# Source code for pymatgen.analysis.surface_analysis

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

    """
    This module defines tools to analyze surface and adsorption related
    quantities as well as related plots. If you use this module, please
    consider citing the following works::

        R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson,
        S. P. Ong, "Surface Energies of Elemental Crystals", Scientific
        Data, 2016, 3:160080, doi: 10.1038/sdata.2016.80.

        and

        Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale
        stabilization of sodium oxides: Implications for Na-O2 batteries.
        Nano Letters, 14(2), 1016–1020. https://doi.org/10.1021/nl404557w

        and

        Montoya, J. H., & Persson, K. A. (2017). A high-throughput framework
            for determining adsorption energies on solid surfaces. Npj
            Computational Materials, 3(1), 14.
            https://doi.org/10.1038/s41524-017-0017-z

    TODO:
        -Still assumes individual elements have their own chempots
            in a molecular adsorbate instead of considering a single
            chempot for a single molecular adsorbate. E.g. for an OH
            adsorbate, the surface energy is a function of delu_O and
            delu_H instead of delu_OH
        -Need a method to automatically get chempot range when
            dealing with non-stoichiometric slabs
        -Simplify the input for SurfaceEnergyPlotter such that the
            user does not need to generate a dict
    """

    import numpy as np
    import itertools
    import warnings
    import random
    import copy
    from sympy import Symbol
    from sympy.solvers import linsolve, solve

    from pymatgen.core.composition import Composition
    from pymatgen.core.surface import get_slab_regions
    from pymatgen.entries.computed_entries import ComputedStructureEntry
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.analysis.wulff import WulffShape
    from pymatgen.util.plotting import pretty_plot
    from pymatgen.io.vasp.outputs import Outcar, Locpot, Poscar

    EV_PER_ANG2_TO_JOULES_PER_M2 = 16.0217656

    __author__ = "Richard Tran"
    __copyright__ = "Copyright 2017, The Materials Virtual Lab"
    __version__ = "0.2"
    __maintainer__ = "Richard Tran"
    __credits__ = "Joseph Montoya, Xianguo Li"
    __email__ = "rit001@eng.ucsd.edu"
    __date__ = "8/24/17"

    class SlabEntry(ComputedStructureEntry):
        """
        A ComputedStructureEntry object encompassing all data relevant to a
            slab for analyzing surface thermodynamics.

        .. attribute:: miller_index

            Miller index of plane parallel to surface.

        .. attribute:: label

            Brief description for this slab.

        .. attribute:: adsorbates

            List of ComputedStructureEntry for the types of adsorbates

        ..attribute:: clean_entry

            SlabEntry for the corresponding clean slab for an adsorbed slab

        ..attribute:: ads_entries_dict

            Dictionary where the key is the reduced composition of the
                adsorbate entry and value is the entry itself
        """

        def __init__(self, structure, energy, miller_index, correction=0.0,
                     parameters=None, data=None, entry_id=None, label=None,
                     adsorbates=None, clean_entry=None, marker=None, color=None):

            """
            Make a SlabEntry containing all relevant surface thermodynamics data.

            Args:
                structure (Slab): The primary slab associated with this entry.
                energy (float): Energy from total energy calculation
                miller_index (tuple(h, k, l)): Miller index of plane parallel
                    to surface
                correction (float): See ComputedSlabEntry
                parameters (dict): See ComputedSlabEntry
                data (dict): See ComputedSlabEntry
                entry_id (obj): See ComputedSlabEntry
                data (dict): See ComputedSlabEntry
                entry_id (str): See ComputedSlabEntry
                label (str): Any particular label for this slab, e.g. "Tasker 2",
                    "non-stoichiometric", "reconstructed"
                adsorbates ([ComputedStructureEntry]): List of reference entries
                    for the adsorbates on the slab, can be an isolated molecule
                    (e.g. O2 for O or O2 adsorption), a bulk structure (eg. fcc
                    Cu for Cu adsorption) or anything.
                clean_entry (ComputedStructureEntry): If the SlabEntry is for an
                    adsorbed slab, this is the corresponding SlabEntry for the
                    clean slab
                marker (str): Custom marker for gamma plots ("--" and "-" are typical)
                color (str or rgba): Custom color for gamma plots
            """

            self.miller_index = miller_index
            self.label = label
            self.adsorbates = [] if not adsorbates else adsorbates
            self.clean_entry = clean_entry
            self.ads_entries_dict = {str(list(ads.composition.as_dict().keys())[0]): ads for ads in self.adsorbates}
            self.mark = marker
            self.color = color

            super().__init__(
                structure, energy, correction=correction,
                parameters=parameters, data=data, entry_id=entry_id)

        def as_dict(self):
            """
            Returns dict which contains Slab Entry data.
            """

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__}
            d["structure"] = self.structure
            d["energy"] = self.energy
            d["miller_index"] = self.miller_index
            d["label"] = self.label
            d["coverage"] = self.coverage
            d["adsorbates"] = self.adsorbates
            d["clean_entry"] = self.clean_entry

            return d

        def gibbs_binding_energy(self, eads=False):
            """
            Returns the adsorption energy or Gibb's binding energy
                of an adsorbate on a surface
            Args:
                eads (bool): Whether to calculate the adsorption energy
                    (True) or the binding energy (False) which is just
                    adsorption energy normalized by number of adsorbates.
            """

            n = self.get_unit_primitive_area
            Nads = self.Nads_in_slab

            BE = (self.energy - n * self.clean_entry.energy) / Nads - sum([ads.energy_per_atom for ads in self.adsorbates])
            return BE * Nads if eads else BE

        def surface_energy(self, ucell_entry, ref_entries=None):
            """
            Calculates the surface energy of this SlabEntry.
            Args:
                ucell_entry (entry): An entry object for the bulk
                ref_entries (list: [entry]): A list of entries for each type
                    of element to be used as a reservoir for nonstoichiometric
                    systems. The length of this list MUST be n-1 where n is the
                    number of different elements in the bulk entry. The chempot
                    of the element ref_entry that is not in the list will be
                    treated as a variable.

            Returns (Add (Sympy class)): Surface energy
            """

            # Set up
            ref_entries = [] if not ref_entries else ref_entries

            # Check if appropriate ref_entries are present if the slab is non-stoichiometric
            # TODO: There should be a way to identify which specific species are
            # non-stoichiometric relative to the others in systems with more than 2 species
            slab_comp = self.composition.as_dict()
            ucell_entry_comp = ucell_entry.composition.reduced_composition.as_dict()
            slab_clean_comp = Composition({el: slab_comp[el] for el in ucell_entry_comp.keys()})
            if slab_clean_comp.reduced_composition != ucell_entry.composition.reduced_composition:
                list_els = [list(entry.composition.as_dict().keys())[0] for entry in ref_entries]
                if not any([el in list_els for el in ucell_entry.composition.as_dict().keys()]):
                    warnings.warn("Elemental references missing for the non-dopant species.")

            gamma = (Symbol("E_surf") - Symbol("Ebulk")) / (2 * Symbol("A"))
            ucell_comp = ucell_entry.composition
            ucell_reduced_comp = ucell_comp.reduced_composition
            ref_entries_dict = {str(list(ref.composition.as_dict().keys())[0]): ref for ref in ref_entries}
            ref_entries_dict.update(self.ads_entries_dict)

            # Calculate Gibbs free energy of the bulk per unit formula
            gbulk = ucell_entry.energy / ucell_comp.get_integer_formula_and_factor()[1]

            # First we get the contribution to the bulk energy
            # from each element with an existing ref_entry.
            bulk_energy, gbulk_eqn = 0, 0
            for el, ref in ref_entries_dict.items():
                N, delu = self.composition.as_dict()[el], Symbol("delu_" + str(el))
                if el in ucell_comp.as_dict().keys():
                    gbulk_eqn += ucell_reduced_comp[el] * (delu + ref.energy_per_atom)
                bulk_energy += N * (Symbol("delu_" + el) + ref.energy_per_atom)

            # Next, we add the contribution to the bulk energy from
            # the variable element (the element without a ref_entry),
            # as a function of the other elements
            for ref_el in ucell_comp.as_dict().keys():
                if str(ref_el) not in ref_entries_dict.keys():
                    break
            refEperA = (gbulk - gbulk_eqn) / ucell_reduced_comp.as_dict()[ref_el]
            bulk_energy += self.composition.as_dict()[ref_el] * refEperA
            se = gamma.subs({Symbol("E_surf"): self.energy, Symbol("Ebulk"): bulk_energy,
                             Symbol("A"): self.surface_area})

            return float(se) if type(se).__name__ == "Float" else se

        @property
        def get_unit_primitive_area(self):
            """
            Returns the surface area of the adsorbed system per
            unit area of the primitive slab system.
            """

