def simplify_all(result, deltas, cumulantE4=False, cumulantE3=False):
for t in result:
t.contractDeltaFuncs_new()
sqa.removeVirtOps_sf(result)
sqa.termChop(result)
sqa.combineTerms(result)
extendedR = []
for t in result:
extendedR += sqa.contractCoreOps_sf(t)
for t in extendedR:
t.contractDeltaFuncs_new()
sqa.termChop(extendedR)
sqa.combineTerms(extendedR)
result = []
for r in extendedR:
item1 = replaceRepeatIndicesWithDeltas(r, deltas)
item2 = replaceSingleKdeltaWithDeltas(item1, deltas)
result.append(replaceAllKdeltaWithDeltas(item2, deltas))
if (cumulantE4):
x1 = sqa.index('Ax1', [sqa.options.active_type], True)
x2 = sqa.index('Ax2', [sqa.options.active_type], True)
x3 = sqa.index('Ax3', [sqa.options.active_type], True)
x4 = sqa.index('Ax4', [sqa.options.active_type], True)
x5 = sqa.index('Ax5', [sqa.options.active_type], True)
x6 = sqa.index('Ax6', [sqa.options.active_type], True)
sqa.decomp_4rdms_to_3rdms_sf(result, 'E4', sqa.sfExOp([x1, x2]),
sqa.sfExOp([x1, x2, x3, x4]),
sqa.sfExOp([x1, x2, x3, x4]),
sqa.sfExOp([x1, x2, x3, x4]),
sqa.sfExOp([x1, x2, x3, x4, x5, x6]))
if (cumulantE3):
x1 = sqa.index('Ax1', [sqa.options.active_type], True)
x2 = sqa.index('Ax2', [sqa.options.active_type], True)
x3 = sqa.index('Ax3', [sqa.options.active_type], True)
x4 = sqa.index('Ax4', [sqa.options.active_type], True)
sqa.decomp_3rdms_to_2rdms_sf(result, 'E3', sqa.sfExOp([x1, x2]),
sqa.sfExOp([x1, x2, x3, x4]))
return result
[gimme('vc'), gimme('vc')], # vvcc
[gimme('vc'), gimme('va')], # vvca
[gimme('ac'), gimme('vc')], # ccav
[gimme('va'), gimme('va')], # vvaa
[gimme('ac'), gimme('ac')], # ccaa
[gimme('vc'), gimme('aa')], # vaca
[gimme('ac'), gimme('va')], # avca
[gimme('va'), gimme('aa')], # vaaa
[gimme('ac'), gimme('aa')]
] # caaa
# Construct |Psi_1> and <Psi_1|
psi1_right = []
psi1_left = []
for i in range(9):
basis1 = sqa.sfExOp(basis[i][0])
basis2 = sqa.sfExOp(basis[i][1])
unique = unique_tensor(reorga_two_to_one(basis1, basis2))
tensor = sqa.tensor('D' + class_names[i], unique, []) #symm(unique)) #NO!
psi1_right.append(sqa.term(1.0, [''], [tensor, basis1, basis2]))
basis1 = sqa.sfExOp([basis[i][1][t] for t in [1, 0]])
basis2 = sqa.sfExOp([basis[i][0][t] for t in [1, 0]])
unique = unique_tensor(reorga_two_to_one(basis1, basis2))
tensor = sqa.tensor('D' + class_names[i], unique, []) #symm(unique)) #NO!
psi1_left.append(sqa.term(1.0, [''], [tensor, basis1, basis2]))
# (LOG if want to debug)
if print_log:
print '//'
print '// With the unique tensors found, |Psi1> is:'
# definitions
tg_c = sqa.options.core_type
tg_a = sqa.options.active_type
tg_v = sqa.options.virtual_type
tg_t = tg_c + tg_a + tg_v
i = [sqa.index('i%i' %j, [tg_c], True) for j in range(8)]
r = [sqa.index('r%i' %j, [tg_a], True) for j in range(8)]
a = [sqa.index('a%i' %j, [tg_v], True) for j in range(8)]
m = [sqa.index('m%i' %j, [tg_t], True) for j in range(8)]
t_sym = [ sqa.symmetry((1,0,3,2),1) ]
W_sym = [ sqa.symmetry((1,0,3,2),1), sqa.symmetry((0,3,2,1),1) ]
t_ts_ket_1 = [ sqa.tensor('t2', [a[0], a[3], i[0], i[1]], t_sym) ]
t_ops_ket_1= [ sqa.sfExOp([i[0], i[1], a[0], a[3]]) ]
W_ts_ket_1 = [ sqa.tensor('W', [a[1], a[2], a[3], i[2]], W_sym) ]
W_ops_ket_1= [ sqa.sfExOp([a[3], i[2], a[1], a[2]]) ]
t_ts_ket_2 = [ sqa.tensor('t2', [a[0], a[1], i[0], i[3]], t_sym) ]
t_ops_ket_2= [ sqa.sfExOp([i[0], i[3], a[0], a[1]]) ]
W_ts_ket_2 = [ sqa.tensor('W', [i[3], a[2], i[1], i[2]], W_sym) ]
W_ops_ket_2= [ sqa.sfExOp([i[1], i[2], i[3], a[2]]) ]
t_ts_bra_1 = [ sqa.tensor('t2', [i[4], i[5], a[4], a[7]], t_sym) ]
t_ops_bra_1= [ sqa.sfExOp([a[4], a[7], i[4], i[5]]) ]
W_ts_bra_1 = [ sqa.tensor('W', [a[7], i[6], a[5], a[6]], W_sym) ]
W_ops_bra_1= [ sqa.sfExOp([a[5], a[6], a[7], i[6]]) ]
t_ts_bra_2 = [ sqa.tensor('t2', [i[4], i[7], a[4], a[5]], t_sym) ]
t_ops_bra_2= [ sqa.sfExOp([a[4], a[5], i[4], i[7]]) ]
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
# Define tensors
K_C = sqa.tensor('int1c', [i1, i2], [hsym])
K_A = sqa.tensor('int1a', [x1, x2], [hsym])
K_V = sqa.tensor('int1v', [a1, a2], [hsym])
V_Al = sqa.tensor('int2Laa', [L, x1, x3], [])
V_Ar = sqa.tensor('int2Laa', [L, x2, x4], [])
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term(1.0, [''], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [''], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [''], [K_V, sqa.sfExOp([a1, a2])])
