Source code for pymatgen.analysis.adsorption

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.


"""
This module provides classes used to enumerate surface sites
and to find adsorption sites on slabs
"""

import numpy as np
from pymatgen import Structure, vis
import itertools
import os
from monty.serialization import loadfn
from scipy.spatial import Delaunay

from pymatgen.core.operations import SymmOp
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.util.coord import in_coord_list_pbc
from pymatgen.analysis.local_env import VoronoiNN
from pymatgen.core.surface import generate_all_slabs
from pymatgen.analysis.structure_matcher import StructureMatcher

from matplotlib import patches
from matplotlib.path import Path

__author__ = "Joseph Montoya"
__copyright__ = "Copyright 2016, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Joseph Montoya"
__credits__ = "Richard Tran"
__email__ = "montoyjh@lbl.gov"
__status__ = "Development"
__date__ = "December 2, 2015"


[docs]class AdsorbateSiteFinder: """ This class finds adsorbate sites on slabs and generates adsorbate structures according to user-defined criteria. The algorithm for finding sites is essentially as follows: 1. Determine "surface sites" by finding those within a height threshold along the miller index of the highest site 2. Create a network of surface sites using the Delaunay triangulation of the surface sites 3. Assign on-top, bridge, and hollow adsorption sites at the nodes, edges, and face centers of the Del. Triangulation 4. Generate structures from a molecule positioned at these sites """ def __init__(self, slab, selective_dynamics=False, height=0.9, mi_vec=None): """ Create an AdsorbateSiteFinder object. Args: slab (Slab): slab object for which to find adsorbate sites selective_dynamics (bool): flag for whether to assign non-surface sites as fixed for selective dynamics height (float): height criteria for selection of surface sites mi_vec (3-D array-like): vector corresponding to the vector concurrent with the miller index, this enables use with slabs that have been reoriented, but the miller vector must be supplied manually """ # get surface normal from miller index if mi_vec: self.mvec = mi_vec else: self.mvec = get_mi_vec(slab) slab = self.assign_site_properties(slab, height) if selective_dynamics: slab = self.assign_selective_dynamics(slab) self.slab = slab
[docs] @classmethod def from_bulk_and_miller(cls, structure, miller_index, min_slab_size=8.0, min_vacuum_size=10.0, max_normal_search=None, center_slab=True, selective_dynamics=False, undercoord_threshold=0.09): """ This method constructs the adsorbate site finder from a bulk structure and a miller index, which allows the surface sites to be determined from the difference in bulk and slab coordination, as opposed to the height threshold. Args: structure (Structure): structure from which slab input to the ASF is constructed miller_index (3-tuple or list): miller index to be used min_slab_size (float): min slab size for slab generation min_vacuum_size (float): min vacuum size for slab generation max_normal_search (int): max normal search for slab generation center_slab (bool): whether to center slab in slab generation selective dynamics (bool): whether to assign surface sites to selective dynamics undercoord_threshold (float): threshold of "undercoordation" to use for the assignment of surface sites. Default is 0.1, for which surface sites will be designated if they are 10% less coordinated than their bulk counterpart """ # TODO: for some reason this works poorly with primitive cells # may want to switch the coordination algorithm eventually vnn_bulk = VoronoiNN(tol=0.05) bulk_coords = [len(vnn_bulk.get_nn(structure, n)) for n in range(len(structure))] struct = structure.copy(site_properties={'bulk_coordinations': bulk_coords}) slabs = generate_all_slabs(struct, max_index=max(miller_index), min_slab_size=min_slab_size, min_vacuum_size=min_vacuum_size, max_normal_search=max_normal_search, center_slab=center_slab) slab_dict = {slab.miller_index: slab