def one_block(L1, L2):
v = -2.0*sum([sqrt(4.0*pi/(2*L+1)) *
y1mat_Yqk((L1, 0), (L, 0), (L2, 0)) *
en_r1mat_L[L]
for L in ls_non_zero_YYY(L1, L2)])
if L1 == L2:
L = L1
t = -0.5 * d2_rmat + L*(L+1)*0.5*r2_rmat
return t+v
else:
return v
def mat_h2_plus(bond_length, bspline_set, l_list):
""" gives hamiltonian matrix and overlap matrix of hydrogem molecule ion
Parameters
----------
bond_length : Double
bond length of hydrogen molecular ion
bspline_set : BSplineSet
l_list: list of non negative integer
list of angular quauntum number to use
Returns
-------
h_mat : numpy.ndarray
hamiltonian matrix
s_mat : numpy.ndarray
overlap pmatrix
"""
# compute r1 matrix (B_i|O|B_j)
# (-1/2 d^2/dr^2, 1, 1/r^2, {s^L/g^{L+1} | L<-l_list})
rs = bspline_set.xs
d2_rmat = bspline_set.d2_mat()
r2_rmat = bspline_set.v_mat(1.0/(rs*rs))
s_rmat = bspline_set.s_mat()
tmp_L_list = uniq(flatten([ls_non_zero_YYY(L1, L2)
for L1 in l_list for L2 in l_list]))
en_r1mat_L = {}
for L in tmp_L_list:
en_r1mat_L[L] = bspline_set.en_mat(L, bond_length/2.0)
# compute y1 matrix (Y_L1|P_L(w_A)|Y_L2)
en_y1mat_L = {}
for L in tmp_L_list:
en_y1mat_L[L] = coo_matrix([[np.sqrt(4.0*np.pi/(2*L+1)) *
y1mat_Yqk((L1, 0), (L, 0), (L2, 0))
for L1 in l_list]
for L2 in l_list])
LL_y1mat = coo_matrix(np.diag([1.0*L*(L+1) for L in l_list]))
diag_y1mat = coo_matrix(np.diag([1 for L in l_list]))
# compute r1y1 matrix
h_r1y1mat = (synthesis_mat(-0.5*d2_rmat, diag_y1mat) +
synthesis_mat(+0.5*r2_rmat, LL_y1mat) - 2.0 *
sum([synthesis_mat(en_r1mat_L[L], en_y1mat_L[L])
for L in tmp_L_list]))
s_r1y1mat = synthesis_mat(s_rmat, diag_y1mat)
return (h_r1y1mat, s_r1y1mat)