easyunfold.unfold

`easyunfold.unfold`#

The main module for unfolding workflow and algorithm

Module Contents#

Classes#

`UnfoldKSet`	High-level interface for unfolding and serialization.
`Unfold`	Low level interface for performing unfolding related calculations. obtain the effective band structure (EBS).

Functions#

`get_symmetry_dataset`	Get the symmetry dataset using spglib
`find_K_from_k`	Get the K vector of the supercell onto which the k vector of the primitive cell folds. The unfolding vector G, which satisfy the following equation, is also returned.
`rotate_kpt`	Apply rotation to a kpoint based on the rotations of the crystals (in the real space)
`expand_K_by_symmetry`	Expand the sampling of the PC kpoints due to symmetry breaking of the supercell cell.
`LorentzSmearing`	Simulate the Delta function by a Lorentzian shape function $$ \Delta(x) = \lim_{\sigma\to 0} Lorentzian $$
`GaussianSmearing`	Simulate the Delta function by a Lorentzian shape function $$ \Delta(x) = \lim_{\sigma\to 0} Gaussian $$
`make_kpath`	Return a list of kpoints defining the path between the given kpoints.
`clean_latex_string`	Clean up latex labels and convert if necessary
`spectral_function_from_weight_sets`	Generate the spectral function
`spectral_weight_multiple_source`	Calculate the spectral weight for a list of kpoints in the primitive BZ from a list of wave function files.
`concatenate_scf_kpoints`	Concatenate SCF kpoints (from IBZKPT) with zero-weighted kpoints
`create_white_colormap`	Create colormap from white to certain colour.
`create_white_colormap_from_existing`	Create a white-based color map from an existing one.
`parse_atoms_idx`	Expanding syntax like `1-2` (inclusive)
`process_projection_options`	Process commandline-style specifications for project
`read_poscar_contcar_if_present`	Return an ase Atoms() object of the POSCAR or CONTCAR file if present in the current directory.
`parse_atoms`	Parse the specified atoms (and orbitals if set) from a comma-separated string (e.g. “Na,Bi”) into a list of strings (e.g. [“Na”, “Bi”]), as well as a list of the corresponding atom indices in the structure and the parse orbital projections.

API#

easyunfold.unfold.get_symmetry_dataset(atoms: ase.Atoms, symprec: float = 1e-05)#: Get the symmetry dataset using spglib

easyunfold.unfold.find_K_from_k(k: numpy.ndarray, M: numpy.ndarray)#

Get the K vector of the supercell onto which the k vector of the primitive cell folds. The unfolding vector G, which satisfy the following equation, is also returned.

\[ \vec{k} = \vec{K} + \vec{G} \]

where G is a reciprocal space vector of supercell

easyunfold.unfold.rotate_kpt(k: numpy.ndarray, opt: numpy.ndarray)#

Apply rotation to a kpoint based on the rotations of the crystals (in the real space)

NOTE: The rotation matrix should be the one that act on fractional coordinates, e.g. from spglib.

easyunfold.unfold.expand_K_by_symmetry(kpt: Union[list, numpy.ndarray], opts_pc: numpy.ndarray, opts_sc: numpy.ndarray, time_reversal: bool = True)#

Expand the sampling of the PC kpoints due to symmetry breaking of the supercell cell.

Returns:: Expanded kpoints and corresponding weights for each primitive cell kpoint.

class easyunfold.unfold.UnfoldKSet(M: numpy.ndarray, kpts_pc: list, pc_latt: numpy.ndarray, pc_opts: numpy.ndarray, sc_opts: numpy.ndarray, time_reversal: bool = True, expand: bool = True, metadata: Union[None, dict] = None, expansion_results: Union[None, dict] = None, calculated_quantities: Union[None, dict] = None, kpoint_labels: Union[None, list] = None, dft_code='vasp')#

Bases: monty.json.MSONable

High-level interface for unfolding and serialization.

Initialization

Instantiate an UnfoldKSet object.

Parameters:

M – The supercell transformation matrix
kpts_pc – A list of kpoints in the PC
pc_latt – A 3x3 matrix of row lattice vectors of the primitive cell
pc_opts – Symmetry operations of the primitive cell
sc_opts – Symmetry operations of the supercell
time_reversal – Whether to assume time-reversal symmetry or not
expand – Whether to expand the kpoint to take account of broken symmetry or not
expansion_results – Using existing results of symmetry expansion
calculated_quantities – Existing calculated quantities
kpoint_labels – Labels of the kpoints as passed in pc_latt as a list of tuples (<idx>, <label>)
dft_code – Name of the DFT code to be used.