for slab in slabs} if miller_index not in slab_dict: raise ValueError("Miller index not in slab dict") this_slab = slab_dict[miller_index] vnn_surface = VoronoiNN(tol=0.05, allow_pathological=True) surf_props, undercoords = [], [] this_mi_vec = get_mi_vec(this_slab) mi_mags = [np.dot(this_mi_vec, site.coords) for site in this_slab] average_mi_mag = np.average(mi_mags) for n, site in enumerate(this_slab): bulk_coord = this_slab.site_properties['bulk_coordinations'][n] slab_coord = len(vnn_surface.get_nn(this_slab, n)) mi_mag = np.dot(this_mi_vec, site.coords) undercoord = (bulk_coord - slab_coord) / bulk_coord undercoords += [undercoord] if undercoord > undercoord_threshold and mi_mag > average_mi_mag: surf_props += ['surface'] else: surf_props += ['subsurface'] new_site_properties = {'surface_properties': surf_props, 'undercoords': undercoords} new_slab = this_slab.copy(site_properties=new_site_properties) return cls(new_slab, selective_dynamics)
[docs] def find_surface_sites_by_height(self, slab, height=0.9, xy_tol=0.05): """ This method finds surface sites by determining which sites are within a threshold value in height from the topmost site in a list of sites Args: site_list (list): list of sites from which to select surface sites height (float): threshold in angstroms of distance from topmost site in slab along the slab c-vector to include in surface site determination xy_tol (float): if supplied, will remove any sites which are within a certain distance in the miller plane. Returns: list of sites selected to be within a threshold of the highest """ # Get projection of coordinates along the miller index m_projs = np.array([np.dot(site.coords, self.mvec) for site in slab.sites]) # Mask based on window threshold along the miller index. mask = (m_projs - np.amax(m_projs)) >= -height surf_sites = [slab.sites[n] for n in np.where(mask)[0]] if xy_tol: # sort surface sites by height surf_sites = [s for (h, s) in zip(m_projs[mask], surf_sites)] surf_sites.reverse() unique_sites, unique_perp_fracs = [], [] for site in surf_sites: this_perp = site.coords - np.dot(site.coords, self.mvec) this_perp_frac = slab.lattice.get_fractional_coords(this_perp) if not in_coord_list_pbc(unique_perp_fracs, this_perp_frac): unique_sites.append(site) unique_perp_fracs.append(this_perp_frac) surf_sites = unique_sites return surf_sites
[docs] def assign_site_properties(self, slab, height=0.9): """ Assigns site properties. """ if 'surface_properties' in slab.site_properties.keys(): return slab else: surf_sites = self.find_surface_sites_by_height(slab, height) surf_props = ['surface' if site in surf_sites else 'subsurface' for site in slab.sites] return slab.copy( site_properties={'surface_properties': surf_props})
[docs] def get_extended_surface_mesh(self, repeat=(5, 5, 1)): """ Gets an extended surface mesh for to use for adsorption site finding by constructing supercell of surface sites Args: repeat (3-tuple): repeat for getting extended surface mesh """ surf_str = Structure.from_sites(self.surface_sites) surf_str.make_supercell(repeat) return surf_str
@property def surface_sites(self): """ convenience method to return a list of surface sites """ return [site for site in self.slab.sites if site.properties['surface_properties'] == 'surface']
[docs] def subsurface_sites(self): """ convenience method to return list of subsurface sites """ return [site for site in self.slab.sites if site.properties['surface_properties'] == 'subsurface']
