Dfttk postprocessing mechanism

Flow controls

Depending on the given condition, postprocessing can take data from

The qha-phonon collection

The qha collection (Debye model)

The phonon 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 difference

If the data quality is very good, fit the free energies use 4-parameter Birch-Murnaghan

If the data quality is good (may use as default), fit the 0-K total energies using 4-parameter Birch-Murnaghan

Fit the finite T part of the free energies by UnivariateSpline

Scheme to calculate derivative

1. 7-point symmetrical central difference

\[Deriv= \frac{1}{3}\sum_{i=1}^{3}{\frac{f(X_{N+i})-f(X_{N-i})}{X_{N+i}-X_{N-i}}}\]

2. 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

1. By entropy derivative

\[\alpha =\frac{1}{B_{T}}\frac{\partial S}{\partial V}\]

where \(B_{T}\) is isothermal bulk modulus

2. By internal energy derivative via Birch-Mannhan fitting

\[\alpha =\frac{1}{B_{T} T}(\frac{\partial U}{\partial V}+P)\]

where \(P\) is pressure

3. When the data quality is fair (~20% cases)

Fit the 0-K total energies using 4-parameter Birch-Murnaghan; and

fit the finite T part of the free energies by linear function f=a+b*V