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.Version 3.0 of PHONONS
.Copyright (C) 1998-2025 ABINIT group (FB,JB).
ABINIT comes with ABSOLUTELY NO WARRANTY.
It is free software, and you are welcome to redistribute it
under certain conditions (GNU General Public License,
see ~abinit/COPYING or http://www.gnu.org/copyleft/gpl.txt).
ABINIT is a project of the Universite Catholique de Louvain,
Corning Inc. and other collaborators, see
~abinit/doc/developers/contributors.txt .
Please read https://docs.abinit.org/theory/acknowledgments for suggested
acknowledgments of the ABINIT effort.
For more information, see http://www.abinit.org .
.Starting date : 13 Sep 2024.
#############################################################################
######################### ECHO OF INPUT FILE ################################
#############################################################################
======================= Define the unitcell =================================
brav 7 -3
natom_unitcell 1
xred_unitcell
0.0000000000 0.0000000000 0.0000000000
typat_unitcell 1
ntypat 1
amu 26.9815390000
======================= Define the supercell ================================
rprimd
22.9089998000 0.0000000000 0.0000000000
0.0000000000 22.9089998000 0.0000000000
0.0000000000 0.0000000000 22.9089998000
multiplicity
-3.0000000000 3.0000000000 3.0000000000
3.0000000000 -3.0000000000 3.0000000000
3.0000000000 3.0000000000 -3.0000000000
natom 108
typat
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
temperature 900.0000000000
======================= Define computational details ========================
nstep_max 20
nstep_min 1
rcut 11.4500000000
======================= Optional input variables ============================
enunit 3 (Phonon frequencies in THz)
USE AVERAGE POSITIONS TO COMPUTE SPECTRUM
-Number of processors 1 1
All quantities are computed from nstep_min= 1
to nstep_max= 20
So, the real number of time steps is nstep= 20
The positions, forces and energies are extracted from the ASCII files: xred.dat, fcart.dat & etot.dat
#############################################################################
########################## Computed quantities ##############################
#############################################################################
acell_unitcell= 7.6363332667 7.6363332667 7.6363332667
rprimd_md= 22.9089998000 0.0000000000 0.0000000000
rprimd_md= 0.0000000000 22.9089998000 0.0000000000
rprimd_md= 0.0000000000 0.0000000000 22.9089998000
bravais= 7 -3 1 -1 0 1 0 1 0 -1 1
See the sym.dat file
#############################################################################
########################## Q points generation #############################
#############################################################################
Generate the BZ path using the Q points defined by default
See the qpt.dat file
#############################################################################
###### Find the matching between ideal and average positions ###############
#############################################################################
Determine ideal positions and distances...
Compute average positions...
Search the unitcell basis of atoms in the MD trajectory...
Compare ideal and average positions using PBC...
Write the xred_average.xyz file with ideal and average positions...
Compute cartesian coordinates and forces...
#############################################################################
###################### Find the symetry operations ##########################
#################### (connecting the atoms together) ########################
#############################################################################
Search the matrix transformation going from (k) to (i)...
Search the matrix transformation going from (k,l) to (i,j)...
See the Indsym*.dat files (if debug)
#############################################################################
####### FIRST ORDER : find the number of coefficients #######################
#############################################################################
Build the ref1at and Isym1at tables...
Build the Shell1at datatype...
Number of shells= 1
============================================================================
Shell number: 1
For atom 1:
Number of independant coefficients in this shell= 0
Number of interactions in this shell= 0
============================================================================
>>>>>> Total number of coefficients at the first order= 0
#############################################################################
###### SECOND ORDER : find the number of coefficients #######################
#############################################################################
Build the ref2at and Isym2at tables...
Build the Shell2at datatype...