HD_A = sqa.term(0.5, [''], [V_Al, V_Ar, sqa.sfExOp([x1, x2, x3, x4])])
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec = sqa.tensor('p', [i, p, q, r], [])
Apvec = sqa.tensor('Ap', [j, u, v, w], [])
Omu = sqa.term(1.0, [''], [pvec, sqa.sfExOp([q, i]), sqa.sfExOp([p, r])])
Onu = sqa.term(1.0, [''], [Apvec, sqa.sfExOp([w, u]), sqa.sfExOp([j, v])])
commutator = []
commutator += sqa.commutator(T_C, Omu)
commutator += sqa.commutator(T_A, Omu)
commutator += sqa.commutator(T_V, Omu)
commutator += sqa.commutator(HD_A, Omu)
import secondQuantizationAlgebra as sqa
from tools_for_sqa import *
from tools_for_pt import *
sqa.options.verbose = False
# Make H0
H=h0('MRLCC',df=True)
# Define Omu
list1=gimme('caav')
list2=[list1[i] for i in [3,0]]
list3=[list1[i] for i in [1,2]]
pvec1 = sqa.tensor('p1', list1, symm(list1))
OmuA = sqa.term(1.0, [''], [pvec1, sqa.sfExOp(list2), sqa.sfExOp(list3)])
list2=[list1[i] for i in [1,0]]
list3=[list1[i] for i in [3,2]]
pvec2 = sqa.tensor('p2', list1, symm(list1))
OmuB = sqa.term(1.0, [''], [pvec2, sqa.sfExOp(list2), sqa.sfExOp(list3)])
# Define Onu
list1=gimme('caav')
list2=[list1[i] for i in [2,1]]
list3=[list1[i] for i in [0,3]]
Apvec1 = sqa.tensor('Ap1', list1, symm(list1))
OnuA = sqa.term(1.0, [''], [Apvec1, sqa.sfExOp(list2), sqa.sfExOp(list3)])
list2=[list1[i] for i in [2,3]]
list3=[list1[i] for i in [0,1]]
Apvec2 = sqa.tensor('Ap2', list1, symm(list1))
OnuB = sqa.term(1.0, [''], [Apvec2, sqa.sfExOp(list2), sqa.sfExOp(list3)])
# Define the normal-ordered A matrix:
import secondQuantizationAlgebra as sqa
import geraldCode
import mussardCode
sqa.options.verbose = False
# Define needed indexes as being core,active,virtual
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
x1 = sqa.index('Ax1', [tag_active], True)
x2 = sqa.index('Ax2', [tag_active], True)
x3 = sqa.index('Ax3', [tag_active], True)
x4 = sqa.index('Ax4', [tag_active], True)
x5 = sqa.index('Ax5', [tag_active], True)
x6 = sqa.index('Ax6', [tag_active], True)
x7 = sqa.index('Ax7', [tag_active], True)
x8 = sqa.index('Ax8', [tag_active], True)
result = sqa.normalOrder(
sqa.term(1.0, [''], [sqa.sfExOp([x1, x2, x3, x4, x5, x6, x7, x8])]))
result += sqa.normalOrder(
sqa.term(1.0, [''], [sqa.sfExOp([x1, x2, x3, x6, x7, x8])]))
result += sqa.normalOrder(sqa.term(1.0, [''], [sqa.sfExOp([x1, x2, x7, x8])]))
result += sqa.normalOrder(sqa.term(1.0, [''], [sqa.sfExOp([x1, x8])]))
for t in result:
print t
print "Test 3 output:"
print test3_string_output
if test3_string_output == test3_correct_answer:
print "Test 3 passed",
else:
print "Test 3 failed",
print " (%.3f seconds)\n" % (time.time() - startTime)
# Test 4: Normal ordering of the spin free operator string E(i0,i1) E(i2,i3,i4,i5) E(i6,i7,i8,i9)
print ""
print "Starting test 4"
print ""
startTime = time.time()
test4_indices = [sqa.index('i%i' % i) for i in range(10)]
test4_term = sqa.term(1.0, [], [
sqa.sfExOp(test4_indices[0:2]),
sqa.sfExOp(test4_indices[2:6]),
sqa.sfExOp(test4_indices[6:10])
])
test4_output = sqa.normalOrder(test4_term)
sqa.combineTerms(test4_output)
test4_string_output = ""
for t in test4_output:
test4_string_output += str(t) + '\n'
test4_correct_answer = " ( 1.00000) kdelta(i1,i2) kdelta(i4,i6) kdelta(i5,i7) E2(i0,i3,i8,i9) \n" + \
" ( 1.00000) kdelta(i1,i2) kdelta(i4,i7) kdelta(i5,i6) E2(i0,i3,i9,i8) \n" + \
" ( 1.00000) kdelta(i1,i3) kdelta(i4,i6) kdelta(i5,i7) E2(i0,i2,i9,i8) \n" + \
" ( 1.00000) kdelta(i1,i3) kdelta(i4,i7) kdelta(i5,i6) E2(i0,i2,i8,i9) \n" + \
" ( 1.00000) kdelta(i1,i2) kdelta(i4,i6) E3(i0,i3,i7,i8,i5,i9) \n" + \
" ( 1.00000) kdelta(i1,i2) kdelta(i4,i7) E3(i0,i3,i6,i9,i5,i8) \n" + \
" ( 1.00000) kdelta(i1,i2) kdelta(i5,i6) E3(i0,i3,i7,i4,i8,i9) \n" + \
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
k = sqa.index('Ak', [tag_active], True)
l = sqa.index('Al', [tag_active], True)
m = sqa.index('Am', [tag_active], True)
c = sqa.index('Vc', [tag_virtual], True)
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
Tsym = sqa.symmetry((0, 1, 2, 3), 1)
E_cmlk = [sqa.sfExOp([c, m, l, k])]
T_klmc = [sqa.tensor('T2', [k, l, m, c], [Tsym])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_cmlk[0], "|Psi>: R !!!!!"
