pymatgen.command_line.critic2_caller — pymatgen 2020.7.3 documentation

# Source code for pymatgen.command_line.critic2_caller

    """
    This module implements an interface to the critic2 Bader analysis code.

    For most Bader analysis purposes, users are referred to
    pymatgen.command_line.bader_caller instead, this module is for advanced
    usage requiring identification of critical points in the charge density.

    This module depends on a compiled critic2 executable available in the path.
    Please follow the instructions at https://github.com/aoterodelaroza/critic2
    to compile.

    New users are *strongly* encouraged to read the critic2 manual first.

    In brief,
    * critic2 searches for critical points in charge density
    * a critical point can be one of four types: nucleus, bond, ring
    or cage
    * it does this by seeding locations for likely critical points
    and then searching in these regions
    * there are two lists of critical points in the output, a list
    of non-equivalent points (with in-depth information about the
    field at those points), and a full list of points generated
    by the appropriate symmetry operations
    * connectivity between these points is also provided when
    appropriate (e.g. the two nucleus critical points linked to
     a bond critical point)
    * critic2 can do many other things besides

    If you use this module, please cite the following:

    A. Otero-de-la-Roza, E. R. Johnson and V. Luaña,
    Comput. Phys. Commun. 185, 1007-1018 (2014)
    (https://doi.org/10.1016/j.cpc.2013.10.026)

    A. Otero-de-la-Roza, M. A. Blanco, A. Martín Pendás and
    V. Luaña, Comput. Phys. Commun. 180, 157–166 (2009)
    (https://doi.org/10.1016/j.cpc.2008.07.018)
    """

    import os
    import subprocess
    import warnings
    import numpy as np
    import glob

    from scipy.spatial import KDTree
    from pymatgen.io.vasp.outputs import Chgcar, VolumetricData
    from pymatgen.io.vasp.inputs import Potcar
    from pymatgen.analysis.graphs import StructureGraph
    from pymatgen.core.periodic_table import DummySpecie
    from monty.os.path import which
    from monty.dev import requires
    from monty.json import MSONable
    from monty.serialization import loadfn
    from monty.tempfile import ScratchDir
    from enum import Enum

    import logging

    logging.basicConfig(level=logging.INFO)
    logger = logging.getLogger(__name__)

    __author__ = "Matthew Horton"
    __maintainer__ = "Matthew Horton"
    __email__ = "mkhorton@lbl.gov"
    __status__ = "Production"
    __date__ = "July 2017"

    class Critic2Caller:
        """
        Class to call critic2 and store standard output for further processing.
        """

        @requires(
            which("critic2"),
            "Critic2Caller requires the executable critic to be in the path. "
            "Please follow the instructions at https://github.com/aoterodelaroza/critic2.",
        )
        def __init__(
            self,
            structure,
            chgcar=None,
            chgcar_ref=None,
            user_input_settings=None,
            write_cml=False,
            write_json=True,
            zpsp=None,
        ):
            """
            Run Critic2 in automatic mode on a supplied structure, charge
            density (chgcar) and reference charge density (chgcar_ref).

            The reason for a separate reference field is that in
            VASP, the CHGCAR charge density only contains valence
            electrons and may be missing substantial charge at
            nuclei leading to misleading results. Thus, a reference
            field is commonly constructed from the sum of AECCAR0
            and AECCAR2 which is the total charge density, but then
            the valence charge density is used for the final analysis.

            If chgcar_ref is not supplied, chgcar will be used as the
            reference field. If chgcar is not supplied, the promolecular
            charge density will be used as the reference field -- this can
            often still give useful results if only topological information
            is wanted.

            User settings is a dictionary that can contain:
            * GRADEPS, float (field units), gradient norm threshold
            * CPEPS, float (Bohr units in crystals), minimum distance between
              critical points for them to be equivalent
            * NUCEPS, same as CPEPS but specifically for nucleus critical
              points (critic2 default is depedent on grid dimensions)
            * NUCEPSH, same as NUCEPS but specifically for hydrogen nuclei
              since associated charge density can be significantly displaced
              from hydrogen nucleus
            * EPSDEGEN, float (field units), discard critical point if any
              element of the diagonal of the Hessian is below this value,
              useful for discarding points in vacuum regions
            * DISCARD, float (field units), discard critical points with field
              value below this value, useful for discarding points in vacuum
              regions
            * SEED, list of strings, strategies for seeding points, default
              is ['WS 1', 'PAIR 10'] which seeds critical points by
              sub-dividing the Wigner-Seitz cell and between every atom pair
              closer than 10 Bohr, see critic2 manual for more options