[docs] def find_adsorption_sites(self, distance=2.0, put_inside=True, symm_reduce=1e-2, near_reduce=1e-2, positions=['ontop', 'bridge', 'hollow'], no_obtuse_hollow=True): """ Finds surface sites according to the above algorithm. Returns a list of corresponding cartesian coordinates. Args: distance (float): distance from the coordinating ensemble of atoms along the miller index for the site (i. e. the distance from the slab itself) put_inside (bool): whether to put the site inside the cell symm_reduce (float): symm reduction threshold near_reduce (float): near reduction threshold positions (list): which positions to include in the site finding "ontop": sites on top of surface sites "bridge": sites at edges between surface sites in Delaunay triangulation of surface sites in the miller plane "hollow": sites at centers of Delaunay triangulation faces "subsurface": subsurface positions projected into miller plane no_obtuse_hollow (bool): flag to indicate whether to include obtuse triangular ensembles in hollow sites """ ads_sites = {k: [] for k in positions} if 'ontop' in positions: ads_sites['ontop'] = [s.coords for s in self.surface_sites] if 'subsurface' in positions: # Get highest site ref = self.slab.sites[np.argmax(self.slab.cart_coords[:, 2])] # Project diff between highest site and subs site into miller ss_sites = [self.mvec * np.dot(ref.coords - s.coords, self.mvec) + s.coords for s in self.subsurface_sites()] ads_sites['subsurface'] = ss_sites if 'bridge' in positions or 'hollow' in positions: mesh = self.get_extended_surface_mesh() sop = get_rot(self.slab) dt = Delaunay([sop.operate(m.coords)[:2] for m in mesh]) # TODO: refactor below to properly account for >3-fold for v in dt.simplices: if -1 not in v: dots = [] for i_corner, i_opp in zip(range(3), ((1, 2), (0, 2), (0, 1))): corner, opp = v[i_corner], [v[o] for o in i_opp] vecs = [mesh[d].coords - mesh[corner].coords for d in opp] vecs = [vec / np.linalg.norm(vec) for vec in vecs] dots.append(np.dot(*vecs)) # Add bridge sites at midpoints of edges of D. Tri if 'bridge' in positions: ads_sites["bridge"].append( self.ensemble_center(mesh, opp)) # Prevent addition of hollow sites in obtuse triangles obtuse = no_obtuse_hollow and (np.array(dots) < 1e-5).any() # Add hollow sites at centers of D. Tri faces if 'hollow' in positions and not obtuse: ads_sites['hollow'].append( self.ensemble_center(mesh, v)) for key, sites in ads_sites.items(): # Pare off outer sites for bridge/hollow if key in ['bridge', 'hollow']: frac_coords = [self.slab.lattice.get_fractional_coords(ads_site) for ads_site in sites] frac_coords = [frac_coord for frac_coord in frac_coords if (frac_coord[0] > 1 and frac_coord[0] < 4 and frac_coord[1] > 1 and frac_coord[1] < 4)] sites = [self.slab.lattice.get_cartesian_coords(frac_coord) for frac_coord in frac_coords] if near_reduce: sites = self.near_reduce(sites, threshold=near_reduce) if put_inside: sites = [put_coord_inside(self.slab.lattice, coord) for coord in sites] if symm_reduce: sites = self.symm_reduce(sites, threshold=symm_reduce) sites = [site + distance * self.mvec for site in sites] ads_sites[key] = sites ads_sites['all'] = sum(ads_sites.values(), []) return ads_sites
[docs] def symm_reduce(self, coords_set, threshold=1e-6): """ Reduces the set of adsorbate sites by finding removing symmetrically equivalent duplicates Args: coords_set: coordinate set in cartesian coordinates threshold: tolerance for distance equivalence, used as input to in_coord_list_pbc for dupl. checking """ surf_sg = SpacegroupAnalyzer(self.slab, 0.1) symm_ops = surf_sg.get_symmetry_operations() unique_coords = [] # Convert to fractional coords_set = [self.slab.lattice.get_fractional_coords(coords) for coords in coords_set] for coords in coords_set: incoord = False for op in symm_ops: if in_coord_list_pbc(unique_coords, op.operate(coords), atol=threshold): incoord = True break if not incoord: unique_coords += [coords] # convert back to cartesian return [self.slab.lattice.get_cartesian_coords(coords) for coords in unique_coords]
[docs] def near_reduce(self, coords_set, threshold=1e-4): """ Prunes coordinate set for coordinates that are within threshold Args: coords_set (Nx3 array-like): list or array of coordinates threshold (float): threshold value for distance """ unique_coords = [] coords_set = [self.slab.lattice.get_fractional_coords(coords) for coords in coords_set] for coord in coords_set: if not in_coord_list_pbc(unique_coords, coord, threshold): unique_coords += [coord] return [self.slab.lattice.get_cartesian_coords(coords) for coords in unique_coords]
