molsym.symtext.character_table
import numpy as np from .point_group import PointGroup from ..symtools import * import re
These functions are deprecated
- deprecated:
- class CharacterTable():
- def __init__(self, pg, irreps, classes, class_orders, chars, irrep_dims) -> None:
print(“Deprecation Warning: Using deprecated CharacterTable class”) self.name = pg self.irreps = irreps self.classes = classes self.class_orders = class_orders self.characters = chars self.irrep_dims = irrep_dims
- def __repr__(self) -> str:
return f”Character Table for {self.name}
Irreps: {self.irreps} Classes: {self.classes} Characters: {self.characters} “
- def __eq__(self, other):
- if len(self.irreps) == len(other.irreps) and len(self.classes) == len(other.classes) and np.shape(self.characters)==np.shape(other.characters):
return (self.irreps == other.irreps).all() and (self.classes == other.classes).all() and np.isclose(self.characters,other.characters,atol=1e-10).all()
- else:
return False
- def pg_to_chartab(PG):
pg = PointGroup.from_string(PG) irreps = [] if pg.family == “C”:
- if pg.subfamily == “s”:
irreps = [“A’”,”A’’”] classes = [“E”, “sigma_h”] chars = np.array([[1.0, 1.0], [1.0, -1.0]])
- elif pg.subfamily == “i”:
irreps = [“Ag”,”Au”] classes = [“E”, “i”] chars = np.array([[1.0, 1.0], [1.0, -1.0]])
- elif pg.subfamily == “v”:
irreps, classes, chars = Cnv_irr(pg.n)
- elif pg.subfamily == “h”:
irreps, classes, chars = Cnh_irr(pg.n)
- else:
#irreps, classes, chars = Cn_irrmat(pg.n) irreps, classes, chars = Cn_irr_complex(pg.n)
- elif pg.family == “D”:
- if pg.subfamily == “d”:
irreps, classes, chars = Dnd_irr(pg.n)
- elif pg.subfamily == “h”:
irreps, classes, chars = Dnh_irr(pg.n)
- else:
irreps, classes, chars = Dn_irr(pg.n)
- elif pg.family == “S”:
irreps, classes, chars = Sn_irr_complex(pg.n)
- else:
cp3 = np.cos(np.pi/3) pr5 = 0.5*(1.0+np.sqrt(5.0)) mr5 = 0.5*(1.0-np.sqrt(5.0)) if pg.family == “T”:
- if pg.subfamily == “h”:
- irreps, classes, chars = ([“Ag”,”Au”,”Eg”,”Eu”,”Tg”,”Tu”],
[“E”, “4C_3”, “4C_3^2”, “3C_2”, “i”, “S_6”, “S_6^5”, “3sigma_h”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0], [2.0, cp3, cp3, 2.0, 2.0, cp3, cp3, 1.0], [2.0, cp3, cp3, 2.0, -2.0, -cp3, -cp3, -1.0], [3.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, -1.0], [3.0, 0.0, 0.0, -1.0, -1.0, 0.0, 0.0, 1.0]]))
- elif pg.subfamily == “d”:
- irreps, classes, chars = ([“A1”,”A2”,”E”,”T1”,”T2”],
[“E”, “8C_3”, “3C_2”, “6S_4”, “6sigma_d”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, -1.0, -1.0], [2.0, -1.0, 2.0, 0.0, 0.0], [3.0, 0.0, -1.0, 1.0, -1.0], [3.0, 0.0, -1.0, -1.0, 1.0]]))
- else:
- irreps, classes, chars = ([“A”,”E”,”T”],
[“E”, “4C_3”, “4C_3^2”, “3C_2”], np.array( [[1.0, 1.0, 1.0, 1.0],
[2.0, cp3, cp3, 2.0], [3.0, 0.0, 0.0, -1.0]]))
- elif pg.family == “O”:
- if pg.subfamily == “h”:
- irreps, classes, chars = ([“A1g”,”A2g”,”Eg”,”T1g”,”T2g”,”A1u”,”A2u”,”Eu”,”T1u”,”T2u”],
