy in term of integration within the Brillouin Zone.
- 3.E.5. A utility for generating wavefunctions with new characteristic (cut-off, k-point) from already existing wavefunctions with different characteristics is available (newsp).

#### 3.F. Automatic determination of input parameters.

- 3.F.1. Many defaults values are provided.
- 3.F.2. The FFT grid parameters can be automatically generated from the cut-off energy and geometry of the system.
- 3.F.3. The number of bands and starting occupation numbers can be automatically generated from the input set of atoms.
- 3.F.4. There is a database of atomic masses.

### 4. The programmer's point of view.

- 4.A. The code is distributed without charge under the GNU General Public Licence (GPL). This garantees that the future modifications of the code stay available to the developpers and users for free. This Copyright is often referred to as a "Copyleft".
- 4.B. The code is written in clean Fortran90. Strict programming rules have been followed. These are documented. Comments are numerous, and all in english.
- 4.C. Quick, fully automatic, testing of the code is available in the makefile, giving diagnostics on the validity of computed energy, forces, stresses and eigenvalues for five typical cases.
- 4.D. More extensive testing is provided in five batteries of tests (altogether more than 350 different runs), with automatic comparison with results of preceding versions. A specialized diff script (called 'fldiff') has been written in order to ease the diagnostic on the suite of tests. A short one-line-per-test file is produced (report file). In addition to tests of the correctness of the execution, for the sequential or parallel version of the main code, as well as some utilities, there are automatic diagnostics of the speed of crucial routines, and the response to a load of up to 4 instances of the main code, running concurrently.
- 4.E. Debugging facilities are provided inside the code, and can be directly accessed from the input file. The compilation can be done in both debugging or normal mode : the C-preprocessed files are either kept or removed automatically.
- 4.F. "Design-by-contract" utility routines are present, as well as a flag to preprocess the sources, and eliminate the design-by-contract features in production mode.

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