Source code for matador.utils.cell_utils

# coding: utf-8
# Distributed under the terms of the MIT License.

""" This submodule implements some useful functions for real/reciprocal
cell manipulation, symmetry checking and sampling (e.g. grids and paths.)

"""

import numpy as np
from periodictable import elements
EPS = 1e-12


[docs]def abc2cart(lattice_abc): """ Converts lattice parameters into Cartesian lattice vectors. Parameters: lattice_abc (list): [[a, b, c], [alpha, beta, gamma]] Returns: list: Cartesian lattice vectors. """ assert len(lattice_abc) == 2 assert len(lattice_abc[0]) == 3 assert len(lattice_abc[1]) == 3 a = lattice_abc[0][0] b = lattice_abc[0][1] c = lattice_abc[0][2] deg2rad = np.pi/180 alpha = lattice_abc[1][0] * deg2rad beta = lattice_abc[1][1] * deg2rad gamma = lattice_abc[1][2] * deg2rad lattice_cart = [] lattice_cart.append([a, 0.0, 0.0]) # vec(b) = (b np.cos(gamma), b np.sin(gamma), 0) bx = b*np.cos(gamma) by = b*np.sin(gamma) tol = 1e-12 if abs(bx) < tol: bx = 0.0 if abs(by) < tol: by = 0.0 cx = c*np.cos(beta) if abs(cx) < tol: cx = 0.0 cy = c*(np.cos(alpha)-np.cos(beta)*np.cos(gamma))/np.sin(gamma) if abs(cy) < tol: cy = 0.0 cz = np.sqrt(c**2 - cx**2 - cy**2) lattice_cart.append([bx, by, 0.0]) lattice_cart.append([cx, cy, cz]) return lattice_cart
[docs]def cart2abcstar(lattice_cart): """ Convert lattice_cart =[[a1,a2,a3],[b1,b2,b3],[c1,c2,c3]] to the reciprocal of the lattice vectors, NOT the reciprocal lattice vectors. Parameters: lattice_cart (list): Cartesian lattice vectors. Returns: list: lattice parameters [[a,b,c],[alpha,beta,gamma]] """ return np.asarray(real2recip(lattice_cart)) / (2*np.pi)
[docs]def cart2volume(lattice_cart): """ Convert lattice_cart to cell volume. Parameters: lattice_cart (list): Cartesian lattice vectors. Returns: float: cell volume in Angstrom^3. """ lattice_cart = np.asarray(lattice_cart) vol = np.abs(np.dot(np.cross(lattice_cart[0], lattice_cart[1]), lattice_cart[2])) return vol
[docs]def cart2abc(lattice_cart): """ Convert Cartesian lattice vectors to lattice parametres. Parameters: lattice_cart (list): Cartesian lattice vectors. Returns: list: lattice parameters [[a,b,c],[alpha,beta,gamma]]. """ vecs = lattice_cart lattice_abc = [] a, b, c = (np.sqrt(sum([val**2 for val in vec])) for vec in vecs) lattice_abc.append([a, b, c]) # np.cos(alpha) = b.c /|b * c| radians2deg = 180.0/np.pi cos_alpha = sum([val_b*val_c for (val_c, val_b) in zip(vecs[2], vecs[1])]) / (b*c) cos_beta = sum([val_c*val_a for (val_c, val_a) in zip(vecs[2], vecs[0])]) / (c*a) cos_gamma = sum([val_a*val_b for (val_a, val_b) in zip(vecs[0], vecs[1])]) / (a*b) alpha = radians2deg * np.arccos(cos_alpha) beta = radians2deg * np.arccos(cos_beta) gamma = radians2deg * np.arccos(cos_gamma) lattice_abc.append([alpha, beta, gamma]) return lattice_abc
[docs]def frac2cart(lattice_cart, positions_frac): """ Convert positions_frac block into positions_abs. Parameters: lattice_cart (list): Cartesian lattice vectors. positions_frac (list): list of fractional position vectors. Returns: list: list of absolute position vectors. """ _positions_frac = np.asarray(positions_frac) reshaped = False if len(np.shape(_positions_frac)) == 1: reshaped = True _positions_frac = _positions_frac.reshape((1, 3)) _lattice_cart = np.asarray(lattice_cart) positions_abs = switch_coords(_lattice_cart, _positions_frac) if reshaped: positions_abs = positions_abs.reshape(-1) return positions_abs.tolist()