            A_ads = self.surface_area
            A_clean = self.clean_entry.surface_area
            n = (A_ads / A_clean)
            return n

        @property
        def get_monolayer(self):
            """
            Returns the primitive unit surface area density of the
                adsorbate.
            """
            unit_a = self.get_unit_primitive_area
            Nsurfs = self.Nsurfs_ads_in_slab
            Nads = self.Nads_in_slab
            return Nads / (unit_a * Nsurfs)

        @property
        def Nads_in_slab(self):
            """
            Returns the TOTAL number of adsorbates in the slab on BOTH sides
            """
            return sum([self.composition.as_dict()[a] for a in self.ads_entries_dict.keys()])

        @property
        def Nsurfs_ads_in_slab(self):
            """
            Returns the TOTAL number of adsorbed surfaces in the slab
            """

            struct = self.structure
            weights = [s.species.weight for s in struct]
            center_of_mass = np.average(struct.frac_coords, weights=weights, axis=0)

            Nsurfs = 0
            # Are there adsorbates on top surface?
            if any([site.species_string in self.ads_entries_dict.keys()
                    for site in struct if site.frac_coords[2] > center_of_mass[2]]):
                Nsurfs += 1
            # Are there adsorbates on bottom surface?
            if any([site.species_string in self.ads_entries_dict.keys()
                    for site in struct if site.frac_coords[2] < center_of_mass[2]]):
                Nsurfs += 1

            return Nsurfs

        @classmethod
        def from_dict(cls, d):
            """
            Returns a SlabEntry by reading in an dictionary
            """

            structure = SlabEntry.from_dict(d["structure"])
            energy = SlabEntry.from_dict(d["energy"])
            miller_index = d["miller_index"]
            label = d["label"]
            coverage = d["coverage"]
            adsorbates = d["adsorbates"]
            clean_entry = d["clean_entry"]

            return SlabEntry(structure, energy, miller_index, label=label,
                             coverage=coverage, adsorbates=adsorbates,
                             clean_entry=clean_entry)

        @property
        def surface_area(self):
            """
            Calculates the surface area of the slab
            """
            m = self.structure.lattice.matrix
            return np.linalg.norm(np.cross(m[0], m[1]))

        @property
        def cleaned_up_slab(self):
            """
            Returns a slab with the adsorbates removed
            """
            ads_strs = list(self.ads_entries_dict.keys())
            cleaned = self.structure.copy()
            cleaned.remove_species(ads_strs)
            return cleaned

        @property
        def create_slab_label(self):
            """
            Returns a label (str) for this particular slab based
                on composition, coverage and Miller index.
            """

            if "label" in self.data.keys():
                return self.data["label"]

            label = str(self.miller_index)
            ads_strs = list(self.ads_entries_dict.keys())

            cleaned = self.cleaned_up_slab
            label += " %s" % (cleaned.composition.reduced_composition)

            if self.adsorbates:
                for ads in ads_strs:
                    label += r"+%s" % (ads)
                label += r", %.3f ML" % (self.get_monolayer)
            return label

        @staticmethod
        def from_computed_structure_entry(entry, miller_index, label=None,
                                          adsorbates=None, clean_entry=None, **kwargs):
            """
            Returns SlabEntry from a ComputedStructureEntry
            """
            return SlabEntry(entry.structure, entry.energy, miller_index, label=label,
                             adsorbates=adsorbates, clean_entry=clean_entry, **kwargs)

    class SurfaceEnergyPlotter:
        """
        A class used for generating plots to analyze the thermodynamics of surfaces
            of a material. Produces stability maps of different slab configurations,
            phases diagrams of two parameters to determine stability of configurations
            (future release), and Wulff shapes.

        .. attribute:: all_slab_entries

            Either a list of SlabEntry objects (note for a list, the SlabEntry must
                have the adsorbates and clean_entry parameter pulgged in) or a Nested
                dictionary containing a list of entries for slab calculations as
                items and the corresponding Miller index of the slab as the key.
                To account for adsorption, each value is a sub-dictionary with the
                entry of a clean slab calculation as the sub-key and a list of
                entries for adsorption calculations as the sub-value. The sub-value
                can contain different adsorption configurations such as a different
                site or a different coverage, however, ordinarily only the most stable
                configuration for a particular coverage will be considered as the
                function of the adsorbed surface energy has an intercept dependent on
                the adsorption energy (ie an adsorption site with a higher adsorption
                energy will always provide a higher surface energy than a site with a
                lower adsorption energy). An example parameter is provided:
                {(h1,k1,l1): {clean_entry1: [ads_entry1, ads_entry2, ...],
                              clean_entry2: [...], ...}, (h2,k2,l2): {...}}
                where clean_entry1 can be a pristine surface and clean_entry2 can be a
                reconstructed surface while ads_entry1 can be adsorption at site 1 with
                a 2x2 coverage while ads_entry2 can have a 3x3 coverage. If adsorption
                entries are present (i.e. if all_slab_entries[(h,k,l)][clean_entry1]), we
                consider adsorption in all plots and analysis for this particular facet.

        ..attribute:: color_dict

            Dictionary of colors (r,g,b,a) when plotting surface energy stability. The
                keys are individual surface entries where clean surfaces have a solid
                color while the corresponding adsorbed surface will be transparent.

        .. attribute:: ucell_entry

            ComputedStructureEntry of the bulk reference for this particular material.

        .. attribute:: ref_entries

            List of ComputedStructureEntries to be used for calculating chemical potential.

        .. attribute:: color_dict

            Randomly generated dictionary of colors associated with each facet.
        """

        def __init__(self, all_slab_entries, ucell_entry, ref_entries=None):
            """
            Object for plotting surface energy in different ways for clean and
                adsorbed surfaces.
            Args:
                all_slab_entries (dict or list): Dictionary or list containing
                    all entries for slab calculations. See attributes.
                ucell_entry (ComputedStructureEntry): ComputedStructureEntry
                    of the bulk reference for this particular material.
                ref_entries ([ComputedStructureEntries]): A list of entries for
                    each type of element to be used as a reservoir for
                    nonstoichiometric systems. The length of this list MUST be
                    n-1 where n is the number of different elements in the bulk
                    entry. The bulk energy term in the grand surface potential can
                    be defined by a summation of the chemical potentials for each
                    element in the system. As the bulk energy is already provided,
                    one can solve for one of the chemical potentials as a function
                    of the other chemical potetinals and bulk energy. i.e. there
                    are n-1 variables (chempots). e.g. if your ucell_entry is for
                    LiFePO4 than your ref_entries should have an entry for Li, Fe,
                    and P if you want to use the chempot of O as the variable.
            """

            self.ucell_entry = ucell_entry
            self.ref_entries = ref_entries
            self.all_slab_entries = all_slab_entries if \
                type(all_slab_entries).__name__ == "dict" else \
                entry_dict_from_list(all_slab_entries)
            self.color_dict = self.color_palette_dict()

            se_dict, as_coeffs_dict = {}, {}
            for hkl in self.all_slab_entries.keys():
                for clean in self.all_slab_entries[hkl].keys():
                    se = clean.surface_energy(self.ucell_entry, ref_entries=self.ref_entries)
                    if type(se).__name__ == "float":
                        se_dict[clean] = se
                        as_coeffs_dict[clean] = {1: se}
                    else:
                        se_dict[clean] = se
                        as_coeffs_dict[clean] = se.as_coefficients_dict()
                    for dope in self.all_slab_entries[hkl][clean]:
                        se = dope.surface_energy(self.ucell_entry, ref_entries=self.ref_entries)
                        if type(se).__name__ == "float":
                            se_dict[dope] = se
                            as_coeffs_dict[dope] = {1: se}
                        else:
                            se_dict[dope] = se
                            as_coeffs_dict[dope] = se.as_coefficients_dict()
            self.surfe_dict = se_dict
            self.as_coeffs_dict = as_coeffs_dict

            list_of_chempots = []
            for k in self.as_coeffs_dict.keys():
                if type(self.as_coeffs_dict[k]).__name__ == "float":
                    continue
                for du in self.as_coeffs_dict[k].keys():
                    if du not in list_of_chempots:
                        list_of_chempots.append(du)
            self.list_of_chempots = list_of_chempots

        def get_stable_entry_at_u(self, miller_index, delu_dict=None, delu_default=0,
                                  no_doped=False, no_clean=False):
            """
            Returns the entry corresponding to the most stable slab for a particular
                facet at a specific chempot. We assume that surface energy is constant
                so all free variables must be set with delu_dict, otherwise they are
                assumed to be equal to delu_default.

            Args:
                miller_index ((h,k,l)): The facet to find the most stable slab in
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                no_doped (bool): Consider stability of clean slabs only.
                no_clean (bool): Consider stability of doped slabs only.

