# mol.basis = {'O': 'sto-3g', 'H': 'cc-pvdz', 'H@2': '6-31G'}
is_atomic = False
mol.build()
_q_ = qmol_func(mol, atomic=is_atomic)
if is_atomic:
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
fer_op = FermionicOperator(h1=_q_.one_body_integrals,
h2=_q_.two_body_integrals)
# s = np.shape(fer_op.h1)
# fer_op.h1 = np.zeros(s)
# print(fer_op.h1)
ref_op = fer_op.mapping('jordan_wigner')
print(ref_op.print_operators())
ee = ExactEigensolver(ref_op, k=1)
ee_result = ee.run()
temp_min_eigvals = ee_result['eigvals']
print(temp_min_eigvals)
exit(0)
def mol_r_matrices(MoleculeFlag,check_r_matrix_flag,is_atomic):
mol = gto.Mole()
#=================================
# Hydrogen molecule
#=================================
if MoleculeFlag == 'H2':
r_matrices=[]
num_particles = 2
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Defining R-matrix --> r
# Swapping the spatial orbitals. This involves swapping both the spin orbitals corresponding to a spatial orbital.
# This could be treated as a reflection symmetry or rotational symmetry.
r1 = np.zeros([4,4])
r1[0,1]=1
r1[1,0]=1
r1[2,3]=1
r1[3,2]=1
# Swapping the spin oritals. Spin symmetry.
r2=np.zeros([4,4])
for i in range(4):
if i<2:
r2[i+2,i]=1.
else:
r2[i-2,i]=1.
r_matrices.append(r1)
r_matrices.append(r2)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Water molecule (with different basis sets)
#=================================
elif MoleculeFlag== 'H2O_L':
r_matrices = []
print(MoleculeFlag)
# Configuration from
# mol.atom = [['O',(0.8638, 0.4573,0.0)], ['H',(0, 0, 0)], ['H',(1.7785,0.0,0.0)]]
# mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
#mol.atom = [['O',(0, 0, 0)], ['H',(0, 1, 0)], ['H@2',(0, 0, 1)]]
#mol.basis = {'O': 'sto-3g', 'H': 'cc-pvdz', 'H@2': '6-31G'}
num_particles=10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Water molecule (with different basis sets)
#=================================
elif MoleculeFlag== 'H2O':
r_matrices=[]
print(MoleculeFlag)
num_particles = 10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['O',(0.0000, 0.0000, 0.0000)],
['H',(0.757, 0.586, 0.0)],
['H',(-0.757, 0.586, 0.0)]]
# mol.atom = [['N', (0.0000, 0.0000, 0.0000)],
# ['H', (0.0000, -1.,-0.3816)],
# ['H', (0.8, 0.6 ,-0.3816)],
# ['H', (-0.8, 0.6 ,-0.3816)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['O',(0.0000, 0.0000, 0.0000)],
['H',(0.757, 0.586, 0.0)],
['H',(-0.757, 0.586, 0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
#Spin symmetry:
r1=np.zeros([14,14])
for i in range(14):
if i<7:
r1[i+7,i]=1.
else:
r1[i-7,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(14)
r2[4,4]=-1
r2[11,11]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and the hydrogen atoms swap.
r3=np.eye(14)
r3[2,2]=-1
r3[9,9]=-1
r3[12,12]=0
r3[13,13]=0
r3[12,13]=1
r3[13,12]=1
r3[5,6]=1
r3[6,5]=1
r3[5,5]=0
r3[6,6]=0
# print(r)
r_matrices.append(r3)
#Axial symmetry about y-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=1
r4[4,4]=-1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=1
r4[11,11]=-1
r4[12,13]=1
r4[13,12]=1
r_matrices.append(r4)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ammonia molecule
#=================================
elif MoleculeFlag=='NH3':
print(MoleculeFlag)
num_particles = 10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['N' , ( 0.0000000, 0.0000000, 0.1493220)],
['H' , ( 0.0000000 , 0.9474830 , -0.3484190)],
['H' , ( 0.8205440 , -0.4737420 , -0.3484190)],
['H' , ( -0.8205440 , -0.4737420 , -0.3484190)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['N' , ( 0.0000000, 0.0000000, 0.1493220)],
['H' , ( 0.0000000 , 0.9474830 , -0.3484190)],
['H' , ( 0.8205440 , -0.4737420 , -0.3484190)],
['H' , ( -0.8205440 , -0.4737420 , -0.3484190)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
r_matrices=[]
#Spin symmetry:
r1=np.zeros([16,16])
for i in range(16):
if i<8:
r1[i+8,i]=1.
else:
r1[i-8,i]=1.