[docs] def ensemble_center(self, site_list, indices, cartesian=True): """ Finds the center of an ensemble of sites selected from a list of sites. Helper method for the find_adsorption_sites algorithm. Args: site_list (list of sites): list of sites indices (list of ints): list of ints from which to select sites from site list cartesian (bool): whether to get average fractional or cartesian coordinate """ if cartesian: return np.average([site_list[i].coords for i in indices], axis=0) else: return np.average([site_list[i].frac_coords for i in indices], axis=0)
[docs] def add_adsorbate(self, molecule, ads_coord, repeat=None, translate=True, reorient=True): """ Adds an adsorbate at a particular coordinate. Adsorbate represented by a Molecule object and is translated to (0, 0, 0) if translate is True, or positioned relative to the input adsorbate coordinate if translate is False. Args: molecule (Molecule): molecule object representing the adsorbate ads_coord (array): coordinate of adsorbate position repeat (3-tuple or list): input for making a supercell of slab prior to placing the adsorbate translate (bool): flag on whether to translate the molecule so that its CoM is at the origin prior to adding it to the surface reorient (bool): flag on whether to reorient the molecule to have its z-axis concurrent with miller index """ molecule = molecule.copy() if translate: # Translate the molecule so that the center of mass of the atoms # that have the most negative z coordinate is at (0, 0, 0) front_atoms = molecule.copy() front_atoms._sites = [s for s in molecule.sites if s.coords[2] == min([s.coords[2] for s in molecule.sites])] x, y, z = front_atoms.center_of_mass molecule.translate_sites(vector=[-x, -y, -z]) if reorient: # Reorient the molecule along slab m_index sop = get_rot(self.slab) molecule.apply_operation(sop.inverse) struct = self.slab.copy() if repeat: struct.make_supercell(repeat) if 'surface_properties' in struct.site_properties.keys(): molecule.add_site_property("surface_properties", ["adsorbate"] * molecule.num_sites) if 'selective_dynamics' in struct.site_properties.keys(): molecule.add_site_property("selective_dynamics", [[True, True, True]] * molecule.num_sites) for site in molecule: struct.append(site.specie, ads_coord + site.coords, coords_are_cartesian=True, properties=site.properties) return struct
[docs] def assign_selective_dynamics(self, slab): """ Helper function to assign selective dynamics site_properties based on surface, subsurface site properties Args: slab (Slab): slab for which to assign selective dynamics """ sd_list = [] sd_list = [[False, False, False] if site.properties['surface_properties'] == 'subsurface' else [True, True, True] for site in slab.sites] new_sp = slab.site_properties new_sp['selective_dynamics'] = sd_list return slab.copy(site_properties=new_sp)
[docs] def generate_adsorption_structures(self, molecule, repeat=None, min_lw=5.0, translate=True, reorient=True, find_args=None): """ Function that generates all adsorption structures for a given molecular adsorbate. Can take repeat argument or minimum length/width of precursor slab as an input Args: molecule (Molecule): molecule corresponding to adsorbate repeat (3-tuple or list): repeat argument for supercell generation min_lw (float): minimum length and width of the slab, only used if repeat is None translate (bool): flag on whether to translate the molecule so that its CoM is at the origin prior to adding it to the surface reorient (bool): flag on whether or not to reorient adsorbate along the miller index find_args (dict): dictionary of arguments to be passed to the call to self.find_adsorption_sites, e.g. {"distance":2.0} """ if repeat is None: xrep = np.ceil(min_lw / np.linalg.norm(self.slab.lattice.matrix[0])) yrep = np.ceil(min_lw / np.linalg.norm(self.slab.lattice.matrix[1])) repeat = [xrep, yrep, 1] structs = [] find_args = find_args or {} for coords in self.find_adsorption_sites(**find_args)['all']: structs.append(self.add_adsorbate(molecule, coords, repeat=repeat, translate=translate, reorient=reorient)) return structs