            Returns:
                SlabEntry, surface_energy (float)
            """

            all_delu_dict = self.set_all_variables(delu_dict, delu_default)

            def get_coeffs(e):
                coeffs = []
                for du in all_delu_dict.keys():
                    if type(self.as_coeffs_dict[e]).__name__ == 'float':
                        coeffs.append(self.as_coeffs_dict[e])
                    elif du in self.as_coeffs_dict[e].keys():
                        coeffs.append(self.as_coeffs_dict[e][du])
                    else:
                        coeffs.append(0)
                return np.array(coeffs)

            all_entries, all_coeffs = [], []
            for entry in self.all_slab_entries[miller_index].keys():
                if not no_clean:
                    all_entries.append(entry)
                    all_coeffs.append(get_coeffs(entry))
                if not no_doped:
                    for ads_entry in self.all_slab_entries[miller_index][entry]:
                        all_entries.append(ads_entry)
                        all_coeffs.append(get_coeffs(ads_entry))

            du_vals = np.array(list(all_delu_dict.values()))
            all_gamma = list(np.dot(all_coeffs, du_vals.T))

            return all_entries[all_gamma.index(min(all_gamma))], float(min(all_gamma))

        def wulff_from_chempot(self, delu_dict=None, delu_default=0, symprec=1e-5,
                               no_clean=False, no_doped=False):
            """
            Method to get the Wulff shape at a specific chemical potential.

            Args:
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                symprec (float): See WulffShape.
                no_doped (bool): Consider stability of clean slabs only.
                no_clean (bool): Consider stability of doped slabs only.

            Returns:
                (WulffShape): The WulffShape at u_ref and u_ads.
            """

            latt = SpacegroupAnalyzer(self.ucell_entry.structure). \
                get_conventional_standard_structure().lattice

            miller_list = self.all_slab_entries.keys()
            e_surf_list = []
            for hkl in miller_list:
                # For all configurations, calculate surface energy as a
                # function of u. Use the lowest surface energy (corresponds
                # to the most stable slab termination at that particular u)
                gamma = self.get_stable_entry_at_u(hkl, delu_dict=delu_dict,
                                                   delu_default=delu_default,
                                                   no_clean=no_clean,
                                                   no_doped=no_doped)[1]
                e_surf_list.append(gamma)

            return WulffShape(latt, miller_list, e_surf_list, symprec=symprec)

        def area_frac_vs_chempot_plot(self, ref_delu, chempot_range, delu_dict=None,
                                      delu_default=0, increments=10, no_clean=False, no_doped=False):
            """
            1D plot. Plots the change in the area contribution
            of each facet as a function of chemical potential.

            Args:
                ref_delu (sympy Symbol): The free variable chempot with the format:
                    Symbol("delu_el") where el is the name of the element.
                chempot_range (list): Min/max range of chemical potential to plot along
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                increments (int): Number of data points between min/max or point
                    of intersection. Defaults to 10 points.

            Returns:
                (Pylab): Plot of area frac on the Wulff shape
                    for each facet vs chemical potential.
            """

            delu_dict = delu_dict if delu_dict else {}
            chempot_range = sorted(chempot_range)
            all_chempots = np.linspace(min(chempot_range), max(chempot_range),
                                       increments)

            # initialize a dictionary of lists of fractional areas for each hkl
            hkl_area_dict = {}
            for hkl in self.all_slab_entries.keys():
                hkl_area_dict[hkl] = []

            # Get plot points for each Miller index
            for u in all_chempots:
                delu_dict[ref_delu] = u
                wulffshape = self.wulff_from_chempot(delu_dict=delu_dict, no_clean=no_clean,
                                                     no_doped=no_doped, delu_default=delu_default)

                for hkl in wulffshape.area_fraction_dict.keys():
                    hkl_area_dict[hkl].append(wulffshape.area_fraction_dict[hkl])

            # Plot the area fraction vs chemical potential for each facet
            plt = pretty_plot(width=8, height=7)
            axes = plt.gca()

            for hkl in self.all_slab_entries.keys():
                clean_entry = list(self.all_slab_entries[hkl].keys())[0]
                # Ignore any facets that never show up on the
                # Wulff shape regardless of chemical potential
                if all([a == 0 for a in hkl_area_dict[hkl]]):
                    continue
                else:
                    plt.plot(all_chempots, hkl_area_dict[hkl],
                             '--', color=self.color_dict[clean_entry],
                             label=str(hkl))

            # Make the figure look nice
            plt.ylabel(r"Fractional area $A^{Wulff}_{hkl}/A^{Wulff}$")
            self.chempot_plot_addons(plt, chempot_range, str(ref_delu).split("_")[1],
                                     axes, rect=[-0.0, 0, 0.95, 1], pad=5, ylim=[0, 1])

            return plt

        def get_surface_equilibrium(self, slab_entries, delu_dict=None):

            """
            Takes in a list of SlabEntries and calculates the chemical potentials
                at which all slabs in the list coexists simultaneously. Useful for
                building surface phase diagrams. Note that to solve for x equations
                (x slab_entries), there must be x free variables (chemical potentials).
                Adjust delu_dict as need be to get the correct number of free variables.
            Args:
                slab_entries (array): The coefficients of the first equation
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.

            Returns:
                (array): Array containing a solution to x equations with x
                    variables (x-1 chemical potential and 1 surface energy)
            """
            # Generate all possible coefficients
            all_parameters = []
            all_eqns = []
            for slab_entry in slab_entries:
                se = self.surfe_dict[slab_entry]

                # remove the free chempots we wish to keep constant and
                # set the equation to 0 (subtract gamma from both sides)
                if type(se).__name__ == "float":
                    all_eqns.append(se - Symbol("gamma"))
                else:

                    se = sub_chempots(se, delu_dict) if delu_dict else se
                    all_eqns.append(se - Symbol("gamma"))
                    all_parameters.extend([p for p in list(se.free_symbols)
                                           if p not in all_parameters])

            all_parameters.append(Symbol("gamma"))
            # Now solve the system of linear eqns to find the chempot
            # where the slabs are at equilibrium with each other

            soln = linsolve(all_eqns, all_parameters)
            if not soln:
                warnings.warn("No solution")
                return soln
            return {p: list(soln)[0][i] for i, p in enumerate(all_parameters)}

        def stable_u_range_dict(self, chempot_range, ref_delu, no_doped=True,
                                no_clean=False, delu_dict={}, miller_index=(),
                                dmu_at_0=False, return_se_dict=False):
            """
            Creates a dictionary where each entry is a key pointing to a
            chemical potential range where the surface of that entry is stable.
            Does so by enumerating through all possible solutions (intersect)
            for surface energies of a specific facet.

            Args:
                chempot_range ([max_chempot, min_chempot]): Range to consider the
                    stability of the slabs.
                ref_delu (sympy Symbol): The range stability of each slab is based
                    on the chempot range of this chempot. Should be a sympy Symbol
                    object of the format: Symbol("delu_el") where el is the name of
                    the element
                no_doped (bool): Consider stability of clean slabs only.
                no_clean (bool): Consider stability of doped slabs only.
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                miller_index (list): Miller index for a specific facet to get a
                    dictionary for.
                dmu_at_0 (bool): If True, if the surface energies corresponding to
                    the chemical potential range is between a negative and positive
                    value, the value is a list of three chemical potentials with the
                    one in the center corresponding a surface energy of 0. Uselful
                    in identifying unphysical ranges of surface energies and their
                    chemical potential range.
                return_se_dict (bool): Whether or not to return the corresponding
                    dictionary of surface energies
            """

            chempot_range = sorted(chempot_range)
            stable_urange_dict, se_dict = {}, {}

            # Get all entries for a specific facet
            for hkl in self.all_slab_entries.keys():
                entries_in_hkl = []
                # Skip this facet if this is not the facet we want
                if miller_index and hkl != tuple(miller_index):
                    continue
                if not no_clean:
                    entries_in_hkl.extend([clean for clean in self.all_slab_entries[hkl]])
                if not no_doped:
                    for entry in self.all_slab_entries[hkl]:
                        entries_in_hkl.extend([ads_entry for ads_entry in
                                               self.all_slab_entries[hkl][entry]])

                for entry in entries_in_hkl:
                    stable_urange_dict[entry] = []
                    se_dict[entry] = []
                # if there is only one entry for this facet, then just give it the
                # default urange, you can't make combinations with just 1 item
                if len(entries_in_hkl) == 1:
                    stable_urange_dict[entries_in_hkl[0]] = chempot_range
                    u1, u2 = delu_dict.copy(), delu_dict.copy()
                    u1[ref_delu], u2[ref_delu] = chempot_range[0], chempot_range[1]
                    se = self.as_coeffs_dict[entries_in_hkl[0]]
                    se_dict[entries_in_hkl[0]] = [sub_chempots(se, u1), sub_chempots(se, u2)]
                    continue

                for pair in itertools.combinations(entries_in_hkl, 2):
                    # I'm assuming ref_delu was not set in delu_dict,
                    # so the solution should be for ref_delu
                    solution = self.get_surface_equilibrium(pair, delu_dict=delu_dict)

