Calculation Inputs

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

Dense uniform band structure and wave function coefficients

AMSET should be run on a vasprun.xml file from a "dense" uniform band structure calculation. Typically a k-point mesh density at least twice that needed to converge the total energy will be necessary to converge transport properties. Note this refers to the initial DFT mesh before Fourier interpolation. In order to obtain accurate band gaps often a hybrid DFT functional such as HSE06 is required.

Wave function coefficients are required to calculate wave function overlaps. This requires the WAVECAR file to be written by VASP (achieved by setting LWAVE = True). Wave function coefficients can then be extracted using the amset wave command. Coefficients are stored in the wavefunction.h5 file.

VASP settings for uniform calculations

ADDGRID = True
EDIFF = 1E-8
PREC = Accurate
NSW = 1
LWAVE = True

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 elastic constants

ADDGRID = True
EDIFF = 1E-8
PREC = Accurate
NSW = 1
IBRION = 6
ISIF = 3

Deformation potentials

The absolute deformation potential describes the change in energy of the bands with change in volume and is calculated as $\mathbf{D}_{n\mathbf{k}} = \delta \varepsilon_{n\mathbf{k}} / \delta S_{\alpha\beta}$ where $\mathbf{S}$ is the uniform stress tensor. The deformation potential should be averaged over contraction (–0.5 %) and expansion (+0.5 %) of the lattice and calculated separately for each component of the strain tensor. To account for shifts in the average electrostatic potential between deformed cells, the eigenvalues are aligned to the average energy level of the core states.

AMSET includes a tool to assist with the calculation of the deformation potentials. The initial input is a "tight" optimised structure as described in the structural relaxation section. Deformed structures are generated using the amset deform create command, which will generate a list of POSCARs each corresponding to a component of the strain tensor. Note that symmetry is automatically used to reduce the number of calculations needed. A single point calculation (no relaxation, i.e., NSW = 0) should be performed for each deformed POSCAR as well as the undeformed structure.

VASP settings for deformation calculations

ADDGRID = True
EDIFF = 1E-8
PREC = Accurate
NSW = 1
ICORELEVEL = 1  # needed to write the core levels to OUTCAR

The deformation potentials can be calculated using the amset deform read command. This requires the paths to the undeformed and deformation calculations as inputs. The undeformed folder should be specified first, followed by the deformation folders. For example,

amset deform read undeformed def-1 def-2 def-3

This will write the deformations potentials to a deformation.h5 file in the current directory. You can specify to use this file when calculating scattering rates by setting the deformation_potential option to "deformation.h5". See the settings page for more details.

Dielectric constants, piezoelectric constants and polar-phonon frequency

Static and high-frequency dielectric constants, piezoelectric 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

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