Number of shells= 5
============================================================================
Shell number: 1
Between atom 1 and 1 the distance is= 0.0000000000
Number of independant coefficients in this shell= 0
Number of interactions in this shell= 1
============================================================================
Shell number: 2
Between atom 1 and 2 the distance is= 5.3997030363
Number of independant coefficients in this shell= 3
Number of interactions in this shell= 12
============================================================================
Shell number: 3
Between atom 1 and 4 the distance is= 7.6363332667
Number of independant coefficients in this shell= 2
Number of interactions in this shell= 6
============================================================================
Shell number: 4
Between atom 1 and 10 the distance is= 9.3525600046
Number of independant coefficients in this shell= 4
Number of interactions in this shell= 24
============================================================================
Shell number: 5
Between atom 1 and 16 the distance is= 10.7994060725
Number of independant coefficients in this shell= 3
Number of interactions in this shell= 12
============================================================================
>>>>>> Total number of coefficients at the second order= 12
#############################################################################
############## Fill the matrices used in the pseudo-inverse #################
#############################################################################
Compute the coefficients (at the 1st order) used in the Moore-Penrose...
------- achieved
Compute the coefficients (at the 2nd order) used in the Moore-Penrose...
------- achieved
#############################################################################
###################### Compute the constraints ##############################
########################## At the 1st order #################################
########################## At the 2nd order #################################
################## Reduce the number of constraints #########################
############### (Solve simultaneously all the orders) #######################
################### And compute the pseudo-inverse ##########################
#############################################################################
The problem is solved
#############################################################################
#### For each shell, list of coefficients (IFC), number of neighbours... ####
#############################################################################
############# List of (first order) IFC for the reference atom= 1
0.000000 0.000000 0.000000
#############################################################################
#### For each shell, list of coefficients (IFC), number of neighbours... ####
#############################################################################
############# List of (second order) IFC for the reference atom= 1
======== NEW SHELL (ishell= 1): There are 1 atoms on this shell at distance= 0.000000
For jatom= 1 ,with type= 1
0.044568 0.000000 0.000000
0.000000 0.044568 0.000000
0.000000 0.000000 0.044568
The components of the vector are: 0.000000 0.000000 0.000000
Trace= 0.133703
======== NEW SHELL (ishell= 2): There are 12 atoms on this shell at distance= 5.399703
For jatom= 2 ,with type= 1
-0.006188 -0.007055 0.000000
-0.007055 -0.006188 0.000000
0.000000 0.000000 0.001595
The components of the vector are: 3.818167 3.818167 0.000000
Trace= -0.010781