                    # Check if this solution is stable
                    if not solution:
                        continue
                    new_delu_dict = delu_dict.copy()
                    new_delu_dict[ref_delu] = solution[ref_delu]
                    stable_entry, gamma = self.get_stable_entry_at_u(hkl, new_delu_dict,
                                                                     no_doped=no_doped,
                                                                     no_clean=no_clean)
                    if stable_entry not in pair:
                        continue

                    # Now check if the solution is within the chempot range
                    if not (chempot_range[0] <= solution[ref_delu] <= chempot_range[1]):
                        continue

                    for entry in pair:
                        stable_urange_dict[entry].append(solution[ref_delu])
                        se_dict[entry].append(gamma)

                # Now check if all entries have 2 chempot values. If only
                # one, we need to set the other value as either the upper
                # limit or lower limit of the user provided chempot_range
                new_delu_dict = delu_dict.copy()
                for u in chempot_range:
                    new_delu_dict[ref_delu] = u
                    entry, gamma = self.get_stable_entry_at_u(hkl, delu_dict=new_delu_dict,
                                                              no_doped=no_doped,
                                                              no_clean=no_clean)
                    stable_urange_dict[entry].append(u)
                    se_dict[entry].append(gamma)

            if dmu_at_0:
                for entry in se_dict.keys():
                    # if se are of opposite sign, determine chempot when se=0.
                    # Useful for finding a chempot range where se is unphysical
                    if not stable_urange_dict[entry]:
                        continue
                    if se_dict[entry][0] * se_dict[entry][1] < 0:
                        # solve for gamma=0
                        se = self.as_coeffs_dict[entry]
                        se_dict[entry].append(0)
                        stable_urange_dict[entry].append(solve(sub_chempots(se, delu_dict),
                                                               ref_delu)[0])

            # sort the chempot ranges for each facet
            for entry in stable_urange_dict.keys():
                se_dict[entry] = [se for i, se in sorted(zip(stable_urange_dict[entry],
                                                             se_dict[entry]))]
                stable_urange_dict[entry] = sorted(stable_urange_dict[entry])

            if return_se_dict:
                return stable_urange_dict, se_dict
            else:
                return stable_urange_dict

        def color_palette_dict(self, alpha=0.35):
            """
            Helper function to assign each facet a unique color using a dictionary.

            Args:
                alpha (float): Degree of transparency

            return (dict): Dictionary of colors (r,g,b,a) when plotting surface
                energy stability. The keys are individual surface entries where
                clean surfaces have a solid color while the corresponding adsorbed
                surface will be transparent.
            """

            color_dict = {}
            for hkl in self.all_slab_entries.keys():
                rgb_indices = [0, 1, 2]
                color = [0, 0, 0, 1]
                random.shuffle(rgb_indices)
                for i, ind in enumerate(rgb_indices):
                    if i == 2:
                        break
                    color[ind] = np.random.uniform(0, 1)

                # Get the clean (solid) colors first
                clean_list = np.linspace(0, 1, len(self.all_slab_entries[hkl]))
                for i, clean in enumerate(self.all_slab_entries[hkl].keys()):
                    c = copy.copy(color)
                    c[rgb_indices[2]] = clean_list[i]
                    color_dict[clean] = c

                    # Now get the adsorbed (transparent) colors
                    for ads_entry in self.all_slab_entries[hkl][clean]:
                        c_ads = copy.copy(c)
                        c_ads[3] = alpha
                        color_dict[ads_entry] = c_ads

            return color_dict

        def chempot_vs_gamma_plot_one(self, plt, entry, ref_delu, chempot_range,
                                      delu_dict={}, delu_default=0, label='', JPERM2=False):
            """
            Helper function to  help plot the surface energy of a
            single SlabEntry as a function of chemical potential.

            Args:
                plt (Plot): A plot.
                entry (SlabEntry): Entry of the slab whose surface energy we want
                    to plot
                ref_delu (sympy Symbol): The range stability of each slab is based
                    on the chempot range of this chempot. Should be a sympy Symbol
                    object of the format: Symbol("delu_el") where el is the name of
                    the element
                chempot_range ([max_chempot, min_chempot]): Range to consider the
                    stability of the slabs.
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                label (str): Label of the slab for the legend.
                JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
                    eV/A^2 (False)

            Returns:
                (Plot): Plot of surface energy vs chemical potential for one entry.
            """

            chempot_range = sorted(chempot_range)

            # use dashed lines for slabs that are not stoichiometric
            # wrt bulk. Label with formula if nonstoichiometric
            ucell_comp = self.ucell_entry.composition.reduced_composition
            if entry.adsorbates:
                s = entry.cleaned_up_slab
                clean_comp = s.composition.reduced_composition
            else:
                clean_comp = entry.composition.reduced_composition

            mark = '--' if ucell_comp != clean_comp else '-'

            delu_dict = self.set_all_variables(delu_dict, delu_default)
            delu_dict[ref_delu] = chempot_range[0]
            gamma_min = self.as_coeffs_dict[entry]
            gamma_min = gamma_min if type(gamma_min).__name__ == "float" else sub_chempots(gamma_min, delu_dict)
            delu_dict[ref_delu] = chempot_range[1]
            gamma_max = self.as_coeffs_dict[entry]
            gamma_max = gamma_max if type(gamma_max).__name__ == "float" else sub_chempots(gamma_max, delu_dict)
            gamma_range = [gamma_min, gamma_max]

            se_range = np.array(gamma_range) * EV_PER_ANG2_TO_JOULES_PER_M2 \
                if JPERM2 else gamma_range

            mark = entry.mark if entry.mark else mark
            c = entry.color if entry.color else self.color_dict[entry]
            plt.plot(chempot_range, se_range, mark, color=c, label=label)

            return plt

        def chempot_vs_gamma(self, ref_delu, chempot_range, miller_index=(),
                             delu_dict={}, delu_default=0, JPERM2=False,
                             show_unstable=False, ylim=[], plt=None,
                             no_clean=False, no_doped=False,
                             use_entry_labels=False, no_label=False):
            """
            Plots the surface energy as a function of chemical potential.
                Each facet will be associated with its own distinct colors.
                Dashed lines will represent stoichiometries different from that
                of the mpid's compound. Transparent lines indicates adsorption.

            Args:
                ref_delu (sympy Symbol): The range stability of each slab is based
                    on the chempot range of this chempot. Should be a sympy Symbol
                    object of the format: Symbol("delu_el") where el is the name of
                    the element
                chempot_range ([max_chempot, min_chempot]): Range to consider the
                    stability of the slabs.
                miller_index (list): Miller index for a specific facet to get a
                    dictionary for.
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
                    eV/A^2 (False)
                show_unstable (bool): Whether or not to show parts of the surface
                    energy plot outside the region of stability.
                ylim ([ymax, ymin]): Range of y axis
                no_doped (bool): Whether to plot for the clean slabs only.
                no_clean (bool): Whether to plot for the doped slabs only.
                use_entry_labels (bool): If True, will label each slab configuration
                    according to their given label in the SlabEntry object.
                no_label (bool): Option to turn off labels.

