Molecular Systems

Under construction. The chiLife.MolSys module is not yet officially supported.

The MolSys object

The chiLife Molecular System, or MolSys and related objects, are how chilife represents molecular systems including proteins, nucleic acids, small molecules, course grained systems and more. MolSys objects are generally created from PDB files, MDAnalysis objects or existing chilife molecular systems. The design of the chiLife molecular system objects are heavily influenced by MDAnalysis and shares many attribute and method names to facilitate a compatible interface.

class MolecularSystemBase

Base class for molecular systems containing attributes universal to

select_atoms(selstr)

Select atoms from MolSys or AtomSelection based on selection a selection string, similar to the select_atoms method from MDAnalysis

Parameters:

selstr (str) – Selection string

Returns:

atoms – Selected atoms

Return type:

AtomSelection

property fname

File name or functional name of the molecular system

property positions

3-Dimensional cartesian coordinates of the atoms in the molecular system

property coords

3-dimensional cartesian coordinates of the atoms in the molecular system

property n_atoms

“Number of atoms in the molecular system

property n_residues

Number of residues in the molecular system

property n_chains

Number of chains in the molecular system

property residues

ResidueSelection for all residues of the molecular system

property segments

SegmentSelection for all segments (chains) of the molecular system

property logic_keywords

Dictionary of logic keywords (strings) pertaining to atom_selection() method. Keywords are mapped to the associated logic function

property molsys_keywords

Dictionary of molecular system keywords (strings) pertaining to atom_selection() method. Keywords are mapped to the associated molecular system attributes

property universe

Wrapper attribute to allow molecular systems to behave like MDAnalysis AtomGroup objects

copy()

Creates a deep copy of the underlying MolSys and returns an AtomSelection from the new copy matching the current selection if it exists.

class MolSys(atomids: ndarray, names: ndarray, altlocs: ndarray, resnames: ndarray, resnums: ndarray, chains: ndarray, trajectory: ndarray, occupancies: ndarray, bs: ndarray, segs: ndarray, atypes: ndarray, charges: ndarray, bonds: ArrayLike | None = None, name: str = 'Noname_MolSys')

An object containing all attributes of a molecular system.

Parameters:

  • atomids (np.ndarray) – Array of atom indices where each index is unique to each atom in the molecular system.

  • names (np.ndarray) – Array of atom names, e.g. ‘N’, ‘CA’ ‘C’.

  • altlocs (np.ndarray) – Array of alternative location identifiers for each atom.

  • resnames (np.ndarray) – Array of residue names for each atom.

  • resnums (np.ndarray) – Array of residue numbers for each atom.

  • chains (np.ndarray) – Array of chain identifiers for each atom.

  • trajectory (np.ndarray) – Cartesian coordinates of each atom for each state of an ensemble or for each timestep of a trajectory.

  • occupancies (np.ndarray) – Occupancy or q-factory for each atom.

  • bs (np.ndarray) – thermal, or b-factors for each atom.

  • segs (np.ndarray) – Segment/chain IDs for each atom.

  • atypes (np.ndarray) – Atom/element types.

  • charges (np.ndarray) – Formal or partial charges assigned to each atom.

  • bonds (ArrayLike) – Array of atom ID pairs corresponding to all atom bonds in the system.

  • name (str) – Name of molecular system

classmethod from_pdb(file_name, sort_atoms=False)

Reads a pdb file and returns a MolSys object

Parameters:

  • file_name (str, Path) – Path to the PDB file to read.

  • sort_atoms (bool) – Presort atoms for consisted internal coordinate definitions

Returns:

cls – Molecular system object of the PDB structure.

Return type:

MolSys

classmethod from_arrays(anames: ArrayLike, atypes: ArrayLike, resnames: ArrayLike, resindices: ArrayLike, resnums: ArrayLike, segindices: ArrayLike, segids: ArrayLike | None = None, trajectory: ArrayLike | None = None, **kwargs) → MolSys

Create a MolSys object from a minimal set of arrays.

Parameters:

  • anames (ArrayLike) – Array of atom names.

  • atypes (ArrayLike) – Array of atom types/elements.

  • resnames (ArrayLike) – Array of residue names for each atom.

  • resindices (ArrayLike) – Array of residue indices for each atom.

  • resnums (ArrayLike) – Array of residue numbers for each atom.

  • segindices (ArrayLike) – Array of segment indices for each atom.

  • segids (ArrayLike) – Array of segment IDs for each atom.