For jatom= 3 ,with type= 1
-0.006188 0.000000 -0.007055
0.000000 0.001595 0.000000
-0.007055 0.000000 -0.006188
The components of the vector are: 3.818167 0.000000 3.818167
Trace= -0.010781
For jatom= 5 ,with type= 1
-0.006188 0.007055 0.000000
0.007055 -0.006188 0.000000
0.000000 0.000000 0.001595
The components of the vector are: -3.818167 3.818167 0.000000
Trace= -0.010781
For jatom= 8 ,with type= 1
-0.006188 0.000000 0.007055
0.000000 0.001595 0.000000
0.007055 0.000000 -0.006188
The components of the vector are: -3.818167 0.000000 3.818167
Trace= -0.010781
For jatom= 9 ,with type= 1
0.001595 0.000000 0.000000
0.000000 -0.006188 -0.007055
0.000000 -0.007055 -0.006188
The components of the vector are: 0.000000 3.818167 3.818167
Trace= -0.010781
For jatom= 19 ,with type= 1
-0.006188 0.007055 0.000000
0.007055 -0.006188 0.000000
0.000000 0.000000 0.001595
The components of the vector are: 3.818167 -3.818167 0.000000
Trace= -0.010781
For jatom= 34 ,with type= 1
-0.006188 0.000000 0.007055
0.000000 0.001595 0.000000
0.007055 0.000000 -0.006188
The components of the vector are: 3.818167 0.000000 -3.818167
Trace= -0.010781
For jatom= 38 ,with type= 1
-0.006188 -0.007055 0.000000
-0.007055 -0.006188 0.000000
0.000000 0.000000 0.001595
The components of the vector are: -3.818167 -3.818167 0.000000
Trace= -0.010781
For jatom= 43 ,with type= 1
0.001595 0.000000 0.000000
0.000000 -0.006188 0.007055
0.000000 0.007055 -0.006188
The components of the vector are: 0.000000 -3.818167 3.818167
Trace= -0.010781
For jatom= 59 ,with type= 1
-0.006188 0.000000 -0.007055
0.000000 0.001595 0.000000
-0.007055 0.000000 -0.006188
The components of the vector are: -3.818167 0.000000 -3.818167
Trace= -0.010781
For jatom= 60 ,with type= 1
0.001595 0.000000 0.000000
0.000000 -0.006188 0.007055
0.000000 0.007055 -0.006188
The components of the vector are: 0.000000 3.818167 -3.818167
Trace= -0.010781
For jatom= 101 ,with type= 1
0.001595 0.000000 0.000000
0.000000 -0.006188 -0.007055
0.000000 -0.007055 -0.006188
The components of the vector are: 0.000000 -3.818167 -3.818167
Trace= -0.010781
======== NEW SHELL (ishell= 3): There are 6 atoms on this shell at distance= 7.636333
For jatom= 4 ,with type= 1
-0.000579 0.000000 0.000000
0.000000 0.000955 0.000000
0.000000 0.000000 0.000955
The components of the vector are: -7.636333 0.000000 0.000000
Trace= 0.001331
For jatom= 6 ,with type= 1
0.000955 0.000000 0.000000
0.000000 -0.000579 0.000000
0.000000 0.000000 0.000955
The components of the vector are: 0.000000 7.636333 0.000000
Trace= 0.001331
For jatom= 11 ,with type= 1
0.000955 0.000000 0.000000
0.000000 0.000955 0.000000
0.000000 0.000000 -0.000579
The components of the vector are: 0.000000 0.000000 7.636333
Trace= 0.001331
For jatom= 14 ,with type= 1
-0.000579 0.000000 0.000000
0.000000 0.000955 0.000000
0.000000 0.000000 0.000955
The components of the vector are: 7.636333 0.000000 0.000000
Trace= 0.001331
For jatom= 18 ,with type= 1
0.000955 0.000000 0.000000
0.000000 -0.000579 0.000000
0.000000 0.000000 0.000955
The components of the vector are: 0.000000 -7.636333 0.000000
Trace= 0.001331
For jatom= 32 ,with type= 1
0.000955 0.000000 0.000000
0.000000 0.000955 0.000000
0.000000 0.000000 -0.000579
The components of the vector are: 0.000000 0.000000 -7.636333
Trace= 0.001331
======== NEW SHELL (ishell= 4): There are 24 atoms on this shell at distance= 9.352560
For jatom= 10 ,with type= 1
-0.000306 0.000038 -0.000026
0.000038 0.000006 0.000038
-0.000026 0.000038 -0.000306
The components of the vector are: 3.818167 7.636333 3.818167
Trace= -0.000606
