def make_nabla(lmax=2):
"""Create the array of derivative intergrals.
::
/ ^ 1-l' d l'
| dr Y r ---(r Y )
/ L dr L'
v
"""
Lmax = (lmax + 1)**2
from gpaw.spherical_harmonics import YL, gam
Y_LLv = np.zeros((Lmax, Lmax, 3))
# Insert new values
for L1 in range(Lmax):
for L2 in range(Lmax):
for v in range(3):
r = 0.0
for c1, n1 in YL[L1]:
for c2, n2 in YL[L2]:
n = [0, 0, 0]
n[0] = n1[0] + n2[0]
n[1] = n1[1] + n2[1]
n[2] = n1[2] + n2[2]
if n2[v] > 0:
# apply derivative
n[v] -= 1
# add integral
r += n2[v] * c1 * c2 * gam(n[0], n[1], n[2])
Y_LLv[L1, L2, v] = r
return Y_LLv
def make_gaunt(lmax=2):
Lmax = (lmax + 1)**2
L2max = (2 * lmax + 1)**2
from gpaw.spherical_harmonics import YL, gam
G_LLL = np.zeros((Lmax, Lmax, L2max))
for L1 in range(Lmax):
for L2 in range(Lmax):
for L in range(L2max):
r = 0.0
for c1, n1 in YL[L1]:
for c2, n2 in YL[L2]:
for c, n in YL[L]:
nx = n1[0] + n2[0] + n[0]
ny = n1[1] + n2[1] + n[1]
nz = n1[2] + n2[2] + n[2]
r += c * c1 * c2 * gam(nx, ny, nz)
G_LLL[L1, L2, L] = r
return G_LLL