            Returns:
                (Plot): Plot of surface energy vs chempot for all entries.
            """

            chempot_range = sorted(chempot_range)

            plt = pretty_plot(width=8, height=7) if not plt else plt
            axes = plt.gca()

            for hkl in self.all_slab_entries.keys():
                if miller_index and hkl != tuple(miller_index):
                    continue
                # Get the chempot range of each surface if we only
                # want to show the region where each slab is stable
                if not show_unstable:
                    stable_u_range_dict = self.stable_u_range_dict(chempot_range, ref_delu,
                                                                   no_doped=no_doped,
                                                                   delu_dict=delu_dict,
                                                                   miller_index=hkl)

                already_labelled = []
                label = ''
                for clean_entry in self.all_slab_entries[hkl]:

                    urange = stable_u_range_dict[clean_entry] if \
                        not show_unstable else chempot_range
                    # Don't plot if the slab is unstable, plot if it is.
                    if urange != []:

                        label = clean_entry.label
                        if label in already_labelled:
                            label = None
                        else:
                            already_labelled.append(label)
                        if not no_clean:
                            if use_entry_labels:
                                label = clean_entry.label
                            if no_label:
                                label = ""
                            plt = self.chempot_vs_gamma_plot_one(plt, clean_entry, ref_delu,
                                                                 urange, delu_dict=delu_dict,
                                                                 delu_default=delu_default,
                                                                 label=label, JPERM2=JPERM2)
                    if not no_doped:
                        for ads_entry in self.all_slab_entries[hkl][clean_entry]:
                            # Plot the adsorbed slabs
                            # Generate a label for the type of slab
                            urange = stable_u_range_dict[ads_entry] \
                                if not show_unstable else chempot_range
                            if urange != []:
                                if use_entry_labels:
                                    label = ads_entry.label
                                if no_label:
                                    label = ""
                                plt = self.chempot_vs_gamma_plot_one(plt, ads_entry,
                                                                     ref_delu, urange,
                                                                     delu_dict=delu_dict,
                                                                     delu_default=delu_default,
                                                                     label=label,
                                                                     JPERM2=JPERM2)

            # Make the figure look nice
            plt.ylabel(r"Surface energy (J/$m^{2}$)") if JPERM2 \
                else plt.ylabel(r"Surface energy (eV/$\AA^{2}$)")
            plt = self.chempot_plot_addons(plt, chempot_range, str(ref_delu).split("_")[1],
                                           axes, ylim=ylim)

            return plt

        def monolayer_vs_BE(self, plot_eads=False):
            """
            Plots the binding energy energy as a function of monolayers (ML), i.e.
                the fractional area adsorbate density for all facets. For each
                facet at a specific monlayer, only plot the lowest binding energy.

            Args:
                plot_eads (bool): Option to plot the adsorption energy (binding
                     energy multiplied by number of adsorbates) instead.

            Returns:
                (Plot): Plot of binding energy vs monolayer for all facets.
            """

            plt = pretty_plot(width=8, height=7)
            for hkl in self.all_slab_entries.keys():
                ml_be_dict = {}
                for clean_entry in self.all_slab_entries[hkl].keys():
                    if self.all_slab_entries[hkl][clean_entry]:
                        for ads_entry in self.all_slab_entries[hkl][clean_entry]:
                            if ads_entry.get_monolayer not in ml_be_dict.keys():
                                ml_be_dict[ads_entry.get_monolayer] = 1000
                            be = ads_entry.gibbs_binding_energy(eads=plot_eads)
                            if be < ml_be_dict[ads_entry.get_monolayer]:
                                ml_be_dict[ads_entry.get_monolayer] = be
                # sort the binding energies and monolayers
                # in order to properly draw a line plot
                vals = sorted(ml_be_dict.items())
                monolayers, BEs = zip(*vals)
                plt.plot(monolayers, BEs, '-o',
                         c=self.color_dict[clean_entry], label=hkl)

            adsorbates = tuple(ads_entry.ads_entries_dict.keys())
            plt.xlabel(" %s" * len(adsorbates) % adsorbates + " Coverage (ML)")
            plt.ylabel("Adsorption Energy (eV)") if plot_eads \
                else plt.ylabel("Binding Energy (eV)")
            plt.legend()
            plt.tight_layout()

            return plt

        def chempot_plot_addons(self, plt, xrange, ref_el, axes, pad=2.4,
                                rect=[-0.047, 0, 0.84, 1], ylim=[]):

            """
            Helper function to a chempot plot look nicer.

            Args:
                plt (Plot) Plot to add things to.
                xrange (list): xlim parameter
                ref_el (str): Element of the referenced chempot.
                axes(axes) Axes object from matplotlib
                pad (float) For tight layout
                rect (list): For tight layout
                ylim (ylim parameter):

            return (Plot): Modified plot with addons.
            return (Plot): Modified plot with addons.
            """

            # Make the figure look nice
            plt.legend(bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0.)
            axes.set_xlabel(r"Chemical potential $\Delta\mu_{%s}$ (eV)" % (ref_el))

            ylim = ylim if ylim else axes.get_ylim()
            plt.xticks(rotation=60)
            plt.ylim(ylim)
            xlim = axes.get_xlim()
            plt.xlim(xlim)
            plt.tight_layout(pad=pad, rect=rect)
            plt.plot([xrange[0], xrange[0]], ylim, '--k')
            plt.plot([xrange[1], xrange[1]], ylim, '--k')
            xy = [np.mean([xrange[1]]), np.mean(ylim)]
            plt.annotate("%s-rich" % (ref_el), xy=xy,
                         xytext=xy, rotation=90, fontsize=17)
            xy = [np.mean([xlim[0]]), np.mean(ylim)]
            plt.annotate("%s-poor" % (ref_el), xy=xy,
                         xytext=xy, rotation=90, fontsize=17)

            return plt

        def BE_vs_clean_SE(self, delu_dict, delu_default=0, plot_eads=False,
                           annotate_monolayer=True, JPERM2=False):
            """
            For each facet, plot the clean surface energy against the most
                stable binding energy.
            Args:
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                plot_eads (bool): Option to plot the adsorption energy (binding
                    energy multiplied by number of adsorbates) instead.
                annotate_monolayer (bool): Whether or not to label each data point
                    with its monolayer (adsorbate density per unit primiitve area)
                JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
                    eV/A^2 (False)

            Returns:
                (Plot): Plot of clean surface energy vs binding energy for
                    all facets.
            """

            plt = pretty_plot(width=8, height=7)
            for hkl in self.all_slab_entries.keys():
                for clean_entry in self.all_slab_entries[hkl].keys():
                    all_delu_dict = self.set_all_variables(delu_dict, delu_default)
                    if self.all_slab_entries[hkl][clean_entry]:
                        clean_se = self.as_coeffs_dict[clean_entry]
                        se = sub_chempots(clean_se, all_delu_dict)
                        for ads_entry in self.all_slab_entries[hkl][clean_entry]:
                            ml = ads_entry.get_monolayer
                            be = ads_entry.gibbs_binding_energy(eads=plot_eads)

                            # Now plot the surface energy vs binding energy
                            plt.scatter(se, be)
                            if annotate_monolayer:
                                plt.annotate("%.2f" % (ml), xy=[se, be],
                                             xytext=[se, be])

            plt.xlabel(r"Surface energy ($J/m^2$)") if JPERM2 \
                else plt.xlabel(r"Surface energy ($eV/\AA^2$)")
            plt.ylabel("Adsorption Energy (eV)") if plot_eads \
                else plt.ylabel("Binding Energy (eV)")
            plt.tight_layout()
            plt.xticks(rotation=60)

            return plt

        def surface_chempot_range_map(self, elements, miller_index, ranges,
                                      incr=50, no_doped=False, no_clean=False,
                                      delu_dict=None, plt=None, annotate=True,
                                      show_unphyiscal_only=False, fontsize=10):
            """
            Adapted from the get_chempot_range_map() method in the PhaseDiagram
                class. Plot the chemical potential range map based on surface
                energy stability. Currently works only for 2-component PDs. At
                the moment uses a brute force method by enumerating through the
                range of the first element chempot with a specified increment
                and determines the chempot rangeo fht e second element for each
                SlabEntry. Future implementation will determine the chempot range
                map first by solving systems of equations up to 3 instead of 2.
            Args:
                elements (list): Sequence of elements to be considered as independent
                    variables. E.g., if you want to show the stability ranges of
                    all Li-Co-O phases wrt to duLi and duO, you will supply
                    [Element("Li"), Element("O")]
                miller_index ([h, k, l]): Miller index of the surface we are interested in
                ranges ([[range1], [range2]]): List of chempot ranges (max and min values)
                    for the first and second element.
                incr (int): Number of points to sample along the range of the first chempot
                no_doped (bool): Whether or not to include doped systems.
                no_clean (bool): Whether or not to include clean systems.
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                annotate (bool): Whether to annotate each "phase" with the label of
                    the entry. If no label, uses the reduced formula
                show_unphyiscal_only (bool): Whether to only show the shaded region where
                    surface energy is negative. Useful for drawing other chempot range maps.
            """

            # Set up
            delu_dict = delu_dict if delu_dict else {}
            plt = pretty_plot(12, 8) if not plt else plt
            el1, el2 = str(elements[0]), str(elements[1])
            delu1 = Symbol("delu_%s" % (str(elements[0])))
            delu2 = Symbol("delu_%s" % (str(elements[1])))
            range1 = ranges[0]
            range2 = ranges[1]

            # Find a range map for each entry (surface). This part is very slow, will
            # need to implement a more sophisticated method of getting the range map
            vertices_dict = {}
            for dmu1 in np.linspace(range1[0], range1[1], incr):
                # Get chemical potential range of dmu2 for each increment of dmu1
                new_delu_dict = delu_dict.copy()
                new_delu_dict[delu1] = dmu1
                range_dict, se_dict = self.stable_u_range_dict(range2, delu2, dmu_at_0=True,
                                                               miller_index=miller_index,
                                                               no_doped=no_doped,
                                                               no_clean=no_clean,
                                                               delu_dict=new_delu_dict,
                                                               return_se_dict=True)