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{yz}. Two hydrogen atoms are swapped and the px orbital picks up
# a negative sign.
r3=np.zeros([16,16])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,5]=1
r3[6,7]=1
r3[7,6]=1
r3[8,8]=1
r3[9,9]=1
r3[10,10]=-1
r3[11,11]=1
r3[12,12]=1
r3[13,13]=1
r3[14,15]=1
r3[15,14]=1
r_matrices.append(r3)
######################################
# The following mtrices commute with Hamiltonian
# and hence are symmetries, but these cannot be used
# to taper off qubits.
theta = -2*np.pi/3
r4 = np.eye(16)
r4[5,5]=r4[6,6]=r4[7,7]=0
r4[13,13]=r4[14,14]=r4[15,15]=0
r4[5,6]=r4[6,7]=r4[7,5]=1
# r4[6,5]=r4[7,6]=r4[5,7]=1
r4[13,14]=r4[14,15]=r4[15,13]=1
# r4[14,13]=r4[15,14]=r4[13,15]=1
r4[2,2]=r4[3,3]=r4[10,10]=r4[11,11]=np.cos(theta)
r4[2,3]= np.sin(theta)
r4[3,2]= -np.sin(theta)
r4[10,11]=np.sin(theta)
r4[11,10]=-np.sin(theta)
r5 = r4.copy()
theta = np.pi/3
r4 = np.eye(16,dtype=complex)
r4[5,5]=r4[6,6]=0
r4[13,13]=r4[14,14]=0
r4[5,6]=r4[6,5]=1
r4[13,14]=r4[14,13]=1
r4[2,2]=r4[10,10]=np.cos(theta)
r4[3,3]=r4[11,11]=-np.cos(theta)
r4[2,3]= np.sin(theta)
r4[3,2]= np.sin(theta)
r4[10,11]=np.sin(theta)
r4[11,10]=np.sin(theta)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Methane molecule
#=================================
elif MoleculeFlag=='CH4':
# print(MoleculeFlag)
mol.atom=[['C', (0.0000 , 0.0000 , 0.0000 )],
['H', (0.6276 , 0.6276 , 0.6276 )],
['H', (0.6276 , -0.6276, -0.6276)],
['H', (-0.6276, 0.6276 , -0.6276)],
['H', (-0.6276, -0.6276, 0.6276 )]]
mol.basis='sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
# Spin symmetry:
r1=np.zeros([18,18])
for i in range(18):
if i<8:
r1[i+9,i]=1.
else:
r1[i-9,i]=1.
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Carbon dioxide molecule
#=================================
elif MoleculeFlag=='CO2':
r_matrices = []
# print(MoleculeFlag)
mol.atom = [['C',(0., 0., 0.)],
['O',(-1.1621, 0., 0.)],
['O',(1.1621, 0., 0.)]]
mol.basis='sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
# Spin symmetry:
r1=np.zeros([30,30])
for i in range(30):
if i<15:
r1[i+15,i]=1.
else:
r1[i-15,i]=1.
r_matrices.append(r1)
# Permutation matrix for inversion. \sigma{yz} All the oxygen orbitals are swapped.
# Oxygen px orbital picks up a negative sign and the px of carbon picks up a
# negative sign.
r2=np.zeros([30,30])
r2[0,0]=1
r2[1,1]=1
r2[3,3]=1
r2[2,2]=-1
r2[4,4]=r2[19,19]=1
r2[5,10]=r2[10,5]=1
r2[11,6]=r2[6,11]=1
r2[7,12]=r2[12,7]=-1
r2[8,13]=r2[13,8]=1
r2[14,9]=r2[9,14]=1
r2[15,15]=1
r2[16,16]=1
r2[17,17]=-1
r2[18,18]=1
r2[20,25]=r2[25,20]=1
r2[21,26]=r2[26,21]=1
r2[22,27]=r2[27,22]=-1
r2[23,28]=r2[28,23]=1
r2[24,29]=r2[29,24]=1
r_matrices.append(r2)
# Permutation matrix for inversion. \sigma{xy}
# pz orbitals of oxygen and carbon pick up negative sign
r3=np.eye(30)
r3[4,4]=-1
r3[19,19]=-1
r3[9,9]=-1
r3[14,14]=-1
r3[24,24]=-1
r3[29,29]=-1
r_matrices.append(r3)
# Permutation matrix for inversion. \sigma{xz}
# py orbitals of oxygen and carbon pick up negative sign
r4=np.eye(30)
r4[3,3]=-1
r4[18,18]=-1
r4[8,8]=-1
r4[13,13]=-1
r4[23,23]=-1
r4[28,28]=-1
r_matrices.append(r4)
# Permutation matrix for axial symmetry. C_2{x}
# pz and py orbitals of oxygen and carbon pick up negative sign
r5=np.eye(30)
r5[3,3]=-1
r5[18,18]=-1
r5[8,8]=-1
r5[13,13]=-1
r5[23,23]=-1
r5[28,28]=-1
r5[4,4]=-1
r5[19,19]=-1
r5[9,9]=-1
r5[14,14]=-1
r5[24,24]=-1
r5[29,29]=-1
r_matrices.append(r5)
