Modematching

Phonon normal mode-matching algorithm used for upscaling low-accuracy semi-empirical (DFTB) phonons to full ab initio (DFT)

This code contains a full suite of finite temperature free energy predictions based on pre-calculated harmonic phonons.

The base functionality takes the output of a Gamma-point DFT and DFTB calculation (xtal.ref.yaml, xtal.shift.yaml files). These are required to contain the normalized eigenvectors and frequencies, and will serve as the initial matching assignnment. A third (xtal.ss.yaml) file containing the frequencies of the raw DFTB supercell calculation containing the entire density of states is required. The differences in the frequencies of the two Gamma-pt calculations will be added here as the "shift", and the full integration of the shifted density of states (DOS) will serve as the upscaled free energy.

An additional correction to the DOS can be applied with the inclusion of acoustic modes via elastic constants and toggled by the \$ACOUSTICS card. This will require either an input of pre-calculated Elastic Constants (xtal.ecs file) or stress/strain files for the ECs to be evaluated here (Toggle CALC ECs TRUE in \$Acoustics, files xtal.stress and xtal.strain). This will ensure convergence of the acoustic modes near Gamma.

This program will also allow for the inclusion of multiple sets of frequencies for Quasiharmonic Approximations (QHA), predicting accurate thermal expansions and sublimation enthalpies. Simply put as many frequency files in the working directory as you wish to be included in the Fvib(V) calculation (For n points: xtal1 - xtaln), as well as the volumes in the same order in the input file, and directories will be made for each match/acoustic treatment.

Finally, ModeMatch can predict solid-state phase diagrams given multiple structures in the working directory. Identify multiple polymorphs by listing more structures in the infile inder \$crystals, and name the input files accordingly.

Installation

Dependencies

• numpy (>= 1.18.1)
• sympy (>= 1.5.1)
• pandas (>=1.0.1)

From pip

First, it is recommended that a virtual environment is created for module control, e.g.:

conda create -n modematch

Modematch can then be installed via pip:

conda activate modematch

pip install modematch

From source

git clone https://github.com/cjcook41/Modematching.git

conda activate modematch

python setup.py sdist

pip install dist/modematch-0.0.12.tar.gz/

Running the Code

The code requires 2 things in the working directory:

1. Input file titled infile containing job control
2. Directory titled datafiles containing all of the necessary data files for the job you're running. More on this in the Input File section.

Run the following commands from a python3 interpreter:

• from modematch import main
• main.RunJob()

Elastic Properties

Control of elastic calcualations is listed under the \$acoustics card. Christoffel true will correct raw frequencies using elastic constants and Christoffel matrices. EC true will evaluate the elastic constants on the fly using input stresses and strains.

Phase Diagrams

For phase diagrams, add another polymorph name under the \$crystals card. NOTE: The names listed under here will need to be the prefix of the input data files! \$P2atoms and \$P2volumes will need to be specified as well, containing atomic information and cell volumes of the second polymorph specified. Volume dependent free energies are evaluated at a series of pressures up to \$Pmax in GigaPascals (0.01GPa steps), and temperatures in Kelvin up to \$Tmax (10K steps). If QHA points are in a large sampled volume range, second order polynomial fits are used to determine the transition temperature at some pressure (where relative thermodynamic stability inverts). Smaller volume ranges use linear fits to avoid erratic behavior in the extrapolation region. "No transition" will result in imaginary temperatures.

Sample Input File

infile is a sample input file for Phase I carbon dioxide. This input file will perform the base normal mode shift, evaluate free energies at multiple volumes of an Alpha xtal, evaluate the corrected acoustic modes using pre-calculated elastic constants, and finally perform the quasiharmonic approximation for thermal expansion.

Outputs

• For 1 polymorph, 1 volume (No QHA):

  • Thermodynamic data / absolute free energies

• 1 polymorph, multiple volumes (QHA):

  • xtal.csv file containing relevent free energies and predicted cell volumes as a function of T

• 2 polymorphs, multiple volumes (QHA + Phase Diagram):

  • xtal.csv file containing relevent free energies and predicted cell volumes as a function of T
  • PhaseDiagram file containing temperatures, enthalpies, and entropies of transition as a function of P

Additional Consideration

Modematching does not account for uniform kpt sampling. The supercell phonons must be along user-defined kpaths within the Brillouin zone. This supplies the code with the well-defined bands to shift during the matching procedure. Future versions will implement uniform sampling.

Citation

Please refer to the following publications for more information and citation:

• https://doi.org/10.1063/5.0032649

Patch Notes

v0.0.8

• Corrected a unit conversion error in Christoffel.py
• Corrected a reciprocal space transform error in Christoffel.py
• Fixed a bug in the kpt sampling directions when assigning the acoustic mode dispersion

v0.0.9

• Added a Tmax parameter to the input file for changing Trange to evaluate
• Changed to linear extrapolation of Fvib vs. V free energy fitting. The polynomial extrapolation gives erratic behavior if the sampled volume points are not far enough from the minimum.

v0.0.10

• Redefined compression and expansion branch evaluation for a finer volume grid. This was done to mitigate the use of fewer points in the initial electronic E(V) curve.

v0.0.11

• Fixed bug for high pressure scan introduced after refining the Vgrid.
• Introduced a dependence on relative volume range for determining order of the Fvib(V) fit. Larger range of volumes == quadratic fit, narrower range == linear fit

v0.0.12

• Reworked the fitting and added comments for ElasticConstants solver. Earlier versions used an average over all strains in a grid, new version solves for the inflection point of positive and negative strains. These are more accurate by ~5%.