For jatom= 12 ,with type= 1
-0.000306 -0.000026 0.000038
-0.000026 -0.000306 0.000038
0.000038 0.000038 0.000006
The components of the vector are: 3.818167 3.818167 7.636333
Trace= -0.000606
For jatom= 21 ,with type= 1
0.000006 -0.000038 -0.000038
-0.000038 -0.000306 -0.000026
-0.000038 -0.000026 -0.000306
The components of the vector are: -7.636333 3.818167 3.818167
Trace= -0.000606
For jatom= 22 ,with type= 1
-0.000306 -0.000038 0.000026
-0.000038 0.000006 0.000038
0.000026 0.000038 -0.000306
The components of the vector are: -3.818167 7.636333 3.818167
Trace= -0.000606
For jatom= 24 ,with type= 1
-0.000306 -0.000038 -0.000026
-0.000038 0.000006 -0.000038
-0.000026 -0.000038 -0.000306
The components of the vector are: 3.818167 -7.636333 3.818167
Trace= -0.000606
For jatom= 26 ,with type= 1
-0.000306 0.000026 -0.000038
0.000026 -0.000306 0.000038
-0.000038 0.000038 0.000006
The components of the vector are: -3.818167 3.818167 7.636333
Trace= -0.000606
For jatom= 33 ,with type= 1
-0.000306 -0.000026 -0.000038
-0.000026 -0.000306 -0.000038
-0.000038 -0.000038 0.000006
The components of the vector are: 3.818167 3.818167 -7.636333
Trace= -0.000606
For jatom= 39 ,with type= 1
0.000006 0.000038 0.000038
0.000038 -0.000306 -0.000026
0.000038 -0.000026 -0.000306
The components of the vector are: 7.636333 3.818167 3.818167
Trace= -0.000606
For jatom= 42 ,with type= 1
-0.000306 0.000038 0.000026
0.000038 0.000006 -0.000038
0.000026 -0.000038 -0.000306
The components of the vector are: -3.818167 -7.636333 3.818167
Trace= -0.000606
For jatom= 49 ,with type= 1
-0.000306 0.000026 0.000038
0.000026 -0.000306 -0.000038
0.000038 -0.000038 0.000006
The components of the vector are: 3.818167 -3.818167 7.636333
Trace= -0.000606
For jatom= 56 ,with type= 1
-0.000306 0.000026 0.000038
0.000026 -0.000306 -0.000038
0.000038 -0.000038 0.000006
The components of the vector are: -3.818167 3.818167 -7.636333
Trace= -0.000606
For jatom= 61 ,with type= 1
-0.000306 0.000038 0.000026
0.000038 0.000006 -0.000038
0.000026 -0.000038 -0.000306
The components of the vector are: 3.818167 7.636333 -3.818167
Trace= -0.000606
For jatom= 66 ,with type= 1
0.000006 0.000038 -0.000038
0.000038 -0.000306 0.000026
-0.000038 0.000026 -0.000306
The components of the vector are: -7.636333 -3.818167 3.818167
Trace= -0.000606
For jatom= 70 ,with type= 1
-0.000306 -0.000026 -0.000038
-0.000026 -0.000306 -0.000038
-0.000038 -0.000038 0.000006
The components of the vector are: -3.818167 -3.818167 7.636333
Trace= -0.000606
For jatom= 81 ,with type= 1
-0.000306 0.000026 -0.000038
0.000026 -0.000306 0.000038
-0.000038 0.000038 0.000006
The components of the vector are: 3.818167 -3.818167 -7.636333
Trace= -0.000606
For jatom= 83 ,with type= 1
0.000006 -0.000038 0.000038
-0.000038 -0.000306 0.000026
0.000038 0.000026 -0.000306
The components of the vector are: -7.636333 3.818167 -3.818167
Trace= -0.000606
For jatom= 84 ,with type= 1
-0.000306 -0.000038 -0.000026
-0.000038 0.000006 -0.000038
-0.000026 -0.000038 -0.000306
The components of the vector are: -3.818167 7.636333 -3.818167
Trace= -0.000606
For jatom= 86 ,with type= 1
-0.000306 -0.000038 0.000026
-0.000038 0.000006 0.000038
0.000026 0.000038 -0.000306
The components of the vector are: 3.818167 -7.636333 -3.818167
Trace= -0.000606
For jatom= 87 ,with type= 1
0.000006 -0.000038 0.000038
-0.000038 -0.000306 0.000026
0.000038 0.000026 -0.000306
The components of the vector are: 7.636333 -3.818167 3.818167
Trace= -0.000606
For jatom= 96 ,with type= 1
-0.000306 -0.000026 0.000038
-0.000026 -0.000306 0.000038
0.000038 0.000038 0.000006