                # Save the chempot range for dmu1 and dmu2
                for entry in range_dict.keys():
                    if not range_dict[entry]:
                        continue
                    if entry not in vertices_dict.keys():
                        vertices_dict[entry] = []

                    selist = se_dict[entry]
                    vertices_dict[entry].append({delu1: dmu1, delu2: [range_dict[entry], selist]})

            # Plot the edges of the phases
            for entry in vertices_dict.keys():

                xvals, yvals = [], []

                # Plot each edge of a phase within the borders
                for ii, pt1 in enumerate(vertices_dict[entry]):

                    # Determine if the surface energy at this lower range
                    # of dmu2 is negative. If so, shade this region.
                    if len(pt1[delu2][1]) == 3:
                        if pt1[delu2][1][0] < 0:
                            neg_dmu_range = [pt1[delu2][0][0], pt1[delu2][0][1]]
                        else:
                            neg_dmu_range = [pt1[delu2][0][1], pt1[delu2][0][2]]
                        # Shade the threshold and region at which se<=0
                        plt.plot([pt1[delu1], pt1[delu1]], neg_dmu_range, 'k--')
                    elif pt1[delu2][1][0] < 0 and pt1[delu2][1][1] < 0:
                        # Any chempot at at this point will result
                        # in se<0, shade the entire y range
                        if not show_unphyiscal_only:
                            plt.plot([pt1[delu1], pt1[delu1]], range2, 'k--')

                    if ii == len(vertices_dict[entry]) - 1:
                        break
                    pt2 = vertices_dict[entry][ii + 1]
                    if not show_unphyiscal_only:
                        plt.plot([pt1[delu1], pt2[delu1]], [pt1[delu2][0][0], pt2[delu2][0][0]], 'k')

                    # Need these values to get a good position for labelling phases
                    xvals.extend([pt1[delu1], pt2[delu1]])
                    yvals.extend([pt1[delu2][0][0], pt2[delu2][0][0]])

                # Plot the edge along the max x value
                pt = vertices_dict[entry][-1]
                delu1, delu2 = pt.keys()
                xvals.extend([pt[delu1], pt[delu1]])
                yvals.extend(pt[delu2][0])
                if not show_unphyiscal_only:
                    plt.plot([pt[delu1], pt[delu1]], [pt[delu2][0][0], pt[delu2][0][-1]], 'k')

                if annotate:
                    # Label the phases
                    x = np.mean([max(xvals), min(xvals)])
                    y = np.mean([max(yvals), min(yvals)])
                    label = entry.label if entry.label else entry.composition.reduced_formula
                    plt.annotate(label, xy=[x, y], xytext=[x, y], fontsize=fontsize)

            # Label plot
            plt.xlim(range1)
            plt.ylim(range2)
            plt.xlabel(r"$\Delta\mu_{%s} (eV)$" % (el1), fontsize=25)
            plt.ylabel(r"$\Delta\mu_{%s} (eV)$" % (el2), fontsize=25)
            plt.xticks(rotation=60)

            return plt

        def set_all_variables(self, delu_dict, delu_default):
            """
            Sets all chemical potential values and returns a dictionary where
                the key is a sympy Symbol and the value is a float (chempot).

            Args:
                entry (SlabEntry): Computed structure entry of the slab
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials

            Returns:
                Dictionary of set chemical potential values
            """

            # Set up the variables
            all_delu_dict = {}
            for du in self.list_of_chempots:
                if delu_dict and du in delu_dict.keys():
                    all_delu_dict[du] = delu_dict[du]
                elif du == 1:
                    all_delu_dict[du] = du
                else:
                    all_delu_dict[du] = delu_default

            return all_delu_dict

            # def surface_phase_diagram(self, y_param, x_param, miller_index):
            #     return
            #
            # def wulff_shape_extrapolated_model(self):
            #     return
            #
            # def surface_pourbaix_diagram(self):
            #
            #     return
            #
            # def surface_p_vs_t_phase_diagram(self):
            #
            #     return
            #
            # def broken_bond_vs_gamma(self):
            #
            #     return

    def entry_dict_from_list(all_slab_entries):
        """
        Converts a list of SlabEntry to an appropriate dictionary. It is
        assumed that if there is no adsorbate, then it is a clean SlabEntry
        and that adsorbed SlabEntry has the clean_entry parameter set.

        Args:
            all_slab_entries (list): List of SlabEntry objects

        Returns:
            (dict): Dictionary of SlabEntry with the Miller index as the main
                key to a dictionary with a clean SlabEntry as the key to a
                list of adsorbed SlabEntry.
        """

        entry_dict = {}

        for entry in all_slab_entries:
            hkl = tuple(entry.miller_index)
            if hkl not in entry_dict.keys():
                entry_dict[hkl] = {}
            if entry.clean_entry:
                clean = entry.clean_entry
            else:
                clean = entry
            if clean not in entry_dict[hkl].keys():
                entry_dict[hkl][clean] = []
            if entry.adsorbates:
                entry_dict[hkl][clean].append(entry)

        return entry_dict

    class WorkFunctionAnalyzer:
        """
        A class used for calculating the work function
            from a slab model and visualizing the behavior
            of the local potential along the slab.

        .. attribute:: efermi

            The Fermi energy

        .. attribute:: locpot_along_c

            Local potential in eV along points along the  axis

        .. attribute:: vacuum_locpot

            The maximum local potential along the c direction for
                the slab model, ie the potential at the vacuum

        .. attribute:: work_function

            The minimum energy needed to move an electron from the
                surface to infinity. Defined as the difference between
                the potential at the vacuum and the Fermi energy.

        .. attribute:: slab

            The slab structure model

        .. attribute:: along_c

            Points along the c direction with same
                increments as the locpot in the c axis

        .. attribute:: ave_locpot

            Mean of the minimum and maximmum (vacuum) locpot along c

        .. attribute:: sorted_sites

            List of sites from the slab sorted along the c direction

        .. attribute:: ave_bulk_p

            The average locpot of the slab region along the c direction
        """

        def __init__(self, structure, locpot_along_c, efermi, shift=0, blength=3.5):
            """
            Initializes the WorkFunctionAnalyzer class.

            Args:
                structure (Structure): Structure object modelling the surface
                locpot_along_c (list): Local potential along the c direction
                outcar (MSONable): Outcar vasp output object
                shift (float): Parameter to translate the slab (and
                    therefore the vacuum) of the slab structure, thereby
                    translating the plot along the x axis.
                blength (float (Ang)): The longest bond length in the material.
                    Used to handle pbc for noncontiguous slab layers
            """

            # ensure shift between 0 and 1
            if shift < 0:
                shift += -1 * int(shift) + 1
            elif shift >= 1:
                shift -= int(shift)
            self.shift = shift

            # properties that can be shifted
            slab = structure.copy()
            slab.translate_sites([i for i, site in enumerate(slab)], [0, 0, self.shift])
            self.slab = slab
            self.sorted_sites = sorted(self.slab, key=lambda site: site.frac_coords[2])

            # Get the plot points between 0 and c
            # increments of the number of locpot points
            self.along_c = np.linspace(0, 1, num=len(locpot_along_c))

            # Get the plot points between 0 and c
            # increments of the number of locpot points
            locpot_along_c_mid, locpot_end, locpot_start = [], [], []
            for i, s in enumerate(self.along_c):
                j = s + self.shift
                if j > 1:
                    locpot_start.append(locpot_along_c[i])
                elif j < 0:
                    locpot_end.append(locpot_along_c[i])
                else:
                    locpot_along_c_mid.append(locpot_along_c[i])
            self.locpot_along_c = locpot_start + locpot_along_c_mid + locpot_end

            # identify slab region
            self.slab_regions = get_slab_regions(self.slab, blength=blength)
            # get the average of the signal in the bulk-like region of the
            # slab, i.e. the average of the oscillating region. This gives
            # a rough appr. of the potential in the interior of the slab
            bulk_p = []
            for r in self.slab_regions:
                bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if r[1] >= self.along_c[i] > r[0]])
            if len(self.slab_regions) > 1:
                bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if self.slab_regions[1][1] <= self.along_c[i]])
                bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if self.slab_regions[0][0] >= self.along_c[i]])
            self.ave_bulk_p = np.mean(bulk_p)