_VERSION#: ‘0.1.0’

check_version()#: Check the version of the program

property is_calculated: bool#: Show the status of the work

property has_averaged_spectral_weights: bool#: Return True if the spectral weights stored is averaged

classmethod from_atoms(M: numpy.ndarray, kpts_pc: list, pc: ase.Atoms, sc: ase.Atoms, time_reversal: bool = True, expand=True, symprec: float = 1e-05, dft_code='vasp')#

Initialise from primitive cell and supercell atoms

Parameters:

M – The supercell transformation matrix
kpts_pc – A list of kpoints in the PC
pc – Primitive cell structure
sc – Supercell structure
time_reversal – Whether to assume time-reversal symmetry or not
expand – Whether to expand the kpoint to take account of broken symmetry or not
symprec – Symmetry detection precision

classmethod from_file(fname: str)#: Load from a file

expand_pc_kpoints() → None#: Compute the pc kpoints to be unfolded into

__repr__() → str#

property nsymm_orig: int#: Number of symmetry operation in the original cell

property nsymm_expand: int#: Number of symmetry operation in the original cell

property nkpts_orig: int#: Total number of unexpanded kpoints

property nkpts_expand: int#: Total number of expanded kpoints

generate_sc_kpoints() → None#: Generate the supercell kpoints to be calculated. Results are stored into self.expansion_results.

write_sc_kpoints(file: str, nk_per_split: Union[None, list] = None, scf_kpoints_and_weights: Union[None, list] = None, **kwargs)#

Write the supercell kpoints to a file.

Parameters:

file – Name of the file
nk_per_split – Number of kpoints per split along the path
scf_kpoints_and_weights – SCF kpoint and their weights needed for split-path calculations

write_pc_kpoints(file: str, expanded: bool = False, **kwargs)#: Write the primitive cell kpoints

_read_weights(wavefunction: Union[str, List[str]], gamma: bool, ncl: bool, gamma_half: str)#

Read the weights from the wave function files for all kpoints

Returns the averaged weights and the original weights per set of kpoints

load_procars(procars: Union[str, List[str]])#: Read in PROCAR for band-based projection

_construct_procar_kmap() → list#: Construct mapping from the set of kpoints to that in the PROCAR

property procar: Union[None, easyunfold.procar.Procar]#: Loaded PROCARS

property procar_kmaps#: Loaded PROCAR kpoint mapping

_get_spectral_weights(wavefunction, npoints=2000, sigma=0.01, emin=None, emax=None, gamma=False, ncl=False, gamma_half='x', also_spectral_function=False, atoms_idx=None, orbitals=None, symm_average=True)#

Fetch spectral weights from a wavecar and compute spectral function is requested

Args:

atomic_projects (tuple): A tuple of atoms and orbitals whose projected weights should be used.

get_band_weight_sets(atoms_idx: List[int], orbitals: List[Union[List[str], str]], procars: Union[None, List[str], str] = None) → list#

Get weights array sets for bands

Construct the weights of each band in same format of the kpoint set. Each item is a numpy array of (nspins, nbands), containing the summed weights over the passed atom indices and orbitals.

Parameters:

atoms_idx – Indices of the atoms to be selected
orbitals – Orbitals to be selected for each atom
procars – Names of the PROCAR files to be loaded

Returns:

A list of weights for each band at each expanded kpoint

get_spectral_function(wavefunction: Union[None, List[str]] = None, npoints: int = 2000, sigma: float = 0.1, gamma: bool = False, ncl: bool = False, gamma_half: str = 'x', symm_average: bool = True, atoms_idx: Union[None, List[int]] = None, orbitals: Union[None, str, List[str]] = None)#

Compute and return the spectral function

Parameters:

wavecar – The wavefunction files to be used
npoints – Number of points for the energy axis
sigma – Smearing width for the Gaussian smearing
gamma – Need to be set to True for Gamma-only calculation
ncl – Need to be set to True for non-collinear magnetism calculation
gamma_half – Flag used for reading WAVECAR
symm_average – Whether to perform symmetry averaging
atoms_idx – Indices for the atoms for projection
orbitals – Orbitals of the atoms for projection

Returns:

A tuple of the energies and the spectral functioin.

get_spectral_weights(wavefunction=None, gamma: bool = False, ncl: bool = False, gamma_half: str = 'x', symm_average: bool = True)#

Return the spectral weights calculated

Parameters:

wavefunction – The wavefunction file(s) for calculation. Not need if the weights has been calculated.
gamma – Whether the wavefunction files are from $\Gamma$-only calculation.

Returns:

An array storing the spectral weights.

as_dict() → dict#: Convert the object into a dictionary representation

get_kpoint_distances()#: Distances between the kpoints along the path in the reciprocal space. This does not take account of the breaking of the path.

Note

The reciprocal lattice vectors includes the $2\pi$ factor, e.g. np.linalg.inv(L).T * 2 * np.pi.

easyunfold.unfold.LorentzSmearing(x, x0, sigma=0.02)#: Simulate the Delta function by a Lorentzian shape function $$ \Delta(x) = \lim_{\sigma\to 0} Lorentzian $$

easyunfold.unfold.GaussianSmearing(x, x0, sigma=0.02)#: Simulate the Delta function by a Lorentzian shape function $$ \Delta(x) = \lim_{\sigma\to 0} Gaussian $$

easyunfold.unfold.make_kpath(kbound: List[float], nseg=40)#: Return a list of kpoints defining the path between the given kpoints.

easyunfold.unfold.clean_latex_string(label: str)#

Clean up latex labels and convert if necessary

Returns:: Cleaned tag string

easyunfold.unfold.spectral_function_from_weight_sets(spectral_weight_sets: numpy.ndarray, kweight_sets: list, nedos: int = 4000, sigma: float = 0.02, emin=None, emax=None, band_weight_sets=None)#

Generate the spectral function

\[ A(k_i, E) = \sum_m P_{Km}(k_i)\Delta(E - Em) \]

Where the \Delta function can be approximated by Lorentzian or Gaussian function.