[“E”, “8C_3”, “6C_2”, “6C_4”, “3C_2”, “i”, “6S_4”, “8S_6”, “3sigma_h”, “6sigma_d”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0], [2.0, -1.0, 0.0, 0.0, 2.0, 2.0, 0.0, -1.0, 2.0, 0.0], [3.0, 0.0, -1.0, 1.0, -1.0, 3.0, 1.0, 0.0, -1.0, -1.0], [3.0, 0.0, 1.0, -1.0, -1.0, 3.0, -1.0, 0.0, -1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0], [1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, 1.0], [2.0, -1.0, 0.0, 0.0, 2.0, -2.0, 0.0, 1.0, -2.0, 0.0], [3.0, 0.0, -1.0, 1.0, -1.0, -3.0, -1.0, 0.0, 1.0, 1.0], [3.0, 0.0, 1.0, -1.0, -1.0, -3.0, 1.0, 0.0, 1.0, -1.0]]))
- else:
- irreps, classes, chars = ([“A1”,”A2”,”E”,”T1”,”T2”],
[“E”, “6C_4”, “3C_2”, “8C_3”, “6C_2”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, -1.0, 1.0, 1.0, -1.0], [2.0, 0.0, 2.0, -1.0, 0.0], [3.0, 1.0, -1.0, 0.0, -1.0], [3.0, -1.0, -1.0, 0.0, 1.0]]))
- elif pg.family == “I”:
- if pg.subfamily == “h”:
- irreps, classes, chars = ([“Ag”,”T1g”,”T2g”,”Gg”,”Hg”,”Au”,”T1u”,”T2u”,”Gu”,”Hu”],
[“E”, “12C_5”, “12C_5^2”, “20C_3”, “15C_2”, “i”, “12S_10”, “12S_10^3”, “20S_6”, “15sigma”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
[3.0, pr5, mr5, 0.0, -1.0, 3.0, mr5, pr5, 0.0, -1.0], [3.0, mr5, pr5, 0.0, -1.0, 3.0, pr5, mr5, 0.0, -1.0], [4.0, -1.0, -1.0, 1.0, 0.0, 4.0, -1.0, -1.0, 1.0, 0.0], [5.0, 0.0, 0.0, -1.0, 1.0, 5.0, 0.0, 0.0, -1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0], [3.0, pr5, mr5, 0.0, -1.0, -3.0, -mr5, -pr5, 0.0, 1.0], [3.0, mr5, pr5, 0.0, -1.0, -3.0, -pr5, -mr5, 0.0, 1.0], [4.0, -1.0, -1.0, 1.0, 0.0, -4.0, 1.0, 1.0, -1.0, 0.0], [5.0, 0.0, 0.0, -1.0, 1.0, -5.0, 0.0, 0.0, 1.0, -1.0]]))
- else:
- irreps, classes, chars = ([“A”,”T1”,”T2”,”G”,”H”],
[“E”, “12C_5”, “12C_5^2”, “20C_3”, “15C_2”], np.array( [[1.0, 1.0, 1.0, 1.0, 1.0],
[3.0, pr5, mr5, 0.0, -1.0], [3.0, mr5, pr5, 0.0, -1.0], [4.0, -1.0, -1.0, 1.0, 0.0], [5.0, 0.0, 0.0, -1.0, 1.0]]))
- else:
raise Exception(f”An invalid point group has been given or unexpected parsing of the point group string has occured: {pg.str}”)
class_orders = grab_class_orders(classes) irr_dims = {} for (irr_idx,irrep) in enumerate(irreps):
- if pg.n == 1:
irr_dims[irrep] = int(chars[0])
- else:
irr_dims[irrep] = int(np.real(chars[irr_idx, 0]))
return CharacterTable(PG, irreps, classes, class_orders, chars, irr_dims)
- def grab_class_orders(classes):
ncls = len(classes) class_orders = np.zeros(ncls) for i in range(ncls): # = 1:ncls
class_orders[i] = grab_order(classes[i])
return class_orders
- def grab_order(class_str):
regex = r”^(d+)” m = re.match(regex, class_str) if m is not None:
return int(m.groups()[0])
- else:
return 1
- def c_class_string(classes, pre, r, s):
“Pushes class string to ‘classes’ for rotations, but ignores superscript if s is one” if s == 1:
classes.append(pre+f”_{r}”)
- else:
classes.append(pre+f”_{r}^{s}”)
- def Cn_irrmat(n):
names = [“A”] classes = [“E”] for c in range(1,n):
r,s = reduce(n,c) c_class_string(classes, “C”, r, s)
chars = np.ones(n) if n % 2 == 0:
names.append(“B”) bi = np.ones(n) #for i=1:n: for i in range(n):
- if (i+1) % 2 == 0:
bi[i] *= -1
chars = np.vstack((chars, bi))
- if 2 < n < 5:
