__________________________________________________
VIBRATIONAL ENTROPY OF CRYSTALLINE SOLIDS FROM
COVARIANCE OF ATOMIC DISPLACEMENTS
Yang Huang
__________________________________________________
<2023-01-18 Wed>
Table of Contents
_________________
1. Purpose
2. Contents
3. Required packages
4. How to install
5. List of tools
6. Pay attention to
1 Purpose
=========
This archive contains tools to calculate entropy from covariance
matrix based on method describe in Huang, Y.; Widom, M. Vibrational
Entropy of Crystalline Solids from Covariance of Atomic Displacements.
Entropy 2022, 24, 618. <https://doi.org/10.3390/e24050618>. These
tools are designed especially for output from MD simulation
implemented in VASP. You are free to modify and redistribute the code
for general purpose.
2 Contents
==========
Following list of files should be contained in the directory:
- README
- install.sh
- src
Contain source files.
- example
Contain examples
- bin
Contain compiled binaries.
3 Required packages
===================
1) GSL - GNU Scientific Library
The GNU Scientific Library (GSL) is a numerical library for C and
C++ programmers. It is free software under the GNU General Public
License. It is installed on most linux systems. To install it,
check <https://www.gnu.org/software/gsl/>.
2) Aflow [optional]
The aflow-sym.sh requires AFLOW codes in order to run properly. To
install it, check <http://aflow.org/install-aflow/>.
3) pos2xyz and xyz2pos from euler
The xdat-ent program is originally written on euler so that it
utilizes certain mgtools on euler. Unfortunately the author is
unwilling to modify these codes to make it more convenient for
general users and you will have to ask for permissions to access
these tools.
The "pos2xyz" converts a POSCAR file to a XYZ file. The "xyz2pos"
converts a XYZ file to a POSCAR file.
4 How to install
================
Go to the main directory and run "./install.sh". It will compile the
source files and put binaries into the bin directory.
After you run the command, you run the test script "./test.sh" in the
examples directory.
5 List of tools
===============
[BEFORE YOU RUN]
- xdat-ent-init.sh
- Description
Preparing "Trun" and "Mass" input files for
"xdat-ent-rhoALL_quantum_mod" commands.
- Input:
- INCAR
- POTCAR
- /home/Tools/src/mgtools/INFO/CHTAB.
- Usage:
xdat-ent-init.sh *Only work on euler.
- Output:
Generate "Trun" and "Mass".
- aflow-sym.sh
- Description
This script utilizes "aflow" tools to help find symmetry
operations. It is recommended to run on a small cell for
efficiency.
- Input:
POSCAR or XYZ file.
- Usage:
aflow-sym.sh [ -x <xyz file> ] [ -p <POSCAR file> ]
- Output:
A "symmetry_operation.dat " which contains number of operations N
and N 3x3 operation matrix in direction space.
[WHEN YOU RUN]
- xdat-ent-rhoALL_quantum_mod tools
- Description
+ xdat-ent-rhoALL_quantum_mod
Pure element crystalline from NVT simulation
+ xdat-ent-rhoALL_quantum_npt
Pure element crystalline from NPT simulation
+ xdat-ent-rhoALL_quantum_alloy
Alloys from NVT simulation.
xdat-ent-rhoALL_quantum_mod has been tested to be robust while
only a few examples have been performed with
xdat-ent-rhoALL_quantum_npt and xdat-ent-rhoALL_quantum_alloy
command. So be careful with these two commands!
- Input:
"example" directory provides examples of input files.
- Trun
This file contains in value which is the temperature of MD
simulation.
- Mass
This file contains three rows:
1. type of species.
2. atomic numbers.
3. atomic masses [a.u.] in atomic units.
- xyzfile
This file contains the ideal structure of a crystal. The first
three rows are lattice constants. The 4th row contains number of
atoms N. The following N rows should obeys: dx,dy,dz,na ...
where dx,dy,dz is directional vector and na is atomic number.
- symmetry-file
This file contains symmetry operation matrices U. The first row
is number of operations N and then it is followed by N 3x3
matrices U each of which is a operation matrix in directional
space (b'=Ub).
- XDATCAR
Output from VASP MD simulations.
- Usage:
xdat-ent-rhoALL_quantum_mod -f xyzfile -s symmetry-file XDATCAR* >
out
- Output:
+ covariance_pair.dat
3x3 covariance matrices in real space of all symmetry
distinguishing pairs.
+ density_matrix.dat
See reference for more mathematical description. A 3Nx3N matrix.
+ force_matrix.dat
See reference for more mathematical description. A 3Nx3N force
matrix.
+ Eigenvalues.dat
A 3Nx2 matrix. The first row are eigenvalues of density matrix.
The second row are frequencies (hbar*omega [eV]) of eigen modes
See reference for mathematical relation.
+ "out":
The last line of "out" reports calculated entropy with S_classic
(classical entropy) and S_quantum (quantum entropy)
[AFTER YOU RUN]
- freq2quan.py
- Description
Calculate free energy F[eV/at], internal energy U [eV/at], entropy
S [kB/at] and heat capacity Cv [kB/at] from Eigenvalues.dat
- Input: "Trun", "Eigenvalues.dat"
- Usage: freq2quan.py
- Output: calculated quantities.
- force2dos
- Description
Calculate free energy F[eV/at], internal energy U [eV/at], entropy
S [kB/at] and heat capacity Cv [kB/at] from Eigenvalues.dat
- Input:
- "Trun", "force_matrix.dat", xyzfile
- KDim (an integer indicate kmesh KDimxKDimxKdim).
- recip_vectors of a primitive cell
3x3 matrix
- Usage:
force2dos xyzfile KDim > out;
- Output:
In "out" file, there are two columns of datas. The first column is
hbar*omega [meV]. The second one is vibrational DOS
[states/atom/meV].
- force2band
- Description
Calculate free energy F[eV/at], internal energy U [eV/at], entropy
S [kB/at] and heat capacity Cv [kB/at] from Eigenvalues.dat
- Input:
- "Trun", "force_matrix.dat", xyzfile
- KDim (an integer indicate kmesh KDimxKDimxKdim).
- recip_vectors of a primitive cell
3x3 matrix
- kpath
- Usage:
force2band xyzfile > out;
- Output:
Eigenvalues along kpath.
6 Pay attention to
==================
- symmetry operations:
Symmetry operations will greatly improve precision of calculated
entropy for a short run at a cost of calculation time. With symmetry
operation turned on, each configuration will be process N times
where N is the number of operations.
This program is known to give incorrect results when applied to
low-symmetry super cell from a highly symmetrical crystalline
structure, e.g. a 5x5x5 primitive cell of BCC Li. Hence, it is
recommended to run simulation at its high-symmetry unit cell. e.g. a
super cell of a 2-atom BCC unit cell or a 4-atom FCC unit cell.
- Eigenvalues.dat:
A reasonable calculation should give 3 zero eigenvalues in the first
column in Eigenvalues.dat and correspondingly 3 nan or large number
in the second column. So be careful with zero or nan values in
Eigenvalues.dat.
Imaginary modes may show up which are denoted as negative
eigenvalues. As long as there are 3 zero eigenvalues, we think the
program is doing its job.