            :param structure: Structure to analyze
            :param chgcar: Charge density to use for analysis. If None, will
                use promolecular density. Should be a Chgcar object or path (string).
            :param chgcar_ref: Reference charge density. If None, will use
                chgcar as reference. Should be a Chgcar object or path (string).
            :param user_input_settings (dict): as explained above
            :param write_cml (bool): Useful for debug, if True will write all
                critical points to a file 'table.cml' in the working directory
                useful for visualization
            :param write_json (bool): Whether to write out critical points
            and YT json. YT integration will be performed with this setting.
            :param zpsp (dict): Dict of element/symbol name to number of electrons
            (ZVAL in VASP pseudopotential), with which to properly augment core regions
            and calculate charge transfer. Optional.
            """

            settings = {"CPEPS": 0.1, "SEED": ["WS", "PAIR DIST 10"]}
            if user_input_settings:
                settings.update(user_input_settings)

            # Load crystal structure
            input_script = ["crystal POSCAR"]

            # Load data to use as reference field
            if chgcar_ref:
                input_script += ["load ref.CHGCAR id chg_ref", "reference chg_ref"]

            # Load data to use for analysis
            if chgcar:
                input_script += ["load int.CHGCAR id chg_int", "integrable chg_int"]
                if zpsp:
                    zpsp_str = " zpsp " + " ".join(
                        ["{} {}".format(symbol, int(zval)) for symbol, zval in zpsp.items()]
                    )
                    input_script[-2] += zpsp_str

            # Command to run automatic analysis
            auto = "auto "
            for k, v in settings.items():
                if isinstance(v, list):
                    for item in v:
                        auto += "{} {} ".format(k, item)
                else:
                    auto += "{} {} ".format(k, v)
            input_script += [auto]

            if write_cml:
                input_script += ["cpreport ../table.cml cell border graph"]

            if write_json:
                input_script += ["cpreport cpreport.json"]

            if write_json and chgcar:
                # requires gridded data to work
                input_script += ["yt"]
                input_script += ["yt JSON yt.json"]

            input_script = "\n".join(input_script)

            with ScratchDir(".") as temp_dir:

                os.chdir(temp_dir)

                with open("input_script.cri", "w") as f:
                    f.write(input_script)

                structure.to(filename="POSCAR")

                if chgcar and isinstance(chgcar, VolumetricData):
                    chgcar.write_file("int.CHGCAR")
                elif chgcar:
                    os.symlink(chgcar, "int.CHGCAR")

                if chgcar_ref and isinstance(chgcar_ref, VolumetricData):
                    chgcar_ref.write_file("ref.CHGCAR")
                elif chgcar_ref:
                    os.symlink(chgcar_ref, "ref.CHGCAR")

                args = ["critic2", "input_script.cri"]
                rs = subprocess.Popen(
                    args, stdout=subprocess.PIPE, stdin=subprocess.PIPE, close_fds=True
                )

                stdout, stderr = rs.communicate()
                stdout = stdout.decode()

                if stderr:
                    stderr = stderr.decode()
                    warnings.warn(stderr)

                if rs.returncode != 0:
                    raise RuntimeError(
                        "critic2 exited with return code {}: {}".format(
                            rs.returncode, stdout
                        )
                    )

                self._stdout = stdout
                self._stderr = stderr

                if os.path.exists("cpreport.json"):
                    cpreport = loadfn("cpreport.json")
                else:
                    cpreport = None

                if os.path.exists("yt.json"):
                    yt = loadfn("yt.json")
                else:
                    yt = None

                self.output = Critic2Analysis(
                    structure,
                    stdout=stdout,
                    stderr=stderr,
                    cpreport=cpreport,
                    yt=yt,
                    zpsp=zpsp,
                )

        @classmethod
        def from_path(cls, path, suffix="", zpsp=None):
            """
            Convenience method to run critic2 analysis on a folder containing
            typical VASP output files.
            This method will:

            1. Look for files CHGCAR, AECAR0, AECAR2, POTCAR or their gzipped
            counterparts.

            2. If AECCAR* files are present, constructs a temporary reference
            file as AECCAR0 + AECCAR2.

            3. Runs critic2 analysis twice: once for charge, and a second time
            for the charge difference (magnetization density).

