Geometry¶

class sisl.Geometry(xyz, atom=None, sc=None)[source]¶

Holds atomic information, coordinates, species, lattice vectors

The Geometry class holds information regarding atomic coordinates, the atomic species, the corresponding lattice-vectors.

It enables the interaction and conversion of atomic structures via simple routine methods.

All lengths are assumed to be in units of Angstrom, however, as long as units are kept same the exact units are irrespective.

>>> square = Geometry([[0.5, 0.5, 0.5]], Atom(1),
...                   sc=SuperCell([1, 1, 10], nsc=[3, 3, 1]))
>>> print(square)
Geometry{na: 1, no: 1,
 Atoms{species: 1,
  Atom{H, Z: 1, mass(au): 1.0079, maxR: -1.00000,
   Orbital{R: -1.0, q0: 0.0}
  }: 1,
 },
 nsc: [3, 3, 1], maxR: -1.0
}

Parameters:	xyz : array_like atomic coordinates `xyz[i, :]` is the atomic coordinate of the i’th atom. atom : array_like or Atoms atomic species retrieved from the `PeriodicTable` sc : SuperCell the unit-cell describing the atoms in a periodic super-cell

See also

Atoms: contained atoms self.atom
Atom: contained atoms are each an object of this

Examples

An atomic cubic lattice of Hydrogen atoms

>>> xyz = [[0, 0, 0],
...        [1, 1, 1]]
>>> sc = SuperCell([2,2,2])
>>> g = Geometry(xyz, Atom('H'), sc)

The following estimates the lattice vectors from the atomic coordinates, although possible, it is not recommended to be used.

>>> xyz = [[0, 0, 0],
...        [1, 1, 1]]
>>> g = Geometry(xyz, Atom('H'))

Attributes:

na: Number of atoms in geometry
xyz : ndarray: atomic coordinates
atom: Atoms for the geometry (Atoms object)
orbitals: List of orbitals per atom
sc : SuperCell: the supercell describing the periodicity of the geometry
no: Number of orbitals
n_s: int: total number of supercells in the supercell
no_s: int: total number of orbitals in the geometry times number of supercells

Attributes

`atom`	Atoms for the geometry (`Atoms` object)
`atoms`	Atoms for the geometry (`Atoms` object)
`cell`	Returns the inherent `SuperCell` objects `cell`
`firsto`	The first orbital on the corresponding atom
`fxyz`	Returns geometry coordinates in fractional coordinates
`icell`	Returns the inherent `SuperCell` objects `icell`
`isc_off`	Returns the inherent `SuperCell` objects `isc_off`
`lasto`	The last orbital on the corresponding atom
`mass`	Returns the mass of all atoms as an array
`n_s`	Returns the inherent `SuperCell` objects `n_s`
`na`	Number of atoms in geometry
`na_s`	Number of supercell atoms
`names`	The named index specifier
`no`	Number of orbitals
`no_s`	Number of supercell orbitals
`nsc`	Returns the inherent `SuperCell` objects `nsc`
`orbitals`	List of orbitals per atom
`origo`	Returns the inherent `SuperCell` objects `origo`
`q0`	Total initial charge in this geometry (sum of q0 in all atoms)
`rcell`	Returns the inherent `SuperCell` objects `rcell`
`sc_off`	Returns the inherent `SuperCell` objects `sc_off`
`volume`	Returns the inherent `SuperCell` objects vol