  • trajectory (ArrayLike) – Array of cartesian coordinates for each atom and each state of an ensemble or frame of a trajectory.

Returns:

cls – Molecular system object of the PDB structure.

Return type:

MolSys

classmethod from_atomsel(atomsel, frames=None)

Create a new MolSys object from an existing AtomSelection or MDAnalysis.AtomGroup object.

Parameters:

  • atomsel (AtomSelection, MDAnalysis.AtomGroup) – The AtomSelection or MDAnalysis.AtomGroup from which to create the new MolSys object.

  • frames (int, Slice, ArrayLike) – Frame index, slice or array of frame indices corresponding to the frames of the atom selection you wish to extract into a new MolSys object.

Returns:

cls – Molecular system object of the PDB structure.

Return type:

MolSys

classmethod from_rdkit(mol)

Create a MolSys from an rdkit Mol object with embedded conformers.

Parameters:

mol

copy()

Create a deep copy of the MolSys.

load_new(coordinates)

Load a new set of 3-dimensional coordinates into the MolSys.

Parameters:

coordinates (ArrayLike) – Set of new coordinates to load into the MolSys

class Trajectory(coordinates: ndarray, molsys: MolSys, timestep: float = 1)

Object containing and managing 3-dimensional coordinates of MolSys objects, particularly when there are multiple states or time steps.

Parameters:

  • coordinates (np.ndarray) – 3-dimensional coordinates for all atoms and all states/frames of the associated MolSys object.

  • molsys (MolSys) – The associated MolSys object.

  • timestep (float) – The time step or change in time between frames/states of the trajectory/ensemble.

load_new(coordinates)

Load a new set (trajectory or ensemble) of 3-dimensional coordinates into the Trajectory.

Parameters:

coordinates (ArrayLike) – Set of new coordinates to load into the MolSys

property frame

The frame number the trajectory is currently on

class AtomSelection(*args)

An object containing a group of atoms from a MolSys object

Parameters:

  • molsys (MolSys) – The MolSys object from which the AtomSelection belongs to.

  • mask (np.ndarray) – An array of atom indices that defines the atoms of molsys that make up the atom selection.

class ResidueSelection(molsys, mask)

An object containing a group of residues and all their atoms from a MolSys object. Note that if one atom of a residue is present in the AtomSelection used to create the group, all atoms of that residue will be present in the ResidueSelection object.

Note

Unlike a regular AtomSelection object, the resnames, resnums, segids and chains attributes of this object are tracked with respect to residue not atom and changes made to these attributes on this object will not be present in the parent object and vice versa.

Parameters:

  • molsys (MolSys) – The MolSys object from which the AtomSelection belongs to.

  • mask (np.ndarray) – An array of atom indices that defines the atoms of molsys that make up the atom selection.

class SegmentSelection(molsys, mask)

An object containing a group of segments and all their atoms from a MolSys object. Note that if one atom of a segment is present in the AtomSelection used to create the group, all atoms of that segment will be present in the SegmentSelection object.

Note

Unlike a regular AtomSelection object, the segids and chains attributes of this object are tracked with respect to segements not atoms and changes made to these attributes on this object will not be present in the parent object and vice versa.

Parameters:

  • molsys (MolSys) – The MolSys object from which the AtomSelection belongs to.

  • mask (np.ndarray) – An array of atom indices that defines the atoms of molsys that make up the atom selection.

class Atom(molsys, mask)

An object containing information for a single atom.

Parameters:

  • molsys (MolSys) – The MolSys object from which the Atom belongs to.

  • mask (np.ndarray) – The index that defines the atoms of molsys that make up the atom selection.

class Residue(molsys, mask)

An object representing a single residue.

Parameters:

  • molsys (MolSys) – The MolSys object from which the Residue belongs to.

  • mask (int) – An array of atom indices that defines the atoms of the residue

phi_selection()

Get an AtomSelection of the atoms defining the Phi backbone dihedral angle of the residue.

Returns:

sel – An AtomSelection object containing the atoms that make up the Phi backbone dihedral angle of the selected residue.

Return type:

AtomSelection

psi_selection()

Get an AtomSelection of the atoms defining the Psi backbone dihedral angle of the residue.

Returns:

sel – An AtomSelection object containing the atoms that make up the Psi backbone dihedral angle of the selected residue.

Return type:

AtomSelection

class Segment(molsys, mask)

An object representing a single segment of a molecular system.

Parameters:

  • molsys (MolSys) – The MolSys object from which the segment belongs to.

