# Phonon bands and related topics

### This page gives hints on how to compute phonon bands, density of states, interatomic force constants, sound velocity ... with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (MT)

Mentioned in topic_Phonons, topic_Temperature, topic_q-points, help_features#6.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

The Fourier transformation of the phonon dynamical matrices generates interatomic force constants in real space, as explained in [Gonze1997a]. Backtransforming to reciprocal space gives the Fourier interpolation of the initial phonon band structure. After such Fourier interpolation, the DOS can be produced (see [Lee1995]), the phonon eigenenergies plotted along lines, the slope of the energy versus cristalline momentum evaluated (to give sound velocity).

The two-phonon sum and difference spectra can also be obtained, see dossum.

For the related computation of temperature-dependent properties, see topic_Temperature.
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### 2. Related lesson(s) of the tutorial.

- The lesson Response-Function 2 (RF2) presents the analysis of the DDBs that have been introduced in the lesson_rf1. The computation of the interatomic forces and the computation of thermodynamical properties is an outcome of this lesson.
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### 3. Related input variables.

Compulsory input variables:

... ifcflag@anaddb [Interatomic Force Constants FLAG]

Basic input variables:

... asr@anaddb [Acoustic Sum Rule]
... atifc@anaddb [AToms for IFC analysis]
... dipdip@anaddb [DIPole-DIPole interaction]
... dossum@anaddb [DOS SUM]
... ndivsm@anaddb [Number of DIVisions for the SMallest segment]
... ngqpt@anaddb [Number of Grids points for Q PoinTs]
... nph1l@anaddb [Number of PHonons in List 1]
... nph2l@anaddb [Number of PHonons in List 2]
... nqpath@anaddb [Number of Q wavevectors defining a PATH]
... prtdos@anaddb [PRinT the phonon Density Of States]
... qpath@anaddb [Q wavevectors defining a PATH]
... qph1l@anaddb [Q for PHonon List 1]
... qph2l@anaddb [PHonon List 2]

Useful input variables:

... brav@anaddb [BRAVais]
... dosdeltae@anaddb [DOS DELTA in Energy]
... dossmear@anaddb [DOS SMEARing value]
... dostol@anaddb [DOS TOLerance]
... eivec@anaddb [EIgenVECtors]
... enunit@anaddb [ENergy UNITs]
... iatprj_bs@anaddb [Indices of the AToms for the PRoJection of the phonon Band Structure]
... ifcana@anaddb [IFC ANAlysis]
... ifcout@anaddb [IFC OUTput]
... natifc@anaddb [Number of AToms for IFC analysis]
... natprj_bs@anaddb [Number of AToms for PRoJection of the Band Structure]
... ng2qpt@anaddb [Number of Grids points for Q PoinTs (grid 2)]
... nqshft@anaddb [Number of Q SHiFTs]
... nsphere@anaddb [Number of atoms in SPHERe]
... nwchan@anaddb [Number of Widths of CHANnels]
... prt_ifc@anaddb [PRinT the Interatomic Force Constants]
... prtddb@anaddb [PRinT the Derivative DataBase files]
... prtphbands@anaddb [PRinT PHonon BANDS]
... prtsrlr@anaddb [PRinT the Short-Range/Long-Range decomposition of phonon FREQuencies]
... prtvol@anaddb [PRinT VOLume]
... q1shft@anaddb [Q shifts for the grid number 1]
... q2shft@anaddb [Q points SHiFTs for the grids 2]
... rifcsph@anaddb [Radius of the Interatomic Force Constant SPHere]
... symdynmat@anaddb [SYMmetrize the DYNamical MATrix]
... vs_qrad_tolkms@anaddb [Speed of Sound Q-radius, TOLerance KiloMeter/Second]

Input variables for experts:

... freeze_displ@anaddb [FREEZE DISPLacement of phonons into supercells]
... nchan@anaddb [Number of CHANnels]
... ngrids@anaddb [Number of GRIDS]
... outboltztrap@anaddb [OUTput files for BOLTZTRAP code]
... outscphon@anaddb [OUTput files for Self Consistent PHONons]
... prtbltztrp@anaddb [PRinT input files for BoLTZTRaP code.]
... qrefine@anaddb [Q-point REFINEment order (experimental)]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v2/Input: t15.in t16.in t17.in t19.in t20.in t22.in t25.in t28.in t29.in t32.in t39.in

tests/v5/Input: t95.in

tests/v6/Input: t76.in
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### 5. References.

[Gonze1997a] 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).
[Lee1995] C. Lee and X. Gonze, "Ab-initio calculation of the thermodynamic properties and atomic temperature factors of SiO2 α-quartz and stishovite", Phys. Rev. B 51, 8610 (1995).

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