[docs]def wrap_frac_coords(positions, remove=False): """ Wrap the given fractional coordinates back into the cell. Parameters: positions (list): list of fractional position vectors, or a single position. Keyword arguments: remove (bool): if True, removes points exterior to the cell. Returns: list: list of wrapped fractional position vectors. """ from copy import deepcopy wrapped = deepcopy(positions) single = False if len(wrapped) == 3 and isinstance(wrapped[0], float): wrapped = [wrapped] single = True if remove: to_remove = len(wrapped)*[False] for ind, pos in enumerate(wrapped): for k in range(3): if pos[k] >= 1 or pos[k] < 0: if remove: to_remove[ind] = True break else: wrapped[ind][k] %= 1 if remove: wrapped = [wrapped[ind] for ind, res in enumerate(to_remove) if not res] if single: return wrapped[0] return wrapped
[docs]def switch_coords(lattice, pos, norm=None): """ Act on coordinates with the relevant lattice vectors to switch from fractional to absolute coordinates. Parameters: lattice (np.ndarray(3, 3)): either lattice_cart or reciprocal lattice_cart pos (np.ndarray(3, :)): input positions to convert Keyword arguments: norm (float): divide final coordinates by normalisation factor, e.g. 2*np.pi when lattice is recip and positions are cartesian. Returns: np.ndarray(3, :): converted positions """ new_pos = np.zeros_like(pos) for ni, _ in enumerate(pos): for j in range(3): new_pos[ni] += lattice[j] * pos[ni][j] if norm is not None: new_pos /= norm return new_pos
[docs]def cart2frac(lattice_cart, positions_abs): """ Convert positions_abs block into positions_frac (and equivalent in reciprocal space). Parameters: lattice_cart (list): Cartesian lattice vectors. positions_abs (list): list of absolute position vectors. Returns: list: list of fractional position vectors with the same shape as the input list. """ _positions_abs = np.asarray(positions_abs, dtype=np.float64) reshaped = False if len(np.shape(_positions_abs)) == 1: reshaped = True _positions_abs = _positions_abs.reshape((1, 3)) recip_lat = np.asarray(real2recip(lattice_cart)) recip_lat = recip_lat.T positions_frac = switch_coords(recip_lat, _positions_abs, norm=2*np.pi) if reshaped: positions_frac = positions_frac.reshape(-1) return positions_frac.tolist()
[docs]def real2recip(real_lat): """ Convert the real lattice in Cartesian basis to the reciprocal space lattice. Parameters: real_lat (list): Cartesian lattice vectors. Returns: list: Cartesian lattice vectors of reciprocal lattice. """ real_lat = np.asarray(real_lat) recip_lat = np.zeros((3, 3)) volume = np.dot(real_lat[0], np.cross(real_lat[1], real_lat[2])) recip_lat[0] = (2*np.pi)*np.cross(real_lat[1], real_lat[2]) recip_lat[1] = (2*np.pi)*np.cross(real_lat[2], real_lat[0]) recip_lat[2] = (2*np.pi)*np.cross(real_lat[0], real_lat[1]) recip_lat /= volume return recip_lat.tolist()
