adsorption.py

# 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."""

from __future__ import annotations

import itertools
import os

import numpy as np
from matplotlib import patches
from matplotlib.path import Path
from monty.serialization import loadfn
from scipy.spatial import Delaunay

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

__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"


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

    @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)

    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

    def assign_site_properties(self, slab, height=0.9):
        """Assigns site properties."""
        if "surface_properties" in slab.site_properties:
            return slab

        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})

    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"]

    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"]

    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

    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]

    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]

    @classmethod
    def ensemble_center(cls, 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)

        return np.average([site_list[i].frac_coords for i in indices], axis=0)

    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:
            molecule.add_site_property("surface_properties", ["adsorbate"] * molecule.num_sites)
        if "selective_dynamics" in struct.site_properties:
            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

    @classmethod
    def assign_selective_dynamics(cls, 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)

    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

    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 {}
        ad_slabss = self.generate_adsorption_structures(
            molecule,
            repeat=repeat,
            min_lw=min_lw,
            translate=translate,
            reorient=reorient,
            find_args=find_args,
        )

        new_ad_slabss = []
        for ad_slabs in ad_slabss:
            # Find the adsorbate sites and indices in each slab
            _, adsorbates, indices = False, [], []
            for i, site in enumerate(ad_slabs.sites):
                if site.surface_properties == "adsorbate":
                    adsorbates.append(site)
                    indices.append(i)

            # Start with the clean slab
            ad_slabs.remove_sites(indices)
            slab = ad_slabs.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 = ad_slabs.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_ad_slabss.append(slab)

        return new_ad_slabss

    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 substitute 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 f"{sym_slab[ii].frac_coords[2]:.6f}" != f"{site.frac_coords[2]:.6f}":
                        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)]


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)


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


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])


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"]}


def plot_slab(
    slab,
    ax,
    scale=0.8,
    repeat=5,
    window=1.5,
    draw_unit_cell=True,
    decay=0.2,
    adsorption_sites=True,
    inverse=False,
):
    """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
        inverse (bool): invert z axis to plot opposite surface
    """
    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]
    # inverse coords, sites, alphas, to show other side of slab
    if inverse:
        alphas = np.array(reversed(alphas))
        sites = list(reversed(sites))
        coords = np.array(reversed(coords))
    # Draw circles at sites and stack them accordingly
    for n, coord in enumerate(coords):
        r = sites[n].species.elements[0].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.elements[0].symbol]
        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)
        if inverse:
            inverse_slab = orig_slab.copy()
            inverse_slab.make_supercell([1, 1, -1])
            asf = AdsorbateSiteFinder(inverse_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, 0.0]]
        verts = [[0.0, 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 / 2.0
    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