            :param path: path to folder to search in
            :param suffix: specific suffix to look for (e.g. '.relax1' for
                'CHGCAR.relax1.gz')
            :param zpsp: manually specify ZPSP if POTCAR not present
            :return:
            """

            def _get_filepath(filename, warning, path=path, suffix=suffix):
                paths = glob.glob(os.path.join(path, filename + suffix + "*"))
                if not paths:
                    warnings.warn(warning)
                    return None
                if len(paths) > 1:
                    # using reverse=True because, if multiple files are present,
                    # they likely have suffixes 'static', 'relax', 'relax2', etc.
                    # and this would give 'static' over 'relax2' over 'relax'
                    # however, better to use 'suffix' kwarg to avoid this!
                    paths.sort(reverse=True)
                    warnings.warn(
                        "Multiple files detected, using {}".format(os.path.basename(path))
                    )
                path = paths[0]
                return path

            chgcar_path = _get_filepath("CHGCAR", "Could not find CHGCAR!")
            chgcar = Chgcar.from_file(chgcar_path)
            chgcar_ref = None

            if not zpsp:

                potcar_path = _get_filepath(
                    "POTCAR",
                    "Could not find POTCAR, will not be able to calculate charge transfer.",
                )

                if potcar_path:
                    potcar = Potcar.from_file(potcar_path)
                    zpsp = {p.element: p.zval for p in potcar}

            if not zpsp:

                # try and get reference "all-electron-like" charge density if zpsp not present
                aeccar0_path = _get_filepath(
                    "AECCAR0",
                    "Could not find AECCAR0, interpret Bader results with caution.",
                )
                aeccar0 = Chgcar.from_file(aeccar0_path) if aeccar0_path else None

                aeccar2_path = _get_filepath(
                    "AECCAR2",
                    "Could not find AECCAR2, interpret Bader results with caution.",
                )
                aeccar2 = Chgcar.from_file(aeccar2_path) if aeccar2_path else None

                chgcar_ref = aeccar0.linear_add(aeccar2) if (aeccar0 and aeccar2) else None

            return cls(chgcar.structure, chgcar, chgcar_ref, zpsp=zpsp)

    class CriticalPointType(Enum):
        """
        Enum type for the different varieties of critical point.
        """

        nucleus = "nucleus"  # (3, -3)
        bond = "bond"  # (3, -1)
        ring = "ring"  # (3, 1)
        cage = "cage"  # (3, 3)
        nnattr = "nnattr"  # (3, -3), non-nuclear attractor

    class CriticalPoint(MSONable):
        """
        Access information about a critical point and the field values at that point.
        """

        def __init__(
            self,
            index,
            type,
            frac_coords,
            point_group,
            multiplicity,
            field,
            field_gradient,
            coords=None,
            field_hessian=None,
        ):
            """
            Class to characterise a critical point from a topological
            analysis of electron charge density.

            Note this class is usually associated with a Structure, so
            has information on multiplicity/point group symmetry.

            :param index: index of point
            :param type: type of point, given as a string
            :param coords: Cartesian co-ordinates in Angstroms
            :param frac_coords: fractional co-ordinates
            :param point_group: point group associated with critical point
            :param multiplicity: number of equivalent critical points
            :param field: value of field at point (f)
            :param field_gradient: gradient of field at point (grad f)
            :param field_hessian: hessian of field at point (del^2 f)
            """
            self.index = index
            self._type = type
            self.coords = coords
            self.frac_coords = frac_coords
            self.point_group = point_group
            self.multiplicity = multiplicity
            self.field = field
            self.field_gradient = field_gradient
            self.field_hessian = field_hessian

        @property
        def type(self):
            """
            Returns: Instance of CriticalPointType
            """
            return CriticalPointType(self._type)

        def __str__(self):
            return "Critical Point: {} ({})".format(self.type.name, self.frac_coords)

        @property
        def laplacian(self):
            """
            Returns: The Laplacian of the field at the critical point
            """
            return np.trace(self.field_hessian)

        @property
        def ellipticity(self):
            """
            Most meaningful for bond critical points,
            can be physically interpreted as e.g. degree
            of pi-bonding in organic molecules. Consult
            literature for more information.
            Returns: The ellpiticity of the field at the critical point
            """
            eig, _ = np.linalg.eig(self.field_hessian)
            eig.sort()
            return eig[0] / eig[1] - 1

    class Critic2Analysis(MSONable):
        """
        Class to process the standard output from critic2 into pymatgen-compatible objects.
        """

        def __init__(
            self, structure, stdout=None, stderr=None, cpreport=None, yt=None, zpsp=None
        ):
            """
            This class is used to store results from the Critic2Caller.