  • mask (int) – An array of atom indices that defines the atoms of the segment.

The MolSysIC object

While the MolSys object contains cartesian coordinate and protein information, the MolSysIC object contains information on internal coordinates.

class MolSysIC(z_matrix: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], z_matrix_idxs: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], protein: MolecularSystemBase | Universe | AtomGroup, **kwargs)

A class for protein internal coordinates.

Parameters:

  • z_matrix (np.ndarray) – Array of z-matricies for all frames of the ensemble/trajectory

  • z_matrix_idxs (np.ndarray) – Indices of the attoms that define the bond lengths, angles, and dihedrals of the z-matrix

  • protein

  • kwargs

zmats

Dictionary of Z-matrices of the molecule. Each entry corresponds to a contiguous segment of bonded atoms.

Type:

dict[np.ndarray]

z_matrix_idxs

Dictionary of Z-matrix indices.

Type:

dict[np.ndarray]

atom_dict

Nested dictionaries containing indices of the atoms that define the coordinates (bond, angle dihedral) objects. Nesting pattern: [coord_type][chain][resi, stem][name] where coord_type is one of ‘bond’, ‘angle’ or ‘dihedral’, chain is the chainid, resi is the residue number, stem is a tuple of the names of the 3 atoms preceding the atom coordinate being defined.

Type:

dict

ICS

Nested dictionaries containing AtomIC objects. Nesting pattern: [chain][resi][stem][name] where chain is the chainid, resi is the residue number, stem is a tuple of the names of the 3 atoms preceding the atom coordinate being defined.

Type:

dict

atoms

List of AtomIC objects making up the protein in order of their indices.

Type:

np.ndarray[AtomIC]

atom_types

Array of atom types (elements) corresponding to the atom indices.

Type:

np.ndarray

atom_names

Array of atom names corresponding to the atom indices.

Type:

np.ndarray

resis

Ordered array of residue numbers.

Type:

np.ndarray

resnames

Dictionary mapping residue numbers to their residue names.

Type:

dict[int]:str

chains

Array of chainids

Type:

np.ndarray

bonded_pairs

Array of index pairs corresponding to atoms that are bonded.

Type:

np.ndarray

perturbed

Indicates if any internal coordinates have changed since the last time cartesian coordinates were calculated.

Type:

bool

dihedral_defs

List of major side chain and backbone dihedral definitions as defined by user defined and supported residues.

Type:

list

classmethod from_atoms(atoms: Universe | AtomGroup | MolecularSystemBase, preferred_dihedrals: List | None = None, bonds: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None = None, **kwargs: Dict)

Generate a MolSysIC object from a AtomSelection or MDAnalysis.AtomGroup object.

Parameters:

  • atoms (MDAnalysis.Universe, MDAnalysis.AtomGroup, MolecularSystemBase) – MDA Universe, AtomGroup or chiLife Molecular System to create the internal coordinates from.

  • preferred_dihedrals (List[List[str]]) – List of preferred dihedral definitions to use when defining the internal coordinate system.

  • bonds (ArrayLike) – Array of tuples defining the atom pairs that are bonded.

  • kwargs (dict) –

    Additional keyword arguments.

    ignore_waterbool

    Ignore atoms that belong to water molecules.

    use_chain_operatorsbool

    Allow for the use of a translation and rotation vectors to orient cains that are not covalently linked.

Returns:

cls – A chiLife internal coordinates molecular system.

Return type:

MDAnalysis.Universe

copy()

Create a deep copy of an MolSysIC instance

property chain_operator_idxs

An array of indices defining the starting and ending indices of the different chains.

property chain_operators

A set of coordinate transformations that can orient multiple chains that are not covalently linked. e.g. structures with missing residues or protein complexes. The chain_operator property is a dictionary mapping chainIDs to a sub-dictionary containing a translation vector, ori and rotation matrix mx that will transform the protein coordinates from tie internal coordinate frame to some global frame.

Type:

dict

property z_matrix

The z-matrix (internal) coordinates of the molecular system for the current frame.

property coords

The cartesian coordinates of the molecular system for the current frame

property nonbonded

Array of atom index pairs of atoms that are not bonded

Type:

np.ndarray

to_cartesian()

Method to convert z-matrix (internal) coordinate to cartesian coordinate

set_dihedral(dihedrals: float | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], resi: int, atom_list: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], chain: int | str | None = None)

Set one or more dihedral angles of a single residue in internal coordinates for the atoms defined in atom list.

