pyxtal.descriptor module

Module for crystal packing descriptor from energy decomposition

pyxtal.descriptor.cart2sph(x, y, z)

convert the x, y, z to spherical coordinates (phi, theta, r) phi: [-pi, pi] theta: [-pi/2, pi/2]

pyxtal.descriptor.correlation(coef1, coef2, angle=None, s=0)

Compute the correlation between to sph coefs

Parameters:

• coef1 – sph coefficients 1
• coef2 – sph coefficients 2
• angle – [alpha, beta, gamma]
• s – starting index of coefs

Returns:

distance scaled in [0, 1]

pyxtal.descriptor.correlation_go(coef1, coef2, M=6, s=0, d_cut=0.92)

global optimization of two coefs based on quasi random sampling

Parameters:

• coef1 – sph coefficients 1
• coef2 – sph coefficients 2
• M – 2^M sampling points
• s – starting index of coefs

Returns:

distance scaled in [0, 1]

pyxtal.descriptor.correlation_opt(coef1, coef2, angle, s=0)

Compute the correlation between two sph coefs

Parameters:

• coef1 – sph coefficients 1
• coef2 – sph coefficients 2
• angle – [alpha, beta, gamma]
• s – starting index of coefs

Returns:

distance scaled in [0, 1]

pyxtal.descriptor.expand_sph(pts, l_max, norm=4, csphase=-1)

pyxtal.descriptor.fibonacci_sphere(N=1000)

Sampling the sphere grids

Parameters:N – number of pts to generate Returns:3D points array in Cartesian coordinates

pyxtal.descriptor.get_alignment(pts, degrees=True)

Here we define the equator is the plane with three most important neighbors. Get the required rotation angles to get that representation.

Parameters:important points (pts;) – Returns:[alpha, beta, gamma] Return type:angles

class pyxtal.descriptor.orientation_order(xtal, max_CN=14)

Bases: object

Computes the Steinhardt orientation order parameters

Parameters:

• xtal – pyxtal structure
• max_d – maximum intermolecular distances
• lmax – maximum bandwidth for spherical harmonic expansion

get_neighbors()

get neighboring molecules

Returns:[N, 3] array, (theta, phi, eng) Return type:pts

get_parameters(ls=[4, 6])

Computes :param center: center xyz coordinate :param neighbors: a list of neighboring xyz coordinates :param weights: a list of weights for each neighbor

Returns:

numpy array(complex128), the complex vector qlm normalized

by the number of nearest neighbors

Return type:q

pyxtal.descriptor.sph2cart(phi, theta, r)

convert spherical coordinates (phi, theta, r) to Cartesian (x, y, z)

class pyxtal.descriptor.spherical_image(xtal, model='molecule', max_d=10, factor=2.2, lmax=13, sigma=0.1, N=10000)

Bases: object

A class to handle the crystal packing descriptor from spherical image

Parameters:

• xtal – pyxtal structure
• model – ‘molecule’ or ‘contact’
• max_d – maximum intermolecular distances
• lmax – maximum bandwidth for spherical harmonic expansion
• sigma – Gaussian width to project into the unit sphere
• N – number of grid points on the unit sphere

align(M=6)

Align spherical image in a way that three most important contributions are parallel to the equatorial plane. Experimental stage now!

Parameters:M – number of power in quasi random sampling

calculate_density(pt, xyzs)

calculate the projected density on the unit sphere

get_contacts()

Compute the spherical images from the neighboring distances

Returns:[N, 3] array, (theta, phi, eng) Return type:pts

get_molecules()

compute the spherical images from neighboring molecules

Returns:[N, 3] array, (theta, phi, eng) Return type:pts

get_similarity(sph2, M=6, cutoff=0.95)

Compute the similarity matrix between two sphs

Parameters:

• sph2 – the 2nd sph class
• M – number of power in quasi random sampling
• cutoff – cutoff similarity to terminate search early

plot_real_image(id=0)

Plot the real molecular contacts in the crystal

plot_sph_images(lmax=None, figname=None, molecule=False)

Plot the spherical images in both 3d and 2d

Parameters:

• lmax – maximum truncation
• figname – name of figure file
• molecule – draw 2D molecule diagram or not

rotate(alpha=0, beta=0, gamma=0)

uniformly rotate the coefs

Parameters:

• alpha – rotation in degrees
• beta – rotation in degress
• gamma – rotation in degress

pyxtal.descriptor.xyz2sph(xyzs, radian=True)

convert the vectors (x, y, z) to the sphere representation (theta, phi)

Parameters:

• xyzs – 3D xyz coordinates
• radian – return in radian (otherwise degree)