mirror of https://github.com/NehZio/Crystal-MEC
396 lines
13 KiB
Python
396 lines
13 KiB
Python
import numpy as np
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import operator
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import sys
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def distance(a,b):
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# Returns the 3D distance between a and b where
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# a and b are array where x, y and z are at the
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# position 0, 1 and 2
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x = a[0]-b[0]
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y = a[1]-b[1]
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z = a[2]-b[2]
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return np.sqrt(x**2+y**2+z**2)
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def get_cell_matrix(a,b,c,alpha,beta,gamma):
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# Computing the volume of the primitive cell
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omega = a*b*c*np.sqrt(1-np.cos(alpha)**2-np.cos(beta)**2-np.cos(gamma)**2+2*np.cos(alpha)*np.cos(beta)*np.cos(gamma))
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# Computing the matrix
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M = [
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[a,b*np.cos(gamma),c*np.cos(beta)],
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[0,b*np.sin(gamma),c*(np.cos(alpha)-np.cos(beta)*np.cos(gamma))/(np.sin(gamma))],
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[0,0,omega/(a*b*np.sin(gamma))]
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]
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return M
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def big_cell(generator,symGenerator,a,b,c,alpha,beta,gamma,nA,nB,nC):
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coords = []
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# Computing the matrix converting fractional to cartesian
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fracToCart = get_cell_matrix(a,b,c,alpha,beta,gamma)
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for gen in generator:
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x = gen[1]
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y = gen[2]
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z = gen[3]
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for sym in symGenerator:
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u = eval(sym[0])
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v = eval(sym[1])
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w = eval(sym[2])
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# Making sure the value is within the range [0,1]
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u = u + 1*(u<0) - 1*(u>1)
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v = v + 1*(v<0) - 1*(v>1)
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w = w + 1*(w<0) - 1*(w>1)
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coords.append([u,v,w,gen[0]])
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# Deleting the redundant atoms
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toDel = []
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for i in range(len(coords)-1):
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for j in range(i+1,len(coords)):
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# Computing the distance using the minimum image convention
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# as described in Appendix B equation 9 of
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# "Statistical Mechanics : Theory and Molecular Simulations
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# Mark E. Tuckerman"
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r1 = np.array(coords[i][:3])
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r2 = np.array(coords[j][:3])
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r12 = r1-r2
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da = np.sqrt(r12[0]**2+r12[1]**2+r12[2]**2)
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r12 = r12 - np.round(r12)
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db = da - np.sqrt(r12[0]**2+r12[1]**2+r12[2]**2)
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r12 = np.matmul(fracToCart,r12)
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d = np.sqrt(r12[0]**2+r12[1]**2+r12[2]**2)
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if(d<1e-2):
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# We check if we don't already want to delete this atom
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if j not in toDel:
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toDel.append(j)
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toDel = sorted(toDel)
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# We delete the atoms in the list
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for i in range(len(toDel)):
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coords.pop(toDel[i]-i)
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newCoords = []
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# We replicate the cell nA, nB, nC times
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for at in coords:
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newCoords.append([at[0],at[1],at[2],at[3]])
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for a in range(1,nA):
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newCoords.append([at[0]+a,at[1],at[2],at[3]])
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for b in range(1,nB):
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newCoords.append([at[0]+a,at[1]+b,at[2],at[3]])
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for c in range(1,nC):
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newCoords.append([at[0]+a,at[1]+b,at[2]+c,at[3]])
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for c in range(1,nC):
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newCoords.append([at[0]+a,at[1],at[2]+c,at[3]])
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for b in range(1,nB):
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newCoords.append([at[0],at[1]+b,at[2],at[3]])
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for c in range(1,nC):
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newCoords.append([at[0],at[1]+b,at[2]+c,at[3]])
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for c in range(1,nC):
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newCoords.append([at[0],at[1],at[2]+c,at[3]])
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# Now we convert the fractionnal coordinates to cartesian coordinates
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coords = []
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for at in newCoords:
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r = [at[0],at[1],at[2]]
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rxyz = np.matmul(fracToCart,r)
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coords.append([rxyz[0],rxyz[1],rxyz[2],at[3],'C'])
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# Returns the list of the atoms [x,y,z,label,second_label]
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return coords
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# Translates all the coordinates with the vector v
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def translate(v,coordinates):
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for c in coordinates:
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c[0] += v[0]
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c[1] += v[1]
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c[2] += v[2]
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return coordinates
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# Finds the point at the center of the given atoms that are the
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# closest to the origin
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def find_center(centerList, coordinates, without=[]):
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centers = []
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for i in range(len(centerList)):
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centers.append([100,100,100]) # Setting a large value for each center
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for c in centers:
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c.append(distance(c,[0,0,0])) # Computing the distance to the origin
