pymatgen.analysis.path_finder module

This module finds diffusion paths through a structure based on a given potential field.

If you use PathFinder algorithm for your research, please consider citing the following work:

Ziqin Rong, Daniil Kitchaev, Pieremanuele Canepa, Wenxuan Huang, Gerbrand
Ceder, The Journal of Chemical Physics 145 (7), 074112

class ChgcarPotential(chgcar, smear=False, normalize=True)

Bases: pymatgen.analysis.path_finder.StaticPotential

Implements a potential field based on the charge density output from VASP.

Parameters

• chgcar – Chgcar object based on a VASP run of the structure of interest (Chgcar.from_file(“CHGCAR”))

• smear – Whether or not to apply a Gaussian smearing to the potential

• normalize – Whether or not to normalize the potential to range from 0 to 1

class FreeVolumePotential(struct, dim, smear=False, normalize=True)

Bases: pymatgen.analysis.path_finder.StaticPotential

Implements a potential field based on geometric distances from atoms in the structure - basically, the potential is lower at points farther away from any atoms in the structure.

Parameters

• struct – Unit cell on which to base the potential

• dim – Grid size for the potential

• smear – Whether or not to apply a Gaussian smearing to the potential

• normalize – Whether or not to normalize the potential to range from 0 to 1

class MixedPotential(potentials, coefficients, smear=False, normalize=True)

Bases: pymatgen.analysis.path_finder.StaticPotential

Implements a potential that is a weighted sum of some other potentials

Parameters

• potentials – List of objects extending the StaticPotential superclass

• coefficients – Mixing weights for the elements of the potentials list

• smear – Whether or not to apply a Gaussian smearing to the potential

• normalize – Whether or not to normalize the potential to range from 0 to 1

class NEBPathfinder(start_struct, end_struct, relax_sites, v, n_images=20, mid_struct=None)

Bases: object

General pathfinder for interpolating between two structures, where the interpolating path is calculated with the elastic band method with respect to the given static potential for sites whose indices are given in relax_sites, and is linear otherwise.

Parameters

• start_struct – Endpoint structures to interpolate

• end_struct – Endpoint structures to interpolate

• relax_sites – List of site indices whose interpolation paths should be relaxed

• v – Static potential field to use for the elastic band relaxation

• n_images – Number of interpolation images to generate

• mid_struct – (optional) additional structure between the start and end structures to help

property images

Returns a list of structures interpolating between the start and endpoint structures.

interpolate()

Finds a set of n_images from self.s1 to self.s2, where all sites except for the ones given in relax_sites, the interpolation is linear (as in pymatgen.core.structure.interpolate), and for the site indices given in relax_sites, the path is relaxed by the elastic band method within the static potential V.

If a mid point is defined we will interpolate from s1–> mid –>s2 The final number of images will still be n_images.

plot_images(outfile)

Generates a POSCAR with the calculated diffusion path with respect to the first endpoint. :param outfile: Output file for the POSCAR

static string_relax(start, end, V, n_images=25, dr=None, h=3.0, k=0.17, min_iter=100, max_iter=10000, max_tol=5e-06)

Implements path relaxation via the elastic band method. In general, the method is to define a path by a set of points (images) connected with bands with some elasticity constant k. The images then relax along the forces found in the potential field V, counterbalanced by the elastic response of the elastic band. In general the endpoints of the band can be allowed to relax also to their local minima, but in this calculation they are kept fixed.

Parameters

• start – Endpoints of the path calculation given in discrete coordinates with respect to the grid in V

• end – Endpoints of the path calculation given in discrete coordinates with respect to the grid in V

• V – potential field through which to calculate the path

• n_images – number of images used to define the path. In general anywhere from 20 to 40 seems to be good.

• dr – Conversion ratio from discrete coordinates to real coordinates for each of the three coordinate vectors

• h – Step size for the relaxation. h = 0.1 works reliably, but is slow. h=10 diverges with large gradients but for the types of gradients seen in CHGCARs, works pretty reliably

• k – Elastic constant for the band (in real units, not discrete)

• min_iter – Number of optimization steps the string will take before exiting (even if unconverged)

• max_iter – Number of optimization steps the string will take before exiting (even if unconverged)

• max_tol – Convergence threshold such that if the string moves by less than max_tol in a step, and at least min_iter steps have passed, the algorithm will terminate. Depends strongly on the size of the gradients in V, but 5e-6 works reasonably well for CHGCARs.

class StaticPotential(struct, pot)

Bases: object

Defines a general static potential for diffusion calculations. Implements grid-rescaling and smearing for the potential grid. Also provides a function to normalize the potential from 0 to 1 (recommended).

Parameters

• struct – atomic structure of the potential

• pot – volumentric data to be used as a potential

gaussian_smear(r)

Applies an isotropic Gaussian smear of width (standard deviation) r to the potential field. This is necessary to avoid finding paths through narrow minima or nodes that may exist in the field (although any potential or charge distribution generated from GGA should be relatively smooth anyway). The smearing obeys periodic boundary conditions at the edges of the cell.

:param r - Smearing width in cartesian coordinates, in the same units

as the structure lattice vectors

get_v()

Returns the potential

normalize()

Sets the potential range 0 to 1.

rescale_field(new_dim)

Changes the discretization of the potential field by linear interpolation. This is necessary if the potential field obtained from DFT is strangely skewed, or is too fine or coarse. Obeys periodic boundary conditions at the edges of the cell. Alternatively useful for mixing potentials that originally are on different grids.

Parameters

new_dim – tuple giving the numpy shape of the new grid