            To explore the bond graph, use the "structure_graph"
            method, which returns a user-friendly StructureGraph
            class with bonding information. By default, this returns
            a StructureGraph with edge weights as bond lengths, but
            can optionally return a graph with edge weights as any
            property supported by the `CriticalPoint` class, such as
            bond ellipticity.

            This class also provides an interface to explore just the
            non-symmetrically-equivalent critical points via the
            `critical_points` attribute, and also all critical
            points (via nodes dict) and connections between them
            (via edges dict). The user should be familiar with critic2
            before trying to understand these.

            Indexes of nucleus critical points in the nodes dict are the
            same as the corresponding sites in structure, with indices of
            other critical points arbitrarily assigned.

            Only one of (stdout, cpreport) required, with cpreport preferred
            since this is a new, native JSON output from critic2.

            :param structure: associated Structure
            :param stdout: stdout from running critic2 in automatic
                mode
            :param stderr: stderr from running critic2 in automatic
                mode
            :param cpreport: json output from CPREPORT command
            :param yt: json output from YT command
            :param zpsp (dict): Dict of element/symbol name to number of electrons
            (ZVAL in VASP pseudopotential), with which to calculate charge transfer.
            Optional.
            """

            self.structure = structure

            self._stdout = stdout
            self._stderr = stderr
            self._cpreport = cpreport
            self._yt = yt
            self._zpsp = zpsp

            self.nodes = {}
            self.edges = {}

            if yt:
                self.structure = self._annotate_structure_with_yt(yt, structure, zpsp)

            if cpreport:
                self._parse_cpreport(cpreport)
            elif stdout:
                self._parse_stdout(stdout)
            else:
                raise ValueError("One of cpreport or stdout required.")

            self._remap_indices()

        def structure_graph(self, include_critical_points=("bond", "ring", "cage")):
            """
            A StructureGraph object describing bonding information
            in the crystal.
            Args:
                include_critical_points: add DummySpecie for
                the critical points themselves, a list of
                "nucleus", "bond", "ring", "cage", set to None
                to disable

            Returns: a StructureGraph
            """

            structure = self.structure.copy()

            point_idx_to_struct_idx = {}
            if include_critical_points:
                # atoms themselves don't have field information
                # so set to 0
                for prop in ("ellipticity", "laplacian", "field"):
                    structure.add_site_property(prop, [0] * len(structure))
                for idx, node in self.nodes.items():
                    cp = self.critical_points[node["unique_idx"]]
                    if cp.type.value in include_critical_points:
                        specie = DummySpecie(
                            "X{}cp".format(cp.type.value[0]), oxidation_state=None
                        )
                        structure.append(
                            specie,
                            node["frac_coords"],
                            properties={
                                "ellipticity": cp.ellipticity,
                                "laplacian": cp.laplacian,
                                "field": cp.field,
                            },
                        )
                        point_idx_to_struct_idx[idx] = len(structure) - 1

            edge_weight = "bond_length"
            edge_weight_units = "Å"

            sg = StructureGraph.with_empty_graph(
                structure,
                name="bonds",
                edge_weight_name=edge_weight,
                edge_weight_units=edge_weight_units,
            )

            edges = self.edges.copy()
            idx_to_delete = []
            # check for duplicate bonds
            for idx, edge in edges.items():
                unique_idx = self.nodes[idx]["unique_idx"]
                # only check edges representing bonds, not rings
                if self.critical_points[unique_idx].type == CriticalPointType.bond:
                    if idx not in idx_to_delete:
                        for idx2, edge2 in edges.items():
                            if idx != idx2 and edge == edge2:
                                idx_to_delete.append(idx2)
                                warnings.warn(
                                    "Duplicate edge detected, try re-running "
                                    "critic2 with custom parameters to fix this. "
                                    "Mostly harmless unless user is also "
                                    "interested in rings/cages."
                                )
                                logger.debug(
                                    "Duplicate edge between points {} (unique point {})"
                                    "and {} ({}).".format(
                                        idx,
                                        self.nodes[idx]["unique_idx"],
                                        idx2,
                                        self.nodes[idx2]["unique_idx"],
                                    )
                                )
            # and remove any duplicate bonds present
            for idx in idx_to_delete:
                del edges[idx]

