# Precision with a planewave basis, PAW/pseudopotentials, and the related real space sampling

### This page gives hints on how to perform numerically precise calculations with planewaves or projector-augmented waves and pseudopotentials with the ABINIT package.

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

Mentioned in topic_TuningSpeed, help_features#2.3.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.

### 1. Introduction.

The numerical precision of the calculations depends on many settings, among which the definition of a basis set is likely the most important. With planewaves, there is one single parameter, ecut that governs the completeness of the basis set.

The wavefunction, density, potentials are represented in both reciprocal space (plane waves) and real space, on a homogeneous grid of points. The transformation from reciprocal space to real space and vice-versa is made thanks to the Fast Fourier Transform (FFT) algorithm. With norm-conserving pseudopotential, ecut is also the main parameter to define the real space FFT grid, In PAW, the sampling for such quantities is governed by a more independent variable, pawecutdg. More precise tuning might be done by using boxcutmin and ngfft.

Avoiding discontinuity issues with changing the size of the planewave basis set is made possible thanks to ecutsm.

The accuracy variable enables to tune the accuracy of a calculation by setting automatically up to seventeen variables.

Many more parameters govern a PAW computation than a norm-conserving pseudopotential calculation. They are described in a specific page topic_PAW. For the settings related to wavelets, see Wavelets.
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### 2. Related lesson(s) of the tutorial.

- The lesson 2 deals again with the H2 molecule: convergence studies, LDA versus GGA
- The lesson 3 deals with crystalline silicon (an insulator): the definition of a k-point grid, the smearing of the cut-off energy, the computation of a band structure, and again, convergence studies ...
- The first lesson on the the projector-augmented wave technique.
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  ### 3. Related input variables.

  Compulsory input variables:

  ... ecut [Energy CUToff]
  ... pawecutdg [PAW - Energy CUToff for the Double Grid]

  Basic input variables:

  ... accuracy [ACCURACY]
  ... ecutsm [Energy CUToff SMearing]

  Useful input variables:

  ... boxcutmin [BOX CUT-off MINimum]
  ... ngfft [Number of Grid points for Fast Fourier Transform]

  Relevant internal variables:

  ... %mgfft [Maximum of nGFFT]
  ... %mgfftdg [Maximum of nGFFT for the Double Grid]
  ... %mpw [Maximum number of Plane Waves]
  ... %nfft [Number of FFT points]
  ... %nfftdg [Number of FFT points for the Double Grid]

  Input variables for experts:

  ... mqgrid [Maximum number of Q-space GRID points for pseudopotentials]
  ... nc_xccc_gspace [Norm-Conserving pseudopotentials - use XC Core-Correction in G-SPACE]
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