print "@@@ SIGMA_0 <-- sum_{klcd} H(0; Vd, Vc, Al, Ak) T(Ak, Al, Vc, Vd)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
p = sqa.index('p', [tag_h1_p], True)
a4 = sqa.index('Vf', [tag_virtual], True)
#h0 one body term
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
K_C = sqa.tensor('int1', [i1,i2], [hsym])
K_A = sqa.tensor('int1', [x1,x2], [hsym])
K_V = sqa.tensor('int1', [a1,a2], [hsym])
V_A = sqa.tensor('int2', [x1,x2, x3,x4], [Dsym_a, Dsym_b, Dsym_c])
HD_A = sqa.term( 0.5, [""], [V_A, sqa.sfExOp([x1,x2,x3,x4])] )
T_C = sqa.term( 1.0, [""], [K_C, sqa.sfExOp([i1,i2])] )
T_A = sqa.term( 1.0, [""], [K_A, sqa.sfExOp([x1,x2])] )
T_V = sqa.term( 1.0, [""], [K_V, sqa.sfExOp([a1,a2])] )
#first excitation
E_aiEbj = sqa.term( 1.0, [""], [sqa.sfExOp([a, i]) , sqa.sfExOp([b,q])])
E_aiEbj2 = sqa.term( 1.0, [""], [sqa.sfExOp([r, d]) , sqa.sfExOp([j,c])])
commutator = []
commutator += sqa.commutator(HD_A, E_aiEbj)
commutator += sqa.commutator(T_C, E_aiEbj)
commutator += sqa.commutator(T_A, E_aiEbj)
commutator += sqa.commutator(T_V, E_aiEbj)
result = []
a1 = sqa.index('Vg', [tag_virtual], True)
a2 = sqa.index('Vh', [tag_virtual], True)
a3 = sqa.index('Ve', [tag_virtual], True)
a4 = sqa.index('Vf', [tag_virtual], True)
#h0 one body term
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
K_C = sqa.tensor('int1', [i1, i2], [hsym])
K_A = sqa.tensor('int1', [x1, x2], [hsym])
K_V = sqa.tensor('int1', [a1, a2], [hsym])
V_A = sqa.tensor('int2', [x1, x2, x3, x4], [Dsym_a, Dsym_b, Dsym_c])
HD_A = sqa.term(0.5, [""], [V_A, sqa.sfExOp([x1, x2, x3, x4])])
T_C = sqa.term(1.0, [""], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [""], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [""], [K_V, sqa.sfExOp([a1, a2])])
#first excitation
E_aiEbj = sqa.term(1.0, [""], [sqa.sfExOp([p, i]), sqa.sfExOp([a, j])])
E_aiEbj2 = sqa.term(1.0, [""], [sqa.sfExOp([l, b]), sqa.sfExOp([k, q])])
commutator = []
commutator += sqa.commutator(HD_A, E_aiEbj)
commutator += sqa.commutator(T_C, E_aiEbj)
commutator += sqa.commutator(T_A, E_aiEbj)
commutator += sqa.commutator(T_V, E_aiEbj)
result = []
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
# Define tensors
K_C = sqa.tensor('Wcc', [i1, i2], [hsym])
K_A = sqa.tensor('Waa', [x1, x2], [hsym])
K_V = sqa.tensor('Wvv', [a1, a2], [hsym])
V_A = sqa.tensor('Waaaa', [x1, x2, x3, x4], [Dsym_a, Dsym_b, Dsym_c])
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term(1.0, [''], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [''], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [''], [K_V, sqa.sfExOp([a1, a2])])
HD_A = sqa.term(0.5, [''], [V_A, sqa.sfExOp([x1, x2, x3, x4])])
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec1 = sqa.tensor('p1', [i, p, q, a], [])
pvec2 = sqa.tensor('p2', [i, p, q, a], [])
Apvec1 = sqa.tensor('Ap1', [j, r, s, b], [])
Apvec2 = sqa.tensor('Ap2', [j, r, s, b], [])
OmuA = sqa.term(1.0, [''], [pvec1, sqa.sfExOp([a, i]), sqa.sfExOp([p, q])])
OmuB = sqa.term(1.0, [''], [pvec2, sqa.sfExOp([p, i]), sqa.sfExOp([a, q])])
OnuA = sqa.term(1.0, [''], [Apvec1, sqa.sfExOp([s, r]), sqa.sfExOp([j, b])])
OnuB = sqa.term(1.0, [''], [Apvec2, sqa.sfExOp([s, b]), sqa.sfExOp([j, r])])
commutator1 = []
# definitions
tg_c = sqa.options.core_type
tg_a = sqa.options.active_type
tg_v = sqa.options.virtual_type
tg_t = tg_c + tg_a + tg_v
i = [sqa.index('i%i' %j, [tg_c], True) for j in range(8)]
r = [sqa.index('r%i' %j, [tg_a], True) for j in range(8)]
a = [sqa.index('a%i' %j, [tg_v], True) for j in range(8)]
m = [sqa.index('m%i' %j, [tg_t], True) for j in range(8)]
t_sym = [ sqa.symmetry((1,0,3,2),1) ]
W_sym = [ sqa.symmetry((1,0,3,2),1), sqa.symmetry((0,3,2,1),1) ]
tW_ts_ket_1 = [ sqa.tensor('t2Wk', [a[0], a[1], a[2], i[0], i[1], i[2]], []) ]
tW_ops_ket_1= [ sqa.sfExOp([i[0], i[1], i[2], a[0], a[1], a[2]]) ]
tW_ts_bra_1 = [ sqa.tensor('t2Wb', [i[3], i[4], i[5], a[3], a[4], a[5]], []) ]
tW_ops_bra_1= [ sqa.sfExOp([a[3], a[4], a[5], i[3], i[4], i[5]]) ]
#
#t_ts_ket_2 = [ sqa.tensor('t2', [a[0], a[1], i[0], i[3]], []) ]
#t_ops_ket_2= [ sqa.sfExOp([i[0], i[3], a[0], a[1]]) ]
#W_ts_ket_2 = [ sqa.tensor('W', [i[3], a[2], i[1], i[2]], W_sym) ]
#W_ops_ket_2= [ sqa.sfExOp([i[1], i[2], i[3], a[2]]) ]
#
#t_ts_bra_1 = [ sqa.tensor('t2', [i[4], i[5], a[4], a[7]], t_sym) ]
#t_ops_bra_1= [ sqa.sfExOp([a[4], a[7], i[4], i[5]]) ]
#W_ts_bra_1 = [ sqa.tensor('W', [a[7], i[6], a[5], a[6]], W_sym) ]
#W_ops_bra_1= [ sqa.sfExOp([a[5], a[6], a[7], i[6]]) ]
#
j = sqa.index('Aj', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
b = sqa.index('Vb', [tag_virtual], False)
k = sqa.index('Ak', [tag_active], True)
l = sqa.index('Al', [tag_active], True)
c = sqa.index('Vc', [tag_virtual], True)
d = sqa.index('Vd', [tag_virtual], True)
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
Tsym = sqa.symmetry((0, 1, 2, 3), 1)
E_ijab = [sqa.sfExOp([i, j, a, b])]
E_dclk = [sqa.sfExOp([d, c, l, k])]
T_dclk = [sqa.tensor('T2', [k, l, c, d], [Tsym])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijab[0], "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Va, Vb) <-- H(Ai, Aj, Va, Vb;0) T(0)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