            for idx, edge in edges.items():
                unique_idx = self.nodes[idx]["unique_idx"]
                # only add edges representing bonds, not rings
                if self.critical_points[unique_idx].type == CriticalPointType.bond:

                    from_idx = edge["from_idx"]
                    to_idx = edge["to_idx"]

                    # have to also check bond is between nuclei if non-nuclear
                    # attractors not in structure
                    skip_bond = False
                    if include_critical_points and "nnattr" not in include_critical_points:
                        from_type = self.critical_points[
                            self.nodes[from_idx]["unique_idx"]
                        ].type
                        to_type = self.critical_points[
                            self.nodes[from_idx]["unique_idx"]
                        ].type
                        skip_bond = (from_type != CriticalPointType.nucleus) or (
                            to_type != CriticalPointType.nucleus
                        )

                    if not skip_bond:
                        from_lvec = edge["from_lvec"]
                        to_lvec = edge["to_lvec"]

                        relative_lvec = np.subtract(to_lvec, from_lvec)

                        # for edge case of including nnattrs in bonding graph when other critical
                        # points also included, indices may get mixed
                        struct_from_idx = point_idx_to_struct_idx.get(from_idx, from_idx)
                        struct_to_idx = point_idx_to_struct_idx.get(to_idx, to_idx)

                        weight = self.structure.get_distance(
                            struct_from_idx, struct_to_idx, jimage=relative_lvec
                        )

                        crit_point = self.critical_points[unique_idx]

                        edge_properties = {
                            "field": crit_point.field,
                            "laplacian": crit_point.laplacian,
                            "ellipticity": crit_point.ellipticity,
                            "frac_coords": self.nodes[idx]["frac_coords"],
                        }

                        sg.add_edge(
                            struct_from_idx,
                            struct_to_idx,
                            from_jimage=from_lvec,
                            to_jimage=to_lvec,
                            weight=weight,
                            edge_properties=edge_properties,
                        )

            return sg

        def get_critical_point_for_site(self, n):
            """
            Args:
                n: Site index n

            Returns: A CriticalPoint instance
            """
            return self.critical_points[self.nodes[n]["unique_idx"]]

        def get_volume_and_charge_for_site(self, n):
            """
            Args:
                n: Site index n

            Returns: A dict containing "volume" and "charge" keys,
            or None if YT integration not performed
            """
            if not self._node_values:
                return None
            return self._node_values[n]

        def _parse_cpreport(self, cpreport):
            def get_type(signature: int, is_nucleus: bool):
                if signature == 3:
                    return "cage"
                elif signature == 1:
                    return "ring"
                elif signature == -1:
                    return "bond"
                elif signature == -3:
                    if is_nucleus:
                        return "nucleus"
                    else:
                        return "nnattr"

            bohr_to_angstrom = 0.529177

            self.critical_points = [
                CriticalPoint(
                    p["id"] - 1,
                    get_type(p["signature"], p["is_nucleus"]),
                    p["fractional_coordinates"],
                    p["point_group"],
                    p["multiplicity"],
                    p["field"],
                    p["gradient"],
                    coords=[x * bohr_to_angstrom for x in p["cartesian_coordinates"]]
                    if cpreport["units"] == "bohr"
                    else None,
                    field_hessian=p["hessian"],
                )
                for p in cpreport["critical_points"]["nonequivalent_cps"]
            ]

            for idx, p in enumerate(cpreport["critical_points"]["cell_cps"]):
                self._add_node(
                    idx=p["id"] - 1,
                    unique_idx=p["nonequivalent_id"] - 1,
                    frac_coords=p["fractional_coordinates"],
                )
                if "attractors" in p:
                    self._add_edge(
                        idx=p["id"] - 1,
                        from_idx=int(p["attractors"][0]["cell_id"]) - 1,
                        from_lvec=p["attractors"][0]["lvec"],
                        to_idx=int(p["attractors"][1]["cell_id"]) - 1,
                        to_lvec=p["attractors"][1]["lvec"],
                    )

        def _remap_indices(self):
            """
            Re-maps indices on self.nodes and self.edges such that node indices match
            that of structure, and then sorts self.nodes by index.
            """