Methods

`Rij`(ia, ja)	Vector between atom ia and ja, atoms can be in super-cell indices
`__init__`(xyz[, atom, sc])	Initialize self.
`a2isc`(ia)	Returns super-cell index for a specific/list atom
`a2o`(ia[, all])	Returns an orbital index of the first orbital of said atom.
`a2sc`(a)	Returns the super-cell offset for a specific atom
`add`(other)	Merge two geometries (or a Geometry and SuperCell) by adding the two atoms together
`add_vacuum`(vacuum, axis)	Add vacuum along the axis lattice vector
`angle`(atom[, dir, ref, rad])	The angle between atom `atom` and the direction dir, with possibility of a reference coordinate ref
`append`(other, axis)	Appends structure along axis.
`as_primary`(na_primary[, ret_super])	Try and reduce the geometry to the primary unit-cell comprising na_primary atoms
`asc2uc`(atom[, uniq])	Returns atom from super-cell indices to unit-cell indices, possibly removing dublicates
`attach`(s_idx, other, o_idx[, dist, axis])	Attaches another `Geometry` at the s_idx index with respect to o_idx using different methods.
`axyz`([atom, isc])	Return the atomic coordinates in the supercell of a given atom.
`bond_correct`(ia, atom[, method])	Corrects the bond between ia and the `atom`.
`center`([atom, what])	Returns the center of the geometry
`close`(xyz_ia[, R, idx, idx_xyz, ret_xyz, …])	Indices of atoms in the entire supercell within a given radius from a given coordinate
`close_all`(xyz_ia[, R, idx, idx_xyz, …])	Indices of atoms in the entire supercell within a given radius from a given coordinate
`close_sc`(xyz_ia[, isc, R, idx, idx_xyz, …])	Indices of atoms in a given supercell within a given radius from a given coordinate
`copy`()	A copy of the object.
`cut`(seps, axis[, seg, rtol, atol])	Returns a subset of atoms from the geometry by cutting the geometry into seps parts along the direction axis.
`distance`([atom, R, tol, method])	Calculate the distances for all atoms in shells of radius tol within max_R
`equal`(other[, R, tol])	Whether two geometries are the same (optional not check of the orbital radius)
`fromASE`(aseg)	Returns geometry from an ASE object.
`iR`([na, iR, R])	Return an integer number of maximum radii (`self.maxR()`) which holds approximately `na` atoms
`insert`(atom, geom)	Inserts other atoms right before index
`is_orthogonal`()	Return true if all cell vectors are linearly independent
`iter`()	An iterator over all atomic indices
`iter_block`([iR, R, atom, method])	Iterator for performance critical loops
`iter_block_rand`([iR, R, atom])	Perform the random block-iteration by randomly selecting the next center of block
`iter_block_shape`([shape, iR, atom])	Perform the grid block-iteration by looping a grid
`iter_orbitals`([atom, local])	Returns an iterator over all atoms and their associated orbitals
`iter_species`([atom])	Iterator over all atoms (or a subset) and species as a tuple in this geometry
`maxR`([all])	Maximum orbital range of the atoms
`mirror`(plane[, atom])	Mirrors the structure around the center of the atoms
`move`(v[, atom, cell])	Translates the geometry by v
`o2a`(io[, uniq])	Atomic index corresponding to the orbital indicies.
`o2isc`(io)	Returns the super-cell index for a specific orbital.
`o2sc`(o)	Returns the super-cell offset for a specific orbital.
`oRij`(io, jo)	Vector between orbital `io` and jo, orbitals can be in super-cell indices
`optimize_nsc`([axis, R])	Optimize the number of supercell connections based on `self.maxR()`
`orij`(io, jo)	Distance between orbital `io` and jo, orbitals can be in super-cell indices
`osc2uc`(orb[, uniq])	Returns orbitals from super-cell indices to unit-cell indices, possibly removing dublicates
`prepend`(other, axis)	Prepends structure along axis.
`read`(sile, args, *kwargs)	Reads geometry from the `Sile` using Sile.read_geometry
`reduce`()	Remove all atoms not currently used in the `self.atom` object
`remove`(atom)	Remove atoms from the geometry.
`reorder`()	Reorders atoms according to first occurence in the geometry
`repeat`(reps, axis)	Create a repeated geometry
`reverse`([atom])	Returns a reversed geometry
`rij`(ia, ja)	Distance between atom ia and ja, atoms can be in super-cell indices
`rotate`(angle, v[, origo, atom, only, rad])	Rotate geometry around vector and return a new geometry
`rotate_miller`(m, v)	Align Miller direction along `v`
`rotatea`(angle[, origo, atom, only, rad])	Rotate around first lattice vector
`rotateb`(angle[, origo, atom, only, rad])	Rotate around second lattice vector
`rotatec`(angle[, origo, atom, only, rad])	Rotate around third lattice vector
`sc2uc`(atom[, uniq])	Returns atom from super-cell indices to unit-cell indices, possibly removing dublicates
`sc_index`(args, *kwargs)	Call local `SuperCell` object `sc_index` function
`scale`(scale)	Scale coordinates and unit-cell to get a new geometry with proper scaling
`set_nsc`(args, *kwargs)	Set the number of super-cells in the `SuperCell` object
`set_sc`(sc)	Overwrites the local supercell
`set_supercell`(sc)	Overwrites the local supercell
`sparserij`([dtype, na_iR, method])	Return the sparse matrix with all distances in the matrix
`sub`(atom[, cell])	Create a new `Geometry` with a subset of this `Geometry`
`swap`(a, b)	Swap a set of atoms in the geometry and return a new one
`swapaxes`(a, b[, swap])	Swap the axis for the atomic coordinates and the cell vectors
`tile`(reps, axis)	Tile the geometry to create a bigger one
`toASE`()	Returns the geometry as an ASE `Atoms` object
`translate`(v[, atom, cell])	Translates the geometry by v
`within`(shapes[, idx, idx_xyz, ret_xyz, ret_rij])	Indices of atoms in the entire supercell within a given shape from a given coordinate
`within_inf`(sc[, periodic, tol, origo])	Find all atoms within a provided supercell
`within_sc`(shapes[, isc, idx, idx_xyz, …])	Indices of atoms in a given supercell within a given shape from a given coordinate
`write`(sile, args, *kwargs)	Writes geometry to the `Sile` using sile.write_geometry

Rij(ia, ja)[source]¶

Vector between atom ia and ja, atoms can be in super-cell indices

Returns the vector between two atoms:

\[R_{ij} = r_j - r_i\]

Parameters:	ia : int or array_like atomic index of first atom ja : int or array_like atomic indices

a2isc(ia)[source]¶

Returns super-cell index for a specific/list atom

Returns a vector of 3 numbers with integers.

a2o(ia, all=False)[source]¶

Returns an orbital index of the first orbital of said atom. This is particularly handy if you want to create TB models with more than one orbital per atom.

Note that this will preserve the super-cell offsets.

Parameters:	ia : array_like Atomic indices all : bool, optional `False`, return only the first orbital corresponding to the atom, `True`, returns list of the full atom

a2sc(a)[source]¶: Returns the super-cell offset for a specific atom

add(other)[source]¶

Merge two geometries (or a Geometry and SuperCell) by adding the two atoms together

If other is a Geometry only the atoms gets added, to also add the supercell vectors simply do geom.add(other).add(other.sc).

