# Recursion

### This page gives hints on how to perform orbital-free calculations with the ABINIT package.

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

Mentioned in help_features#2.4.

### Table of content:

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

### 1. Introduction.

It is possible to use Thomas-Fermi kinetic functional (explicit functional of the density) or Thomas-Fermi-Weizsacker kinetic functional (with Gradient Corrections) instead of Kohn-Sham kinetic energy functional (implicit functional of the density through Kohn-Sham wavefunctions).
See [Perrot1979].
The Recursion Method may be used in order to compute electronic density, entropy, Fermi energy and eigenvalues energy. This method computes the density without computing any orbital, is efficient at high temperature, with a efficient parallelization (almost perfect scalability).

At present, it only works for local pseudopotentials, severely restricting the use of this method.
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### 2. Related input variables.

Compulsory input variables:

... tfkinfunc [Thomas-Fermi KINetic energy FUNCtional]

Basic input variables:

... rectolden [RECursion - TOLerance on the difference of electronic DENsity]

Useful input variables:

... recefermi [RECursion - initial guess of the FERMI Energy]
... recgratio [RECursion - Grid RATIO]
... recrcut [RECursion - CUTing Radius]
... tfw_toldfe [Thomas-Fermi-Weizsacker: TOLerance on the DiFference of total Energy, for initialization steps]

Relevant internal variables:

... %userec [USE RECursion]

Input variables for experts:

... recnpath [RECursion - Number of point for PATH integral calculations]
... recnrec [RECursion - Number of RECursions]
... recptrott [RECursion - TROTTer parameter]
... rectesteg [RECursion - TEST on Electron Gas]
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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/mpiio/Input: t42.in

tests/paral/Input: t42.in

tests/v4/Input: t97.in

tests/v5/Input: t75.in t76.in

tests/v7/Input: t11.in
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### 4. References.

[Perrot1979] F. Perrot, "Gradient correction to the statistical electronic free energy at non-zero temperatures: Application to equation-of-state calculations", Phys. Rev. A 20, 586-594 (1979).

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