# No label associated with E if n < 5 names.append(“E”) theta = 2*np.pi / n v = np.zeros(n) for j in range(n):
v[j] += 2*np.cos(j*theta)
chars = np.vstack((chars, v))
- elif n >= 5:
theta = 2*np.pi / n l = round(((n-len(names))/2)) for i in range(l):#= 1:l:
names.append(f”E{i+1}”) v = np.zeros(n) for j in range(n):
v[j] += 2*np.cos((i+1)*j*theta)
chars = np.vstack((chars, v))
return names, classes, chars
- def Cn_irr_complex(n):
names = [“A”] classes = [“E”] for c in range(1,n):
r,s = reduce(n,c) c_class_string(classes, “C”, r, s)
chars = np.ones(n) if n % 2 == 0:
names.append(“B”) bi = np.ones(n) #for i=1:n: for i in range(n):
- if (i+1) % 2 == 0:
bi[i] *= -1
chars = np.vstack((chars, bi))
- if 2 < n < 5:
# No label associated with E if n < 5 names.append(“E_1”) names.append(“E_2”) theta = np.exp(2*np.pi*1j / n) v1 = np.zeros(n, dtype=np.complex128) v2 = np.zeros(n, dtype=np.complex128) for a in range(n):
v1[a] += theta**a v2[a] += np.conj(theta**a)
chars = np.vstack((chars, v1)) chars = np.vstack((chars, v2))
- elif n >= 5:
theta = 2*np.pi / n l = round(((n-len(names))/2)) for a in range(l):#= 1:l:
names.append(f”E{a+1}_1”) names.append(f”E{a+1}_2”) theta = np.exp(2*np.pi*1j*(a+1) / n) v1 = np.zeros(n, dtype=np.complex128) v2 = np.zeros(n, dtype=np.complex128) for b in range(n):
v1[b] += theta**b v2[b] += np.conj(theta**b)
chars = np.vstack((chars, v1)) chars = np.vstack((chars, v2))
return names, classes, chars
- def Cnv_irr(n):
names, classes, chars = Cn_irrmat(n) classes = [“E”] if n % 2 == 0:
- for c in range(1,n>>1): # = 1:(n>>1)-1:
r,s = reduce(n,c) c_class_string(classes, “2C”, r, s)
classes.append(“C_2”) if n>>1 == 1:
classes.append(“sigma_v(xz)”) classes.append(“sigma_d(yz)”)
- else:
classes.append(f”{n>>1}sigma_v”) classes.append(f”{n>>1}sigma_d”)
- else:
- for c in range(1,(n>>1)+1): # = 1:n>>1:
r,s = reduce(n,c) c_class_string(classes, “2C”, r, s)
classes.append(f”{n}sigma_v”)
names[0] = “A1” names.insert(1, “A2”) chars = np.vstack((chars[0,:], chars[0,:], chars[1:,:])) for i in range(1,n):# = 2:n:
- if i >= n-i:
break
#deleteat!(classes, n-i+2) chars = chars[:,[j for j in range(np.shape(chars)[1]) if j != n-i]] #chars[:,1:-1.!=n-i+2]
- if n % 2 == 0:
nirr = round((n/2)+3) names[2] = “B1” names.insert(3, “B2”) chars = np.vstack((chars[0:3,:], chars[2,:], chars[3:,:])) sigma_v = np.zeros(nirr) sigma_d = np.zeros(nirr) sigma_v[0:4] = np.array([1,-1,1,-1]) sigma_d[0:4] = np.array([1,-1,-1,1]) chars = np.hstack((chars, sigma_v[:,None], sigma_d[:,None]))
- else:
nirr = round((n-1)/2+2) sigma_v = np.zeros(nirr) sigma_v[0:2] = np.array([1, -1]) chars = np.hstack((chars, sigma_v[:,None]))
return names, classes, chars
- def Cnh_irr(n):
#names, classes, cnchars = Cn_irrmat(n) names, classes, cnchars = Cn_irr_complex(n) if n % 2 == 0:
classes.append(“i”) for i in range(1,n): # = 1:n-1:
- if i == n>>1:
classes.append(“sigma_h”)
- else:
r,s = reduce(n, (i+(n>>1))%n) if s % 2 == 0:
s += r
c_class_string(classes, “S”, r, s)
- else:
classes.append(“sigma_h”) for i in range(1,n): # = 1:n-1:
