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)
def mat_h2_lil(bond_length, bspline_set, y_list):
"""gives hamiltonian matrix and overlap matrix of hydrogen molecule"""
# settings
qmax = 2*max([y.L1 for y in y_list])
qs = range(qmax+1)
# compute r1 matrix
s_r1mat = bspline_set.s_mat()
d2_r1mat = bspline_set.d2_mat()
rs = bspline_set.xs
r2_r1mat = bspline_set.v_mat(1.0/(rs*rs))
ra_r1mat_q = dict([(q, bspline_set.en_mat(q, bond_length/2.0))
for q in qs])
# compute r2 matrix
s_r2mat = synthesis_mat(s_r1mat, s_r1mat)
d2_1_r2mat = synthesis_mat(d2_r1mat, s_r1mat)
d2_2_r2mat = synthesis_mat(s_r1mat, d2_r1mat)
r2_1_r2mat = synthesis_mat(r2_r1mat, s_r1mat)
r2_2_r2mat = synthesis_mat(s_r1mat, r2_r1mat)
ra_1_r2mat_q = dict([(q, synthesis_mat(ra, s_r1mat))
for (q, ra) in ra_r1mat_q.items()])
ra_2_r2mat_q = dict([(q, synthesis_mat(s_r1mat, ra))
for (q, ra) in ra_r1mat_q.items()])
eri_r2mat_q = dict([(q, bspline_set.eri_mat(q)) for q in qs])
# compute y2 matrix
def ymat(o):
return dict([(q, coo_matrix([[o(y1, q, y2)
for y1 in y_list] for y2 in y_list]))
for q in qs])
y2mat_Pq_r12_q = ymat(y2mat_Pq_r12)
y2mat_Pq_r1A_q = ymat(y2mat_Pq_r1A)
y2mat_Pq_r2A_q = ymat(y2mat_Pq_r2A)
y2mat_LL1 = coo_matrix(np.diag([y.L1*(y.L1+1) for y in y_list]))
y2mat_LL2 = coo_matrix(np.diag([y.L2*(y.L2+1) for y in y_list]))
y2mat_diag = coo_matrix(np.diag([1 for y in y_list]))
# compute r2y2 matrix
h_mat = lil_matrix(-0.5*synthesis_mat(d2_1_r2mat, y2mat_diag))
h_mat += lil_matrix(-0.5*synthesis_mat(d2_2_r2mat, y2mat_diag))
h_mat += lil_matrix(0.5*synthesis_mat(r2_1_r2mat, y2mat_LL1))
h_mat += lil_matrix(0.5*synthesis_mat(r2_2_r2mat, y2mat_LL2))
for q in qs:
h_mat += lil_matrix(-2.0*synthesis_mat(ra_1_r2mat_q[q],
y2mat_Pq_r1A_q[q]))
h_mat += lil_matrix(-2.0*synthesis_mat(ra_2_r2mat_q[q],
y2mat_Pq_r2A_q[q]))
h_mat += lil_matrix(synthesis_mat(eri_r2mat_q[q],
y2mat_Pq_r12_q[q]))
s_mat = synthesis_mat(s_r2mat, y2mat_diag)
return (h_mat, s_mat)