Parameters:

  • dihedrals (float, ArrayLike) – Angle or array of angles to set the dihedral(s) to.

  • resi (int) – Residue number of the site being altered

  • atom_list (ArrayLike) – Names or array of names of atoms involved in the dihedral(s)

  • chain (int, str, optional) – Chain containing the atoms that are defined by the dihedrals that are being set. Only necessary when there is more than one chain in the proteinIC object.

Returns:

self – ProteinIC object with new dihedral angle(s)

Return type:

MolSysIC

batch_set_dihedrals(idxs: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], dihedrals: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], resi: int, atom_list: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], chain: int | str | None = None)

Sets dihedral angles of a single residue in internal coordinates for the atoms defined in atom list and in trajectory indices in idxs.

Parameters:

  • idxs (ArrayLike) – an array in indices corresponding to the progenitor structure in the MolSysIC trajectory.

  • dihedrals (ArrayLike) – an array of angles for each idx in idxs and for each dihedral in atom_list. Should have the shape (len(idxs), len(atom_list))

  • resi (int) – Residue number of the site being altered

  • atom_list (ArrayLike) – Names or array of names of atoms involved in the dihedrals

  • chain (int, str, optional) – Chain containing the atoms that are defined by the dihedrals that are being set. Only necessary when there is more than one chain in the proteinIC object.

Returns:

z_matrix – the z_matrix for every frame in idxs with the new dihedral angel values defined in dihedrals

Return type:

ArrayLike

get_dihedral(resi: int, atom_list: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], chain: int | str | None = None)

Get the dihedral angle(s) of one or more atom sets at the specified residue. Dihedral angles are returned in radians

Parameters:

  • resi (int) – Residue number of the site being altered

  • atom_list (ArrayLike) – Names or array of names of atoms involved in the dihedral(s)

  • chain (int, str) – Chain identifier. required if there is more than one chain in the protein. Default value = None

Returns:

angles – Array of dihedral angles corresponding to the atom sets in atom list.

Return type:

numpy.ndarray

get_z_matrix_idxs(resi: int, atom_list: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], chain: int | str | None = None)

Get the z-matrix indices of the dihedral angle(s) defined by atom_list and the specified residue and chain. Dihedral angles are returned in radians.

Parameters:

  • resi (int) – Residue number of the site being altered

  • atom_list (ArrayLike) – Names or array of names of atoms involved in the dihedral(s)

  • chain (int, str) – Chain identifier. required if there is more than one chain in the protein. Default value = None

Returns:

dihedral_idxs – Array of dihedral angles corresponding to the atom sets in atom list.

Return type:

numpy.ndarray

has_clashes(distance: float = 1.5) → bool

Checks for an internal clash between non-bonded atoms.

Parameters:

distance (float) – Minimum distance allowed between non-bonded atoms in angstroms. (Default value = 1.5).

Returns:

has_clashes – True if there are any atoms within distance angstroms from each other that would constitute a clash otherwise False

Return type:

bool

phi_idxs(resnums: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None = None, chain: int | str | None = None)

Method to return the Z-matrix indices of Phi backbone dihedrals

Parameters:

  • resnums (int, ArrayLike[int]) – Residues for which to return the Phi value index of the z-matrix

  • chain (int, str) – Chain corresponding to the resnums of interest

Returns:

idxs – Array of indices corresponding to the phi dihedral angles of the selected residues on the chain

Return type:

ndarray[int]

psi_idxs(resnums: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None = None, chain: int | str | None = None)

Method to return the Z-matrix indices of Psi backbone dihedrals

Parameters:

  • resnums (int, ArrayLike[int]) – Residues for which to return the Psi value index of the z-matrix

  • chain (int, str) – Chain corresponding to the resnums of interest

Returns:

idxs – Array of indices corresponding to the Psi dihedral angles of the selected residues on the chain

Return type:

ndarray[int]

omega_idxs(resnums: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None = None, chain: int | str | None = None)

Method to return the Z-matrix indices of Psi backbone dihedrals

Parameters:

  • resnums (int, ArrayLike[int]) – Residues for which to return the Psi value index of the z-matrix

  • chain (int, str) – Chain corresponding to the resnums of interest

Returns:

idxs – Array of indices corresponding to the Psi dihedral angles of the selected residues on the chain

Return type:

ndarray[int]

chi_idxs(resnums: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None = None, chain: int | str | None = None)

Create a list of index arrays corresponding the Z-matrix indices of flexible side chain (chi) dihedrals. Note that only chi dihedrals defined in chilife.dihedral_defs will be considered.

