# Wavelets

### This page gives hints on how to perform calculations on a wavelet basis with the ABINIT package.

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

Mentioned in topic_PAW, topic_Planewaves, help_features#2.3.

### Table of content:

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

### 1. Introduction.

A wavelet basis (instead of a plane wave basis) can be used in ABINIT. With a wavelet basis, one can perform basic static DFT calculations with selected norm-conserving pseudopotentials (HGH or GTH pseudopotentials [Genovese2008]), but also with PAW atomic data [Rangel2016]). Available also : the finite size corrections to the total energy, restart on wavefunctions following the ETSF norm and geometry relaxation using BFGS. Molecular dynamic is also available for test purposes.

However, DFPT or excited-state calculations (except Δ-SCF) cannot be performed.
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### 2. Related lesson(s) of the tutorial.

- Parallelism for ground-state calculations, with wavelets presents the parallelism of ABINIT, when wavelets are used as a basis function instead of planewaves, for the computation of total energy, density, and ground state properties
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### 3. Related input variables.

Compulsory input variables:

... usewvl [Use WaVeLet basis set]

Basic input variables:

... wvl_crmult [WaVeLet Coarse grid Radius MULTiplier]
... wvl_frmult [WaVeLet Fine grid Radius MULTiplier]
... wvl_hgrid [WaVeLet H step GRID]

Useful input variables:

... nwfshist [Number of WaveFunctionS HISTory]
... tl_radius [TaiL expansion RADIUS]

Input variables for experts:

... tl_nprccg [TaiL maximum Number of PReConditionner Conjugate Gradient iterations]
... wvl_bigdft_comp [WaVeLet BigDFT Comparison]
... wvl_ngauss [WaVeLet Number of GAUSSians]
... wvl_nprccg [WaVeLet maximum Number of PReConditionner Conjugate Gradient iterations]
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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/bigdft/Input: t01.in t02.in t03.in t04.in t05.in t06.in t07.in t09.in t10.in t11.in t12.in t14.in t16.in t17.in t18.in t31.in t32.in t33.in t34.in

tests/bigdft_paral/Input: t01.in t02.in
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### 5. References.

[Genovese2008] L. Genovese, L. Neelov, S. Goedecker, T. Deutsch, S. Alireza Ghasemi, A. Willand, D. Caliste, O. Zilberberg, M. Rayson, A. Bergman and R. Schneider, "Daubechies wavelets as a basis set for density functional pseudopotential calculations", J. Chem. Phys. 129, 014109 (2008).
[Rangel2016] T. Rangel, D. Caliste, L. Genovese and M. Torrent, "A wavelet-based Projector Augmented-Wave (PAW) method: Reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set", Computer Physics Communication 208, 1-8 (2016).

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