Difference between revisions of "Supercell"

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<source lang="python">
 
<source lang="python">
run supercell.py
+
# import psico.xtal, or run the standalone script:
 +
run https://raw.githubusercontent.com/speleo3/pymol-psico/master/psico/xtal.py
 +
 
 
fetch 2x19, async=0
 
fetch 2x19, async=0
 
supercell 2,1,1, 2x19, green
 
supercell 2,1,1, 2x19, green
 
supercell 1,1,2, 2x19, orange, name=super2
 
supercell 1,1,2, 2x19, orange, name=super2
</source>
 
 
== The Code ==
 
 
<source lang="python">
 
'''
 
(c) 2010 Thomas Holder
 
 
PyMOL python script (load with `run supercell.py`)
 
Usage: See "help supercell" and "help symexpcell"
 
'''
 
 
from pymol import cmd, cgo, xray
 
from math import cos, sin, radians, sqrt
 
import numpy
 
 
def cellbasis(angles, edges):
 
'''
 
For the unit cell with given angles and edge lengths calculate the basis
 
transformation (vectors) as a 4x4 numpy.array
 
'''
 
rad = [radians(i) for i in angles]
 
basis = numpy.identity(4)
 
basis[0][1] = cos(rad[2])
 
basis[1][1] = sin(rad[2])
 
basis[0][2] = cos(rad[1])
 
basis[1][2] = (cos(rad[0]) - basis[0][1]*basis[0][2])/basis[1][1]
 
basis[2][2] = sqrt(1 - basis[0][2]**2 - basis[1][2]**2)
 
edges.append(1.0)
 
return basis * edges # numpy.array multiplication!
 
 
def supercell(a=1, b=1, c=1, object=None, color='blue', name='supercell', withmates=1):
 
'''
 
DESCRIPTION
 
 
    Draw a supercell, as requested by Nicolas Bock on the pymol-users
 
    mailing list (Subject: [PyMOL] feature request: supercell construction
 
    Date: 04/12/2010 10:12:17 PM (Mon, 12 Apr 2010 14:12:17 -0600))
 
 
USAGE
 
 
    supercell a, b, c [, object [, color [, name [, withmates]]]]
 
 
ARGUMENTS
 
 
    a, b, c = integer: repeat cell in x,y,z direction a,b,c times
 
    {default: 1,1,1}
 
 
    object = string: name of object to take cell definition from
 
 
    color = string: color of cell {default: blue}
 
 
    name = string: name of the cgo object to create {default: supercell}
 
 
    withmates = bool: also create symmetry mates in displayed cells
 
    {default: 1}
 
 
SEE ALSO
 
 
    show cell
 
 
'''
 
if object is None:
 
object = cmd.get_object_list()[0]
 
withmates = int(withmates)
 
 
sym = cmd.get_symmetry(object)
 
cell_edges = sym[0:3]
 
cell_angles = sym[3:6]
 
 
basis = cellbasis(cell_angles, cell_edges)
 
assert isinstance(basis, numpy.ndarray)
 
 
ts = list()
 
for i in range(int(a)):
 
for j in range(int(b)):
 
for k in range(int(c)):
 
ts.append([i,j,k])
 
 
obj = [
 
cgo.BEGIN,
 
cgo.LINES,
 
cgo.COLOR,
 
]
 
obj.extend(cmd.get_color_tuple(color))
 
 
for t in ts:
 
shift = basis[0:3,0:3] * t
 
shift = shift[:,0] + shift[:,1] + shift[:,2]
 
 
for i in range(3):
 
vi = basis[0:3,i]
 
vj = [
 
numpy.array([0.,0.,0.]),
 
basis[0:3,(i+1)%3],
 
basis[0:3,(i+2)%3],
 
basis[0:3,(i+1)%3] + basis[0:3,(i+2)%3]
 
]
 
for j in range(4):
 
obj.append(cgo.VERTEX)
 
obj.extend((shift + vj[j]).tolist())
 
obj.append(cgo.VERTEX)
 
obj.extend((shift + vj[j] + vi).tolist())
 
 
if withmates:
 
symexpcell('m%d%d%d_' % tuple(t), object, *t)
 
 
obj.append(cgo.END)
 
 
cmd.delete(name)
 
cmd.load_cgo(obj, name)
 
 
def symexpcell(prefix='mate', object=None, a=0, b=0, c=0):
 
'''
 
DESCRIPTION
 
 
    Creates all symmetry-related objects for the specified object that
 
    occur with their bounding box center within the unit cell.
 
 
USAGE
 
 
    symexpcell prefix, object, [a, b, c]
 
 
ARGUMENTS
 
 
    prefix = string: prefix of new objects
 
 
    object = string: object for which to create symmetry mates
 
 
    a, b, c = integer: create neighboring cell {default: 0,0,0}
 
 
SEE ALSO
 
 
    symexp, http://www.pymolwiki.org/index.php/SuperSym
 
'''
 
if object is None:
 
object = cmd.get_object_list()[0]
 
 
sym = cmd.get_symmetry(object)
 
cell_edges = sym[0:3]
 
cell_angles = sym[3:6]
 
spacegroup = sym[6]
 
 
basis = cellbasis(cell_angles, cell_edges)
 
basis = numpy.matrix(basis)
 
 
extent = cmd.get_extent(object)
 
center = sum(numpy.array(extent)) * 0.5
 
center = numpy.matrix(center.tolist() + [1.0]).T
 
center_cell = basis.I * center
 
 
extra_shift = [[float(i)] for i in (a,b,c)]
 
 
i = 0
 
matrices = xray.sg_sym_to_mat_list(spacegroup)
 
for mat in matrices:
 
i += 1
 
 
mat = numpy.matrix(mat)
 
shift = numpy.floor(mat * center_cell)
 
mat[0:3,3] -= shift[0:3,0]
 
mat[0:3,3] += extra_shift
 
 
mat = basis * mat * basis.I
 
mat_list = list(mat.flat)
 
 
name = '%s%d' % (prefix, i)
 
cmd.create(name, object)
 
cmd.transform_object(name, mat_list, 0)
 
cmd.color(i+1, name)
 
 
cmd.extend('symexpcell', symexpcell)
 
cmd.extend('supercell', supercell)
 
 
# tab-completion of arguments
 
cmd.auto_arg[3]['supercell'] = [ cmd.object_sc, 'object', '']
 
 
</source>
 
</source>
  

Latest revision as of 04:24, 1 July 2020

Included in psico
This command or function is available from psico, which is a PyMOL extension.

Module psico.xtal
Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19

supercell can display multiple copies of the unit cell. Can also fill the unit cell (and its copies) with symmetry mates.

See thread on pymol-users mailing list.

Requires numpy.

Example

# import psico.xtal, or run the standalone script:
run https://raw.githubusercontent.com/speleo3/pymol-psico/master/psico/xtal.py

fetch 2x19, async=0
supercell 2,1,1, 2x19, green
supercell 1,1,2, 2x19, orange, name=super2

See Also