[docs]def calc_mp_grid(lattice_cart, spacing): """ Return correct Monkhorst-Pack grid based on lattice vectors and desired spacing. Parameters: lattice_cart (list): Cartesian lattice vectors. spacing (float): desired maximum grid spacing. Returns: list: list of 3 integers defining the MP grid. """ recip_lat = real2recip(lattice_cart) recip_len = np.zeros((3)) recip_len = np.sqrt(np.sum(np.power(recip_lat, 2), axis=1)) mp_grid = recip_len / (2 * np.pi * spacing) return [int(np.ceil(elem)) for elem in mp_grid]
[docs]def shift_to_include_gamma(mp_grid): """ Calculate the shift required to include $\\Gamma$. in the Monkhorst-Pack grid. Parameters: mp_grid (:obj:`list` of :obj:`int`): number of grid points in each reciprocal space direction. Returns: :obj:`list` of :obj:`float`: shift required to include $\\Gamma$. """ shift = [0, 0, 0] for ind, val in enumerate(mp_grid): if val % 2 == 0: shift[ind] = 1.0/(val*2) return shift
[docs]def shift_to_exclude_gamma(mp_grid): """ Calculate the shift required to exclude $\\Gamma$. in the Monkhorst-Pack grid. Returns the "minimal shift", i.e. only one direction will be shifted. Parameters: mp_grid (:obj:`list` of :obj:`int`): number of grid points in each reciprocal space direction. Returns: :obj:`list` of :obj:`float`: shift required to exclude $\\Gamma$. """ shift = [0, 0, 0] if all([val % 2 == 1 for val in mp_grid]): for ind, val in enumerate(mp_grid): if val % 2 == 1: shift[ind] = 1.0/(val*2) break return shift
[docs]def get_best_mp_offset_for_cell(doc): """ Calculates the "best" kpoint_mp_offset to use for the passed cell. If the crystal has a hexagonal space group, then the offset returned will shift the grid to include $\\Gamma$ point, and vice versa for non-hexagonal cells. Parameters: doc (dict): matador document to consider, containing structural information and a "kpoints_mp_spacing" key. Returns: :obj:`list` of :obj:`float`: the desired kpoint_mp_offset. """ gamma = False if '6' in get_spacegroup_spg(doc, symprec=1e-5): gamma = True print(doc) if 'lattice_cart' not in doc or 'kpoints_mp_spacing' not in doc: raise RuntimeError('Unable to calculate offset without lattice or spacing') mp_grid = calc_mp_grid(doc['lattice_cart'], doc['kpoints_mp_spacing']) if gamma: return shift_to_include_gamma(mp_grid) return shift_to_exclude_gamma(mp_grid)
[docs]def calc_mp_spacing(real_lat, mp_grid, prec=3): """ Convert real lattice in Cartesian basis and the kpoint_mp_grid into a grid spacing. Parameters: real_lat (list): Cartesian lattice vectors. mp_grid (:obj:`list` of :obj:`int`): 3 integers defining the MP grid. Keyword arguments: prec (int): desired decimal precision of output. Returns: float: mp_spacing rounded to `prec`. """ recip_lat = real2recip(real_lat) recip_len = np.zeros((3)) recip_len = np.sqrt(np.sum(np.power(recip_lat, 2), axis=1)) spacing = recip_len / (2*np.pi*np.asarray(mp_grid)) max_spacing = np.max(spacing) exponent = round(np.log10(max_spacing) - prec) return round(max_spacing + 0.5*10**exponent, prec)