            # shift independent quantities
            self.efermi = efermi
            self.vacuum_locpot = max(self.locpot_along_c)
            # get the work function
            self.work_function = self.vacuum_locpot - self.efermi
            # for setting ylim and annotating
            self.ave_locpot = (self.vacuum_locpot - min(self.locpot_along_c)) / 2

        def get_locpot_along_slab_plot(self, label_energies=True,
                                       plt=None, label_fontsize=10):
            """
            Returns a plot of the local potential (eV) vs the
                position along the c axis of the slab model (Ang)

            Args:
                label_energies (bool): Whether to label relevant energy
                    quantities such as the work function, Fermi energy,
                    vacuum locpot, bulk-like locpot
                plt (plt): Matplotlib pylab object
                label_fontsize (float): Fontsize of labels

            Returns plt of the locpot vs c axis
            """

            plt = pretty_plot(width=6, height=4) if not plt else plt

            # plot the raw locpot signal along c
            plt.plot(self.along_c, self.locpot_along_c, 'b--')

            # Get the local averaged signal of the locpot along c
            xg, yg = [], []
            for i, p in enumerate(self.locpot_along_c):
                # average signal is just the bulk-like potential when in the slab region
                in_slab = False
                for r in self.slab_regions:
                    if r[0] <= self.along_c[i] <= r[1]:
                        in_slab = True
                if len(self.slab_regions) > 1:
                    if self.along_c[i] >= self.slab_regions[1][1]:
                        in_slab = True
                    if self.along_c[i] <= self.slab_regions[0][0]:
                        in_slab = True

                if in_slab:
                    yg.append(self.ave_bulk_p)
                    xg.append(self.along_c[i])
                elif p < self.ave_bulk_p:
                    yg.append(self.ave_bulk_p)
                    xg.append(self.along_c[i])
                else:
                    yg.append(p)
                    xg.append(self.along_c[i])
            xg, yg = zip(*sorted(zip(xg, yg)))
            plt.plot(xg, yg, 'r', linewidth=2.5, zorder=-1)

            # make it look nice
            if label_energies:
                plt = self.get_labels(plt, label_fontsize=label_fontsize)
            plt.xlim([0, 1])
            plt.ylim([min(self.locpot_along_c),
                      self.vacuum_locpot + self.ave_locpot * 0.2])
            plt.xlabel(r"Fractional coordinates ($\hat{c}$)", fontsize=25)
            plt.xticks(fontsize=15, rotation=45)
            plt.ylabel(r"Potential (eV)", fontsize=25)
            plt.yticks(fontsize=15)

            return plt

        def get_labels(self, plt, label_fontsize=10):
            """
            Handles the optional labelling of the plot with relevant quantities
            Args:
                plt (plt): Plot of the locpot vs c axis
                label_fontsize (float): Fontsize of labels
            Returns Labelled plt
            """

            # center of vacuum and bulk region
            if len(self.slab_regions) > 1:
                label_in_vac = (self.slab_regions[0][1] + self.slab_regions[1][0]) / 2
                if abs(self.slab_regions[0][0] - self.slab_regions[0][1]) > \
                        abs(self.slab_regions[1][0] - self.slab_regions[1][1]):
                    label_in_bulk = self.slab_regions[0][1] / 2
                else:
                    label_in_bulk = (self.slab_regions[1][1] + self.slab_regions[1][0]) / 2
            else:
                label_in_bulk = (self.slab_regions[0][0] + self.slab_regions[0][1]) / 2
                if self.slab_regions[0][0] > 1 - self.slab_regions[0][1]:
                    label_in_vac = self.slab_regions[0][0] / 2
                else:
                    label_in_vac = (1 + self.slab_regions[0][1]) / 2

            plt.plot([0, 1], [self.vacuum_locpot] * 2, 'b--', zorder=-5, linewidth=1)
            xy = [label_in_bulk, self.vacuum_locpot + self.ave_locpot * 0.05]
            plt.annotate(r"$V_{vac}=%.2f$" % (self.vacuum_locpot), xy=xy,
                         xytext=xy, color='b', fontsize=label_fontsize)

            # label the fermi energy
            plt.plot([0, 1], [self.efermi] * 2, 'g--',
                     zorder=-5, linewidth=3)
            xy = [label_in_bulk, self.efermi + self.ave_locpot * 0.05]
            plt.annotate(r"$E_F=%.2f$" % (self.efermi), xytext=xy,
                         xy=xy, fontsize=label_fontsize, color='g')

            # label the bulk-like locpot
            plt.plot([0, 1], [self.ave_bulk_p] * 2, 'r--', linewidth=1., zorder=-1)
            xy = [label_in_vac, self.ave_bulk_p + self.ave_locpot * 0.05]
            plt.annotate(r"$V^{interior}_{slab}=%.2f$" % (self.ave_bulk_p),
                         xy=xy, xytext=xy, color='r', fontsize=label_fontsize)

            # label the work function as a barrier
            plt.plot([label_in_vac] * 2, [self.efermi, self.vacuum_locpot],
                     'k--', zorder=-5, linewidth=2)
            xy = [label_in_vac, self.efermi + self.ave_locpot * 0.05]
            plt.annotate(r"$\Phi=%.2f$" % (self.work_function),
                         xy=xy, xytext=xy, fontsize=label_fontsize)

            return plt

        def is_converged(self, min_points_frac=0.015, tol=0.0025):
            """
            A well converged work function should have a flat electrostatic
                potential within some distance (min_point) about where the peak
                electrostatic potential is found along the c direction of the
                slab. This is dependent on the size of the slab.
            Args:
                min_point (fractional coordinates): The number of data points
                    +/- the point of where the electrostatic potential is at
                    its peak along the c direction.
                tol (float): If the electrostatic potential stays the same
                    within this tolerance, within the min_points, it is converged.

            Returns a bool (whether or not the work function is converged)
            """

            conv_within = tol * (max(self.locpot_along_c) - min(self.locpot_along_c))
            min_points = int(min_points_frac * len(self.locpot_along_c))
            peak_i = self.locpot_along_c.index(self.vacuum_locpot)
            all_flat = []
            for i in range(len(self.along_c)):
                if peak_i - min_points < i < peak_i + min_points:
                    if abs(self.vacuum_locpot - self.locpot_along_c[i]) > conv_within:
                        all_flat.append(False)
                    else:
                        all_flat.append(True)
            return all(all_flat)

        @staticmethod
        def from_files(poscar_filename, locpot_filename, outcar_filename, shift=0, blength=3.5):
            """

            :param poscar_filename: POSCAR file
            :param locpot_filename: LOCPOT file
            :param outcar_filename: OUTCAR file
            :param shift: shift
            :param blength: The longest bond length in the material.
                Used to handle pbc for noncontiguous slab layers
            :return: WorkFunctionAnalyzer
            """
            p = Poscar.from_file(poscar_filename)
            l = Locpot.from_file(locpot_filename)
            o = Outcar(outcar_filename)
            return WorkFunctionAnalyzer(p.structure, l.get_average_along_axis(2),
                                        o.efermi, shift=shift, blength=blength)

    class NanoscaleStability:
        """
        A class for analyzing the stability of nanoparticles of different
            polymorphs with respect to size. The Wulff shape will be the
            model for the nanoparticle. Stability will be determined by
            an energetic competition between the weighted surface energy
            (surface energy of the Wulff shape) and the bulk energy. A
            future release will include a 2D phase diagram (e.g. wrt size
            vs chempot for adsorbed or nonstoichiometric surfaces). Based
            on the following work:

            Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale
                stabilization of sodium oxides: Implications for Na-O2
                batteries. Nano Letters, 14(2), 1016–1020.
                https://doi.org/10.1021/nl404557w

        .. attribute:: se_analyzers

            List of SurfaceEnergyPlotter objects. Each item corresponds to a
                different polymorph.

        .. attribute:: symprec

            See WulffShape.
        """

        def __init__(self, se_analyzers, symprec=1e-5):

            """
            Analyzes the nanoscale stability of different polymorphs.
            """

            self.se_analyzers = se_analyzers
            self.symprec = symprec

        def solve_equilibrium_point(self, analyzer1, analyzer2,
                                    delu_dict={}, delu_default=0, units="nanometers"):
            """
            Gives the radial size of two particles where equilibrium is reached
                between both particles. NOTE: the solution here is not the same
                as the solution visualized in the plot because solving for r
                requires that both the total surface area and volume of the
                particles are functions of r.

