# The tdep utility¶

The Temperature Dependent Effective Potential (TDEP) method has been developped by O. Hellman et al. [Hellman2011], [Hellman2013], [Hellman2013a] in 2011 and the a-TDEP implementation in ABINIT has been performed and used for the first time in 2015 by J. Bouchet and F. Bottin [Bouchet2015], [Bouchet2017].

This manual can be found as a pdf file: TDEP guide

## Prerequisite and theory¶

The approach used in this code is detailed in a publication dedicated to the development of all formula (see TDEP paper). We strongly encourage all the users to carefully read this paper before beginning. All the vibrational, elastic and thermodynamic quantities computed by a-TDEP are presented with the same writing conventions as the ones used in the output files of a-TDEP . In the same manner, a comprehensive understanding of some ABINIT basic variables is also required in order to fill the input file and read the output file of a-TDEP .

In addition, this paper is also useful to understand the limitations and convergences which are inherent to the present method. These particular points are sometimes discussed in the article, with some references and illustrating examples.

## The ABINIT computation¶

To run a-TDEP , a preliminary ABINIT simulation is needed. This one could be a molecular dynamic trajectory or a set of “ground state” calculations on specific configurations (representative of a given thermodynamic state). After that, all the configurations have to be merged: (i) in a single NetCDF file HIST.nc or (ii) in three separated ASCII files fcart.dat, xred.dat and etot.dat (forces in cartesian coordinates, positions in reduced coordinates, total energies in Ha), as they are written in the output file of ABINIT. In the later case, the 3 files can be built easily by concatenating in each one all the time steps or configurations (using agrep shell instruction, for example).

## The a-TDEP computation¶

In a same manner as performed for ABINIT, the use of a-TDEP is quite simple. One has just to execute tdep as follows:

    tdep < input.files > log


with the input.files file containing 3 lines. The first one defines the input file, the second one is the NetCDF file (if present, see above) and the third one defines the root of all the output files:

input.in
HIST.nc
output


The detection of the HIST.nc file is performed at the beginning; so, if this one is absent, the code will automatically search the 3 ASCII.dat files.

## The input files¶

An example of a a-TDEP calculation (in the special case where the NetCDF file HIST.nc is employed) can be found in v8[37]. The 2 input files are given in the tests/v8/Input directory.
Let us describe briefly this v8[37] file:

The input file format is fixed. So:

1. This file begins with a NormalMode or DebugMode keyword and finishes with TheEnd (all the lines after are not read).
2. All the lines between # Unit cell definition and # Optional inputs are fixed.
3. Between # Optional inputs and TheEnd, the format is free.

More details:

• The section # Unit cell definition defines the bravais lattice brav (here, a simple cubic), the number of atoms in the unit cell natom_unitcell (here, 5 atoms), their reduced coordinates in the unit cell xred_unitcell (here, a perovskite) and the type of atoms in the unit cell typat_unitcell (here, one atom A, one atom B and 3 atoms C).
• The section # Supercell definition defines the multiplicity of the supercell with respect to the unit cell multiplicity (here, it is a simple 2x2x2 multiplication of the unit cell) and the temperature of the system temperature(here, 495.05 K).
• The section # Computation details defines the range nstep_maxnstep_min of time steps or configurations (here, 100 time steps) and the cutoff radius for the pair interactions Rcut (here, all the interaction pairs with a bond length larger than 7.426 bohr will not be considered).
• The section # Optional inputs can define a large number of optional keywords (here ngqpt2 defining the q-point grid for the vDOS integration is set to 2 2 2 in order to have a test sufficiently fast, which means that all the thermodynamic quantities have no sense.) All the input variables are defined in the tdep section of the input variables description. Note that some input variables, not defined in the input.in file, are obtained from the HIST.nc file. In particular, the features of the supercell.

TODO: Explain the extra input variables when the 3 ASCII files are employed.

## The output files¶

A large number of output files are obtained after an execution of a-TDEP .

1. *.out is the main output file. It includes an echo of the input variables, some intermediary results, the definition of the various shells of interaction, the second order IFCs for all the atoms in each shell, the elastic constants and moduli, the energy of the model…
2. *omega.dat contains the dispersion of phonon frequencies (in meV) along a path in the Brillouin Zone.
3. *thermo.dat lists all the thermodynamic quantities obtained by considering the system as a quantum harmonic crystal: specific heat, vibrational energy, entropy and free energy. It also gives all these contributions as a function of temperature in the harmonic approximation.
4. sym.dat details all the symmetry operations of the bravais lattice,
5. qpt.dat defines the q-point grid used to compute the phonon frequencies contained in the omega.dat file.
6. xredaverage.xyz includes the ideal and average positions in the supercell.
7. Indym*.dat contain all the symmetry relations between one or two atoms in the unit cell or the supercell.
8. vdos.dat displays the vibrational density of states (in meV).
9. dij.dat lists the dynamical matrices for a particular set of q-points.
10. etotMDvsTDEP2.dat compares the MD trajectory with the one computed using the second order IFCs (these ones must be superimposed, as much as possible).
11. fcartMDvsTDEP2.dat plots the MD forces wrt the forces computed using the second order IFCs (the cloud of points must be closer to the first bisector).
12. eigenvectors.dat lists all the eigenvectors for a particular set of q-points.
13. nbcoeff-phij.dat shows how the number of IFC coefficients are reduced (for each shell and each symmetry).