r,s = reduce(n,i) if i % 2 == 0:
c_class_string(classes, “S”, r, s+n)
- else:
c_class_string(classes, “S”, r, s)
- if n % 2 == 0:
newnames = [] for i in range(len(names)):# = 1:length(names):
newnames.append(names[i]+”u”) names[i] = names[i]+”g”
names += newnames cncharsi = -1 * cnchars top = np.hstack((cnchars, cnchars)) bot = np.hstack((cnchars, cncharsi)) chars = np.vstack((top, bot))
- else:
newnames = [] for i in range(len(names)):# = 1:length(names):
newnames.append(names[i]+”’’”) names[i] = names[i]+”’”
names += newnames cncharsi = -1 * cnchars top = np.hstack((cnchars, cnchars)) bot = np.hstack((cnchars, cncharsi)) chars = np.vstack((top, bot))
return names, classes, chars
- def Sn_irr(n):
- if n % 4 == 0:
names, classes, chars = Cn_irrmat(n) for i in range(n): # = 1:n:
- if (i+1) % 2 == 0:
classes[i] = “S”+classes[i][1:]
- elif n % 2 == 0:
ni = round(n/2) names, classes, cnchars = Cn_irrmat(ni) classes = [“E”] for i in range(1,n>>1): # = 1:n>>1-1:
r,s = reduce(n>>1, i) c_class_string(classes, “C”, r, s)
classes.append(“i”) for i in range(1,n>>1): # = 1:n>>1-1:
r,s = reduce(n, ((i<<1)+(n>>1))%n) c_class_string(classes, “S”, r, s)
newnames = [] for i in range(len(names)): # = 1:length(names):
newnames.append(names[i]+”u”) names[i] = names[i]+”g”
names += newnames cncharsi = -1 * cnchars top = np.hstack((cnchars, cnchars)) bot = np.hstack((cnchars, cncharsi)) chars = np.vstack((top, bot))
- else:
raise Exception(“Odd number n for S group”)
return names, classes, chars
- def Sn_irr_complex(n):
- if n % 4 == 0:
names, classes, chars = Cn_irr_complex(n) for i in range(n): # = 1:n:
- if (i+1) % 2 == 0:
classes[i] = “S”+classes[i][1:]
- elif n % 2 == 0:
ni = round(n/2) names, classes, cnchars = Cn_irr_complex(ni) classes = [“E”] for i in range(1,n>>1): # = 1:n>>1-1:
r,s = reduce(n>>1, i) c_class_string(classes, “C”, r, s)
classes.append(“i”) for i in range(1,n>>1): # = 1:n>>1-1:
r,s = reduce(n, ((i<<1)+(n>>1))%n) c_class_string(classes, “S”, r, s)
newnames = [] for i in range(len(names)): # = 1:length(names):
newnames.append(names[i]+”u”) names[i] = names[i]+”g”
names += newnames cncharsi = -1 * cnchars top = np.hstack((cnchars, cnchars)) bot = np.hstack((cnchars, cncharsi)) chars = np.vstack((top, bot))
- else:
raise Exception(“Odd number n for S group”)
return names, classes, chars
- def Dn_irr(n):
- if n == 2:
names = [“A”, “B1”, “B2”, “B3”] classes = [“E”, “C_2(z)”, “C_2(y)”, “C_2(x)”] chars = np.array([[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]]) return names, classes, chars
names, garbage_classes, chars = Cn_irrmat(n) garbage_names, classes, garbage_chars = Cnv_irr(n) if n % 2 == 0:
classes[-2] = classes[-2][0]+”C_2’” classes[-1] = classes[-1][0]+”C_2’’”
- else:
classes[-1] = classes[-1][0]+”C_2”
names[0] = “A1” names.insert(1, “A2”) chars = np.vstack((chars[0,:], chars[0,:], chars[1:,:])) for i in range(1,n): # = 2:n:
- if i == n-i or i > n-i:
break
#deleteat!(classes, n-i+2) chars = chars[:,[j for j in range(np.shape(chars)[1]) if j != n-i]] # chars[:,0:-1.!=n-i+2]
