# Calculating Materials Properties¶

## Structural relaxation¶

In order to obtain accurate results, the crystal structure should first be relaxed using "tight" calculation settings including high force and energy convergence criteria. Note, that this can often be expensive for very large structures.

VASP settings for tight convergence

ADDGRID = True
EDIFF = 1E-8
EDIFFG = -5E-4
PREC = Accurate
NSW = 100
ISIF = 3
NELMIN = 5


## Dielectric constants and polar-phonon frequency¶

Static and high-frequency dielectric constants and the "effective polar phonon frequency" can be obtained using density functional perturbation theory (DFPT). It is very important to first relax the structure using tight convergence settings, as described in the structural relaxation section. Details on DFPT in VASP can be found on the IBRION and LEPSILON documentation pages.

VASP settings for dielectric constants and phonon frequency

ADDGRID = True
EDIFF = 1E-8
PREC = Accurate
NSW = 1
IBRION = 8
LEPSILON = True


Note, DFPT cannot be used with hybrid exchange-correlation functionals. In these cases the LCALCEPS flag should be used in combination with IBRION = 6.

The dielectric constants and polar phonon frequency can be extracted from the VASP outputs using the command:

amset phonon-frequency

The command should be run in a folder containing the vasprun.xml file output from the DFPT calculation.

The effective phonon frequency is determined from the phonon frequencies $\omega_{\mathbf{q}\nu}$ (where $\nu$ is a phonon branch and $\mathbf{q}$ is a phonon wave vector) and eigenvectors $\mathbf{e}_{\kappa\nu}(\mathbf{q})$ (where $\kappa$ is an atom in the unit cell). In order to capture scattering from the full phonon band structure in a single phonon frequency, each phonon mode is weighted by the dipole moment it produces according to

$w_{\nu} = \sum_\kappa \left [ \frac{1}{M_\kappa \omega_{\mathbf{q}\nu}} \right]^{1/2} \times \left[ \mathbf{q} \cdot \mathbf{Z}_\kappa^* \cdot \mathbf{e}_{\kappa\nu}(\mathbf{q}) \right ]$

where $\mathbf{Z}_\kappa^*$ is the Born effective charge. This naturally suppresses the contributions from transverse-optical and acoustic modes in the same manner as the more general formalism for computing Frölich based electron-phonon coupling.

The weight is calculated only for $\Gamma$-point phonon frequencies and averaged over the full unit sphere to capture both the polar divergence at $\mathbf{q} \rightarrow 0$ and any anisotropy in the dipole moments. The effective phonon frequency is calculated as the weighted sum over all $\Gamma$-point phonon modes according to

$\omega_\mathrm{po} = \frac{\omega_{\Gamma\nu} w_{\nu}}{\sum_{\nu} w_\nu}.$

## Elastic constants¶

Elastic constants can be calculated using finite differences in VASP. It is very important to first relax the structure using tight convergence settings, as described in the structural relaxation section. Details on the finite difference approach in VASP can be found on the IBRION documentation page.

VASP settings for dielectric constants and phonon frequency

ADDGRID = True
EDIFF = 1E-8
PREC = Accurate
NSW = 1
IBRION = 6