Parameters:	other : Geometry or SuperCell Other geometry class which is added

See also

append: appending geometries
prepend: prending geometries
attach: attach a geometry
insert: insert a geometry

add_vacuum(vacuum, axis)¶

Add vacuum along the axis lattice vector

Parameters:	vacuum : float amount of vacuum added, in Ang axis : int the lattice vector to add vacuum along

angle(atom, dir=(1.0, 0, 0), ref=None, rad=False)[source]¶

The angle between atom atom and the direction dir, with possibility of a reference coordinate ref

The calculated angle can be written as this

\[\alpha = \arccos \frac{(\mathrm{atom} - \mathrm{ref})\cdot \mathrm{dir}} {|\mathrm{atom}-\mathrm{ref}||\mathrm{dir}|}\]

and thus lies in the interval \([0 ; \pi]\) as one cannot distinguish orientation without additional vectors.

Parameters:	atom : int or array_like atomic index dir : str, int or vector the direction from which the angle is calculated from, default to `x` ref : int or coordinate, optional the reference point from which the vectors are drawn, default to origo rad : bool, optional whether the returned value is in radians

append(other, axis)[source]¶

Appends structure along axis. This will automatically add the self.cell[axis,:] to all atomic coordiates in the other structure before appending.

The basic algorithm is this:

>>> oxa = other.xyz + self.cell[axis,:][None,:] 
>>> self.xyz = np.append(self.xyz,oxa) 
>>> self.cell[axis,:] += other.cell[axis,:] 

NOTE: The cell appended is only in the axis that is appended, which means that the other cell directions need not conform.

Parameters:	other : Geometry or SuperCell Other geometry class which needs to be appended If a `SuperCell` only the super cell will be extended axis : int Cell direction to which the other geometry should be appended.

See also

add: add geometries
prepend: prending geometries
attach: attach a geometry
insert: insert a geometry

as_primary(na_primary, ret_super=False)[source]¶

Try and reduce the geometry to the primary unit-cell comprising na_primary atoms

This will basically try and find the tiling/repetitions required for the geometry to only have na_primary atoms in the unit cell.

Parameters:	na_primary : int number of atoms in the primary unit cell ret_super : bool, optional also return the number of supercells used in each direction
Returns:	Geometry : the primary unit cell supercell : the tiled supercell numbers used to find the primary unit cell
Raises:	SislError : in case the algorithm fails.

asc2uc(atom, uniq=False)¶

Returns atom from super-cell indices to unit-cell indices, possibly removing dublicates

Parameters:	atom : array_like or int the atomic indices converted from supercell indices to unit-cell indices uniq : bool, optional If True the returned indices are unique and sorted.

atom¶: Atoms for the geometry (Atoms object)

atoms¶: Atoms for the geometry (Atoms object)

attach(s_idx, other, o_idx, dist='calc', axis=None)[source]¶

Attaches another Geometry at the s_idx index with respect to o_idx using different methods.

Parameters:

s_idx : int: atomic index which is the base position of the attachment. The distance between s_idx and o_idx are dist.
other : Geometry: the other Geometry to attach at the given point. In this case dist from s_idx.
o_idx : int: the index of the atom in other that is inserted at s_idx.
dist : array_like or float or str, optional: the distance (in Ang) between the attached coordinates. If dist is arraylike it should be the vector between the atoms; if `dist is float the argument axis is required and the vector will be calculated along the corresponding latticevector; else if dist is str this will correspond to the method argument of the Atom.radius class of the two atoms. Here axis is also required.
axis : int: specify the direction of the lattice vectors used. Not used if dist is an array-like argument.

axyz(atom=None, isc=None)[source]¶

Return the atomic coordinates in the supercell of a given atom.

The Geometry[...] slicing is calling this function with appropriate options.

Parameters:	atom : int or array_like atom(s) from which we should return the coordinates, the atomic indices may be in supercell format. isc : array_like, optional Returns the atomic coordinates shifted according to the integer parts of the cell. Defaults to the unit-cell

Examples

>>> geom = Geometry([[0, 0, 0], [0.5, 0, 0]], sc=1.)
>>> print(geom.axyz(isc=[1,0,0])) 
[[1.   0.   0. ]
 [1.5  0.   0. ]]

>>> geom = Geometry([[0, 0, 0], [0.5, 0, 0]], sc=1.)
>>> print(geom.axyz(0)) 
[0.  0.  0.]

bond_correct(ia, atom, method='calc')[source]¶

Corrects the bond between ia and the atom.

Corrects the bond-length between atom ia and atom in such a way that the atomic radius is preserved. I.e. the sum of the bond-lengths minimizes the distance matrix.

Only atom ia is moved.

Parameters:	ia : int The atom to be displaced according to the atomic radius atom : array_like or int The atom(s) from which the radius should be reduced. method : str, float, optional If str will use that as lookup in `Atom.radius`. Else it will be the new bond-length.

cell¶: Returns the inherent SuperCell objects cell

center(atom=None, what='xyz')[source]¶

Returns the center of the geometry

By specifying what one can control whether it should be:

xyz|position: Center of coordinates (default)
mm(xyz): Center of minimum/maximum of coordinates
mass: Center of mass
cell: Center of cell

Parameters:	atom : array_like list of atomic indices to find center of what : {‘xyz’, ‘mm(xyz)’, ‘mass’, ‘cell’} determine whether center should be of ‘cell’, mass-centered (‘mass’), center of minimum/maximum position of atoms or absolute center of the positions.

close(xyz_ia, R=None, idx=None, idx_xyz=None, ret_xyz=False, ret_rij=False)[source]¶

Indices of atoms in the entire supercell within a given radius from a given coordinate

This heavily relies on the close_sc method.