The components of the vector are: -3.818167 -3.818167 -7.636333
Trace= -0.000606
For jatom= 97 ,with type= 1
0.000006 0.000038 -0.000038
0.000038 -0.000306 0.000026
-0.000038 0.000026 -0.000306
The components of the vector are: 7.636333 3.818167 -3.818167
Trace= -0.000606
For jatom= 100 ,with type= 1
-0.000306 0.000038 -0.000026
0.000038 0.000006 0.000038
-0.000026 0.000038 -0.000306
The components of the vector are: -3.818167 -7.636333 -3.818167
Trace= -0.000606
For jatom= 107 ,with type= 1
0.000006 0.000038 0.000038
0.000038 -0.000306 -0.000026
0.000038 -0.000026 -0.000306
The components of the vector are: -7.636333 -3.818167 -3.818167
Trace= -0.000606
For jatom= 108 ,with type= 1
0.000006 -0.000038 -0.000038
-0.000038 -0.000306 -0.000026
-0.000038 -0.000026 -0.000306
The components of the vector are: 7.636333 -3.818167 -3.818167
Trace= -0.000606
======== NEW SHELL (ishell= 5): There are 12 atoms on this shell at distance=10.799406
For jatom= 16 ,with type= 1
-0.000007 -0.000080 0.000000
-0.000080 -0.000007 0.000000
0.000000 0.000000 0.000199
The components of the vector are: -7.636333 7.636333 0.000000
Trace= 0.000185
For jatom= 25 ,with type= 1
-0.000007 0.000000 -0.000080
0.000000 0.000199 0.000000
-0.000080 0.000000 -0.000007
The components of the vector are: -7.636333 0.000000 7.636333
Trace= 0.000185
For jatom= 27 ,with type= 1
0.000199 0.000000 0.000000
0.000000 -0.000007 0.000080
0.000000 0.000080 -0.000007
The components of the vector are: 0.000000 7.636333 7.636333
Trace= 0.000185
For jatom= 35 ,with type= 1
-0.000007 0.000080 0.000000
0.000080 -0.000007 0.000000
0.000000 0.000000 0.000199
The components of the vector are: 7.636333 7.636333 0.000000
Trace= 0.000185
For jatom= 37 ,with type= 1
-0.000007 0.000080 0.000000
0.000080 -0.000007 0.000000
0.000000 0.000000 0.000199
The components of the vector are: -7.636333 -7.636333 0.000000
Trace= 0.000185
For jatom= 44 ,with type= 1
-0.000007 0.000000 0.000080
0.000000 0.000199 0.000000
0.000080 0.000000 -0.000007
The components of the vector are: 7.636333 0.000000 7.636333
Trace= 0.000185
For jatom= 48 ,with type= 1
0.000199 0.000000 0.000000
0.000000 -0.000007 -0.000080
0.000000 -0.000080 -0.000007
The components of the vector are: 0.000000 -7.636333 7.636333
Trace= 0.000185
For jatom= 55 ,with type= 1
-0.000007 0.000000 0.000080
0.000000 0.000199 0.000000
0.000080 0.000000 -0.000007
The components of the vector are: -7.636333 0.000000 -7.636333
Trace= 0.000185
For jatom= 57 ,with type= 1
0.000199 0.000000 0.000000
0.000000 -0.000007 -0.000080
0.000000 -0.000080 -0.000007
The components of the vector are: 0.000000 7.636333 -7.636333
Trace= 0.000185
For jatom= 62 ,with type= 1
-0.000007 -0.000080 0.000000
-0.000080 -0.000007 0.000000
0.000000 0.000000 0.000199
The components of the vector are: 7.636333 -7.636333 0.000000
Trace= 0.000185
For jatom= 76 ,with type= 1
-0.000007 0.000000 -0.000080
0.000000 0.000199 0.000000
-0.000080 0.000000 -0.000007
The components of the vector are: 7.636333 0.000000 -7.636333
Trace= 0.000185
For jatom= 80 ,with type= 1
0.000199 0.000000 0.000000
0.000000 -0.000007 0.000080
0.000000 0.000080 -0.000007
The components of the vector are: 0.000000 -7.636333 -7.636333
Trace= 0.000185
#############################################################################
############## Compute the phonon spectrum, the DOS, ########################
############## the dynamical matrix and write them ########################
#############################################################################
#############################################################################