i = sqa.index('Ai', [tag_active], False)
j = sqa.index('Aj', [tag_active], False)
k = sqa.index('Ak', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
Tsym = sqa.symmetry((0,1, 2,3), 1)
E_ijka = [sqa.sfExOp([i, j, k, a])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijka , "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Ak, Va) <-- H(Ai, Aj, Ak, Va;0) T(0)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
p = sqa.index('p', [tag_h1_p], True)
q = sqa.index('q', [tag_h1_q], True)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
# Define tensors
K_C = sqa.tensor('int1c', [i1,i2], [hsym])
K_A = sqa.tensor('int1a', [x1,x2], [hsym])
K_V = sqa.tensor('int1v', [a1,a2], [hsym])
V_Al = sqa.tensor('int2Laa', [L,x1,x3], [])
V_Ar = sqa.tensor('int2Laa', [L,x2,x4], [])
deltaC = sqa.tensor('deltac', [i1,i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1,x2], [hsym])
deltaV = sqa.tensor('deltav', [a1,a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term( 1.0, [''], [K_C, sqa.sfExOp([i1,i2])] )
T_A = sqa.term( 1.0, [''], [K_A, sqa.sfExOp([x1,x2])] )
T_V = sqa.term( 1.0, [''], [K_V, sqa.sfExOp([a1,a2])] )
HD_A = sqa.term( 0.5, [''], [V_Al,V_Ar, sqa.sfExOp([x1,x2,x3,x4])] )
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec = sqa.tensor('p', [a,b,i,q], [])
Apvec = sqa.tensor('Ap', [c,d,j,r], [])
Omu = sqa.term( 1.0, [''], [pvec, sqa.sfExOp([a, i]) , sqa.sfExOp([b, q])])
Onu = sqa.term( 1.0, [''], [Apvec, sqa.sfExOp([r, d]) , sqa.sfExOp([j, c])])
commutator = []
commutator += sqa.commutator(T_C, Omu)
commutator += sqa.commutator(T_A, Omu)
commutator += sqa.commutator(T_V, Omu)
commutator += sqa.commutator(HD_A, Omu)
import secondQuantizationAlgebra as sqa
from tools_for_sqa import *
from tools_for_pt import *
sqa.options.verbose = False
# Make H0
H = h0('NEVPT', df=True)
# Define Omu
list1 = gimme('vaaa')
list2 = [list1[i] for i in [0, 2]]
list3 = [list1[i] for i in [1, 3]]
pvec = sqa.tensor('p', list1, []) #symm(list1))
Omu = sqa.term(1.0, [''], [pvec, sqa.sfExOp(list2), sqa.sfExOp(list3)])
# Define Onu
list1 = gimme('vaaa')
list2 = [list1[i] for i in [3, 1]]
list3 = [list1[i] for i in [2, 0]]
Apvec = sqa.tensor('Ap', list1, []) #symm(list1))
Onu = sqa.term(1.0, [''], [Apvec, sqa.sfExOp(list2), sqa.sfExOp(list3)])
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
commutator = []
for Hterm in H:
commutator += sqa.commutator(Hterm, Omu)
result = []
for t in commutator:
result += sqa.normalOrder(sqa.multiplyTerms(Onu, t))
result = simplify_all(result, [deltaC, deltaA, deltaV], cumulantE4=True)
# Define symmetry classes
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
# Define tensors
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define the normal-ordered overlap
Cin = sqa.tensor('V', [a, p, q, r], [])
Cout = sqa.tensor('b', [b, u, v, w], [])
if (withC):
Op1 = sqa.term(1.0, [''], [Cin, sqa.sfExOp([a, q]), sqa.sfExOp([p, r])])
Op2 = sqa.term(1.0, [''], [Cout, sqa.sfExOp([w, u]), sqa.sfExOp([v, b])])
else:
Op1 = sqa.term(1.0, [''], [sqa.sfExOp([a, q]), sqa.sfExOp([p, r])])
Op2 = sqa.term(1.0, [''], [sqa.sfExOp([w, u]), sqa.sfExOp([v, b])])
result = sqa.normalOrder(sqa.multiplyTerms(Op2, Op1))
# Simplify the result
for t in result:
t.contractDeltaFuncs_new()
sqa.removeVirtOps_sf(result)
sqa.termChop(result)
sqa.combineTerms(result)
extendedR = []
for t in result:
extendedR += sqa.contractCoreOps_sf(t)
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
i = sqa.index('Ai', [tag_active], False)
j = sqa.index('Aj', [tag_active], False)
k = sqa.index('Ak', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
E_ijka = [sqa.sfExOp([i, j, k, a])]
E_bnml = [sqa.sfExOp([a, k, j, i])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements based on"
print "the spin-free generator and the commutator technique"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijka[0],", ",E_bnml[0], "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Ak, Va) <-- H(Ai, Aj, Ak, Va; Vb, Am, Al, Ak) T(Ak, Al, Am, Vb)"
print ""
result = []
# One-body part ....
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
a1 = sqa.index('Vg', [tag_virtual], True)
a2 = sqa.index('Vh', [tag_virtual], True)
a3 = sqa.index('Ve', [tag_virtual], True)
a4 = sqa.index('Vf', [tag_virtual], True)
#h0 one body term
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
K_C = sqa.tensor('int1', [i1, i2], [hsym])
K_A = sqa.tensor('int1', [x1, x2], [hsym])
K_V = sqa.tensor('int1', [a1, a2], [hsym])
V_A = sqa.tensor('int2', [x1, x2, x3, x4], [Dsym_a, Dsym_b, Dsym_c])
HD_A = sqa.term(0.5, [""], [V_A, sqa.sfExOp([x1, x2, x3, x4])])
T_C = sqa.term(1.0, [""], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [""], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [""], [K_V, sqa.sfExOp([a1, a2])])
#first excitation
E_aiEbj1a = sqa.term(1.0, [""], [sqa.sfExOp([a, i]), sqa.sfExOp([p, q])])
E_aiEbj1b = sqa.term(1.0, [""], [sqa.sfExOp([p, i]), sqa.sfExOp([a, q])])