Note that if a connection is made in a neighbouring super-cell then the atomic index is shifted by the super-cell index times number of atoms. This allows one to decipher super-cell atoms from unit-cell atoms.

Parameters:

xyz_ia : coordinate/index

Either a point in space or an index of an atom. If an index is passed it is the equivalent of passing the atomic coordinate close_sc(self.xyz[xyz_ia,:]).

R : (None), float/tuple of float

The radii parameter to where the atomic connections are found. If R is an array it will return the indices: in the ranges:

>>> ( x <= R[0] , R[0] < x <= R[1], R[1] < x <= R[2] ) 

If a single float it will return:

>>> x <= R 

idx : array_like, optional

List of indices for atoms that are to be considered

idx_xyz : array_like, optional

The atomic coordinates of the equivalent idx variable (idx must also be passed)

ret_xyz : bool, optional

If true this method will return the coordinates for each of the couplings.

ret_rij : bool, optional

If true this method will return the distances from the xyz_ia for each of the couplings.

close_all(xyz_ia, R=None, idx=None, idx_xyz=None, ret_xyz=False, ret_rij=False)¶

Indices of atoms in the entire supercell within a given radius from a given coordinate

This heavily relies on the close_sc method.

Note that if a connection is made in a neighbouring super-cell then the atomic index is shifted by the super-cell index times number of atoms. This allows one to decipher super-cell atoms from unit-cell atoms.

Parameters:

xyz_ia : coordinate/index

Either a point in space or an index of an atom. If an index is passed it is the equivalent of passing the atomic coordinate close_sc(self.xyz[xyz_ia,:]).

R : (None), float/tuple of float

The radii parameter to where the atomic connections are found. If R is an array it will return the indices: in the ranges:

>>> ( x <= R[0] , R[0] < x <= R[1], R[1] < x <= R[2] ) 

If a single float it will return:

>>> x <= R 

idx : array_like, optional

List of indices for atoms that are to be considered

idx_xyz : array_like, optional

The atomic coordinates of the equivalent idx variable (idx must also be passed)

ret_xyz : bool, optional

If true this method will return the coordinates for each of the couplings.

ret_rij : bool, optional

If true this method will return the distances from the xyz_ia for each of the couplings.

close_sc(xyz_ia, isc=(0, 0, 0), R=None, idx=None, idx_xyz=None, ret_xyz=False, ret_rij=False)[source]¶

Indices of atoms in a given supercell within a given radius from a given coordinate

This returns a set of atomic indices which are within a sphere of radius R.

If R is a tuple/list/array it will return the indices: in the ranges:

>>> ( x <= R[0] , R[0] < x <= R[1], R[1] < x <= R[2] ) 

Parameters:

xyz_ia : array_like of floats or int: Either a point in space or an index of an atom. If an index is passed it is the equivalent of passing the atomic coordinate close_sc(self.xyz[xyz_ia,:]).
isc : array_like, optional: The super-cell which the coordinates are checked in.
R : float or array_like, optional: The radii parameter to where the atomic connections are found. If R is an array it will return the indices: in the ranges ( x <= R[0] , R[0] < x <= R[1], R[1] < x <= R[2] ). If a single float it will return x <= R.
idx : array_like of int, optional: List of atoms that will be considered. This can be used to only take out a certain atoms.
idx_xyz : array_like of float, optional: The atomic coordinates of the equivalent idx variable (idx must also be passed)
ret_xyz : bool, optional: If True this method will return the coordinates for each of the couplings.
ret_rij : bool, optional: If True this method will return the distance for each of the couplings.

copy()[source]¶: A copy of the object.

cut(seps, axis, seg=0, rtol=0.0001, atol=0.0001)[source]¶

Returns a subset of atoms from the geometry by cutting the geometry into seps parts along the direction axis.

This will effectively change the unit-cell in the axis as-well as removing self.na/seps atoms. It requires that self.na % seps == 0.

REMARK: You need to ensure that all atoms within the first cut out region are within the primary unit-cell.

Doing geom.cut(2, 1).tile(2, 1), could for symmetric setups, be equivalent to a no-op operation. A UserWarning will be issued if this is not the case.

This method may be regarded as the opposite of tile.

Parameters:	seps : int number of times the structure will be cut. axis : int the axis that will be cut seg : int, optional returns the i’th segment of the cut structure Currently the atomic coordinates are not translated, this may change in the future. rtol : (tolerance for checking tiling, see `numpy.allclose`) atol : (tolerance for checking tiling, see `numpy.allclose`)

See also

tile: opposite method of this

Examples

>>> g = sisl.geom.graphene()
>>> gxyz = g.tile(4, 0).tile(3, 1).tile(2, 2)
>>> G = gxyz.cut(2, 2).cut(3, 1).cut(4, 0)
>>> np.allclose(g.xyz, G.xyz)
True

distance(atom=None, R=None, tol=0.1, method='average')[source]¶

Calculate the distances for all atoms in shells of radius tol within max_R

Parameters:

atom : int or array_like, optional

only create list of distances from the given atoms, default to all atoms

R : float, optional

the maximum radius to consider, default to self.maxR(). To retrieve all distances for atoms within the supercell structure you can pass numpy.inf.

tol : float or array_like, optional

the tolerance for grouping a set of atoms. This parameter sets the shell radius for each shell. I.e. the returned distances between two shells will be maximally 2*tol, but only if atoms are within two consecutive lists. If this is a list, the shells will be of unequal size.

