def contract_1e_soc(f1e, fcivec, norb, nelec):
fcinew = numpy.zeros_like(fcivec, dtype=numpy.complex64)
goffset = 0
for neleca in range(nelec + 1):
nelecb = nelec - neleca
link_indexa = cistring_soc.gen_linkstr_index_o0(range(norb), neleca)
link_indexb = cistring_soc.gen_linkstr_index_o0(range(norb), nelecb)
na = cistring_soc.num_strings(norb, neleca)
nb = cistring_soc.num_strings(norb, nelecb)
ci0 = fcivec[goffset:goffset + na * nb].reshape(na, nb)
t1 = numpy.zeros((norb, norb, na, nb), dtype=numpy.complex64)
for str0, tab in enumerate(link_indexa):
for a, i, str1, sign in tab:
t1[a, i, str1] += sign * ci0[str0]
for str0, tab in enumerate(link_indexb):
for a, i, str1, sign in tab:
t1[a, i, :, str1] += sign * ci0[:, str0]
ci0 = numpy.dot(f1e.reshape(-1), t1.reshape(-1, na * nb))
fcinew[goffset:goffset + na * nb] = ci0.reshape(-1)
goffset += na * nb
return fcinew.reshape(fcivec.shape)
def kernel(h1e, hsoc, g2e, norb, nelec):
h2e = absorb_h1e_soc(h1e, g2e, norb, nelec, .5)
def hop(c):
hc = contract_2e_soc(h2e, c, norb, nelec) + contract_1esoc_soc(
hsoc, c, norb, nelec)
return hc.reshape(-1)
e = 0.0
hdiag = make_hdiag_soc(h1e, g2e, norb, nelec)
na = hdiag.shape[0]
ci0 = numpy.zeros(na, numpy.complex64)
#Need to allow mixing otherwise no overlap
#This will not be an issue with SOC switched on
goffset = 0
for neleca in range(nelec + 1):
nelecb = nelec - neleca
na = cistring_soc.num_strings(norb, neleca)
nb = cistring_soc.num_strings(norb, nelecb)
goffset += na * nb
ci0 = numpy.random.random(goffset)
ci0 /= numpy.linalg.norm(ci0)
precond = lambda x, e, *args: x / (hdiag - e + 1e-4)
e, c = pyscf.lib.davidson(hop,
ci0.reshape(-1),
precond,
max_cycle=100,
max_space=100,
tol=1.e-15)
return e, c
def contract_1esoc_soc(f1e, fcivec, norb, nelec):
fcinew = numpy.zeros_like(fcivec, dtype=numpy.complex64)
goffset = 0
for neleca in range(nelec + 1):
nelecb = nelec - neleca
na = cistring_soc.num_strings(norb, neleca)
nb = cistring_soc.num_strings(norb, nelecb)
ci0 = fcivec[goffset:goffset + na * nb].reshape(na, nb)
if (nelecb > 0):
#c+_a c_b
link_index, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 0)
nna = cistring_soc.num_strings(norb, neleca + 1)
nnb = cistring_soc.num_strings(norb, nelecb - 1)
t1 = numpy.zeros((norb, norb, nna, nnb), dtype=numpy.complex64)
for str0, tab in enumerate(link_index):
for loc, (a, i, target, sign) in enumerate(tab):
t1[a, i, target[0],
target[1]] += sign * ci0[vv[str0][loc], str0]
ci0 = numpy.dot(f1e[0].reshape(-1), t1.reshape(-1, nna * nnb))
fcinew[goffset + na * nb:goffset + na * nb +
nna * nnb] += ci0.reshape(-1)
#c+_b c_a
if (neleca > 0):
ci0 = fcivec[goffset:goffset + na * nb].reshape(na, nb)
link_index, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 1)
nna = cistring_soc.num_strings(norb, neleca - 1)
nnb = cistring_soc.num_strings(norb, nelecb + 1)
t1 = numpy.zeros((norb, norb, nna, nnb), dtype=numpy.complex64)
for str0, tab in enumerate(link_index):
for loc, (a, i, target, sign) in enumerate(tab):
t1[a, i, target[0],
target[1]] += sign * ci0[str0, vv[str0][loc]]
ci0 = numpy.dot(f1e[1].reshape(-1), t1.reshape(-1, nna * nnb))
fcinew[goffset - nna * nnb:goffset] += ci0.reshape(-1)
goffset += na * nb
return fcinew.reshape(fcivec.shape)
def make_rdm12(fcivec, norb, nelec, opt=None):
goffset = 0
t1 = numpy.zeros((2, 2, len(fcivec), norb, norb), dtype=numpy.complex64)
for neleca in range(nelec + 1):
nelecb = nelec - neleca
link_indexa = cistring_soc.gen_linkstr_index_o0(range(norb), neleca)
link_indexb = cistring_soc.gen_linkstr_index_o0(range(norb), nelecb)
na = cistring_soc.num_strings(norb, neleca)
nb = cistring_soc.num_strings(norb, nelecb)
ci0 = fcivec[goffset:goffset + na * nb].reshape(na, nb)
#sector a,a
#spin a