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for at in coordinates:
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w = True
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for a in without:
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if distance(at, a) < 1e-6:
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w = False
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break
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if not w:
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continue
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if at[3] in centerList:
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centers = sorted(centers, key=operator.itemgetter(3)) # Sorting the list with respect to the distance to the origin
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d = distance(at,[0,0,0])
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if d <= centers[-1][-1] and d > 0.0:
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centers[-1] = [at[0],at[1],at[2],d]
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center = np.mean(centers,axis=0)[:3] # Computing the barycenter
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return center
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# Defines a rotation matrix that will put r1 at the position r2
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def rotation_matrix(r1,r2):
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r1 = np.array(r1)/np.linalg.norm(r1)
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r2 = np.array(r2)/np.linalg.norm(r2)
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# Computing the cross product which is the vector around which
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# the rotation is done
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crossProduct = np.cross(r1,r2)
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crossProduct = crossProduct/np.linalg.norm(crossProduct)
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# Computing the angle of the rotation
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a = np.arccos(np.dot(r1,r2))
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c = np.cos(a)
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s = np.sin(a)
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x = crossProduct[0]
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y = crossProduct[1]
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z = crossProduct[2]
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M = [
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[x**2*(1-c)+c,x*y*(1-c)-z*s,x*z*(1-c)+y*s],
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[x*y*(1-c)+z*s,y**2*(1-c)+c,y*z*(1-c)-x*s],
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[x*z*(1-c)-y*s,y*z*(1-c)+x*s,z**2*(1-c)+c]
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]
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return M
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# Rotates all the coordinates using the rotation matric M
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def rotate(M,coordinates):
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for i in range(len(coordinates)):
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r = [coordinates[i][0],coordinates[i][1],coordinates[i][2]]
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rV = np.matmul(M,r)
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coordinates[i][0] = rV[0]
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coordinates[i][1] = rV[1]
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coordinates[i][2] = rV[2]
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return coordinates
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# Cuts a sphere centered on the origin in the coordinates
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def cut_sphere(coordinates,r):
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sphere = []
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for i in range(len(coordinates)):
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if distance(coordinates[i],[0,0,0]) <= r:
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sphere.append(coordinates[i])
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return sphere
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# Finds the fragment in the coordinates
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def find_fragment(coordinates, patterns, npatterns,notInFrag):
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inFrag = []
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for n in range(len(patterns)):
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pattern = patterns[n]
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npattern = npatterns[n]
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for i in range(npattern):
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c = [100,100,100]
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dc = distance([0,0,0],c)
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inPattern = []
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# Finding the closest atom of the first type in the pattern
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for at in coordinates:
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if at[3] == pattern[1]:
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d = distance([0,0,0],at)
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if d > 10:
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break
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if d < dc :
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accept = True
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for exc in notInFrag:
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d = distance(exc,at)
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if d < 1e-5:
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accept = False
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if accept and coordinates.index(at) not in inFrag:
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c = [at[0],at[1],at[2],0.0, coordinates.index(at)]
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dc = distance([0,0,0],c)
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# Finding the rest of the pattern around the atom previously found
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atIn = []
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for j in range(0,len(pattern),2):
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d = distance(c,[100,100,100])
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# Initializing the atoms
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for k in range(pattern[j]):
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atIn.append([100,100,100,d])
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for at in coordinates:
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if distance(at,[0,0,0]) > 10:
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break
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if at[3] == pattern[j+1]:
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atIn = sorted(atIn,key=operator.itemgetter(3))
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d = distance(at,c)
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trial = [at[0],at[1],at[2],d,coordinates.index(at)]
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if d < atIn[-1][3] and trial not in atIn:
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accept = True
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for exc in notInFrag:
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d = distance(exc,trial)
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if d < 1e-5:
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accept = False
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if accept:
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atIn[-1] = trial
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for at in atIn:
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inPattern.append(at[4])
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for at in inPattern:
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if at not in inFrag:
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inFrag.append(at)
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for at in inFrag:
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coordinates[at][4] = 'O'
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return len(inFrag), coordinates
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# Finds the pseudopotential layer around
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# the fragment
