3.20 what='elastic_constants_geo'

With this option the code can compute the elastic constants and elastic compliances as a function of temperature using the quasi-harmonic approximation. For the same geometries that are used to compute the elastic constants with the elastic_algorithm='energy_std' or elastic_algorithm= 'energy', the code can compute the phonon dispersions and compute the elastic constants at each temperature as the second derivatives of the Helmholtz free energy with respect to strain. The second derivatives are corrected so that the stress-strain elastic constants are shown in the plots and in output. The temperature dependent elastic constants are calculated on a regular grid of unperturbed geometries, the same geometries chosen by the option what='mur_lc', and written on separate files, one for each unperturbed geometry, inside the directory anhar_files. In order to plot the elastic constants as a function of temperature within the `quasi-harmonic' approximation, it is necessary to make another calculation with what='mur_lc_t' having on files the elastic constants calculated for each geometry with the present option. In this case thermo_pw will be able to calculate the anharmonic properties using temperature dependent elastic constants and bulk moduli obtained by interpolating the ``fixed-geometry quasi-harmonic'' elastic constants computed by this option at the crystal parameters found at each temperature from the minimization of the free energy. The variables fact_ngeo and ngeo_ph are not available with this option. Using start_geometry_qha and last_geometry_qha it is possible to compute the temperature dependent elastic constants for selected or for a single unperturbed configuration. The use of start_geometry and last_geometry is also allowed but it refers to the global number of geometries necessary to compute the elastic constants in all the grid.

Since the calculation of the Helmholtz free energy derivatives is quite heavy, it has to be requested explicitly using the flag use_free_energy=.TRUE..
By default, the code computes only the elastic constants at T = 0 K as second derivatives of the energy and writes them on files in the directory elastic_ constants. A run of thermo_pw using what='mur_lc_t' having on files the T = 0 K elastic constants in the directory elastic_constants allows the calculation of the anharmonic properties using temperature dependent elastic constants and bulk moduli obtained by interpolating (within the ``quasi-static approximation") the elastic constants computed by this option at the crystal parameters that, at each temperature, minimize the free energy. When both the T = 0 K and the temperature dependent elastic constants are on file in the directory elastic_constants and anhar_files respectively, the latter are used. When both use_free_energy=.TRUE. and lel_free_energy=.TRUE. the electronic free energy is added to the free energy before computing the elastic constants. In this case the code expects to find on file (in therm_files) the electronic thermodynamic properties for each perturbed geometry. These files are produced with this same option and the flags use_free_energy=.FALSE. and lel_free_energy= .TRUE.. In this case the code computes the electronic thermodynamic properties at each perturbed geometry and writes them on file, without calculating the elastic constants. Note that the user must be careful to use the same value for the lel_free_energy flag with this option and in the following mur_lc_t calculation that interpolates the elastic constants. After computing the elastic constants at T = 0 K with the present option one can also run another thermo_pw calculation with the option what='mur_lc' computing the crystal parameters for a range of pressures (using pmax and pmin input variables). If the elastic constants are found in the directory elastic_constants they are interpolated at the pressure dependent crystal parameters and plotted on output. The variables that control this run are:

use_free_energy : when .TRUE. computes the elastic constants 
              as second derivatives of the Helmholtz free 
              energy with respect to strain. When .FALSE. 
              the elastic constants are computed as second 
              derivatives of the energy or using the 
              stress-strain algorithms.
              Default: .FALSE.
start_geometry_qha : Among the geometries considered by the 
              option mur_lc_t the calculations of elastic 
              constants are done starting from this geometry.
              Default: integer 1
last_geometry_qha : Among the geometries considered by the 
              option mur_lc_t the calculations of elastic 
              constants are done only up to this geometry.
              Default: integer total number of geometries.

An example for this option with use_free_energy=.FALSE. can be found in example22 while an example with use_free_energy=.TRUE. can be found in example23.
Number of tasks for this option: The product of the number of tasks needed by the what='scf_elastic_constants' option and the number of geometries used with what=mur_lc_t when use_free_energy=.FALSE.. When use_free_ energy=.TRUE. and all_geometries_together=.TRUE. the number of tasks of the previous case is further multiplied by the number of tasks needed to compute a phonon dispersion (see above the option what='scf_ph').
When use_free_energy=.TRUE. and all_geometries_together=.FALSE. the number of tasks of this option is equal to the number of tasks needed to compute a phonon dispersion.