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2.py
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2.py
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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)
# 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)
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)
D = G_convert.T
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)
# D[n_sph:,n_sph:] = np.eye(n_car-n_sph, dtype = np.float32)
print(D)
for i in range(0, n_car - n_sph):
b = np.zeros(n_car, dtype = np.float32)
b[n_sph+i] = 1
# D[n_sph+i] = np.random.random(D.shape[1]).astype(np.float32)
v = np.linalg.solve(D, b)
v /= np.linalg.norm(v)
D[n_sph+i] = v
print(D)
a = np.arange(n_sph)
b = a @ G_convert.T
c = b @ D.I[:,:n_sph]
print(a, b, c)