Dfttk postprocessing mechanism
Flow controls
Depending on the given condition, postprocessing can take data from
Theqha-phonon
collectionTheqha
collection (Debye model)Thephonon
collection (in case of qha-phonon calculations failed)
Then, invoke Yphon
to recalculate the phonon properties based on the force constants obtained from the database
Scheme to find equilibrium volume
If the data quality is excellent, use central symmetric 7-point differenceIf the data quality is very good, fit the free energies use 4-parameter Birch-MurnaghanIf the data quality is good (may use as default), fit the 0-K total energies using 4-parameter Birch-MurnaghanFit the finite T part of the free energies by UnivariateSpline
Scheme to calculate derivative
7-point symmetrical central difference
\[Deriv= \frac{1}{3}\sum_{i=1}^{3}{\frac{f(X_{N+i})-f(X_{N-i})}{X_{N+i}-X_{N-i}}}\]
Birch-Mannhan Euqations of state fitting
\[Deriv=-\frac{2}{3}bx^{-\frac{5}{3}}-\frac{4}{3}cx^{-\frac{7}{3}}-\frac{6}{3}dx^{-\frac{9}{3}}\]
Scheme for LTC
By entropy derivative
\[\alpha =\frac{1}{B_{T}}\frac{\partial S}{\partial V}\]
where \(B_{T}\) is isothermal bulk modulus
By internal energy derivative via Birch-Mannhan fitting
\[\alpha =\frac{1}{B_{T} T}(\frac{\partial U}{\partial V}+P)\]
where \(P\) is pressure
When the data quality is fair (~20% cases)
Fit the 0-K total energies using 4-parameter Birch-Murnaghan; andfit the finite T part of the free energies by linear function f=a+b*V