E_aiEbj2a = sqa.term(1.0, [""], [sqa.sfExOp([s, r]), sqa.sfExOp([j, b])])
E_aiEbj2b = sqa.term(1.0, [""], [sqa.sfExOp([s, b]), sqa.sfExOp([j, r])])
commutator = []
commutator += sqa.commutator(HD_A, E_aiEbj1a)
commutator += sqa.commutator(T_C, E_aiEbj1a)
commutator += sqa.commutator(T_A, E_aiEbj1a)
commutator += sqa.commutator(T_V, E_aiEbj1a)
sqa.options.verbose = False
# definitions
tg_core = sqa.options.core_type
tg_active = sqa.options.active_type
tg_virtual = sqa.options.virtual_type
a1 = sqa.index('a1', [tg_active], False)
b1 = sqa.index('b1', [tg_active], False)
a2 = sqa.index('a2', [tg_active], False)
b2 = sqa.index('b2', [tg_active], False)
a3 = sqa.index('a3', [tg_active], False)
b3 = sqa.index('b3', [tg_active], False)
a4 = sqa.index('a4', [tg_active], False)
b4 = sqa.index('b4', [tg_active], False)
a = sqa.index('a', [tg_active], True)
result = []
term = sqa.term(1.0, [], [sqa.sfExOp([a1, b1])] + [sqa.sfExOp([a2, b2])] +
[sqa.sfExOp([a3, b3])])
result += sqa.normalOrder(term)
for t in result:
t.contractDeltaFuncs()
sqa.combineTerms(result)
print "results"
for t in result:
print t
i = sqa.index('Ai', [tag_active], False)
j = sqa.index('Aj', [tag_active], False)
k = sqa.index('Ak', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
l = sqa.index('Al', [tag_active], True)
m = sqa.index('Am', [tag_active], True)
n = sqa.index('An', [tag_active], True)
b = sqa.index('Vb', [tag_virtual], True)
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
E_ijka = [sqa.sfExOp([i, j, k, a])]
E_bnml = [sqa.sfExOp([b, n, m, l])]
T_bnml = [sqa.tensor('T2', [l, m, n, b])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements based on"
print "the spin-free generator and the commutator technique"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijka[0], ", ", E_bnml[
0], "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Ak, Va) <-- H(Ai, Aj, Ak, Va; Vb, Am, Al, Ak) T(Ak, Al, Am, Vb)"
print ""
result = []
# One-body part
K_V = sqa.tensor('int1v', [a1, a2], [hsym])
V_A = sqa.tensor('int2a', [x1, x2, x3, x4], [Dsym_a, Dsym_b, Dsym_c])
V_C = sqa.tensor('int2c', [i1, i2, i3, i4], [Dsym_a, Dsym_b, Dsym_c])
V_V = sqa.tensor('int2v', [a1, a2, a3, a4], [Dsym_a, Dsym_b, Dsym_c])
V_CA1 = sqa.tensor('int2ca1', [i1, x1, i2, x2], [Dsym_a, Dsym_b])
V_CA2 = sqa.tensor('int2ca2', [i1, x1, x2, i2], [])
V_CV1 = sqa.tensor('int2cv1', [i1, a1, i2, a2], [Dsym_a, Dsym_b])
V_CV2 = sqa.tensor('int2cv2', [i1, a1, a2, i2], [])
V_AV1 = sqa.tensor('int2av1', [x1, a1, x2, a2], [Dsym_a, Dsym_b])
V_AV2 = sqa.tensor('int2av2', [x1, a1, a2, x2], [])
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term(1.0, [''], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [''], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [''], [K_V, sqa.sfExOp([a1, a2])])
HD_A = sqa.term(0.5, [''], [V_A, sqa.sfExOp([x1, x2, x3, x4])])
HD_C = sqa.term(0.5, [''], [V_C, sqa.sfExOp([i1, i2, i3, i4])])
HD_V = sqa.term(0.5, [''], [V_V, sqa.sfExOp([a1, a2, a3, a4])])
HD_CA1 = sqa.term(1.0, [''], [V_CA1, sqa.sfExOp([i1, x1, i2, x2])])
HD_CA2 = sqa.term(1.0, [''], [V_CA2, sqa.sfExOp([i1, x1, x2, i2])])
HD_CV1 = sqa.term(1.0, [''], [V_CV1, sqa.sfExOp([i1, a1, i2, a2])])
HD_CV2 = sqa.term(1.0, [''], [V_CV2, sqa.sfExOp([i1, a1, a2, i2])])
HD_AV1 = sqa.term(1.0, [''], [V_AV1, sqa.sfExOp([x1, a1, x2, a2])])
HD_AV2 = sqa.term(1.0, [''], [V_AV2, sqa.sfExOp([x1, a1, a2, x2])])
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec1 = sqa.tensor('p1', [i, p, q, a], [])
# Define symmetry classes
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
# Define tensors
deltaC = sqa.tensor('deltac', [i1,i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1,x2], [hsym])
deltaV = sqa.tensor('deltav', [a1,a2], [hsym])
# Define the normal-ordered overlap
Cin = sqa.tensor('V', [a,b,i,q], [])
Cout = sqa.tensor('b', [c,d,j,r], [])
if (withC):
Op1 = sqa.term( 1.0, [''], [Cin, sqa.sfExOp([a, i]) , sqa.sfExOp([b, q])])
Op2 = sqa.term( 1.0, [''], [Cout, sqa.sfExOp([r, d]) , sqa.sfExOp([j, c])])
else:
Op1 = sqa.term( 1.0, [''], [sqa.sfExOp([a, i]) , sqa.sfExOp([b, q])])
Op2 = sqa.term( 1.0, [''], [sqa.sfExOp([r, d]) , sqa.sfExOp([j, c])])
result = sqa.normalOrder(sqa.multiplyTerms(Op2, Op1))
# Simplify the result
for t in result:
t.contractDeltaFuncs_new()
sqa.removeVirtOps_sf(result)
sqa.termChop(result)
sqa.combineTerms(result)
extendedR=[]
for t in result:
extendedR += sqa.contractCoreOps_sf(t)
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
i = sqa.index('Ai', [tag_active], False)
j = sqa.index('Aj', [tag_active], False)
k = sqa.index('Ak', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
E_ijka = [sqa.sfExOp([i, j, k, a])]
E_bnml = [sqa.sfExOp([a, k, j, i])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements based on"
print "the spin-free generator and the commutator technique"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijka[0], ", ", E_bnml[
0], "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Ak, Va) <-- H(Ai, Aj, Ak, Va; Vb, Am, Al, Ak) T(Ak, Al, Am, Vb)"
print ""
result = []
