# Dfttk postprocessing mechanism

## Flow controls

Depending on the given condition, postprocessing can take data from

The`qha-phonon`

collectionThe`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 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