Authors: John Kendrick and Andrew Burnett
The Python package PDielec calculates the infrared absorption characteristics of a crystalline material supported in a non absorbing medium by post processesing the output of solid state quantum mechanical and molecular mechanical calculations of the phonons or dielectric response of the crystalline material. The package calculates the internal electric field arising from different particle morphologies and calculates the resulting shift in absorption frequency and intensity arising from the coupling between a phonon and the internal field. The theory of the approach has been published. Any use of the package should cite; PDielec: The calculation of infrared and terahertz absorption for powdered crystals John Kendrick and Andrew D. Burnett Journal of Computational Chemistry 2016, vol 27, 1491-1504 DOI: 10.1002/jcc.24344
The molecular and solid state quantum mechanical calculations of response properties such as the frequencies and intensities of infrared (IR) and terahertz (THz) radiation absorption has become generally available in many molecular and solid state computer programs. A common approach is to assume the harmonic approximation and calculate the mass weighted force constant matrix (for molecules) or the dynamical matrix at the gamma point (for periodic solids). Diagonalisation of the matrix gives the frequencies for absorption and the normal modes (molecules) or phonon displacements (periodic solids). The calculation of the absorption intensity for each mode requires the calculation of the change in dipole moment caused by the displacement of the atoms for that mode. For solids where there is a large separation of charge, there can be a large coupling between a phonon mode and the internal field within a particle resulting from its morphology. The PDielec program is written in Python and post processes the output of solid state quantum mechanical (QM) and molecular mechanics (MM) based codes such as VASP, CASTEP, CRYSTAL14, Abinit, QuantumEspresso and GULP to predict the infrared absorption of crystalline insulator materials whose crystal size is small compared with the wavelength of the absorbing radiation. The package is suited for the calculation of the complex, frequency dependent permittivity and its associated absorption of infrared radiation for a finely ground crystalline material dispersed in a low loss dielectric medium such KBr or PTFE. A particular feature of the program is its ability to take into account the constant permittivity of the supporting medium and the particle shape through an effective medium theory.
The pdielec package is written in Python 2 and has been tested using python 2.7 on Linux and in Windows 10. The package is available on GitHub and can be downloaded from https://github.com/JohnKendrick/PDielec
git clone https://github.com/JohnKendrick/PDielec.git
Install Python 2 using the package manager for your version of Linux. In addition install python2 versions of numpy, scipy and matplotlib. In Ubuntu they are installed by;
sudo apt-get install python-dev python-numpy python-scipy python-matplotlib
Put the PDielec directory in your executable path, eg;
export PATH=~/PDielec;$PATH
Where python3 and python2 have been installed, it is important to ensure that the python command runs python2.
Install a version of Python 2.7 which incorporates SciPy. The program has been tested with the Anaconda system which is available from https://www.continuum.io/why-anaconda Anaconda includes all of the Python packages required by PDielec. On Windows install a version of Git. www.git-scm.com has a version of git based on mingw once this has been installed, a git shell can be used to clone a copy of PDielec from GitHub.
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PDielec/ is the home directory and contains the
pdieleccommand -
PDielec/Python holds the source for the modules used by the pdielec command
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PDielec/Examples a set of examples are available for CASTEP, GULP and VASP. Each example directory holds the input files to the QM/MM program and the relevant output files which are post processed by PDielec
Each example directory has the relevant input data sets use to run the QM/MM program and the output files from that run which are post-processed by PDielec. There is a file command.sh which contains a typical example of a PDielec command line and which has been used to create the reference output files command.ref.out and csvfile.ref.csv. The example can be run
bash command.sh
The output can be compared with the reference data to see if the program is working correctly.
The main Examples/ directory also has a Makefile file which can be used to verify the correct working of the package. Simply by typing make in the Examples directory each example will be run automatically and the output compared with the reference files. To remove the intermediate files after running the tests automatically, type make clean.
pdielec -method ap -method maxwell -sphere -plate 0 0 1 -needle 0 0 1 .