Parameters:

  • resnums (int, ArrayLike[int]) – Residues for which to return the Psi value index of the z-matrix

  • chain (int, str) – Chain corresponding to the resnums of interest

Returns:

chi_idxs – list of arrays containing the indices of the z-matrix dihedrals corresponding to the chi dihedrals. Each array in the list refers to a specific dihedral: [χ1, χ2, ... χn]. because different residues will have different numbers of chi dihedrals the arrays will not be the same size, but they can be concatenated using numpy: chi_idxs = np.concatenate(IC.chi_idxs(...))).

Return type:

List[np.ndarray]

load_new(z_matrix, **kwargs)

Replace the current z-matrix ensemble/trajectory with new one.

Parameters:

  • z_matrix (np.ndarray) – New z-matrix to load into the MolSysIC

  • kwargs (dict) –

    Additional keyword arguments.

    opdict

    New chain operators for the new z-matrix.

apply_chain_operators(idx=None, from_list=False)

Apply chain operators to the specified frames (idx) of the MolSysIC trajectory. If no idx is provided then all chain operators will be applied to all frames. :param from_list: A boolean argument to specify whether each frame previously had its own chain operators. :type from_list: bool :param idx: Frames or array of frames that should have the chain operators applied. :type idx: int, Array

use_frames(idxs)

Remove all frames except those specified by idxs :param idxs: Index or array if indices to keep :type idxs: int, ArrayLike

set_cartesian_coords(coords, mask)

Alter the coordinates of the current frame by assigning new cartwsian coordinates to the atoms set to True and mask.

Parameters:

  • coords (np.ndarray) – Cartesian coordinates to apply to the atoms defined by mask of the current frame.

  • mask (np.ndarray) – Array of bool values defining which atoms of the MolSysIC are being set.

shift_resnum(delta: int)

Alter the residue number of all residues in the MolSysIC by adding delta.

Parameters:

delta (int) – Amount to shift residue numbers by. Can be positive or negative.

reconfigure_cap(cap, atom_idxs, bonds)

Helper function to reconfigure the “cap” region of bifunctional labels so that the internal coordinates are defined correctly.

Parameters:

  • cap (ArrayLike) – Indices of the cap atoms in the molecule with atoms defined in atom_idxs.

  • atom_idxs (ArrayLike) – Indices of all atoms to be considered for reconfiguration containing the cap.

  • bonds (ArrayLike) – Array of tuples defining the bonds between atoms in atom_idxs.

Returns:

atom_idxs – Array of atom indices rearranged so that the cap is terminal to the rest of the atoms.

Return type:

ArrayLike

zmatrix_idxs_to_local(zmatrix_idxs)

Convert Z-matrix indices so that they reference the indices of the z-matrix rather than the parental atom selection that was used to construct the z-matrix and may have an index offset or missing atoms.

Parameters:

zmatrix_idxs (ArrayLike) – z-matrix indices

Returns:

zmatrix_idxs – Array of indices modified for internal reference.

Return type:

ArrayLike

get_chainbreak_idxs(z_matrix_idxs)

Get indices of atoms that chain breaks :param z_matrix_idxs: index map of z_matrix :type z_matrix_idxs: ArrayLike

Returns:

indices of atoms that start new chains

Return type:

chainbreak_idxs

ic_mx(*p: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) → Tuple[_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]]

Calculates a rotation matrix and translation to transform a set of atoms to global coordinate frame from a local coordinated frame defined by p. This function is a wrapper to quickly and easily transform cartesian coordinates, made from internal coordinates, to their appropriate location in the global frame.

Parameters:

p (ArrayLike) – Coordinates of the three atoms defining the local coordinate frame of the IC object

Returns:

  • rotation_matrix (np.ndarray) – Rotation matrix to rotate from the internal coordinate frame to the global frame

  • origin (np.ndarray) – New origin position in 3-dimensional space

get_z_matrix(coords, z_matrix_idxs, chain_operator_idxs=None)

Given a set of cartesian coordinates and indices defining a z-matrix, calcualte the z-matrix.

Parameters:

  • coords (np.ndarray) – Array of cartesian coordinates.

  • z_matrix_idxs (np.ndarray) – Array of indices defining bond-angle-torsions of the z-matrix.

  • chain_operator_idxs (np.ndarray) – Array of indices defining different chains.

Returns:

z_matrix – Z-matrix (internal) coordinates.

Return type:

np.ndarray