# Permutation matrix for axial symmetry. C_2{y} All the oxygen orbitals are swapped.
# Oxygen px and pz orbital picks up a negative sign and the px and pz of carbon picks up a
# negative sign.
r6=np.zeros([30,30])
r6[0,0]=r6[1,1]=1
r6[3,3]=r6[18,18]=1
r6[17,17]=r6[2,2]=-1
r6[4,4]=r6[19,19]=-1
r6[5,10]=r6[10,5]=1
r6[11,6]=r6[6,11]=1
r6[7,12]=r6[12,7]=-1
r6[8,13]=r6[13,8]=1
r6[14,9]=r6[9,14]=-1
r6[15,15]=r6[16,16]=1
r6[20,25]=r6[25,20]=1
r6[21,26]=r6[26,21]=1
r6[22,27]=r6[27,22]=-1
r6[23,28]=r6[28,23]=1
r6[24,29]=r6[29,24]=-1
r_matrices.append(r6)
# Permutation matrix for axial symmetry. C_2{z} All the oxygen orbitals are swapped.
# Oxygen px and py orbital picks up a negative sign and the px and py of carbon picks up a
# negative sign.
r7=np.zeros([30,30])
r7[0,0]=r7[1,1]=1
r7[3,3]=r7[18,18]=-1
r7[17,17]=r7[2,2]=-1
r7[4,4]=r7[19,19]=1
r7[5,10]=r7[10,5]=1
r7[11,6]=r7[6,11]=1
r7[7,12]=r7[12,7]=-1
r7[8,13]=r7[13,8]=-1
r7[14,9]=r7[9,14]=1
r7[15,15]=r7[16,16]=1
r7[20,25]=r7[25,20]=1
r7[21,26]=r7[26,21]=1
r7[22,27]=r7[27,22]=-1
r7[23,28]=r7[28,23]=-1
r7[24,29]=r7[29,24]=1
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ethyne molecule
#=================================
elif MoleculeFlag=='C2H2':
r_matrices =[]
print(MoleculeFlag)
num_particles = 14
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['C',(-0.6000, 0.0000, 0.0000 )],
['C',(0.6000, 0.0000, 0.0000 )],
['H',(-1.6650,0.0000, 0.000 )],
['H',(1.6650,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['C',(-0.6000, 0.0000, 0.0000 )],
['C',(0.6000, 0.0000, 0.0000 )],
['H',(-1.6650,0.0000, 0.000 )],
['H',(1.6650,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Spin symmetry:
r1=np.zeros([24,24])
for i in range(24):
if i<12:
r1[i+12,i]=1.
else:
r1[i-12,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(24)
r2[4,4]=-1
r2[9,9]=-1
r2[16,16]=-1
r2[21,21]=-1
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r3=np.eye(24)
r3[3,3]=-1
r3[8,8]=-1
r3[15,15]=-1
r3[20,20]=-1
# R-matrix for plane of symmetry \sigma_{yz}.
r4=np.zeros([24,24])
#Swapping px picks up a negative sign
r4[2,7]=r4[7,2]=-1
r4[14,19]=r4[19,14]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r4[0,5]=r4[5,0]=1
