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basis.py
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basis.py
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from distutils.command.build import build
import numpy as np
from math import sqrt, factorial, pi
S_convert = np.matrix([
[1.00000000,],
], dtype = np.float32)
P_convert = np.matrix([
[1.00000000, 0.00000000, 0.00000000],
[0.00000000, 1.00000000, 0.00000000],
[0.00000000, 0.00000000, 1.00000000],
], dtype = np.float32)
D_convert = np.matrix([
# D 0, D+1, D-1, D+2, D-2, S
[-0.50000000, 0.00000000, 0.00000000, 0.86602540, 0.00000000], #xx
[-0.50000000, 0.00000000, 0.00000000,-0.86602540, 0.00000000], #yy
[ 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #zz
[ 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000], #xy
[ 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000], #xz
[ 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000], #yz
], dtype = np.float32).T
# 这是专用orca的转换矩阵。相对于multiwfn提供的表格，orca的F+3和G+4轨道的相位是反着的。因此对于其他程序可能要把转移矩阵的后两列乘以-1
F_convert = np.matrix([
# F+0, F+1, F-1, F+2, F-2, F+3, F-3, px, py, pz
[ 0.00000000,-0.61237244, 0.00000000, 0.00000000, 0.00000000,-0.79056942, 0.00000000], #xxx
[ 0.00000000, 0.00000000,-0.61237244, 0.00000000, 0.00000000, 0.00000000, 0.79056942], #yyy
[ 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #zzz
[ 0.00000000,-0.27386127, 0.00000000, 0.00000000, 0.00000000, 1.06066017, 0.00000000], #xyy
[ 0.00000000, 0.00000000,-0.27386127, 0.00000000, 0.00000000, 0.00000000,-1.06066017], #xxy
[-0.67082039, 0.00000000, 0.00000000, 0.86602540, 0.00000000, 0.00000000, 0.00000000], #xxz
[ 0.00000000, 1.09544511, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #xzz
[ 0.00000000, 0.00000000, 1.09544511, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #yzz
[-0.67082039, 0.00000000, 0.00000000,-0.86602540, 0.00000000, 0.00000000, 0.00000000], #yyz
[ 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000], #xyz
], dtype = np.float32).T
G_convert = np.matrix([
# G+0,G+1,G-1G+2,G-2,G+3,G-3,G+4,G-4, D+0, D+1, D-1, D+2, D-2, S
[ 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #zzzz
[ 0.00000000, 0.00000000, 1.19522860, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #yzzz
[-0.87831006, 0.00000000, 0.00000000,-0.98198050, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #yyzz
[ 0.00000000, 0.00000000,-0.89642145, 0.00000000, 0.00000000, 0.00000000,-0.79056941, 0.00000000, 0.00000000], #yyyz
[ 0.37500000, 0.00000000, 0.00000000, 0.55901699, 0.00000000, 0.00000000, 0.00000000,-0.73950997, 0.00000000], #yyyy
[ 0.00000000, 1.19522860, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #xzzz
[ 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.13389341, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #xyzz
[ 0.00000000,-0.40089186, 0.00000000, 0.00000000, 0.00000000,-1.06066017, 0.00000000, 0.00000000, 0.00000000], #xyyz
[ 0.00000000, 0.00000000, 0.00000000, 0.00000000,-0.42257712, 0.00000000, 0.00000000, 0.00000000, 1.11803398], #xyyy
[-0.87831006, 0.00000000, 0.00000000, 0.98198050, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000], #xxzz
[ 0.00000000, 0.00000000,-0.40089186, 0.00000000, 0.00000000, 0.00000000, 1.06066017, 0.00000000, 0.00000000], #xxyz
[ 0.21957751, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.29903810, 0.00000000], #xxyy
[ 0.00000000,-0.89642145, 0.00000000, 0.00000000, 0.00000000, 0.79056941, 0.00000000, 0.00000000, 0.00000000], #xxxz
[ 0.00000000, 0.00000000, 0.00000000, 0.00000000,-0.42257712, 0.00000000, 0.00000000, 0.00000000,-1.11803398], #xxxy
[ 0.37500000, 0.00000000, 0.00000000,-0.55901699, 0.00000000, 0.00000000, 0.00000000, 0.73950997, 0.00000000], #xxxx