The first shell size will be tol * .5 or tol[0] * .5 if tol is a list.

method : {‘average’, ‘mode’, ‘<numpy.func>’, func}

How the distance in each shell is determined. A list of distances within each shell is gathered and the equivalent method will be used to extract a single quantity from the list of distances in the shell. If ‘mode’ is chosen it will use scipy.stats.mode. If a string is given it will correspond to getattr(numpy, method), while any callable function may be passed. The passed function will only be passed a list of unsorted distances that needs to be processed.

Returns:

numpy.ndarray: an array of positive numbers yielding the distances from the atoms in reduced form

See also

sparserij: return a sparse matrix will all distances between atoms

Examples

>>> geom = Geometry([0]*3, Atom(1, R=1.), sc=SuperCell(1., nsc=[5, 5, 1]))
>>> geom.distance() # use geom.maxR() 
array([1.])
>>> geom.distance(tol=[0.5, 0.4, 0.3, 0.2])
array([1.])
>>> geom.distance(R=2, tol=[0.5, 0.4, 0.3, 0.2]) 
array([1.        ,  1.41421356,  2.        ])
>>> geom.distance(R=2, tol=[0.5, 0.7]) # the R = 1 and R = 2 ** .5 gets averaged 
array([1.20710678,  2.        ])

equal(other, R=True, tol=0.0001)[source]¶

Whether two geometries are the same (optional not check of the orbital radius)

Parameters:	other : Geometry the other Geometry to check against R : bool, optional if True also check if the orbital radii are the same (see `Atom.equal`) tol : float, optional tolerance for checking the atomic coordinates

firsto¶: The first orbital on the corresponding atom

classmethod fromASE(aseg)[source]¶

Returns geometry from an ASE object.

Parameters:	aseg : ASE `Atoms` object which contains the following routines: `get_atomic_numbers`, `get_positions`, `get_cell`. From those methods a `Geometry` object will be created.

fxyz¶: Returns geometry coordinates in fractional coordinates

iR(na=1000, iR=20, R=None)[source]¶

Return an integer number of maximum radii (self.maxR()) which holds approximately na atoms

Parameters:	na : int, optional number of atoms within the radius iR : int, optional initial `iR` value, which the sphere is estitametd from R : float, optional the value used for atomic range (defaults to `self.maxR()`)
Returns:	int : number of radius needed to contain `na` atoms. Minimally 2 will be returned.

icell¶: Returns the inherent SuperCell objects icell

insert(atom, geom)[source]¶

Inserts other atoms right before index

We insert the geom Geometry before atom. Note that this will not change the unit cell.

Parameters:	atom : int the index at which atom the other geometry is inserted geom : Geometry the other geometry to be inserted

See also

add: add geometries
append: appending geometries
prepend: prending geometries
attach: attach a geometry

is_orthogonal()¶: Return true if all cell vectors are linearly independent

isc_off¶: Returns the inherent SuperCell objects isc_off

iter()[source]¶

An iterator over all atomic indices

This iterator is the same as:

>>> for ia in range(len(self)): 
...    <do something> 

or equivalently

>>> for ia in self: 
...    <do something> 

See also

iter_species: iterate across indices and atomic species
iter_orbitals: iterate across atomic indices and orbital indices

iter_block(iR=20, R=None, atom=None, method='rand')[source]¶

Iterator for performance critical loops

NOTE: This requires that R has been set correctly as the maximum interaction range.

I.e. the loop would look like this:

>>> for ias, idxs in self.iter_block(): 
...    for ia in ias: 
...        idx_a = self.close(ia, R = R, idx = idxs) 

This iterator is intended for systems with more than 1000 atoms.

Remark that the iterator used is non-deterministic, i.e. any two iterators need not return the same atoms in any way.

Parameters:

iR : int, optional: the number of R ranges taken into account when doing the iterator
R : float, optional: enables overwriting the local R quantity. Defaults to self.maxR()
atom : array_like, optional: enables only effectively looping a subset of the full geometry
method : {‘rand’, ‘sphere’, ‘cube’}: select the method by which the block iteration is performed. Possible values are:

rand: a spherical object is constructed with a random center according to the internal atoms sphere: a spherical equispaced shape is constructed and looped cube: a cube shape is constructed and looped

Returns:

Two lists with ``[0]`` being a list of atoms to be looped and ``[1]`` being the atoms that
need searched.

iter_block_rand(iR=20, R=None, atom=None)[source]¶: Perform the random block-iteration by randomly selecting the next center of block

iter_block_shape(shape=None, iR=20, atom=None)[source]¶: Perform the grid block-iteration by looping a grid

iter_orbitals(atom=None, local=True)[source]¶

Returns an iterator over all atoms and their associated orbitals

>>> for ia, io in self.iter_orbitals(): 

with ia being the atomic index, io the associated orbital index on atom ia. Note that io will start from 0.

Parameters:	atom : int or array_like, optional only loop on the given atoms, default to all atoms local : bool, optional whether the orbital index is the global index, or the local index relative to the atom it resides on.