            # Order of nuclei provided by critic2 doesn't
            # necessarily match order of sites in Structure.
            # This is because critic2 performs a symmetrization step.
            # We perform a mapping from one to the other,
            # and re-index all nodes accordingly.
            node_mapping = {}  # critic2_index:structure_index
            # ensure frac coords are in [0,1] range
            frac_coords = np.array(self.structure.frac_coords) % 1
            kd = KDTree(frac_coords)

            node_mapping = {}
            for idx, node in self.nodes.items():
                if (
                    self.critical_points[node["unique_idx"]].type
                    == CriticalPointType.nucleus
                ):
                    node_mapping[idx] = kd.query(node["frac_coords"])[1]

            if len(node_mapping) != len(self.structure):
                warnings.warn(
                    "Check that all sites in input structure ({}) have "
                    "been detected by critic2 ({}).".format(
                        len(self.structure), len(node_mapping)
                    )
                )

            self.nodes = {
                node_mapping.get(idx, idx): node for idx, node in self.nodes.items()
            }

            for edge in self.edges.values():
                edge["from_idx"] = node_mapping.get(edge["from_idx"], edge["from_idx"])
                edge["to_idx"] = node_mapping.get(edge["to_idx"], edge["to_idx"])

        @staticmethod
        def _annotate_structure_with_yt(yt, structure, zpsp):

            volume_idx = None
            charge_idx = None

            for prop in yt["integration"]["properties"]:
                if prop["label"] == "Volume":
                    volume_idx = prop["id"] - 1  # 1-indexed, change to 0
                elif prop["label"] == "$chg_int":
                    charge_idx = prop["id"] - 1

            def get_volume_and_charge(nonequiv_idx):
                attractor = yt["integration"]["attractors"][nonequiv_idx - 1]
                if attractor["id"] != nonequiv_idx:
                    raise ValueError(
                        "List of attractors may be un-ordered (wanted id={}): {}".format(
                            nonequiv_idx, attractor
                        )
                    )
                return (
                    attractor["integrals"][volume_idx],
                    attractor["integrals"][charge_idx],
                )

            volumes = []
            charges = []
            charge_transfer = []

            for idx, site in enumerate(yt["structure"]["cell_atoms"]):
                if not np.allclose(
                    structure[idx].frac_coords, site["fractional_coordinates"]
                ):
                    raise IndexError(
                        "Site in structure doesn't seem to match site in YT integration:\n{}\n{}".format(
                            structure[idx], site
                        )
                    )
                volume, charge = get_volume_and_charge(site["nonequivalent_id"])
                volumes.append(volume)
                charges.append(charge)
                if zpsp:
                    if structure[idx].species_string in zpsp:
                        charge_transfer.append(charge - zpsp[structure[idx].species_string])
                    else:
                        raise ValueError(
                            "ZPSP argument does not seem compatible with species in structure ({}): {}".format(
                                structure[idx].species_string, zpsp
                            )
                        )

            structure = structure.copy()
            structure.add_site_property("bader_volume", volumes)
            structure.add_site_property("bader_charge", charges)

            if zpsp:
                if len(charge_transfer) != len(charges):
                    warnings.warn(
                        "Something went wrong calculating charge transfer: {}".format(
                            charge_transfer
                        )
                    )
                else:
                    structure.add_site_property("bader_charge_transfer", charge_transfer)

            return structure

        def _parse_stdout(self, stdout):

            warnings.warn(
                "Parsing critic2 standard output is deprecated and will not be maintained, "
                "please use the native JSON output in future."
            )

            stdout = stdout.split("\n")

            # NOTE WE ARE USING 0-BASED INDEXING:
            # This is different from critic2 which
            # uses 1-based indexing, so all parsed
            # indices have 1 subtracted.