], dtype = np.float32).T
H_convert = np.eye(11, 21, dtype = np.float32)
def build_reverse_matrix(M):
D = np.empty_like(M, dtype = np.float32)
D[:,:] = M
n_car, n_sph = D.shape[1], D.shape[0]
D = np.concatenate((D, np.random.random((n_car-n_sph, n_car)).astype(np.float32)), axis = 0)
for i in range(0, n_car - n_sph):
b = np.zeros(n_car, dtype = np.float32)
b[n_sph+i] = 1
v = np.linalg.solve(D, b)
v /= np.linalg.norm(v)
D[n_sph+i] = v
return D.I[:,:n_sph]
D_inverse = build_reverse_matrix(D_convert)
F_inverse = build_reverse_matrix(F_convert)
G_inverse = build_reverse_matrix(G_convert)
H_inverse = np.eye(21, 11, dtype = np.float32)
class GTF:
def __init__(self, p, c, a, i, j, k):
self.c, self.a, self.p = c, a, p
self.i, self.j, self.k = i, j, k
self.__calculate_normalize_coeff()
def __call__(self, x, y, z):
dx, dy, dz = x-self.p[0], y-self.p[1], z-self.p[2]
return self.c * (dx**self.i * dy**self.j * dz**self.k) * np.exp(-self.a * (dx**2 + dy**2 + dz**2))
def __calculate_normalize_coeff(self):
L = self.i + self.j + self.k
i = L // 3
j = i + (L % 3) // 2
k = L - i - j
N0 = (2*self.a/pi)**0.75 * sqrt((8*self.a)**L*factorial(i)*factorial(j)*factorial(k)/(factorial(2*i)*factorial(2*j)*factorial(2*k)))
N1 = (2*self.a/pi)**0.75 * sqrt((8*self.a)**L*factorial(self.i)*factorial(self.j)*factorial(self.k)/(factorial(2*self.i)*factorial(2*self.j)*factorial(2*self.k)))
self.c = self.c * N1 / N0
class GTO:
def __init__(self, position, contracts, coefficients, px, py, pz, atomidx):
self.c = coefficients
self.a = contracts
self.p = position
self.px = px
self.py = py
self.pz = pz
self.atomidx = atomidx
self.funcs = [GTF(self.p, c, a, px, py, pz) for c, a in zip(self.c, self.a)]
def __call__(self, x, y, z):
a = 0
for f in self.funcs:
a += f(x, y, z)
return a
class GTOShell:
def __init__(self, orbital_type = "s", contracts = [1.0,], coefficients = [1.0,], position = [0.0, 0.0, 0.0], atomidx = 0, gtotype = "spherical"):
self.s = orbital_type
self.c = np.array(coefficients, dtype = np.float32)
self.a = np.array(contracts, dtype = np.float32)
self.p = np.array(position, dtype = np.float32)
self.atomidx = atomidx
self.type = gtotype
self.gtos = []
self.generate_orbitals()
def generate_orbitals(self):
if self.s == "s":
self.gtos.append(GTO(self.p, self.a, self.c, 0, 0, 0, self.atomidx))
elif self.s == "p":
self.gtos.append(GTO(self.p, self.a, self.c, 1, 0, 0, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 0, 1, 0, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 0, 0, 1, self.atomidx))
elif self.s == "d":
self.gtos.append(GTO(self.p, self.a, self.c, 2, 0, 0, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 0, 2, 0, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 0, 0, 2, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 1, 1, 0, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 1, 0, 1, self.atomidx))
self.gtos.append(GTO(self.p, self.a, self.c, 0, 1, 1, self.atomidx))
elif self.s == "f":
idx = [3,0,0,1,2,2,1,0,0,1]
idy = [0,3,0,2,1,0,0,1,2,1]
idz = [0,0,3,0,0,1,2,2,1,1]
for x, y, z in zip(idx, idy, idz):
self.gtos.append(GTO(self.p, self.a, self.c, x, y, z, self.atomidx))
elif self.s == "g":
idx = [0,0,0,0,0,1,1,1,1,2,2,2,3,3,4]
idy = [0,1,2,3,4,0,1,2,3,0,1,2,0,1,0]
idz = [4,3,2,1,0,3,2,1,0,2,1,0,1,0,0]
for x, y, z in zip(idx, idy, idz):
self.gtos.append(GTO(self.p, self.a, self.c, x, y, z, self.atomidx))
elif self.s == "h":
idx = [0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5]
idy = [0,1,2,3,4,5,0,1,2,3,4,0,1,2,3,0,1,2,0,1,0]
idz = [5,4,3,2,1,0,4,3,2,1,0,3,2,1,0,2,1,0,1,0,0]
for x, y, z in zip(idx, idy, idz):
self.gtos.append(GTO(self.p, self.a, self.c, x, y, z, self.atomidx))