See also

iter: iterate over atomic indices
iter_species: iterate across indices and atomic species

iter_species(atom=None)[source]¶

Iterator over all atoms (or a subset) and species as a tuple in this geometry

>>> for ia, a, idx_specie in self.iter_species(): 
...     isinstance(ia, int) == True 
...     isinstance(a, Atom) == True 
...     isinstance(idx_specie, int) == True 

with ia being the atomic index, a the Atom object, idx_specie is the index of the specie

Parameters:	atom : int or array_like, optional only loop on the given atoms, default to all atoms

See also

iter: iterate over atomic indices
iter_orbitals: iterate across atomic indices and orbital indices

lasto¶: The last orbital on the corresponding atom

mass¶: Returns the mass of all atoms as an array

maxR(all=False)[source]¶: Maximum orbital range of the atoms

mirror(plane, atom=None)[source]¶: Mirrors the structure around the center of the atoms

move(v, atom=None, cell=False)[source]¶

Translates the geometry by v

One can translate a subset of the atoms by supplying atom.

Returns a copy of the structure translated by v.

Parameters:	v : array_like the vector to displace all atomic coordinates atom : int or array_like, optional only displace the given atomic indices, if not specified, all atoms will be displaced cell : bool, optional If True the supercell also gets enlarged by the vector

n_s¶: Returns the inherent SuperCell objects n_s

na¶: Number of atoms in geometry

na_s¶: Number of supercell atoms

names¶: The named index specifier

no¶: Number of orbitals

no_s¶: Number of supercell orbitals

nsc¶: Returns the inherent SuperCell objects nsc

o2a(io, uniq=False)[source]¶

Atomic index corresponding to the orbital indicies.

This is a particurlaly slow algorithm due to for-loops.

Note that this will preserve the super-cell offsets.

Parameters:	io: array_like List of indices to return the atoms for uniq : bool, optional If True only return the unique atoms.

o2isc(io)[source]¶

Returns the super-cell index for a specific orbital.

Returns a vector of 3 numbers with integers.

o2sc(o)[source]¶: Returns the super-cell offset for a specific orbital.

oRij(io, jo)[source]¶

Vector between orbital io and jo, orbitals can be in super-cell indices

Returns the vector between two orbitals:

\[R_{ij} = r_j - r_i\]

Parameters:	io : int or array_like orbital index of first orbital jo : int or array_like orbital indices

optimize_nsc(axis=None, R=None)[source]¶

Optimize the number of supercell connections based on self.maxR()

After this routine the number of supercells may not necessarily be the same.

This is an in-place operation.

Parameters:	axis : int or array_like, optional only optimize the specified axis (default to all) R : float, optional the maximum connection radius for each atom

orbitals¶: List of orbitals per atom

origo¶: Returns the inherent SuperCell objects origo

orij(io, jo)[source]¶

Distance between orbital io and jo, orbitals can be in super-cell indices

Returns the distance between two orbitals:

\[r_{ij} = |r_j - r_i|\]

Parameters:	io : int or array_like orbital index of first orbital jo : int or array_like orbital indices

osc2uc(orb, uniq=False)[source]¶

Returns orbitals from super-cell indices to unit-cell indices, possibly removing dublicates

Parameters:	orb : array_like or int the orbital indices converted from supercell indices to unit-cell indices uniq : bool, optional If True the returned indices are unique and sorted.

prepend(other, axis)[source]¶

Prepends structure along axis. This will automatically add the self.cell[axis,:] to all atomic coordiates in the other structure before prepending.

The basic algorithm is this:

>>> oxa = other.xyz 
>>> self.xyz = np.append(oxa, self.xyz + other.cell[axis,:][None,:]) 
>>> self.cell[axis,:] += other.cell[axis,:] 

NOTE: The cell prepended is only in the axis that is prependend, which means that the other cell directions need not conform.

Parameters:	other : Geometry or SuperCell Other geometry class which needs to be prepended If a `SuperCell` only the super cell will be extended axis : int Cell direction to which the other geometry should be prepended

See also

add: add geometries
append: appending geometries
attach: attach a geometry
insert: insert a geometry

q0¶: Total initial charge in this geometry (sum of q0 in all atoms)

rcell¶: Returns the inherent SuperCell objects rcell

static read(sile, *args, **kwargs)[source]¶

Reads geometry from the Sile using Sile.read_geometry

Parameters:	sile : `Sile` or str a `Sile` object which will be used to read the geometry if it is a string it will create a new sile using `get_sile`.

See also

write: writes a Geometry to a given Sile/file

reduce()[source]¶

Remove all atoms not currently used in the self.atom object

Notes

This is an in-place operation.

remove(atom)[source]¶

Remove atoms from the geometry.

Indices passed MUST be unique.

Negative indices are wrapped and thus works.

Parameters:	atom : array_like indices of all atoms to be removed.

See also

sub: the negative of this routine, i.e. retain a subset of atoms

reorder()[source]¶

Reorders atoms according to first occurence in the geometry

Notes

This is an in-place operation.

repeat(reps, axis)[source]¶

Create a repeated geometry

The atomic indices are NOT retained for the base structure.

The expansion of the atoms are basically performed using this algorithm:

>>> ja = 0 
>>> for ia in range(self.na): 
...     for id,r in args: 
...        for i in range(r): 
...           ja = ia + cell[id,:] * i 

This method allows to utilise Bloch’s theorem when creating Hamiltonian parameter sets for TBtrans.

For geometries with a single atom this routine returns the same as tile.

It is adviced to only use this for electrode Bloch’s theorem purposes as tile is faster.