################### vibrational Density OF States (vDOS) ####################
#############################################################################
See the vdos.dat and TDEP_PHDOS* files
Write the IFC of TDEP in ifc_out.dat (and ifc_out.nc)
------- achieved
Compute the vDOS
------- achieved
(Please, pay attention to convergency wrt the BZ mesh : the ngqpt2 input variable)
See the dij.dat, omega.dat and eigenvectors files
See also the DDB file
#############################################################################
######################### Elastic constants #################################
################ Bulk and Shear modulus--Sound velocities ###################
#############################################################################
========== Using the formulation proposed by Wallace (using the IFC) =========
Cijkl [in GPa]=
| C11 C12 C13 C14 C15 C16 | 113.760 61.649 61.649 0.000 0.000 0.000
| C21 C22 C23 C24 C25 C26 | 61.649 113.760 61.649 0.000 0.000 0.000
| C31 C32 C33 C34 C35 C36 | 61.649 61.649 113.760 0.000 0.000 0.000
| C41 C42 C43 C44 C45 C46 | = 0.000 0.000 0.000 38.243 0.000 0.000
| C51 C52 C53 C54 C55 C56 | 0.000 0.000 0.000 0.000 38.243 0.000
| C61 C62 C63 C64 C65 C66 | 0.000 0.000 0.000 0.000 0.000 38.243
========== For an Anisotropic Material =======================================
Sijkl [in GPa-1]=
| S11 S12 S13 S14 S15 S16 | 0.014 -0.005 -0.005 0.000 0.000 -0.000
| S21 S22 S23 S24 S25 S26 | -0.005 0.014 -0.005 0.000 0.000 -0.000
| S31 S32 S33 S34 S35 S36 | -0.005 -0.005 0.014 0.000 0.000 -0.000
| S41 S42 S43 S44 S45 S46 | = 0.000 0.000 0.000 0.026 0.000 -0.000
| S51 S52 S53 S54 S55 S56 | 0.000 0.000 0.000 0.000 0.026 -0.000
| S61 S62 S63 S64 S65 S66 | 0.000 0.000 0.000 0.000 0.000 0.026
========== For an Orthotropic Material (see B. M. Lempriere (1968)) ==========
Young modulus E1, E2 and E3 [in GPa]= 70.427 70.427 70.427
Poisson ratio Nu21, Nu31, Nu23, Nu12, Nu13 and Nu32= 0.351 0.351 0.351 0.351 0.351 0.351
Shear modulus G23, G13 and G12 [in GPa]= 38.243 38.243 38.243
Sijkl [in GPa-1]=
| S11 S12 S13 S14 S15 S16 | 0.014 -0.005 -0.005 0.000 0.000 0.000
| S21 S22 S23 S24 S25 S26 | -0.005 0.014 -0.005 0.000 0.000 0.000
| S31 S32 S33 S34 S35 S36 | -0.005 -0.005 0.014 0.000 0.000 0.000
| S41 S42 S43 S44 S45 S46 | = 0.000 0.000 0.000 0.026 0.000 0.000
| S51 S52 S53 S54 S55 S56 | 0.000 0.000 0.000 0.000 0.026 0.000
| S61 S62 S63 S64 S65 S66 | 0.000 0.000 0.000 0.000 0.000 0.026
For density rho [in kg.m-3]= 2715.988
========================= Voigt average (constant strain) ===================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 79.019 and Shear G= 33.368
Average of Young modulus E [in GPa]= 87.752 Lame modulus Lambda [in GPa]= 56.774 and Poisson ratio Nu= 0.315
Velocities [in m.s-1]: compressional Vp= 6743.529 shear Vs= 3505.115 and bulk Vphi= 5393.893
Debye velocity [in m.s-1]= 3922.618 and temperature [in K]= 458.761
========================= Reuss average (constant stress) ===================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 79.019 and Shear G= 32.216
Average of Young modulus E [in GPa]= 85.084 Lame modulus Lambda [in GPa]= 57.542 and Poisson ratio Nu= 0.321
Velocities [in m.s-1]: compressional Vp= 6701.449 shear Vs= 3444.053 and bulk Vphi= 5393.893
Debye velocity [in m.s-1]= 3857.101 and temperature [in K]= 451.098
============================== Hill average =================================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 79.019 and Shear G= 32.792