- if n % 2 == 0:
nirr = round((n/2)+3) names[2] = “B1” names.insert(3, “B2”) chars = np.vstack((chars[0:3,:], chars[2,:], chars[3:,:])) C2p = np.zeros(nirr) C2pp = np.zeros(nirr) C2p[0:4] = np.array([1,-1,1,-1]) C2pp[0:4] = np.array([1,-1,-1,1]) chars = np.hstack((chars, C2p[:,None], C2pp[:,None]))
- else:
nirr = round((n-1)/2+2) C2p = np.zeros(nirr) C2p[0:2] = np.array([1, -1]) chars = np.hstack((chars, C2p[:,None]))
return names, classes, chars
- def Dnh_irr(n):
names, classes, dnchars = Dn_irr(n) if n % 2 == 0:
classes.append(“i”) if n == 2:
classes.append(“sigma(xy)”) classes.append(“sigma(xz)”) classes.append(“sigma(yz)”)
- else:
- for i in range(1,n>>1): # = 1:n>>1-1:
a = i+(n>>1) if a > (n>>1):
a = n - a
r,s = reduce(n, a) c_class_string(classes, “2S”, r, s)
classes.append(“sigma_h”) if n % 4 == 0:
classes.append(f”{n>>1}sigma_v”) classes.append(f”{n>>1}sigma_d”)
- else:
classes.append(f”{n>>1}sigma_d”) classes.append(f”{n>>1}sigma_v”)
newnames = [] for i in range(len(names)): # = 1:length(names):
newnames.append(names[i]+”u”) names[i] = names[i]+”g”
names += newnames dncharsi = -1 * dnchars top = np.hstack((dnchars, dnchars)) bot = np.hstack((dnchars, dncharsi)) chars = np.vstack((top, bot))
- else:
classes.append(“sigma_h”) for i in range(1,(n>>1)+1): # = 1:n>>1:
- if i % 2 == 0:
r,s = reduce(n, n-i)
- else:
r,s = reduce(n ,i)
c_class_string(classes, “2S”, r, s)
classes.append(f”{n}sigma_v”) newnames = [] for i in range(len(names)): # = 1:length(names):
newnames.append(names[i]+”’’”) names[i] = names[i]+”’”
names += newnames dncharsi = -1 * dnchars top = np.hstack((dnchars, dnchars)) bot = np.hstack((dnchars, dncharsi)) chars = np.vstack((top, bot))
return names, classes, chars
- def Dnd_irr(n):
- if n % 2 == 0:
n2 = 2*n names, classes, chars = Sn_irr(n2) #classes = collect(1:2*n2) classes = classes[0:n+1] for i in range(1,n): # = 2:n:
classes[i] = “2”+classes[i]
classes.append(f”{n}C_2’”) classes.append(f”{n}sigma_d”) names[0] = “A1” names.insert(1, “A2”) chars = np.vstack((chars[0,:], chars[0,:], chars[1:,:])) for i in range(1,n2): # = 2:n2:
- if i >= n2-i:
break
chars = chars[:,[j for j in range(np.shape(chars)[1]) if j != n2-i]] # chars[:,0:-1.!=n2-i+2]
nirr = n+3 names[2] = “B1” names.insert(3, “B2”) chars = np.vstack((chars[0:3,:], chars[2,:], chars[3:,:])) C2p = np.zeros(nirr) sigma_d = np.zeros(nirr) C2p[0:4] = np.array([1,-1,1,-1]) sigma_d[0:4] = np.array([1,-1,-1,1]) chars = np.hstack((chars, C2p[:,None], sigma_d[:,None]))
- else:
names, classes, dnchars = Dn_irr(n) classes.append(“i”) for i in range(1,(n>>1)+1): # = 1:n>>1:
r,s = reduce(2*n, 2*i+n) if s > n:
s = 2*n-s
c_class_string(classes, “2S”, r, s)
classes.append(f”{n}sigma_d”) newnames = [] for i in range(len(names)): # = 1:length(names):
newnames.append(names[i]+”u”) names[i] = names[i]+”g”
names += newnames dncharsi = -1 * dnchars top = np.hstack((dnchars, dnchars)) bot = np.hstack((dnchars, dncharsi)) chars = np.vstack((top, bot))
return names, classes, chars