DFT

Module to handle ab initio electrostatic potentials from the DFT code GPAW.

class abtem.dft.GPAWPotential(calculator, gpts=None, sampling=None, origin=None, orthogonal_cell=None, periodic_z=True, slice_thickness=0.5, core_size=0.005, plane='xy', storage='cpu', precalculate=True)[source]

GPAW DFT potential object

The GPAW potential object is used to calculate electrostatic potential of a converged GPAW calculator object.

Parameters:

  • calculator (GPAW object) – A converged GPAW calculator.

  • origin (two float, optional) – xy-origin of the electrostatic potential relative to the xy-origin of the Atoms object [Å].

  • gpts (one or two int) – Number of grid points describing each slice of the potential.

  • sampling (one or two float) – Lateral sampling of the potential [1 / Å].

  • slice_thickness (float) – Thickness of the potential slices in Å for calculating the number of slices used by the multislice algorithm. Default is 0.5 Å.

  • core_size (float) – The standard deviation of the Gaussian function representing the atomic core.

build(first_slice=0, last_slice=None, energy=None, max_batch=None, pbar=False)

Precalcaulate the potential as a potential array.

Parameters:

  • first_slice (int) – First potential slice to generate.

  • last_slice (int, optional) – Last potential slice generate.

  • energy (float) – Electron energy [eV]. If given, the transmission functions will be returned.

  • max_batch (int) – Maximum number of potential slices calculated in parallel.

  • pbar (bool) – If true, show progress bar.

Returns:

Return type:

PotentialArray object

check_slice_idx(i)

Raises an error if i is greater than the number of slices.

copy()

Make a copy.

property extent

Grid extent in each dimension [Å].

generate_slices(first_slice=0, last_slice=None, max_batch=1)[source]

Generate the potential slices.

Parameters:

  • first_slice (int) – First potential slice to generate.

  • last_slice (int, optional) – Last potential slice generate.

  • max_batch (int) – Maximum number of potential slices calculated in parallel.

Returns:

Return type:

generator of PotentialArray objects

generate_transmission_functions(energy, first_slice=0, last_slice=None, max_batch=1)

Generate the transmission functions one slice at a time.

Parameters:

  • energy (float) – Electron energy [eV].

  • first_slice (int) – First potential slice to generate.

  • last_slice (int, optional) – Last potential slice generate.

  • max_batch (int) – Maximum number of potential slices calculated in parallel.

Returns:

Return type:

generator of PotentialArray objects

get_slice_thickness(i)[source]

Get the slice thickness [Å].

Parameters:

i (int) – Slice index.

property gpts

Number of grid points in each dimension.

property num_slices

The number of projected potential slices.

property sampling

Grid sampling in each dimension [1 / Å].

abtem.dft.get_paw_corrections(atom_index, calculator, rcgauss=0.005)[source]

PAW corrections function

Function to calculate the projector-augmented wave corrections to the electrostatic potential, needed to calculate the all-electron potential from a converged calculation. This is implemented independently in abTEM to enable dealing with non-orthogonal cells, and to allow working with slices of large potentials.

Parameters:

  • atom_index (int) – Index of the atom for which the corrections are calculated.

  • calculator (GPAW object) – Converged GPAW calculation.

  • rcgauss (float) – Radius of the Gaussian smearing of the nuclear potentials [Å]. Default value is 0.005 Å.

Returns:

The evaluation points and values of the core contribution to the electronstatic potential.

Return type:

two 1d arrays

abtem.dft.interpolate_rectangle(array, cell, extent, gpts, origin=None)[source]

Interpolation to rectangle function

A function to interpolate an array to a given rectangle, here used to convert electrostatic potentials from non-orthogonal cells to rectangular ones for use in abTEM multislice simulations.

Parameters:

  • array (ndarray) – Electrostatic potential array to be interpolated.

  • cell (ndarray) – ASE atoms simulation cell.

  • extent (Sequence[float]) – Extent of the rectangle [Å].

  • gpts (Sequence[int]) – Number of interpolation grid points.

  • origin (Optional[Sequence[float]]) – Origin of the rectangle. Default is (0,0).