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def find_pseudo(coordinates, rPP, notInPseudo):
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for at in coordinates:
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if at[4] != 'O':
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continue
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for i in range(len(coordinates)):
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if coordinates[i][4] != 'C':
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continue
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d = distance(at,coordinates[i])
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if d < rPP:
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coordinates[i][4] = 'Cl'
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return coordinates
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# Creates lists containing the neighbours of each
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# atom
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def find_neighbours(coordinates, atoms):
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neighbourList = [[] for i in range(len(coordinates))]
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atoms = np.array(atoms).flatten()
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for i in range(len(coordinates)-1):
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for j in range(i+1,len(coordinates)):
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li = coordinates[i][3] # Label of the atom i
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lj = coordinates[j][3] # Label of the atom j
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ii = np.where(atoms==li)[0]
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jj = np.where(atoms==lj)[0]
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ci = float(atoms[ii+1]) # Charge of the atom i
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cj = float(atoms[jj+1]) # Charge of the atom j
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if ci*cj < 0: # Checking if the charges have opposite signs
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d = distance(coordinates[i],coordinates[j])
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if d < float(atoms[ii+3]) and d < float(atoms[jj+3]):
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neighbourList[i].append(j)
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neighbourList[j].append(i)
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return neighbourList
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# For each atom, finds if it has the correct number of neighbours,
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# if not, modify its charge
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def evjen_charges(coordinates,atoms):
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neighbourList = find_neighbours(coordinates,atoms)
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atoms = np.array(atoms).flatten()
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charges = []
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for i in range(len(coordinates)):
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li = coordinates[i][3]
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ii = np.where(atoms==li)[0]
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nr = len(neighbourList[i])
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nt = int(atoms[ii+2])
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ci = float(atoms[ii+1])
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if nr > nt:
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print("Error : too much neighbours for atom n°%i, count %i neighbours where it should have a maximum of %i"%(i,nr,nt))
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sys.exit()
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charges.append(ci*nr/nt)
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return charges
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# Computes the nuclear repulsion
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def nuclear_repulsion(coordinates,charges):
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rep = 0.0
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for i in range(len(coordinates)-1):
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for j in range(i+1,len(coordinates)):
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rij = distance(coordinates[i],coordinates[j])
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ci = charges[i]
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cj = charges[j]
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if(rij < 1):
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print(i,j,"\n",coordinates[i],"\n",coordinates[j],"\n",rij)
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rep += (ci*cj)/rij
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return rep
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# Computes the symmetry in the whole system
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def compute_symmetry(coordinates,charges,symmetry):
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symmetrizedCoordinates = []
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symmetrizedCharges = []
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uniqueIndexList = [] # The list containing the indexes of the unique atoms
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treated = [] # Will store the index of the atoms already treated
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symOp = []
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# Storing all the symmetry operations
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for s in symmetry:
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if s == 'C2x':
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symOp.append(np.array([1,-1,-1]))
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elif s == 'C2y':
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symOp.append(np.array([-1,1,-1]))
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elif s == 'C2z':
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symOp.append(np.array([-1,-1,1]))
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elif s == 'xOy':
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symOp.append(np.array([1,1,-1]))
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elif s == 'xOz':
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symOp.append(np.array([1,-1,1]))
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elif s == 'yOz':
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symOp.append(np.array([-1,1,1]))
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elif s == 'i':
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symOp.append(np.array([-1,-1,-1]))
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for i in range(len(coordinates)):
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if i in treated:
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continue
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treated.append(i)
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at1 = np.array(coordinates[i][:3])
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symmetrizedCoordinates.append(coordinates[i])
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symmetrizedCharges.append(charges[i])
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uniqueIndexList.append(len(symmetrizedCoordinates)-1)
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for j in range(len(coordinates)):
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if j in treated or coordinates[i][3] != coordinates[j][3]:
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continue
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at2 = np.array(coordinates[j][:3])
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for s in symOp:
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if distance(at1,at1*s) > 1e-4 and distance(at2,at1*s) < 1e-4: # Checking if op.at1 != at1 and that op.at2 = at1
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p = at1*s
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treated.append(j)
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symmetrizedCoordinates.append([p[0],p[1],p[2],coordinates[i][3],coordinates[i][4]])
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symmetrizedCharges.append(charges[i])
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break
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return symmetrizedCoordinates,symmetrizedCharges,uniqueIndexList
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