[docs] def adsorb_both_surfaces(self, molecule, repeat=None, min_lw=5.0, translate=True, reorient=True, find_args=None): """ Function that generates all adsorption structures for a given molecular adsorbate on both surfaces of a slab. This is useful for calculating surface energy where both surfaces need to be equivalent or if we want to calculate nonpolar systems. Args: molecule (Molecule): molecule corresponding to adsorbate repeat (3-tuple or list): repeat argument for supercell generation min_lw (float): minimum length and width of the slab, only used if repeat is None reorient (bool): flag on whether or not to reorient adsorbate along the miller index find_args (dict): dictionary of arguments to be passed to the call to self.find_adsorption_sites, e.g. {"distance":2.0} """ # Get the adsorbed surfaces first find_args = find_args or {} adslabs = self.generate_adsorption_structures(molecule, repeat=repeat, min_lw=min_lw, translate=translate, reorient=reorient, find_args=find_args) new_adslabs = [] for adslab in adslabs: # Find the adsorbate sites and indices in each slab _, adsorbates, indices = False, [], [] for i, site in enumerate(adslab.sites): if site.surface_properties == "adsorbate": adsorbates.append(site) indices.append(i) # Start with the clean slab adslab.remove_sites(indices) slab = adslab.copy() # For each site, we add it back to the slab along with a # symmetrically equivalent position on the other side of # the slab using symmetry operations for adsorbate in adsorbates: p2 = adslab.get_symmetric_site(adsorbate.frac_coords) slab.append(adsorbate.specie, p2, properties={"surface_properties": "adsorbate"}) slab.append(adsorbate.specie, adsorbate.frac_coords, properties={"surface_properties": "adsorbate"}) new_adslabs.append(slab) return new_adslabs
[docs] def generate_substitution_structures(self, atom, target_species=None, sub_both_sides=False, range_tol=1e-2, dist_from_surf=0): """ Function that performs substitution-type doping on the surface and returns all possible configurations where one dopant is substituted per surface. Can substitute one surface or both. Args: atom (str): atom corresponding to substitutional dopant sub_both_sides (bool): If true, substitute an equivalent site on the other surface target_species (list): List of specific species to substitute range_tol (float): Find viable substitution sites at a specific distance from the surface +- this tolerance dist_from_surf (float): Distance from the surface to find viable substitution sites, defaults to 0 to substitute at the surface """ target_species = target_species or [] # Get symmetrized structure in case we want to substitue both sides sym_slab = SpacegroupAnalyzer(self.slab).get_symmetrized_structure() # Define a function for substituting a site def substitute(site, i): slab = self.slab.copy() props = self.slab.site_properties if sub_both_sides: # Find an equivalent site on the other surface eq_indices = [indices for indices in sym_slab.equivalent_indices if i in indices][0] for ii in eq_indices: if "%.6f" % (sym_slab[ii].frac_coords[2]) != \ "%.6f" % (site.frac_coords[2]): props["surface_properties"][ii] = "substitute" slab.replace(ii, atom) break props["surface_properties"][i] = "substitute" slab.replace(i, atom) slab.add_site_property("surface_properties", props["surface_properties"]) return slab # Get all possible substitution sites substituted_slabs = [] # Sort sites so that we can define a range relative to the position of the # surface atoms, i.e. search for sites above (below) the bottom (top) surface sorted_sites = sorted(sym_slab, key=lambda site: site.frac_coords[2]) if sorted_sites[0].surface_properties == "surface": d = sorted_sites[0].frac_coords[2] + dist_from_surf else: d = sorted_sites[-1].frac_coords[2] - dist_from_surf for i, site in enumerate(sym_slab): if d - range_tol < site.frac_coords[2] < d + range_tol: if target_species and site.species_string in target_species: substituted_slabs.append(substitute(site, i)) elif not target_species: substituted_slabs.append(substitute(site, i)) matcher = StructureMatcher() return [s[0] for s in matcher.group_structures(substituted_slabs)]