[docs]def get_seekpath_kpoint_path( doc, standardize=True, explicit=True, spacing=0.01, threshold=1e-7, debug=False, symmetry_tol=None ): """ Return the conventional kpoint path of the relevant crystal system according to the definitions by "HKPOT" in Comp. Mat. Sci. 128, 2017: http://dx.doi.org/10.1016/j.commatsci.2016.10.015 Parameters: doc (dict/tuple): matador doc or spglib tuple to find kpoint path for. Keyword arguments: spacing (float): desired kpoint spacing threshold (float): internal seekpath threshold symmetry_tol (float): spglib symmetry tolerance Returns: dict: standardized version of input doc list: list of kpoint positions dict: full dictionary of all seekpath results """ try: from seekpath import get_explicit_k_path, get_path except ImportError: raise ImportError("SeeK-Path dependency missing, please install it with `pip install seekpath`.") if symmetry_tol is None: symmetry_tol = 1e-5 if isinstance(doc, tuple): spg_structure = doc else: if standardize: spg_structure = doc2spg(standardize_doc_cell(doc, symprec=symmetry_tol)) else: spg_structure = doc2spg(doc) if explicit: seekpath_results = get_explicit_k_path(spg_structure, reference_distance=spacing, with_time_reversal=True, symprec=symmetry_tol, threshold=threshold) kpt_path = seekpath_results['explicit_kpoints_rel'] else: seekpath_results = get_path(spg_structure) kpt_path = [] primitive_doc = dict() primitive_doc['lattice_cart'] = seekpath_results['primitive_lattice'] primitive_doc['positions_frac'] = seekpath_results['primitive_positions'] primitive_doc['atom_types'] = [str(elements[i]) for i in seekpath_results['primitive_types']] primitive_doc['num_atoms'] = len(primitive_doc['atom_types']) primitive_doc['lattice_abc'] = cart2abc(primitive_doc['lattice_cart']) primitive_doc['cell_volume'] = cart2volume(primitive_doc['lattice_cart']) if debug: print('Found lattice type {}'.format(seekpath_results['bravais_lattice_extended'])) print('Old lattice:\n', np.asarray(doc['lattice_cart'])) print('Contained {} atoms'.format(doc['num_atoms'])) print('New lattice:\n', np.asarray(primitive_doc['lattice_cart'])) print('Contains {} atoms'.format(primitive_doc['num_atoms'])) print('k-point path contains {} points.'.format(len(kpt_path))) if 'site_occupancy' in doc: if min(doc['site_occupancy']) < 1 - EPS: print('Ignoring any site occupancy found in this cell.') primitive_doc['site_occupancy'] = [1 for atom in primitive_doc['atom_types']] return primitive_doc, kpt_path, seekpath_results
[docs]def doc2spg(doc, check_occ=True): """ Return an spglib input tuple from a matador doc. Parameters: doc (dict or :class:`Crystal`): matador document or Crystal object. Keyword arguments: check_occ (bool): check for partial occupancy and raise an error if present. Returns: tuple: spglib-style tuple of lattice, positions and types. """ from matador.utils.chem_utils import get_atomic_number try: if 'lattice_cart' not in doc: doc['lattice_cart'] = abc2cart(doc['lattice_abc']) except KeyError: raise RuntimeError("doc2spg failed: unable to find lattice in document.") required_keys = ("lattice_cart", "positions_frac", "atom_types") if all(key in doc for key in required_keys): if 'lattice_cart' not in doc: doc['lattice_cart'] = abc2cart(doc['lattice_abc']) cell = (doc['lattice_cart'], doc['positions_frac'], [get_atomic_number(elem) for elem in doc['atom_types']]) if check_occ and np.min(doc.get('site_occupancy', [1.0])) < 1.0: raise RuntimeError("spglib does not support partial occupancy.") return cell else: raise RuntimeError(f"Unable to use doc2spg, one of {required_keys} was missing.")