Parameters:	reps : int number of repetitions axis : int direction of repetition, 0, 1, 2 according to the cell-direction

See also

tile: equivalent but different ordering of final structure

Examples

>>> geom = Geometry([[0, 0, 0], [0.5, 0, 0]], sc=1)
>>> g = geom.repeat(2,axis=0)
>>> print(g.xyz) 
[[0.   0.   0. ]
 [1.   0.   0. ]
 [0.5  0.   0. ]
 [1.5  0.   0. ]]
>>> g = geom.repeat(2,0).repeat(2,1)
>>> print(g.xyz) 
[[0.   0.   0. ]
 [0.   1.   0. ]
 [1.   0.   0. ]
 [1.   1.   0. ]
 [0.5  0.   0. ]
 [0.5  1.   0. ]
 [1.5  0.   0. ]
 [1.5  1.   0. ]]

reverse(atom=None)[source]¶

Returns a reversed geometry

Also enables reversing a subset of the atoms.

Parameters:	atom : int or array_like, optional only reverse the given atomic indices, if not specified, all atoms will be reversed

rij(ia, ja)[source]¶

Distance between atom ia and ja, atoms can be in super-cell indices

Returns the distance between two atoms:

\[r_{ij} = |r_j - r_i|\]

Parameters:	ia : int or array_like atomic index of first atom ja : int or array_like atomic indices

rotate(angle, v, origo=None, atom=None, only='abc+xyz', rad=False)[source]¶

Rotate geometry around vector and return a new geometry

Per default will the entire geometry be rotated, such that everything is aligned as before rotation.

However, by supplying only = 'abc|xyz' one can designate which part of the geometry that will be rotated.

Parameters:

angle : float: the angle in radians of which the geometry should be rotated
v : array_like: the normal vector to the rotated plane, i.e. v = [1,0,0] will rotate the yz plane
origo : int or array_like, optional: the origin of rotation. Anything but [0, 0, 0] is equivalent to a self.move(-origo).rotate(…).move(origo). If this is an int it corresponds to the atomic index.
atom : int or array_like, optional: only rotate the given atomic indices, if not specified, all atoms will be rotated.
only : {‘abc+xyz’, ‘xyz’, ‘abc’}: which coordinate subject should be rotated, if abc is in this string the cell will be rotated if xyz is in this string the coordinates will be rotated
rad : bool, optional: if True the angle is provided in radians (rather than degrees)

See also

Quaternion: class to rotate
rotatea: generic function for rotating around first lattice vector
rotateb: generic function for rotating around second lattice vector
rotatec: generic function for rotating around third lattice vector

rotate_miller(m, v)[source]¶

Align Miller direction along v

Rotate geometry and cell such that the Miller direction points along the Cartesian vector v.

rotatea(angle, origo=None, atom=None, only='abc+xyz', rad=False)[source]¶

Rotate around first lattice vector

See also

rotate: generic function of this, this routine calls rotate with v = self.cell[0, :]

rotateb(angle, origo=None, atom=None, only='abc+xyz', rad=False)[source]¶

Rotate around second lattice vector

See also

rotate: generic function of this, this routine calls rotate with v = self.cell[1, :]

rotatec(angle, origo=None, atom=None, only='abc+xyz', rad=False)[source]¶

Rotate around third lattice vector

See also

rotate: generic function of this, this routine calls rotate with v = self.cell[2, :]

sc2uc(atom, uniq=False)[source]¶

Returns atom from super-cell indices to unit-cell indices, possibly removing dublicates

Parameters:	atom : array_like or int the atomic indices converted from supercell indices to unit-cell indices uniq : bool, optional If True the returned indices are unique and sorted.

sc_index(*args, **kwargs)¶: Call local SuperCell object sc_index function

sc_off¶: Returns the inherent SuperCell objects sc_off

scale(scale)[source]¶

Scale coordinates and unit-cell to get a new geometry with proper scaling

Parameters:	scale : float the scale factor for the new geometry (lattice vectors, coordinates and the atomic radii are scaled).

set_nsc(*args, **kwargs)¶

Set the number of super-cells in the SuperCell object

See set_nsc for allowed parameters.

See also

SuperCell.set_nsc: the underlying called method

set_sc(sc)¶: Overwrites the local supercell

set_supercell(sc)¶: Overwrites the local supercell

sparserij(dtype=<class 'numpy.float64'>, na_iR=1000, method='rand')[source]¶

Return the sparse matrix with all distances in the matrix

The sparse matrix will only be defined for the elements which have orbitals overlapping with other atoms.

Parameters:	dtype : numpy.dtype, numpy.float64 the data-type of the sparse matrix na_iR : int, 1000 number of atoms within the sphere for speeding up the `iter_block` loop. method : str, optional see `iter_block` for details
Returns:	SparseAtom sparse matrix with all rij elements

See also

iter_block: the method for looping the atoms
distance: create a list of distances

sub(atom, cell=None)[source]¶

Create a new Geometry with a subset of this Geometry

Indices passed MUST be unique.

Negative indices are wrapped and thus works.

Parameters:	atom : array_like indices of all atoms to be removed. cell : array_like or SuperCell, optional the new associated cell of the geometry (defaults to the same cell)

See also

SuperCell.fit: update the supercell according to a reference supercell
remove: the negative of this routine, i.e. remove a subset of atoms

swap(a, b)[source]¶

Swap a set of atoms in the geometry and return a new one

This can be used to reorder elements of a geometry.