[docs]def get_mi_vec(slab): """ Convenience function which returns the unit vector aligned with the miller index. """ mvec = np.cross(slab.lattice.matrix[0], slab.lattice.matrix[1]) return mvec / np.linalg.norm(mvec)
[docs]def get_rot(slab): """ Gets the transformation to rotate the z axis into the miller index """ new_z = get_mi_vec(slab) a, b, c = slab.lattice.matrix new_x = a / np.linalg.norm(a) new_y = np.cross(new_z, new_x) x, y, z = np.eye(3) rot_matrix = np.array([np.dot(*el) for el in itertools.product([x, y, z], [new_x, new_y, new_z])]).reshape(3, 3) rot_matrix = np.transpose(rot_matrix) sop = SymmOp.from_rotation_and_translation(rot_matrix) return sop
[docs]def put_coord_inside(lattice, cart_coordinate): """ converts a cartesian coordinate such that it is inside the unit cell. """ fc = lattice.get_fractional_coords(cart_coordinate) return lattice.get_cartesian_coords([c - np.floor(c) for c in fc])
[docs]def reorient_z(structure): """ reorients a structure such that the z axis is concurrent with the normal to the A-B plane """ struct = structure.copy() sop = get_rot(struct) struct.apply_operation(sop) return struct
# Get color dictionary colors = loadfn(os.path.join(os.path.dirname(vis.__file__), "ElementColorSchemes.yaml")) color_dict = {el: [j / 256.001 for j in colors["Jmol"][el]] for el in colors["Jmol"].keys()}
[docs]def plot_slab(slab, ax, scale=0.8, repeat=5, window=1.5, draw_unit_cell=True, decay=0.2, adsorption_sites=True): """ Function that helps visualize the slab in a 2-D plot, for convenient viewing of output of AdsorbateSiteFinder. Args: slab (slab): Slab object to be visualized ax (axes): matplotlib axes with which to visualize scale (float): radius scaling for sites repeat (int): number of repeating unit cells to visualize window (float): window for setting the axes limits, is essentially a fraction of the unit cell limits draw_unit_cell (bool): flag indicating whether or not to draw cell decay (float): how the alpha-value decays along the z-axis """ orig_slab = slab.copy() slab = reorient_z(slab) orig_cell = slab.lattice.matrix.copy() if repeat: slab.make_supercell([repeat, repeat, 1]) coords = np.array(sorted(slab.cart_coords, key=lambda x: x[2])) sites = sorted(slab.sites, key=lambda x: x.coords[2]) alphas = 1 - decay * (np.max(coords[:, 2]) - coords[:, 2]) alphas = alphas.clip(min=0) corner = [0, 0, slab.lattice.get_fractional_coords(coords[-1])[-1]] corner = slab.lattice.get_cartesian_coords(corner)[:2] verts = orig_cell[:2, :2] lattsum = verts[0] + verts[1] # Draw circles at sites and stack them accordingly for n, coord in enumerate(coords): r = sites[n].specie.atomic_radius * scale ax.add_patch(patches.Circle(coord[:2] - lattsum * (repeat // 2), r, color='w', zorder=2 * n)) color = color_dict[sites[n].species_string] ax.add_patch(patches.Circle(coord[:2] - lattsum * (repeat // 2), r, facecolor=color, alpha=alphas[n], edgecolor='k', lw=0.3, zorder=2 * n + 1)) # Adsorption sites if adsorption_sites: asf = AdsorbateSiteFinder(orig_slab) ads_sites = asf.find_adsorption_sites()['all'] sop = get_rot(orig_slab) ads_sites = [sop.operate(ads_site)[:2].tolist() for ads_site in ads_sites] ax.plot(*zip(*ads_sites), color='k', marker='x', markersize=10, mew=1, linestyle='', zorder=10000) # Draw unit cell if draw_unit_cell: verts = np.insert(verts, 1, lattsum, axis=0).tolist() verts += [[0., 0.]] verts = [[0., 0.]] + verts codes = [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY] verts = [(np.array(vert) + corner).tolist() for vert in verts] path = Path(verts, codes) patch = patches.PathPatch(path, facecolor='none', lw=2, alpha=0.5, zorder=2 * n + 2) ax.add_patch(patch) ax.set_aspect("equal") center = corner + lattsum / 2. extent = np.max(lattsum) lim_array = [center - extent * window, center + extent * window] x_lim = [ele[0] for ele in lim_array] y_lim = [ele[1] for ele in lim_array] ax.set_xlim(x_lim) ax.set_ylim(y_lim) return ax