[docs]def get_space_group_label_latex(label): """ Return the LaTeX format of the passed space group label. Takes any string, leaves the first character upright, italicses the rest, handles subscripts and bars over numbers. Parameters: label (str): a given space group in "standard" plain text format, e.g. P-63m. Returns: str: the best attempt to convert the label to LaTeX. """ latex_label = '$' if not isinstance(label, str): raise RuntimeError("Space group label must be a string, not {}".format(label)) skip = False for ind, char in enumerate(label): if skip: skip = False continue if char == '-': # add the next char inside the bar latex_label += "\\bar{" + label[ind+1] + "}" skip = True else: latex_label += char latex_label += "$" return latex_label
[docs]def standardize_doc_cell(doc, primitive=True, symprec=1e-2): """ Return standardized cell data from matador doc. Parameters: doc (dict or :class:`Crystal`): matador document or Crystal object. Keyword arguments: primitive (bool): whether to reduce cell to primitive. symprec (float): spglib symmetry tolerance. Returns: dict: matador document containing standardized cell. """ import spglib as spg from matador.crystal import Crystal from matador.utils.chem_utils import get_atomic_symbol from copy import deepcopy spg_cell = doc2spg(doc) spg_standardized = spg.standardize_cell(spg_cell, to_primitive=primitive, symprec=symprec) if not isinstance(doc, Crystal): std_doc = deepcopy(doc) else: std_doc = deepcopy(doc._data) std_doc['lattice_cart'] = [list(vec) for vec in spg_standardized[0]] std_doc['lattice_abc'] = cart2abc(std_doc['lattice_cart']) std_doc['positions_frac'] = [list(atom) for atom in spg_standardized[1]] std_doc['atom_types'] = [get_atomic_symbol(atom) for atom in spg_standardized[2]] std_doc['site_occupancy'] = len(std_doc['positions_frac']) * [1] std_doc['cell_volume'] = cart2volume(std_doc['lattice_cart']) std_doc['space_group'] = get_spacegroup_spg(std_doc, symprec=symprec) # if the original document was a crystal, return a new one if isinstance(doc, Crystal): std_doc = Crystal(std_doc) return std_doc
[docs]def get_spacegroup_spg(doc, symprec=0.01, check_occ=True): """ Return spglib spacegroup for a cell. Parameters: doc (dict or :class:`Crystal`): matador document or Crystal object. Keyword arguments: symprec (float): spglib symmetry tolerance. Returns: str: spacegroup symbol of structure. """ import spglib as spg spg_cell = doc2spg(doc, check_occ=check_occ) space_group = spg.get_spacegroup(spg_cell, symprec=symprec) if space_group is None: raise RuntimeError('Spglib was unable to calculate space group.') return space_group.split(' ')[0]
[docs]def add_noise(doc, amplitude=0.1): """ Add random noise to the positions of structure contained in doc. Useful for force convergence tests. Parameters: doc (dict): dictionary containing matador structure. Keyword arguments: amplitude (float): maximum amplitude of noise vector. Raises: KeyError if (`lattice_cart` and `positions_frac`) or `positions_abs` are missing. Returns: dict: the randomised structure. """ poscart = np.asarray(doc.get('positions_abs') or frac2cart(doc['lattice_cart'], doc['positions_frac'])) for atom in poscart: noise_vector = np.random.rand(3) noise_vector /= np.sqrt(np.sum(noise_vector**2)) noise_vector *= amplitude*(np.random.rand()) atom += noise_vector doc['positions_abs'] = poscart.tolist() doc['positions_frac'] = cart2frac(doc['lattice_cart'], doc['positions_abs']) return doc
[docs]def calc_pairwise_distances_pbc(poscart, images, lattice, rmax, poscart_b=None, compress=False, debug=False, filter_zero=False, per_image=False): """ Calculate PBC distances with SciPy's cdist, given the image cell vectors. Parameters: poscart (numpy.ndarray): list or array of absolute atomic coordinates. images: iterable of lattice vector multiples (e.g. [2, -1, 3]) required to obtain the translation to desired image cells. lattice (:obj:`list` if :obj:`list`): list of lattice vectors of the real cell. rmax (float): maximum value after which to mask the array. Keyword arguments: poscart_b (numpy.ndarray): absolute positions of another type of atom, where only A-B distances will be calculated. debug (bool): print timing data