# One-body part ....
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
i = sqa.index('Ai', [tag_active], False)
j = sqa.index('Aj', [tag_active], False)
k = sqa.index('Ak', [tag_active], False)
l = sqa.index('Al', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
b = sqa.index('Vb', [tag_virtual], False)
c = sqa.index('Vc', [tag_virtual], False)
d = sqa.index('Vd', [tag_virtual], False)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
E_iajb = [sqa.sfExOp([i, j, a, b])]
E_dlck = [sqa.sfExOp([b, a, j, i])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_iajb[0], E_dlck[0], "|Psi>: R !!!!!"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
p = sqa.index('p', [tag_h1_p], True)
q = sqa.index('q', [tag_h1_q], True)
"A", "A", "H"]
pDomains = "\tint f(int i) {\n"
pDomains += "\t\treturn 2*i;\n"
pDomains += "\t}\n"
pDomains += "\tFDomainDecl DomainDecls[1] = {\n"
pDomains += "\t\t{\"A\", \"a\", f}\n"
pDomains += "\t};"
CommentKey = {}
print "namespace MRLCC_CAAV {\n"
for tc in list(zip(AllTensors, CommentTensors)):
CommentKey[tc[0]] = tc[1]
geraldCode.writeTensors(AllTensors, CommentKey, Domains, Usage)
HD_C = sqa.term( 0.5, [""], [V_C, sqa.sfExOp([i1,i2,i3,i4])] )
HD_A = sqa.term( 0.5, [""], [V_A, sqa.sfExOp([x1,x2,x3,x4])] )
HD_V = sqa.term( 0.5, [""], [V_V, sqa.sfExOp([a1,a2,a3,a4])] )
HD_CA1 = sqa.term( 1.0, [""], [V_CA1, sqa.sfExOp([i1,x1,i2,x2])] )
HD_CA2 = sqa.term( 1.0, [""], [V_CA2, sqa.sfExOp([i1,x1,x2,i2])] )
HD_CV1 = sqa.term( 1.0, [""], [V_CV1, sqa.sfExOp([i1,a1,i2,a2])] )
HD_CV2 = sqa.term( 1.0, [""], [V_CV2, sqa.sfExOp([i1,a1,a2,i2])] )
HD_AV1 = sqa.term( 1.0, [""], [V_AV1, sqa.sfExOp([x1,a1,x2,a2])] )
HD_AV2 = sqa.term( 1.0, [""], [V_AV2, sqa.sfExOp([x1,a1,a2,x2])] )
T_C = sqa.term( 1.0, [""], [K_C, sqa.sfExOp([i1,i2])] )
T_A = sqa.term( 1.0, [""], [K_A, sqa.sfExOp([x1,x2])] )
T_V = sqa.term( 1.0, [""], [K_V, sqa.sfExOp([a1,a2])] )
listnu = indExOp_Psi1[nu][4:8]
if is_non_zero(code(listnu) + code_rearrange(listtau)):
# H
if indExOp_H4[tau][-1] == 'other' or indExOp_H4[tau][
-1] == 'h0':
name = 'WO' + indTens_H4[tau][-1]
elif indExOp_H4[tau][-1] == 'heff4':
name = 'WE' + indTens_H4[tau][-1]
else:
name = 'WC' + indTens_H4[tau][-1]
Wtau = sqa.tensor(name, indTens_H4[tau][:4],
symm(indTens_H4[tau][:4]))
Vtau = sqa.term(factor[code(listtau)] * 0.5, [''],
[Wtau, sqa.sfExOp(listtau)])
# <Psi1|
bnu = sqa.tensor('b' + indTens_Psi1[nu][-1],
indTens_Psi1[nu][4:8],
symm(indTens_Psi1[nu][4:8]))
Onu = sqa.term(
1.0, [''],
[bnu, sqa.sfExOp(listnu[:2]),
sqa.sfExOp(listnu[2:4])])
#Onu = sqa.term( 1.0, [''], [bnu, sqa.sfExOp([listnu[i] for i in [0,2,3,1]])])
# Define the normal-ordered: W_nu = <O^T_nu V_tau> W_tau
term = sqa.multiplyTerms(Onu, Vtau)
#print term
result = sqa.normalOrder(term)
j = sqa.index('Aj', [tag_active], False)
a = sqa.index('Va', [tag_virtual], False)
b = sqa.index('Vb', [tag_virtual], False)
k = sqa.index('Ak', [tag_active], True)
l = sqa.index('Al', [tag_active], True)
c = sqa.index('Vc', [tag_virtual], True)
d = sqa.index('Vd', [tag_virtual], True)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
Tsym = sqa.symmetry((0,1, 2,3), 1)
E_ijab = [sqa.sfExOp([i, j, a, b])]
E_dclk = [sqa.sfExOp([d, c, l, k])]
T_dclk = [sqa.tensor('T2', [k, l, c, d], [Tsym])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_ijab[0], E_dclk[0], "|Psi>: R !!!!!"
print "@@@ SIGMA(Ai, Aj, Va, Vb) <-- sum_{klcd} H(Ai, Aj, Va, Vb; Vd, Vc, Al, Ak) T(Ak, Al, Vc, Vd)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
# Define symmetry classes
hsym = sqa.symmetry((1, 0), 1)
Dsym_a = sqa.symmetry((2, 1, 0, 3), 1)
Dsym_b = sqa.symmetry((0, 3, 2, 1), 1)
Dsym_c = sqa.symmetry((1, 0, 3, 2), 1)
# Define tensors
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define the normal-ordered overlap
Cin = sqa.tensor('V', [a, b, i, j], [Dsym_c])
Cout = sqa.tensor('b', [c, d, l, k], [Dsym_c])
if (withC):
Op1 = sqa.term(1.0, [''], [Cin, sqa.sfExOp([a, i]), sqa.sfExOp([b, j])])
Op2 = sqa.term(1.0, [''], [Cout, sqa.sfExOp([k, d]), sqa.sfExOp([l, c])])
else:
Op1 = sqa.term(1.0, [''], [sqa.sfExOp([a, i]), sqa.sfExOp([b, j])])
Op2 = sqa.term(1.0, [''], [sqa.sfExOp([k, d]), sqa.sfExOp([l, c])])
result = sqa.normalOrder(sqa.multiplyTerms(Op2, Op1))
# Simplify the result
for t in result:
t.contractDeltaFuncs_new()
sqa.removeVirtOps_sf(result)
sqa.termChop(result)
sqa.combineTerms(result)
extendedR = []
for t in result:
extendedR += sqa.contractCoreOps_sf(t)
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
k = sqa.index('Ak', [tag_active], True)
l = sqa.index('Al', [tag_active], True)
m = sqa.index('Am', [tag_active], True)
c = sqa.index('Vc', [tag_virtual], True)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
Tsym = sqa.symmetry((0,1, 2,3), 1)
E_cmlk = [sqa.sfExOp([c, m, l, k])]
T_klmc = [sqa.tensor('T2', [k, l, m, c], [Tsym])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_cmlk[0], "|Psi>: R !!!!!"
