# Coulomb interaction and charged cells

### This page gives hints on how to treat adequately the Coulomb interaction, especially in charged cells, with the ABINIT package.

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

Mentioned in help_features#2.2.

### Table of content:

- 1. Introduction.
- 2. Related input variables.
- 3. Selected input files.
- 4. References.

### 1. Introduction.

ABINIT can treat charged systems (e.g. either for molecules, or for dopants in a supercell), using the charge input variable. A careful convergence study with respect to the cell size must however be done.

Depending on the dimension, different treatment of the Coulomb interaction can be enforced, governed by icoulomb for grouns-state calculations, and by icutcoul for GW calculations. Some development effort is needed in ABINIT to rationalize the situation.

Additional information concerning usepotzero. It is well known that the electrostatic potential (arising from ion-ion, ion-electron, and electron-electron interactions) is ill-defined within periodic boundary conditions. However, it is less well known that the total energy of a charged cell is also ill-defined. In fact, after a careful derivation in [Bruneval2014], it was shown that the above two statements are tightly linked: when the number of electrons differs from the number of protons in a cell, the necessary compensating background that enforces the overall charge neutrality is sensitive to the arbitrary average electrostatic potential.

ABINIT offers the possibility to choose which convention to use for the average electrostatic potential with the keyword usepotzero.

In PAW, one can choose among 3 options:

- the average of smooth electrostatic potential is set to zero;
- the average of all-electron electrostatic potential is set to zero;
- the average of smooth electrostatic potential is set to a finite value, which follows the Quantum Espresso implementation (see [Giannozzi2009] for more details).

Only options 1 and 3 are valid for the NCPP case.

None of these conventions is intrinsically more correct than the other ones. This is just an arbitrary choice, but ABINIT now permits a straight comparison to the other codes.
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### 2. Related input variables.

Basic input variables:

... charge [CHARGE]

Useful input variables:

... icoulomb [Index for the Coulomb TReaTMenT]
... icutcoul [Integer that governs the CUT-off for COULomb interaction]
... usepotzero [USE POTential ZERO]

Input variables for experts:

... nscforder [Nth - SCaling Function ORDER]
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### 3. 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/v7/Input: t26.in
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### 4. References.

[Bruneval2014] F. Bruneval, J.-P. Crocombette, X. Gonze, B. Dorado, M. Torrent and F. Jollet, "Consistent treatment of charged systems within periodic boundary conditions: The projector augmented-wave and pseudopotential methods revisited", Phys. Rev. B 89, 045116 (2014).
DOI: 10.1103/PhysRevB.89.045116.
[Giannozzi2009] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari and R.M. Wentzcovitch, "QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials", J. Phys.: Cond. Matt. 21, 395502 (2009).
URL: http://iopscience.iop.org/article/10.1088/0953-8984/21/39/395502.

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