I've written a script that lets you take two structures and align and superimpose them so that only the atoms that take part in the reaction move.
It works by you defining a minimum of four atoms that aren't supposed to move /relative to each other/ (i.e. they can be translated/rotated --- just not relative to each other) between the two structures. Four atoms far from each other are ideal. You need to make sure that they also don't lie in the same plane, but form a three-dimensional space.
I've tried this on real molecules too and it works better than I'd ever dared to hope for. The more 'stationary' atoms that you can use to make up the transformation matrix, the better.
Example:
In this example atom F is in a different location in structures a and b. The structures have also been rotated relative to each other.
a.xyz6 A A 0.00000 0.00000 1.00000 B 0.00000 1.00000 0.00000 C 1.00000 0.00000 0.00000 D -1.00000 0.00000 0.00000 E 0.00000 0.00000 -1.00000 F 0.00000 0.500000 0.00000
b.xyz6 B A 1 0 0 B 0 1 0 C 0 0 -1 D 0 0 1 E -1 0 0 F 0 -1 0
./autorotate.py a.xyz b.xyz '1,2,3,4'Selected atoms in molecules 1 and 2 ['A', 0.0, 0.0, 1.0] ['A', 1.0, 0.0, 0.0] ['B', 0.0, 1.0, 0.0] ['B', 0.0, 1.0, 0.0] ['C', 1.0, 0.0, 0.0] ['C', 0.0, 0.0, -1.0] ['D', -1.0, 0.0, 0.0] ['D', 0.0, 0.0, 1.0] Transformation max error: 3.33066907388e-16 Writing to a.rot.xyz
a.rot.xyzThis is how it looks (note that the axis aren't aligned with (1,0,0; 0,1,0; 0,0,1) but seem to go through the centre of the molecule):6 A A 1.00000 0.00000 0.00000 B -0.00000 1.00000 -0.00000 C -0.00000 0.00000 -1.00000 D -0.00000 0.00000 1.00000 E -1.00000 -0.00000 -0.00000 F -0.00000 0.50000 -0.00000
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| a.xyz |
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| a.rot.xyz |
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| b.xyz |
Code:
#!/usr/bin/python
import sys
import numpy as np
#autorotate input_1.xyz input_2.xyz '1,2,3,4'
# need to pick at least four atoms that are not in the same plane
# input_1.xyz will be rotated to align with input_2.xyz
# you pick at least four atoms that should have the same positions
# relative to one another (i.e. distance and relative geometry). These
# are then used to calculate an affine transform matrix which is used
# to rotate and translate structure input_1.xyz to overlap with
# structure 2
def formatinput(argument):
infile1=sys.argv[1]
atoms=sys.argv[3]
atoms=atoms.split(',')
coord_sys=[]
for n in atoms:
coord_sys+=[int(n)-1]
try:
infile2=sys.argv[2]
except:
infile2=''
infile=[infile1,infile2]
return infile,coord_sys
def getrawdata(infile):
f=open(infile,'r')
n=0
preamble=[]
struct=[]
for line in f:
if n<2: data-blogger-escaped-if="" data-blogger-escaped-line.rstrip="" data-blogger-escaped-n="" data-blogger-escaped-preamble="">1:
line=line.rstrip()
struct+=[line]
n+=1
xyz=[struct]
return xyz, preamble
def getcoords(rawdata,preamble,atoms):
n=0
cartesian=[]
for structure in rawdata:
n=n+1
num="%03d" % (n,)
for item in structure:
coordx=filter(None,item.split(' '))
coordy=filter(None,item.split('\t'))
if len(coordx)>len(coordy):
coords=coordx
else:
coords=coordy
coordinates=[float(coords[1]),float(coords[2]),float(coords[3])]
element=coords[0]
cartesian+=[[element,float(coords[1]),float(coords[2]),float(coords[3])]]
return cartesian
def getstructures(rawdata,preamble):
n=0
cartesian=[]
for structure in rawdata:
n=n+1
num="%03d" % (n,)
for item in structure:
coordx=filter(None,item.split(' '))
coordy=filter(None,item.split('\t'))
if len(coordx)>len(coordy):
coords=coordx
else:
coords=coordy
coordinates=[float(coords[1]),float(coords[2]),float(coords[3])]
element=coords[0]
cartesian+=[coordinates]
return cartesian
def affine_transform(atoms,structures):
# from http://stackoverflow.com/questions/20546182/how-to-perform-coordinates-affine-transformation-using-python-part-2
primaryatomcoords=[]
for n in atoms:
primaryatomcoords+=[structures[0][n]]
secondaryatomcoords=[]
for n in atoms:
secondaryatomcoords+=[structures[1][n]]
primary = np.array(primaryatomcoords)
secondary = np.array(secondaryatomcoords)
primaryfull = np.array(structures[0])
# Pad the data with ones, so that our transformation can do translations too
n = primary.shape[0]
pad = lambda x: np.hstack([x, np.ones((x.shape[0], 1))])
unpad = lambda x: x[:,:-1]
X = pad(primary)
Y = pad(secondary)
Xp= pad(primaryfull)
# Solve the least squares problem X * A = Y
# to find our transformation matrix A
A, res, rank, s = np.linalg.lstsq(X, Y)
transform = lambda x: unpad(np.dot(pad(x), A))
# print "Max error should be as small as possible if the rotation is successful"
# print "If max error is large you may have selected a bad set of atoms"
print "Transformation max error:", np.abs(secondary - transform(primary)).max()
secondaryfull=transform(primaryfull)
return secondaryfull
def transform_xyz(tmatrix,newxyz):
final_xyz=[]
for n in newxyz:
coord=np.mat(str(n[0])+';'+str(n[1])+';'+str(n[2]))
newcoord=np.dot(tmatrix,coord)
newcoord=np.matrix.tolist(newcoord)
final_xyz+=[[ newcoord[0][0],newcoord[1][0],newcoord[2][0]]]
return final_xyz
def genxyzstring(coords,elementnumber):
x_str='%10.5f'% coords[0]
y_str='%10.5f'% coords[1]
z_str='%10.5f'% coords[2]
element=elementnumber
xyz_string=element+(3-len(element))*' '+10*' '+\
(8-len(x_str))*' '+x_str+10*' '+(8-len(y_str))*' '+y_str+10*' '+(8-len(z_str))*' '+z_str+'\n'
return xyz_string
def write_aligned(aligned_structure,atom_coords,preamble,outfile):
outfile=outfile.replace('.xyz','.rot.xyz')
print "Writing to ",outfile
g=open(outfile,'w')
g.write(str(preamble[0])+'\n'+str(preamble[1])+'\n')
for n in range(0,len(aligned_structure)):
xyzstring=genxyzstring(aligned_structure[n],atom_coords[n][0])
g.write(xyzstring)
g.close()
return 0
if __name__ == "__main__":
infile,atoms=formatinput(sys.argv)
xyz=['','']
preamble=['','']
#get raw data
xyz[0],preamble[0]=getrawdata(infile[0])
xyz[1],preamble[1]=getrawdata(infile[1])
atom_coords=[getcoords(xyz[0],preamble[0],atoms)]
atom_coords+=[getcoords(xyz[1],preamble[1],atoms)]
#collect structures from raw data
structures=[getstructures(xyz[0],preamble[0])]
structures+=[getstructures(xyz[1],preamble[1])]
print "Selected atoms in molecules 1 and 2"
for n in atoms:
print atom_coords[0][n],atom_coords[1][n]
#transform structure
aligned_structure=affine_transform(atoms,structures)
write_aligned(aligned_structure,atom_coords[0],preamble[0],str(infile[0]))