print "@@@ SIGMA_0 <-- sum_{klcd} H(0; Vd, Vc, Al, Ak) T(Ak, Al, Vc, Vd)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
p = sqa.index('p', [tag_h1_p], True)
sqa.options.verbose = False
# definitions
tg_core = sqa.options.core_type
tg_active = sqa.options.active_type
tg_virtual = sqa.options.virtual_type
a1 = sqa.index('a1', [tg_active], False)
b1 = sqa.index('b1', [tg_active], False)
a2 = sqa.index('a2', [tg_active], False)
b2 = sqa.index('b2', [tg_active], False)
a3 = sqa.index('a3', [tg_active], False)
b3 = sqa.index('b3', [tg_active], False)
a4 = sqa.index('a4', [tg_active], False)
b4 = sqa.index('b4', [tg_active], False)
a = sqa.index('a', [tg_active], True)
result = []
term = sqa.term(1.0, [], [sqa.sfExOp([a1,b1])] + [sqa.sfExOp([a2,b2])] + [sqa.sfExOp([a3,b3])])
result += sqa.normalOrder(term)
for t in result:
t.contractDeltaFuncs()
sqa.combineTerms(result)
print "results"
for t in result:
print t
"A", "A", "A", "H", "D", "D", "D", "A"]
pDomains = "\tint f(int i) {\n"
pDomains += "\t\treturn 2*i;\n"
pDomains += "\t}\n"
pDomains += "\tFDomainDecl DomainDecls[1] = {\n"
pDomains += "\t\t{\"A\", \"a\", f}\n"
pDomains += "\t};"
CommentKey = {}
print "namespace MRLCC_CCVV {\n"
for tc in list(zip(AllTensors, CommentTensors)):
CommentKey[tc[0]] = tc[1]
geraldCode.writeTensors(AllTensors, CommentKey, Domains, Usage)
HD_C = sqa.term( 0.5, [""], [V_C, sqa.sfExOp([i1,i2,i3,i4])] )
HD_A = sqa.term( 0.5, [""], [V_A, sqa.sfExOp([x1,x2,x3,x4])] )
HD_V = sqa.term( 0.5, [""], [V_V, sqa.sfExOp([a1,a2,a3,a4])] )
HD_CA1 = sqa.term( 1.0, [""], [V_CA1, sqa.sfExOp([i1,x1,i2,x2])] )
HD_CA2 = sqa.term( 1.0, [""], [V_CA2, sqa.sfExOp([i1,x1,x2,i2])] )
HD_CV1 = sqa.term( 1.0, [""], [V_CV1, sqa.sfExOp([i1,a1,i2,a2])] )
HD_CV2 = sqa.term( 1.0, [""], [V_CV2, sqa.sfExOp([i1,a1,a2,i2])] )
HD_AV1 = sqa.term( 1.0, [""], [V_AV1, sqa.sfExOp([x1,a1,x2,a2])] )
HD_AV2 = sqa.term( 1.0, [""], [V_AV2, sqa.sfExOp([x1,a1,a2,x2])] )
T_C = sqa.term( 1.0, [""], [K_C, sqa.sfExOp([i1,i2])] )
T_A = sqa.term( 1.0, [""], [K_A, sqa.sfExOp([x1,x2])] )
T_V = sqa.term( 1.0, [""], [K_V, sqa.sfExOp([a1,a2])] )
V_AV1l = sqa.tensor('int2Laa', [L,x1,x2], [])
V_AV1r = sqa.tensor('int2Lvv', [L,a1,a2], [])
V_AV2l = sqa.tensor('int2Lav', [L,x1,a2], [])
V_AV2r = sqa.tensor('int2Lva', [L,a1,x2], [])
V_Cl = sqa.tensor('int2Lcc', [L,i1,i3], [])
V_Cr = sqa.tensor('int2Lcc', [L,i2,i4], [])
V_Al = sqa.tensor('int2Laa', [L,x1,x3], [])
V_Ar = sqa.tensor('int2Laa', [L,x2,x4], [])
V_Vl = sqa.tensor('int2Lvv', [L,a1,a3], [])
V_Vr = sqa.tensor('int2Lvv', [L,a2,a4], [])
deltaC = sqa.tensor('deltac', [i1,i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1,x2], [hsym])
deltaV = sqa.tensor('deltav', [a1,a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term( 1.0, [''], [K_C, sqa.sfExOp([i1,i2])] )
T_A = sqa.term( 1.0, [''], [K_A, sqa.sfExOp([x1,x2])] )
T_V = sqa.term( 1.0, [''], [K_V, sqa.sfExOp([a1,a2])] )
HD_C = sqa.term( 0.5, [''], [V_Cl,V_Cr, sqa.sfExOp([i1,i2,i3,i4])] )
HD_A = sqa.term( 0.5, [''], [V_Al,V_Ar, sqa.sfExOp([x1,x2,x3,x4])] )
HD_V = sqa.term( 0.5, [''], [V_Vl,V_Vr, sqa.sfExOp([a1,a2,a3,a4])] )
HD_CA1 = sqa.term( 1.0, [''], [V_CA1l,V_CA1r, sqa.sfExOp([i1,x1,i2,x2])] )
HD_CA2 = sqa.term( 1.0, [''], [V_CA2l,V_CA2r, sqa.sfExOp([i1,x1,x2,i2])] )
HD_CV1 = sqa.term( 1.0, [''], [V_CV1l,V_CV1r, sqa.sfExOp([i1,a1,i2,a2])] )
HD_CV2 = sqa.term( 1.0, [''], [V_CV2l,V_CV2r, sqa.sfExOp([i1,a1,a2,i2])] )
HD_AV1 = sqa.term( 1.0, [''], [V_AV1l,V_AV1r, sqa.sfExOp([x1,a1,x2,a2])] )
HD_AV2 = sqa.term( 1.0, [''], [V_AV2l,V_AV2r, sqa.sfExOp([x1,a1,a2,x2])] )
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec = sqa.tensor('p', [a,b,p,q], [Dsym_c])
K_V = sqa.tensor('Wvv', [a1, a2], [hsym])
V_A = sqa.tensor('Waaaa', [x1, x2, x3, x4], [Dsym_a, Dsym_b, Dsym_c])
V_C = sqa.tensor('Wcccc', [i1, i2, i3, i4], [Dsym_a, Dsym_b, Dsym_c])
V_V = sqa.tensor('Wvvvv', [a1, a2, a3, a4], [Dsym_a, Dsym_b, Dsym_c])
V_CA1 = sqa.tensor('Wcaca', [i1, x1, i2, x2], [Dsym_a, Dsym_b])
V_CA2 = sqa.tensor('Wcaac', [i1, x1, x2, i2], [])
V_CV1 = sqa.tensor('Wcvcv', [i1, a1, i2, a2], [Dsym_a, Dsym_b])
V_CV2 = sqa.tensor('Wcvvc', [i1, a1, a2, i2], [])
V_AV1 = sqa.tensor('Wavav', [x1, a1, x2, a2], [Dsym_a, Dsym_b])
V_AV2 = sqa.tensor('Wavva', [x1, a1, a2, x2], [])
deltaC = sqa.tensor('deltac', [i1, i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1, x2], [hsym])