Parameters:	a : array_like the first list of atomic coordinates b : array_like the second list of atomic coordinates

swapaxes(a, b, swap='cell+xyz')[source]¶

Swap the axis for the atomic coordinates and the cell vectors

If swapaxes(0,1) it returns the 0 and 1 values swapped in the cell variable.

Parameters:	a : int axes 1, swaps with b b : int axes 2, swaps with a swap : {‘cell+xyz’, ‘cell’, ‘xyz’} decide what to swap, if ‘cell’ is in `swap` then the cell axis are swapped. if ‘xyz’ is in `swap` then the xyz (Cartesian) axis are swapped. Both may be in `swap`.

tile(reps, axis)[source]¶

Tile the geometry to create a bigger one

The atomic indices are retained for the base structure.

Parameters:	reps : int number of tiles (repetitions) axis : int direction of tiling, 0, 1, 2 according to the cell-direction

See also

repeat: equivalent but different ordering of final structure
cut: opposite method of this

Examples

>>> geom = Geometry([[0, 0, 0], [0.5, 0, 0]], sc=1.)
>>> g = geom.tile(2,axis=0)
>>> print(g.xyz) 
[[0.   0.   0. ]
 [0.5  0.   0. ]
 [1.   0.   0. ]
 [1.5  0.   0. ]]
>>> g = geom.tile(2,0).tile(2,axis=1)
>>> print(g.xyz) 
[[0.   0.   0. ]
 [0.5  0.   0. ]
 [1.   0.   0. ]
 [1.5  0.   0. ]
 [0.   1.   0. ]
 [0.5  1.   0. ]
 [1.   1.   0. ]
 [1.5  1.   0. ]]

toASE()[source]¶: Returns the geometry as an ASE Atoms object

translate(v, atom=None, cell=False)¶

Translates the geometry by v

One can translate a subset of the atoms by supplying atom.

Returns a copy of the structure translated by v.

Parameters:	v : array_like the vector to displace all atomic coordinates atom : int or array_like, optional only displace the given atomic indices, if not specified, all atoms will be displaced cell : bool, optional If True the supercell also gets enlarged by the vector

volume¶: Returns the inherent SuperCell objects vol

within(shapes, idx=None, idx_xyz=None, ret_xyz=False, ret_rij=False)[source]¶

Indices of atoms in the entire supercell within a given shape from a given coordinate

This heavily relies on the within_sc method.

Note that if a connection is made in a neighbouring super-cell then the atomic index is shifted by the super-cell index times number of atoms. This allows one to decipher super-cell atoms from unit-cell atoms.

Parameters:

shapes : Shape, list of Shape
idx : array_like, optional: List of indices for atoms that are to be considered
idx_xyz : array_like, optional: The atomic coordinates of the equivalent idx variable (idx must also be passed)
ret_xyz : bool, optional: If true this method will return the coordinates for each of the couplings.
ret_rij : bool, optional: If true this method will return the distances from the xyz_ia for each of the couplings.

within_inf(sc, periodic=None, tol=1e-05, origo=None)[source]¶

Find all atoms within a provided supercell

Note this function is rather different from close and within. Specifically this routine is returning all indices for the infinite periodic system (where self.nsc > 1 or periodic is true).

Atomic coordinates lying on the boundary of the supercell will be duplicated on the neighbouring supercell images. Thus performing geom.within_inf(geom.sc) may result in more atoms than in the structure.

Parameters:

sc : SuperCell or SuperCellChild: the supercell in which this geometry should be expanded into.
periodic : list of bool: explicitly define the periodic directions, by default the periodic directions are only where self.nsc > 1.
tol : float, optional: length tolerance for the fractional coordinates to be on a duplicate site (in Ang). This allows atoms within tol of the cell boundaries to be taken as inside the cell.
origo : (3, ) of float: origo that is the basis for comparison

Returns:

ia : numpy.ndarray: unit-cell atomic indices which are inside the sc cell
xyz : numpy.ndarray: atomic coordinates for the ia atoms (including supercell offsets)
isc : numpy.ndarray: integer supercell offsets for ia atoms

Notes

The name of this function may change. Currently it should only be used internally in sisl.

within_sc(shapes, isc=None, idx=None, idx_xyz=None, ret_xyz=False, ret_rij=False)[source]¶

Indices of atoms in a given supercell within a given shape from a given coordinate

This returns a set of atomic indices which are within a sphere of radius R.

If R is a tuple/list/array it will return the indices: in the ranges:

>>> ( x <= R[0] , R[0] < x <= R[1], R[1] < x <= R[2] ) 

Parameters:

shapes : Shape or list of Shape

A list of increasing shapes that define the extend of the geometric volume that is searched. It is vital that:

shapes[0] in shapes[1] in shapes[2] ...

isc : array_like, optional

The super-cell which the coordinates are checked in. Defaults to [0, 0, 0]

idx : array_like, optional

List of atoms that will be considered. This can be used to only take out a certain atoms.

idx_xyz : array_like, optional

The atomic coordinates of the equivalent idx variable (idx must also be passed)

ret_xyz : bool, optional

If True this method will return the coordinates for each of the couplings.

ret_rij : bool, optional

If True this method will return the distance for each of the couplings.

write(sile, *args, **kwargs)[source]¶

Writes geometry to the Sile using sile.write_geometry

Parameters:	sile : Sile or str a `Sile` object which will be used to write the geometry if it is a string it will create a new sile using `get_sile` args, *kwargs: Any other args will be passed directly to the underlying routine

See also

read: reads a Geometry from a given Sile/file