Average of Young modulus E [in GPa]= 86.421 Lame modulus Lambda [in GPa]= 57.158 and Poisson ratio Nu= 0.318
Velocities [in m.s-1]: compressional Vp= 6722.522 shear Vs= 3474.718 and bulk Vphi= 5393.893
Debye velocity [in m.s-1]= 3890.016 and temperature [in K]= 454.948
========================= Elastic anisotropy =================================
Elastic anisotropy index : A_U= 5*G_V/G_R + K_V/K_R - 6 = 0.179
Bulk anisotropy ratio : A_B= (B_V-B_R)/(B_V+B_R) = 0.000
Shear anisotropy ratio : A_G= (G_V-G_R)/(G_V+G_R) = 0.018
#############################################################################
######################### Energies, errors,... #############################
#############################################################################
Thermodynamic quantities and convergence parameters of THE MODEL,
as a function of the step number (energies in eV/atom and forces in Ha/bohr) :
<U_TDEP> = U_0 + U_1 + U_2
with U_0 = < U_MD - sum_i Phi1 ui - 1/2 sum_ij Phi2 ui uj >
and U_1 = < sum_i Phi1 ui >
and U_2 = < 1/2 sum_ij Phi2 ui uj >
Delta_U = < U_MD - U_TDEP >
Delta_U2= (< (U_MD - U_TDEP)^2 >)**0.5
Delta_F2= (< (F_MD - F_TDEP)^2 >)**0.5
Sigma = (< (F_MD - F_TDEP)^2 >/<F_MD**2>)**0.5
<U_MD> U_0 U_1 U_2 Delta_U Delta_U2 Delta_F2 Sigma
-56.30133 -56.40725 0.00000 0.10592 0.00000 0.38259 0.00631 0.50615
NOTE : in the harmonic and classical limit (T>>T_Debye), U_2=3/2*kB*T= 0.11633
See the etotMDvsTDEP.dat & fcartMDvsTDEP.dat files
#############################################################################
################# Thermodynamic quantities: Free energy,...##################
#############################################################################
See the thermo.dat file
#############################################################################
######################### CALCULATION COMPLETED #############################
#############################################################################
Suggested references for the acknowledgment of ABINIT usage.
The users of ABINIT have little formal obligations with respect to the ABINIT group
(those specified in the GNU General Public License, http://www.gnu.org/copyleft/gpl.txt).
However, it is common practice in the scientific literature,
to acknowledge the efforts of people that have made the research possible.
In this spirit, please find below suggested citations of work written by ABINIT developers,
corresponding to implementations inside of ABINIT that you have used in the present run.
Note also that it will be of great value to readers of publications presenting these results,
to read papers enabling them to understand the theoretical formalism and details
of the ABINIT implementation.
For information on why they are suggested, see also https://docs.abinit.org/theory/acknowledgments.
[1] a-TDEP: Temperature Dependent Effective Potential for Abinit
-- Lattice dynamic properties including anharmonicity
F. Bottin, J. Bieder and J. Bouchet, Comput. Phys. Comm. 254, 107301 (2020).
Strong suggestion to cite this paper in your publications.
[2] Thermal evolution of vibrational properties of alpha-U
J. Bouchet and F. Bottin, Phys. Rev. B 92, 174108 (2015).
Strong suggestion to cite this paper in your publications.
[3] Lattice dynamics of anharmonic solids from first principles
O. Hellman, I.A. Abrikosov and S.I. Simak, Phys. Rev. B 84, 180301(R) (2011).
[4] Temperature dependent effective potential method for accurate free energy calculations of solids
O. Hellman, P. Steneteg, I.A. Abrikosov and S.I. Simak, Phys. Rev. B 87, 104111 (2013).
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