Performs a calculation using the Averaged-Permittivity and Maxwell-Garnett mixing rules for spherical particles, plate-like particles with a surface (001) and needle-like particles with a unique direction lying along the [001] direction. The supporting matrix is taken to be PTFE and the default volume fraction (10%) is used. The results of a VASP calculation are stored in the current directory. There is no absorption output from this command as neither the -plot nor the -csv options were specified.
pdielec -vmin 300 -vmax 800 -sphere -dielectric 3 -vf 0.1 -vf 0.2 -sigma 10 -csv mgo.csv phonon
Performs a calculation for spherical particles varying the frequency from 300 to 800 cm 1, the permittivity of the supporting media is 3, two volume fractions are considered and a damping factor of 10 cm-1 is used. The results of a CASTEP calculation with the seed-name “phonon” are analysed and the results stored in mgo.csv for further analysis using a spreadsheet. In this example a Maxwell-Garnett mixing rule is used by default. If visual inspection of the results is required then the following will perform the same calculation but a graph shown the molar absorption coefficients will be displayed.
pdielec -vmin 300 -vmax 800 -sphere -kbr 3 -vf 0.1 -vf 0.2 -sigma 10 -csv mgo.csv -plot molar_absorption phonon
The followng command performs a calculation of the absorption spectrum resulting from a GULP calculation. The supporting matrix density and permittivity are those of high density polyethylene, the frequency range is 0 to 2000 cm-1, the volume fraction considered is 10%, the mixing rules used are Averaged-Permittivity and Maxwell-Garnett. Spheres and plates with the (1 ̅1 ̅2 ̅) surface are considered.
pdielec -matrix hdpe -method ap -method maxwell -sphere -plate -1 -1 -2 -vmax 2000 -vf 0.1 calcite.gout -csv calcite.csv
Option |
Default |
Purpose |
Repeatable? |
-program s |
Specifies the program used in generating the output which will be analysed |
No |
|
-method s |
maxwell |
The method is given by the string s and may be either ap, maxwell or bruggeman |
Yes |
-sphere |
The inclusion is a sphere, the default if no other shape is given |
No |
|
-needle h k l |
The inclusion is a needle whose unique direction is given by [hkl] |
Yes |
|
-plate h k l |
The inclusion is a plate whose surface is defined by (hkl) |
Yes |
|
-ellipse h k l z |
The inclusion is an ellipsoid whose unique direction is given by [hkl] and the eccentricity is given by z |
Yes |
|
-vf z |
0.1 |
z specifies the volume fraction |
Yes |
-mf z |
0.0 |
z specifies the mass fraction |
Yes |
-matrix s |
ptfe |
The supporting matrix is defined by the string s. Options are ptfe, kbr, nujol, air, vacuum, ldpe, mdpe, hdpe |
Yes |
-density z |
2.2 |
z defines the density of the supporting matrix |
No |
-dielectric z |
2.0 |
z defines the dielectric of the supporting matrix |
No |
-sigma z |
5.0 |
z specifies the damping factor (or width) of the Lorentzian in cm-1 |
No |
-mode_sigma k z |
The kth mode is assigned a width of z cm-1 |
Yes |
|
-LO h k l |
The longitudinal optic frequencies are calculated for (hkl) |
Yes |
|
-LO_cart x y z |
The longitudinal optic frequencies are calculated for the cartesian direction x, y, z |
Yes |
|
-vmin z |
0.0 |
The starting wavenumber for the frequency range |
No |
-vm z |
300.0 |
The final wavenumber for the frequency range |
No |
-i z |
0.2 |
The increment wavenumber used to cover the frequency range |
No |
-plot s |
A plot is requested the string s can be absorption, molar_absorption, real, or imaginary |
Yes |
|
-csv s |
Output is sent to a comma delimited file specified by the string s |
No |
|
Additional output is printed regarding the QM/MM program |
No |
||
-ignore k |
Ignore the k’th mode. Any mode less than 5 cm-1 is ignored automatically |
Yes |
|
-mode k |
Only using the kth mode in the calculation |
Yes |
|
-optical z1 z2 z3 |
z1, z2 and z3 are the diagonal elements of the optical permittivity tensor |
No |
|
-optical_tensor z1 z2 ..z9 |
z1, z2 .. Z9 define the full optical permittivity tensor |
No |
|
-eckart |
The translationa modes will be projected from the hessian |
No |
|
-neutral |
The Born charge matrices will be modified to make the system overall charge neutral |
No |
|
-hessian s |
If the string "s" is "crystal" symmetrisation of the hessian will be performed using the Crystal14 convention. Otherwise if the string is "symm" the default method will be used |
No |
The supporting matrix is often selected from a small range of materials which have little or no absorption in the frequency range of interest. The properties of the materials known to the program are summarised in the table below.
Name |
Density |
Permittivity |
Description |
ptfe |
2.2 |
2.0 |
Polytetrafluoroethylene |
air |
0.0 |
1.0 |
Air |
vacuum |
0.0 |
1.0 |
Vacuum |
kbr |
2.75 |
2.25 |
Potassium bromide |
nujol |
0.838 |
2.155 |
Nujol |
hdpe |
0.955 |
2.25 |
High density polyethylene |
mdpe |
0.933 |
2.25 |
Medium density polyethylene |
ldpe |
0.925 |
2.25 |
Low density polyethylene |