            Args:
                analyzer1 (SurfaceEnergyPlotter): Analyzer associated with the
                    first polymorph
                analyzer2 (SurfaceEnergyPlotter): Analyzer associated with the
                    second polymorph
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                units (str): Can be nanometers or Angstrom

            Returns:
                Particle radius in nm
            """

            # Set up
            wulff1 = analyzer1.wulff_from_chempot(delu_dict=delu_dict,
                                                  delu_default=delu_default,
                                                  symprec=self.symprec)
            wulff2 = analyzer2.wulff_from_chempot(delu_dict=delu_dict,
                                                  delu_default=delu_default,
                                                  symprec=self.symprec)

            # Now calculate r
            delta_gamma = wulff1.weighted_surface_energy - wulff2.weighted_surface_energy
            delta_E = self.bulk_gform(analyzer1.ucell_entry) - self.bulk_gform(analyzer2.ucell_entry)
            r = ((-3 * delta_gamma) / (delta_E))

            return r / 10 if units == "nanometers" else r

        def wulff_gform_and_r(self, wulffshape, bulk_entry, r, from_sphere_area=False,
                              r_units="nanometers", e_units="keV", normalize=False,
                              scale_per_atom=False):
            """
            Calculates the formation energy of the particle with arbitrary radius r.

            Args:
                wulffshape (WulffShape): Initial, unscaled WulffShape
                bulk_entry (ComputedStructureEntry): Entry of the corresponding bulk.
                r (float (Ang)): Arbitrary effective radius of the WulffShape
                from_sphere_area (bool): There are two ways to calculate the bulk
                    formation energy. Either by treating the volume and thus surface
                    area of the particle as a perfect sphere, or as a Wulff shape.
                r_units (str): Can be nanometers or Angstrom
                e_units (str): Can be keV or eV
                normalize (bool): Whether or not to normalize energy by volume
                scale_per_atom (True): Whether or not to normalize by number of
                    atoms in the particle

            Returns:
                particle formation energy (float in keV), effective radius
            """

            # Set up
            miller_se_dict = wulffshape.miller_energy_dict
            new_wulff = self.scaled_wulff(wulffshape, r)
            new_wulff_area = new_wulff.miller_area_dict

            # calculate surface energy of the particle
            if not from_sphere_area:
                # By approximating the particle as a Wulff shape
                w_vol = new_wulff.volume
                tot_wulff_se = 0
                for hkl in new_wulff_area.keys():
                    tot_wulff_se += miller_se_dict[hkl] * new_wulff_area[hkl]
                Ebulk = self.bulk_gform(bulk_entry) * w_vol
                new_r = new_wulff.effective_radius

            else:
                # By approximating the particle as a perfect sphere
                w_vol = (4 / 3) * np.pi * r ** 3
                sphere_sa = 4 * np.pi * r ** 2
                tot_wulff_se = wulffshape.weighted_surface_energy * sphere_sa
                Ebulk = self.bulk_gform(bulk_entry) * w_vol
                new_r = r

            new_r = new_r / 10 if r_units == "nanometers" else new_r
            e = (Ebulk + tot_wulff_se)
            e = e / 1000 if e_units == "keV" else e
            e = e / ((4 / 3) * np.pi * new_r ** 3) if normalize else e
            bulk_struct = bulk_entry.structure
            density = len(bulk_struct) / bulk_struct.lattice.volume
            e = e / (density * w_vol) if scale_per_atom else e

            return e, new_r

        def bulk_gform(self, bulk_entry):
            """
            Returns the formation energy of the bulk
            Args:
                bulk_entry (ComputedStructureEntry): Entry of the corresponding bulk.
            """
            return bulk_entry.energy / bulk_entry.structure.lattice.volume

        def scaled_wulff(self, wulffshape, r):
            """
            Scales the Wulff shape with an effective radius r. Note that the resulting
                Wulff does not neccesarily have the same effective radius as the one
                provided. The Wulff shape is scaled by its surface energies where first
                the surface energies are scale by the minimum surface energy and then
                multiplied by the given effective radius.

            Args:
                wulffshape (WulffShape): Initial, unscaled WulffShape
                r (float): Arbitrary effective radius of the WulffShape

            Returns:
                WulffShape (scaled by r)
            """

            # get the scaling ratio for the energies
            r_ratio = r / wulffshape.effective_radius
            miller_list = wulffshape.miller_energy_dict.keys()
            # Normalize the magnitude of the facet normal vectors
            # of the Wulff shape by the minimum surface energy.
            se_list = np.array(list(wulffshape.miller_energy_dict.values()))
            # Scale the magnitudes by r_ratio
            scaled_se = se_list * r_ratio

            return WulffShape(wulffshape.lattice, miller_list,
                              scaled_se, symprec=self.symprec)

        def plot_one_stability_map(self, analyzer, max_r, delu_dict=None, label="",
                                   increments=50, delu_default=0, plt=None,
                                   from_sphere_area=False, e_units="keV",
                                   r_units="nanometers", normalize=False,
                                   scale_per_atom=False):
            """
            Returns the plot of the formation energy of a particle against its
                effect radius

            Args:
                analyzer (SurfaceEnergyPlotter): Analyzer associated with the
                    first polymorph
                max_r (float): The maximum radius of the particle to plot up to.
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                label (str): Label of the plot for legend
                increments (int): Number of plot points
                delu_default (float): Default value for all unset chemical potentials
                plt (pylab): Plot
                from_sphere_area (bool): There are two ways to calculate the bulk
                    formation energy. Either by treating the volume and thus surface
                    area of the particle as a perfect sphere, or as a Wulff shape.
                r_units (str): Can be nanometers or Angstrom
                e_units (str): Can be keV or eV
                normalize (str): Whether or not to normalize energy by volume
            """

            plt = plt if plt else pretty_plot(width=8, height=7)

            wulffshape = analyzer.wulff_from_chempot(delu_dict=delu_dict,
                                                     delu_default=delu_default,
                                                     symprec=self.symprec)

            gform_list, r_list = [], []
            for r in np.linspace(1e-6, max_r, increments):
                gform, r = self.wulff_gform_and_r(wulffshape, analyzer.ucell_entry,
                                                  r, from_sphere_area=from_sphere_area,
                                                  r_units=r_units, e_units=e_units,
                                                  normalize=normalize,
                                                  scale_per_atom=scale_per_atom)
                gform_list.append(gform)
                r_list.append(r)

            ru = "nm" if r_units == "nanometers" else r"\AA"
            plt.xlabel(r"Particle radius ($%s$)" % (ru))
            eu = "$%s/%s^3$" % (e_units, ru)
            plt.ylabel(r"$G_{form}$ (%s)" % (eu))

            plt.plot(r_list, gform_list, label=label)

            return plt

        def plot_all_stability_map(self, max_r, increments=50, delu_dict=None,
                                   delu_default=0, plt=None, labels=None,
                                   from_sphere_area=False, e_units="keV",
                                   r_units="nanometers", normalize=False,
                                   scale_per_atom=False):
            """
            Returns the plot of the formation energy of a particles
                of different polymorphs against its effect radius

            Args:
                max_r (float): The maximum radius of the particle to plot up to.
                increments (int): Number of plot points
                delu_dict (Dict): Dictionary of the chemical potentials to be set as
                    constant. Note the key should be a sympy Symbol object of the
                    format: Symbol("delu_el") where el is the name of the element.
                delu_default (float): Default value for all unset chemical potentials
                plt (pylab): Plot
                labels (list): List of labels for each plot, corresponds to the
                    list of se_analyzers
                from_sphere_area (bool): There are two ways to calculate the bulk
                    formation energy. Either by treating the volume and thus surface
                    area of the particle as a perfect sphere, or as a Wulff shape.
            """

            plt = plt if plt else pretty_plot(width=8, height=7)

            for i, analyzer in enumerate(self.se_analyzers):
                label = labels[i] if labels else ""
                plt = self.plot_one_stability_map(analyzer, max_r, delu_dict,
                                                  label=label, plt=plt,
                                                  increments=increments,
                                                  delu_default=delu_default,
                                                  from_sphere_area=from_sphere_area,
                                                  e_units=e_units, r_units=r_units,
                                                  normalize=normalize,
                                                  scale_per_atom=scale_per_atom)

            return plt

            # class GetChempotRange:
            #     def __init__(self, entry):
            #         self.entry = entry
            #
            #
            # class SlabEntryGenerator:
            #     def __init__(self, entry):
            #         self.entry = entry

    def sub_chempots(gamma_dict, chempots):
        """
        Uses dot product of numpy array to sub chemical potentials
            into the surface grand potential. This is much faster
            than using the subs function in sympy.
        Args:
            gamma_dict (dict): Surface grand potential equation
                as a coefficient dictionary
            chempots (dict): Dictionary assigning each chemical
                potential (key) in gamma a value
        Returns:
            Surface energy as a float
        """

        coeffs = [gamma_dict[k] for k in gamma_dict.keys()]
        chempot_vals = []
        for k in gamma_dict.keys():
            if k not in chempots.keys():
                chempot_vals.append(k)
            elif k == 1:
                chempot_vals.append(1)
            else:
                chempot_vals.append(chempots[k])

        return np.dot(coeffs, chempot_vals)