and how many distances were masked. compress (bool): whether or not to compressed the output array, useful when e.g. creating PDFs but not when atom ID is important. filter_zero (bool): whether or not to filter out the "self-interaction" zero distances. per_image (bool): return a list of distances per image, as opposed to one large flat. This preserves atom IDs for use elsewhere. Returns: distances (numpy.ndarray): pairwise 2-D d_ij masked array with values or stripped 1-D array containing just the distances, or a list of numpy arrays if per_image is True. """ from scipy.spatial.distance import cdist import time if debug: start = time.time() _lattice = np.asarray(lattice) _poscart = np.asarray(poscart) image_distances = [] if poscart_b is None: _poscart_b = _poscart else: _poscart_b = np.asarray(poscart_b) num_pairs = len(_poscart) * len(_poscart_b) if per_image: for image_ind, prod in enumerate(images): distances = cdist(_poscart, _poscart_b + prod @ _lattice) distances = np.ma.masked_where(distances > rmax, distances, copy=False) image_distances.append(distances) distances = image_distances else: array_size = (len(_poscart) * len(images) * len(_poscart_b)) distances = np.empty(array_size) for image_ind, prod in enumerate(images): distances[image_ind*num_pairs:(image_ind+1)*num_pairs] = cdist(_poscart, _poscart_b + prod @ _lattice).flatten() distances = np.ma.masked_where(distances > rmax, distances, copy=False) if filter_zero: distances = np.ma.masked_where(distances < EPS, distances, copy=False) if debug: print('Calculated: {}, Used: {}, Ignored: {}'.format(len(distances), np.ma.count(distances), np.ma.count_masked(distances))) if compress: distances = distances.compressed() if debug: end = time.time() print('Calculated distances in {} s'.format(end - start)) return distances
[docs]def create_simple_supercell(doc, extension, standardize=False, symmetric=False): """ Return a document with new supercell, given extension vector. Parameters: doc (dict): matador doc to construct cell from. extension (:obj:`tuple` of :obj:`int`): multiplicity of each lattice vector, e.g. (2,2,1). Keyword arguments: standardize (bool): whether or not to use spglib to standardize the cell first. symmetric (bool): whether or not centre the new cell on the origin. Returns: supercell_doc (dict): matador document containing supercell. """ from itertools import product from copy import deepcopy if not all([elem >= 1 for elem in extension]) or extension == (1, 1, 1): raise RuntimeError('Bad/null supercell {} requested...'.format(extension)) supercell_doc = deepcopy(doc) # standardize cell with spglib if standardize: supercell_doc = standardize_doc_cell(supercell_doc) # copy new doc and delete data that will not be corrected keys_to_copy = set(['positions_frac', 'lattice_cart', 'atom_types', 'source', 'stoichiometry']) supercell_doc = {key: supercell_doc[key] for key in keys_to_copy} for i, elem in enumerate(extension): for k in range(3): supercell_doc['lattice_cart'][i][k] = elem * supercell_doc['lattice_cart'][i][k] for ind, atom in enumerate(supercell_doc['positions_frac']): supercell_doc['positions_frac'][ind][i] /= elem images = product(*[list(range(elem)) for elem in extension]) new_positions = [] new_atoms = [] for image in images: if image != (0, 0, 0): for ind, atom in enumerate(supercell_doc['atom_types']): new_pos = deepcopy(supercell_doc['positions_frac'][ind]) for i, elem in enumerate(image): new_pos[i] += image[i] / extension[i] new_positions.append(new_pos) new_atoms.append(atom) supercell_doc['atom_types'].extend(new_atoms) supercell_doc['positions_frac'].extend(new_positions) if symmetric: supercell_doc['positions_frac'] = np.asarray(supercell_doc['positions_frac']) supercell_doc['positions_frac'] -= np.mean(supercell_doc['positions_frac'], axis=0) supercell_doc['positions_frac'] = supercell_doc['positions_frac'].tolist() supercell_doc['num_atoms'] = len(supercell_doc['atom_types']) supercell_doc['cell_volume'] = cart2volume(supercell_doc['lattice_cart']) supercell_doc['lattice_abc'] = cart2abc(supercell_doc['lattice_cart']) assert np.isclose(supercell_doc['cell_volume'], np.prod(extension)*cart2volume(doc['lattice_cart'])) return supercell_doc