deltaV = sqa.tensor('deltav', [a1, a2], [hsym])
# Define Hamilonian terms
T_C = sqa.term(1.0, [''], [K_C, sqa.sfExOp([i1, i2])])
T_A = sqa.term(1.0, [''], [K_A, sqa.sfExOp([x1, x2])])
T_V = sqa.term(1.0, [''], [K_V, sqa.sfExOp([a1, a2])])
HD_A = sqa.term(0.5, [''], [V_A, sqa.sfExOp([x1, x2, x3, x4])])
HD_C = sqa.term(0.5, [''], [V_C, sqa.sfExOp([i1, i2, i3, i4])])
HD_V = sqa.term(0.5, [''], [V_V, sqa.sfExOp([a1, a2, a3, a4])])
HD_CA1 = sqa.term(1.0, [''], [V_CA1, sqa.sfExOp([i1, x1, i2, x2])])
HD_CA2 = sqa.term(1.0, [''], [V_CA2, sqa.sfExOp([i1, x1, x2, i2])])
HD_CV1 = sqa.term(1.0, [''], [V_CV1, sqa.sfExOp([i1, a1, i2, a2])])
HD_CV2 = sqa.term(1.0, [''], [V_CV2, sqa.sfExOp([i1, a1, a2, i2])])
HD_AV1 = sqa.term(1.0, [''], [V_AV1, sqa.sfExOp([x1, a1, x2, a2])])
HD_AV2 = sqa.term(1.0, [''], [V_AV2, sqa.sfExOp([x1, a1, a2, x2])])
# Define the normal-ordered A matrix:
# Apvec_nu = < O^T_nu [H,O_mu] >.pvec_mu
pvec = sqa.tensor('p', [i, p, q, r], [])
tg_c = sqa.options.core_type
tg_a = sqa.options.active_type
tg_v = sqa.options.virtual_type
tg_t = tg_c + tg_a + tg_v
i = [sqa.index('i%i' % j, [tg_c], True) for j in range(8)]
r = [sqa.index('r%i' % j, [tg_a], True) for j in range(8)]
a = [sqa.index('a%i' % j, [tg_v], True) for j in range(8)]
m = [sqa.index('m%i' % j, [tg_t], True) for j in range(8)]
n = [sqa.index('n%i' % j, [tg_t], True) for j in range(8)]
t_sym = [sqa.symmetry((1, 0, 3, 2), 1)]
W_sym = [sqa.symmetry((1, 0, 3, 2), 1), sqa.symmetry((0, 3, 2, 1), 1)]
W_ts_ket = [sqa.tensor('W', [a[2], a[3], i[2], i[3]], W_sym)]
W_ops_ket = [sqa.sfExOp([i[2], i[3], a[2], a[3]])]
t_ts_bra = [sqa.tensor('t2', [i[0], i[1], a[0], a[1]], t_sym)]
t_ops_bra = [sqa.sfExOp([a[0], a[1], i[0], i[1]])]
terms = []
#Op1 = t_ts_ket_1 + t_ops_ket_1 + W_ts_ket_1 + W_ops_ket_1 + W_ts_bra_1 + W_ops_bra_1 + t_ts_bra_1 + t_ops_bra_1
#terms.append( sqa.term( 1.0, [], Op1) )
#Op2 = t_ts_ket_2 + t_ops_ket_2 + W_ts_ket_2 + W_ops_ket_2 + W_ts_bra_1 + W_ops_bra_1 + t_ts_bra_1 + t_ops_bra_1
#terms.append( sqa.term( 1.0, [], Op2) )
#Op3 = t_ts_ket_1 + t_ops_ket_1 + W_ts_ket_1 + W_ops_ket_1 + W_ts_bra_2 + W_ops_bra_2 + t_ts_bra_2 + t_ops_bra_2
#terms.append( sqa.term( 1.0, [], Op3) )
#Op4 = t_ts_ket_2 + t_ops_ket_2 + W_ts_ket_2 + W_ops_ket_2 + W_ts_bra_2 + W_ops_bra_2 + t_ts_bra_2 + t_ops_bra_2
#Op4 = t_ops_ket_2 + W_ops_ket_2 + W_ops_bra_2 + t_ops_bra_2
#Op4 = t_ops_ket_2 + W_ops_ket_2
Op4 = W_ts_ket + W_ops_ket + t_ts_bra + t_ops_bra
# Define symmetry classes
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
# Define tensors
deltaC = sqa.tensor('deltac', [i1,i2], [hsym])
deltaA = sqa.tensor('deltaa', [x1,x2], [hsym])
deltaV = sqa.tensor('deltav', [a1,a2], [hsym])
# Define the normal-ordered overlap
Cin = sqa.tensor('V', [i,j,p,a], [])
Cout = sqa.tensor('b', [k,l,q,b], [])
if (withC):
Op1 = sqa.term( 1.0, [''], [Cin, sqa.sfExOp([p, i]) , sqa.sfExOp([a, j])])
Op2 = sqa.term( 1.0, [''], [Cout, sqa.sfExOp([l, b]) , sqa.sfExOp([k, q])])
else:
Op1 = sqa.term( 1.0, [''], [sqa.sfExOp([p, i]) , sqa.sfExOp([a, j])])
Op2 = sqa.term( 1.0, [''], [sqa.sfExOp([l, b]) , sqa.sfExOp([k, q])])
result = sqa.normalOrder(sqa.multiplyTerms(Op2, Op1))
# Simplify the result
for t in result:
t.contractDeltaFuncs_new()
sqa.removeVirtOps_sf(result)
sqa.termChop(result)
sqa.combineTerms(result)
extendedR=[]
for t in result:
extendedR += sqa.contractCoreOps_sf(t)
tag_core = sqa.options.core_type
tag_active = sqa.options.active_type
tag_virtual = sqa.options.virtual_type
k = sqa.index('Ak', [tag_active], True)
l = sqa.index('Al', [tag_active], True)
c = sqa.index('Vc', [tag_virtual], True)
d = sqa.index('Vd', [tag_virtual], True)
hsym = sqa.symmetry((1,0), 1)
Dsym_a = sqa.symmetry((2,1, 0,3), 1)
Dsym_b = sqa.symmetry((0,3, 2,1), 1)
Dsym_c = sqa.symmetry((1,0, 3,2), 1)
Tsym = sqa.symmetry((0,1, 2,3), 1)
E_dclk = [sqa.sfExOp([d, c, l, k])]
T_klcd = [sqa.tensor('T2', [k, l, c, d], [Tsym])]
print ""
print "Evaluation of the IC-MRCI Hamiltonian elements"
print "based on the spin-free generator"
print ""
print "!!!!! The operator space is L: <Psi|", E_dclk[0], "|Psi>: R !!!!!"
print "@@@ SIGMA_0 <-- sum_{klcd} H(0; Vd, Vc, Al, Ak) T(Ak, Al, Vc, Vd)"
print ""
result = []
for tag_h1_p in [tag_active, tag_virtual]:
for tag_h1_q in [tag_active, tag_virtual]:
p = sqa.index('p', [tag_h1_p], True)