# Vibrational and dielectric properties

### This page gives hints on how to compute phonon frequencies and modes, IR and Raman spectra, Born effective charges, IR reflectivity ... with the ABINIT package.

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

Mentioned in topic_nonlinear, 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 computation of the second-order derivative of the total energy with respect to atomic displacements at an arbitrary wavevector, using DFPT, opens the possibility to compute the dynamical matrix at that wavevector, and hence, to compute the phonon eigenfrequency and eigendisplacements. When the wavevector is (0,0,0), usually denoted as the Gamma point, the combination of the atomic displacements and electric field type perturbations opens also the access to Born effective charges, electronic (for frequencies lower than the electronic band gap) dielectric constants, and then, to infra-red reflectivity of materials (in the infinite lifetime approximation). See [Gonze1997a] for the presentation of the theory with DFPT.

In ABINIT, with one dataset for a fixed wavevector (see topic_q-points), one can compute all such second-order derivatives. ABINIT will already perform some post-processing treatment of the second-order derivatives (e.g. computation of the dynamical matrix, and corresponding eigenenergies and eigendisplacements), although the most extended post-processing treatment is provided by ANADDB. Thus, there is some overlap of the two executables, with some common input variables. Usually, the action of an input variable with the same name in the two executables is very similar, although there are some input variables that govern more options in ANADDB then in ABINIT, because of the previously mentioned difference in capabilities. In the database of input variables, the input variables related to ABINIT or ANADDB are clearly distinguished.

The band-by-band decomposition of the Born effective charge tensors can be computed thanks to prtbbb. The related localization tensor (see [Veithen2002] can also be computed.

Phonon calculations are arbitrary q-points can be done under finite electric field (topic_Berry).

It will be the easiest to discover the capabilities of these two executables through the lesson_rf1 of the tutorial.

See topic_DFPT for the general information about DFPT, topic_q-points for the specification of q-points, and topic_PhononBands for the computation of full phonon bands.
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### 2. Related lesson(s) of the tutorial.

- The lesson Response-Function 1 (RF1) presents the basics of DFPT calculations within ABINIT. The example given is the study of dynamical and dielectric properties of AlAs (an insulator): phonons at Gamma, dielectric constant, Born effective charges, LO-TO splitting, phonons in the whole Brillouin zone. The creation of the "Derivative Data Base" (DDB) is presented.
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### 3. Related input variables.

Compulsory input variables:

... rfatpol [Response Function : ATomic POLarisation]
... rfdir [Response Function : DIRections]

Basic input variables:

... asr@anaddb [Acoustic Sum Rule]
... dieflag@anaddb [DIElectric FLAG]
... ngqpt@anaddb [Number of Grids points for Q PoinTs]
... rfasr [Response Function : Acoustic Sum Rule]

Useful input variables:

... amu [Atomic Mass Units]
... chneut [CHarge NEUTrality treatment ]
... chneut@anaddb [Integer for CHarge NEUTrality treatment]
... dipdip [DIPole-DIPole interaction ]
... eivec@anaddb [EIgenVECtors]
... enunit@anaddb [ENergy UNITs]
... frmax@anaddb [FRequency MAXimum]
... frmin@anaddb [FRequency MINimum]
... nfreq@anaddb [Number of FREQuencies]
... prtvol@anaddb [PRinT VOLume]
... q1shft@anaddb [Q shifts for the grid number 1]
... symdynmat [SYMmetrize the DYNamical MATrix]
... symdynmat@anaddb [SYMmetrize the DYNamical MATrix]

Input variables for experts:

... rfmeth@anaddb [Response-Function METHod]
... selectz@anaddb [SeLECT Z]
... thermal_supercell@anaddb [THERMALized SUPERCELL lattice vectors]
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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: t13.in t15.in t16.in t17.in t18.in t19.in t20.in t21.in t39.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).
[Veithen2002] M. Veithen, X. Gonze and Ph. Ghosez, "Electron localization: Band-by-band decomposition and application to oxides", Physical Review B - Condensed Matter and Materials Physics 66, 235113:1-10 (2002).

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