Parameters:: band_weight_sets – Additional weighting for each band, used for generating projection onto atomic orbitals.

class easyunfold.unfold.Unfold(M=None, fname: str = 'WAVECAR', gamma: bool = False, lsorbit: bool = False, gamma_half: str = 'x', verbose=False, time_reversal=False, dft_code='vasp')#

Low level interface for performing unfolding related calculations. obtain the effective band structure (EBS).

Reference

“Extracting E versus k effective band structure from supercell calculations on alloys and impurities” Phys. Rev. B 85, 085201 (2012)

Initialization

Initialization.

M is the transformation matrix between supercell and primitive cell:

M = np.dot(A, np.linalg.inv(a))

In real space, the basis vectors of Supercell (A) and those of the primitive cell (a) satisfy:

A = np.dot(M, a);      a = np.dot(np.linalg.inv(M), A)

Whereas in reciprocal space

b = np.dot(M.T, B);    B = np.dot(np.linalg.inv(M).T, b)

get_vbm_cbm(thresh: float = 1e-08) → Tuple[float, float]#: Locate the VBM from the wave function data

get_ovlap_G(ikpt: int = 1, epsilon: float = 1e-05) → Tuple[numpy.ndarray, numpy.ndarray]#: Get subset of the reciprocal space vectors of the supercell, specifically the ones that match the reciprocal space vectors of the primitive cell.

find_K_index(K0: numpy.ndarray) → int#: Find the (one-based) index of a point K0.

spectral_weight_k(k0, whichspin=1)#

Spectral weight for a given $k$:

\[ P_{Km}(k) = \sum_n |<Km | kn>|^2 \]

which is equivalent to $$ P_{Km}(k) = \sum_{G} |C_{Km}(G + k - K)|^2 $$

where $G$ is a subset of the reciprocal space vectors of the supercell.

spectral_weight(kpoints: List)#: Calculate the spectral weight for a list of kpoints in the primitive BZ.

spectral_function(nedos: int = 4000, sigma: float = 0.02)#

Generate the spectral function

\[ A(k_i, E) = \sum_m P_{Km}(k_i)\Delta(E - Em) \]

Where the $\Delta$ function can be approximated by Lorentzian or Gaussian function.

easyunfold.unfold.spectral_weight_multiple_source(kpoints: list, unfold_objs: List[easyunfold.unfold.Unfold], transform_matrix: numpy.ndarray)#: Calculate the spectral weight for a list of kpoints in the primitive BZ from a list of wave function files.

easyunfold.unfold.concatenate_scf_kpoints(scf_kpts: list, scf_weights: list, kpoints: list)#: Concatenate SCF kpoints (from IBZKPT) with zero-weighted kpoints

easyunfold.unfold.create_white_colormap(color: Union[str, tuple, list]) → matplotlib.colors.ListedColormap#

Create colormap from white to certain colour.

Args: color (str, tuple, list): HEX color string or tuple/list of RGB color.

easyunfold.unfold.create_white_colormap_from_existing(name: str) → matplotlib.colors.ListedColormap#: Create a white-based color map from an existing one.

easyunfold.unfold.parse_atoms_idx(atoms_idx: str) → List[int]#

Expanding syntax like 1-2 (inclusive)

For example, 1,2,3,4-6 will be expanded as 1,2,3,4,5,6.

Parameters:: atoms_idx – A string encode atom indices
Returns:: A list of atom indices

easyunfold.unfold.process_projection_options(atoms_idx: str, orbitals: str) → Tuple[list, list]#

Process commandline-style specifications for project

Parameters:

atoms_idx – A comma- or hyphen-separated string of atom projections
orbitals – A comma-separated string of orbital projections

Returns:

A tuple of atom indices and the orbitals selected for projection.

easyunfold.unfold.read_poscar_contcar_if_present(poscar: str = 'POSCAR')#

Return an ase Atoms() object of the POSCAR or CONTCAR file if present in the current directory.

Returns:: ASE Atoms() object

easyunfold.unfold.parse_atoms(atoms_to_project: str, orbitals: str, poscar: str)#

Parse the specified atoms (and orbitals if set) from a comma-separated string (e.g. “Na,Bi”) into a list of strings (e.g. [“Na”, “Bi”]), as well as a list of the corresponding atom indices in the structure and the parse orbital projections.

Parameters:

atoms_to_project – A comma-separted string of atom symbols to project
orbitals – A “|”-separated string of orbital projections
poscar – The POSCAR file to read atom indices from

Returns:

A tuple of lists of atoms, atom indices and the orbitals selected for projection.

easyunfold.unfold

Contents

easyunfold.unfold#

Module Contents#

Classes#

Functions#

API#

`easyunfold.unfold`#