for str0, tab in enumerate(link_indexa):
for a, i, str1, sign in tab:
for k in range(nb):
t1[0, 0, goffset + str1 * nb + k, a,
i] += sign * ci0[str0, k]
#sector b,b
#spin b
for str0, tab in enumerate(link_indexb):
for a, i, str1, sign in tab:
for k in range(na):
t1[1, 1, goffset + k * nb + str1, a,
i] += sign * ci0[k, str0]
#sector a,b
if (nelecb > 0):
#c+_a c_b
link_indexa, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 0)
nna = cistring_soc.num_strings(norb, neleca + 1)
nnb = cistring_soc.num_strings(norb, nelecb - 1)
for str0b, tab in enumerate(link_indexa):
for loc, (a, i, target, sign) in enumerate(tab):
str0a = vv[str0][loc]
#print a,i,target,sign, str0, vv[str0], ci0[tstr,str0], ciT[target[0],target[1]]
targetloc = goffset + na * nb + nnb * target[0] + target[1]
t1[0, 1, targetloc, a, i] += sign * ci0[str0a, str0b]
if (neleca > 0):
#c+_b c_a
link_indexb, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 1)
nna = cistring_soc.num_strings(norb, neleca - 1)
nnb = cistring_soc.num_strings(norb, nelecb + 1)
for str0a, tab in enumerate(link_indexb):
for loc, (a, i, target, sign) in enumerate(tab):
str0b = vv[str0][loc]
targetloc = goffset - nna * nnb + nnb * target[0] + target[
1]
t1[1, 0, targetloc, a, i] += sign * ci0[str0a, str0b]
goffset += na * nb
#Now construct the different sectors for rdm2
rdm1 = numpy.zeros((2, 2, norb, norb), dtype=numpy.complex64)
rdm2 = numpy.zeros((2, 2, 2, 2, norb, norb, norb, norb),
dtype=numpy.complex64)
for a in range(2):
for b in range(2):
rdm1[a, b] = numpy.einsum('m,mij->ij', fcivec.conjugate(), t1[a,
b])
for c in range(2):
for d in range(2):
rdm2[a, b, c,
d] = numpy.einsum('mij,mkl->jikl',
t1[a, b].conjugate(), t1[c, d])
#Remove additional contribution
for a in range(2):
for b in range(2):
for c in range(2):
for k in range(norb):
rdm2[a, b, b, c, :, k, k, :] -= rdm1[a, c]
return rdm1, rdm2
def make_rdm1(fcivec, norb, nelec, opt=None):
rdm1 = numpy.zeros((2, 2, norb, norb), dtype=numpy.complex64)
goffset = 0
for neleca in range(nelec + 1):
nelecb = nelec - neleca
link_indexa = cistring_soc.gen_linkstr_index_o0(range(norb), neleca)
link_indexb = cistring_soc.gen_linkstr_index_o0(range(norb), nelecb)
na = cistring_soc.num_strings(norb, neleca)
nb = cistring_soc.num_strings(norb, nelecb)
ci0 = fcivec[goffset:goffset + na * nb].reshape(na, nb)
#sector a,a
#spin a
for str0, tab in enumerate(link_indexa):
for a, i, str1, sign in tab:
rdm1[0, 0, a,
i] += sign * numpy.dot(ci0[str1].conjugate(), ci0[str0])
#sector b,b
#spin b
for str0, tab in enumerate(link_indexb):
for k in range(na):
for a, i, str1, sign in tab:
rdm1[1, 1, a,
i] += sign * ci0[k, str1].conjugate() * ci0[k, str0]
#sector a,b
if (nelecb > 0):
#c+_a c_b
link_indexa, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 0)
nna = cistring_soc.num_strings(norb, neleca + 1)
nnb = cistring_soc.num_strings(norb, nelecb - 1)
ciT = fcivec[goffset + na * nb:goffset + na * nb +
nna * nnb].reshape(nna, nnb)
for str0, tab in enumerate(link_indexa):
for loc, (a, i, target, sign) in enumerate(tab):
#print a,i,target,sign, str0, vv[str0], ci0[tstr,str0], ciT[target[0],target[1]]
tstr = vv[str0][loc]
rdm1[0, 1, a,
i] += sign * ci0[tstr,
str0] * ciT[target[0],
target[1]].conjugate()
if (neleca > 0):
#c+_b c_a
link_indexb, vv = cistring_soc.gen_linkstr_index_o0_soc(
range(norb), neleca, nelecb, 1)
nna = cistring_soc.num_strings(norb, neleca - 1)
nnb = cistring_soc.num_strings(norb, nelecb + 1)
ciT = fcivec[goffset - nna * nnb:goffset].reshape(nna, nnb)
for str0, tab in enumerate(link_indexb):
for loc, (a, i, target, sign) in enumerate(tab):
#for tstr in vv[str0]:
tstr = vv[str0][loc]
rdm1[1, 0, a,
i] += sign * ci0[str0,
tstr] * ciT[target[0],
target[1]].conjugate()
goffset += na * nb
return rdm1