            # Parsing happens in two stages:

            # 1. We construct a list of unique critical points
            #    (i.e. non-equivalent by the symmetry of the crystal)
            #   and the properties of the field at those points

            # 2. We construct a list of nodes and edges describing
            #    all critical points in the crystal

            # Steps 1. and 2. are essentially independent, except
            # that the critical points in 2. have a pointer to their
            # associated unique critical point in 1. so that more
            # information on that point can be retrieved if necessary.

            unique_critical_points = []

            # parse unique critical points
            for i, line in enumerate(stdout):
                if "mult  name            f             |grad|           lap" in line:
                    start_i = i + 1
                elif "* Analysis of system bonds" in line:
                    end_i = i - 2
            # if start_i and end_i haven't been found, we
            # need to re-evaluate assumptions in this parser!

            for i, line in enumerate(stdout):
                if i >= start_i and i <= end_i:
                    l = line.replace("(", "").replace(")", "").split()

                    unique_idx = int(l[0]) - 1
                    point_group = l[1]
                    # type = l[2]  # type from definition of critical point e.g. (3, -3)
                    critical_point_type = l[3]  # type from name, e.g. nucleus
                    frac_coords = [float(l[4]), float(l[5]), float(l[6])]
                    multiplicity = float(l[7])
                    # name = float(l[8])
                    field = float(l[9])
                    field_gradient = float(l[10])
                    # laplacian = float(l[11])

                    point = CriticalPoint(
                        unique_idx,
                        critical_point_type,
                        frac_coords,
                        point_group,
                        multiplicity,
                        field,
                        field_gradient,
                    )
                    unique_critical_points.append(point)

            for i, line in enumerate(stdout):
                if "+ Critical point no." in line:
                    unique_idx = int(line.split()[4]) - 1
                elif "Hessian:" in line:
                    l1 = list(map(float, stdout[i + 1].split()))
                    l2 = list(map(float, stdout[i + 2].split()))
                    l3 = list(map(float, stdout[i + 3].split()))
                    hessian = [
                        [l1[0], l1[1], l1[2]],
                        [l2[0], l2[1], l2[2]],
                        [l3[0], l3[1], l3[2]],
                    ]
                    unique_critical_points[unique_idx].field_hessian = hessian

            self.critical_points = unique_critical_points

            # parse graph connecting critical points
            for i, line in enumerate(stdout):
                if "#cp  ncp   typ        position " in line:
                    start_i = i + 1
                elif "* Attractor connectivity matrix" in line:
                    end_i = i - 2
            # if start_i and end_i haven't been found, we
            # need to re-evaluate assumptions in this parser!

            for i, line in enumerate(stdout):
                if i >= start_i and i <= end_i:

                    l = line.replace("(", "").replace(")", "").split()

                    idx = int(l[0]) - 1
                    unique_idx = int(l[1]) - 1
                    frac_coords = [float(l[3]), float(l[4]), float(l[5])]

                    self._add_node(idx, unique_idx, frac_coords)
                    if len(l) > 6:
                        from_idx = int(l[6]) - 1
                        to_idx = int(l[10]) - 1
                        self._add_edge(
                            idx,
                            from_idx=from_idx,
                            from_lvec=(int(l[7]), int(l[8]), int(l[9])),
                            to_idx=to_idx,
                            to_lvec=(int(l[11]), int(l[12]), int(l[13])),
                        )

        def _add_node(self, idx, unique_idx, frac_coords):
            """
            Add information about a node describing a critical point.

            :param idx: index
            :param unique_idx: index of unique CriticalPoint,
                used to look up more information of point (field etc.)
            :param frac_coord: fractional co-ordinates of point
            :return:
            """
            self.nodes[idx] = {"unique_idx": unique_idx, "frac_coords": frac_coords}

        def _add_edge(self, idx, from_idx, from_lvec, to_idx, to_lvec):
            """
            Add information about an edge linking two critical points.

            This actually describes two edges:

            from_idx ------ idx ------ to_idx

            However, in practice, from_idx and to_idx will typically be
            atom nuclei, with the center node (idx) referring to a bond
            critical point. Thus, it will be more convenient to model
            this as a single edge linking nuclei with the properties
            of the bond critical point stored as an edge attribute.

            :param idx: index of node
            :param from_idx: from index of node
            :param from_lvec: vector of lattice image the from node is in
                as tuple of ints
            :param to_idx: to index of node
            :param to_lvec:  vector of lattice image the to node is in as
                tuple of ints
            :return:
            """
            self.edges[idx] = {
                "from_idx": from_idx,
                "from_lvec": from_lvec,
                "to_idx": to_idx,
                "to_lvec": to_lvec,
            }