r4[1,6]=r4[6,1]=1
r4[12,17]=r4[17,12]=1
r4[13,18]=r4[18,13]=1
r4[3,8]=r4[8,3]=1
r4[15,20]=r4[20,15]=1
r4[21,16]=r4[16,21]=1
r4[9,4]=r4[4,9]=1
#Swapping 1s of hydrogen
r4[10,11]=r4[11,10]=1
r4[22,23]=r4[23,22]=1
# R-matrix for axis of symmetry C_2 around y axis.
r5=np.zeros([24,24])
#Swapping px picks up a negative sign
r5[2,7]=r5[7,2]=-1
r5[14,19]=r5[19,14]=-1
r5[21,16]=r5[16,21]=-1
r5[9,4]=r5[4,9]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r5[0,5]=r5[5,0]=1
r5[1,6]=r5[6,1]=1
r5[12,17]=r5[17,12]=1
r5[13,18]=r5[18,13]=1
r5[3,8]=r5[8,3]=1
r5[15,20]=r5[20,15]=1
#Swapping 1s of hydrogen
r5[10,11]=r5[11,10]=1
r5[22,23]=r5[23,22]=1
# R-matrix for axis of symmetry C_2 around z axis.
r6=np.zeros([24,24])
#Swapping px picks up a negative sign
r6[2,7]=r6[7,2]=-1
r6[14,19]=r6[19,14]=-1
r6[15,20]=r6[20,15]=-1
r6[3,8]=r6[8,3]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r6[0,5]=r6[5,0]=1
r6[1,6]=r6[6,1]=1
r6[12,17]=r6[17,12]=1
r6[13,18]=r6[18,13]=1
r6[9,4]=r6[4,9]=1
r6[21,16]=r6[16,21]=1
#Swapping 1s of hydrogen
r6[10,11]=r6[11,10]=1
r6[22,23]=r6[23,22]=1
# R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
r7=np.eye(24)
r7[3,3]=-1
r7[4,4]=-1
r7[8,8]=-1
r7[9,9]=-1
r7[16,16]=-1
r7[15,15]=-1
r7[20,20]=-1
r7[21,21]=-1
r_matrices.append(r7)
r_matrices.append(r6)
r_matrices.append(r5)
r_matrices.append(r2)
r_matrices.append(r3)
r_matrices.append(r4)
r_matrices.append(r1)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ethylene molecule
#=================================
elif MoleculeFlag=='C2H4':
r_matrices =[]
print(MoleculeFlag)
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['C',( 0.6695, 0.0000 , 0.0000)],
['C',(-0.6695, 0.0000 , 0.0000)],
['H',( 1.2321, 0.9289 , 0.0000)],
['H',( 1.2321, -0.9289, 0.0000)],
['H',(-1.2321, 0.9289 , 0.0000)],
['H',(-1.2321, -0.9289, 0.0000)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
fer_op = FermionicOperator(h1=one_b, h2=two_b)
r_matrices = []
# Spin symmetry:
r1=np.zeros([28,28])
for i in range(28):
if i<14:
r1[i+14,i]=1.
else:
r1[i-14,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(28)
r2[4,4]=-1
r2[9,9]=-1
r2[18,18]=-1
r2[23,23]=-1
# R-matrix for plane of symmetry \sigma_{xz}.
r3=np.eye(28)
r3[3,3]=-1
r3[8,8]=-1
r3[17,17]=-1
r3[22,22]=-1
r3[10,10]=r3[11,11]=r3[12,12]=r3[13,13]=0
r3[24,24]=r3[25,25]=r3[26,26]=r3[27,27]=0
r3[10,11]=r3[11,10]=r3[12,13]=r3[13,12]=1
r3[24,25]=r3[25,24]=r3[26,27]=r3[27,26]=1
# R-matrix for plane of symmetry \sigma_{yz}.
r4=np.zeros([28,28])
# #Swapping px picks up a negative sign
r4[2,7]=r4[7,2]=-1
r4[16,21]=r4[21,16]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
r4[0,5]=r4[5,0]=1
r4[1,6]=r4[6,1]=1
r4[3,8]=r4[8,3]=1
r4[4,9]=r4[9,4]=1
r4[14,19]=r4[19,14]=1
r4[15,20]=r4[20,15]=1
r4[17,22]=r4[22,17]=1
r4[18,23]=r4[23,18]=1
# #Swapping 1s of hydrogen
r4[10,12]=r4[12,10]=1
r4[24,26]=r4[26,24]=1
r4[11,13]=r4[13,11]=1
r4[25,27]=r4[27,25]=1
# R-matrix for axis of symmetry C_2 around y axis.
r5=np.zeros([28,28])
#Swapping px picks up a negative sign
r5[2,7]=r5[7,2]=-1
r5[4,9]=r5[9,4]=-1
r5[16,21]=r5[21,16]=-1
r5[18,23]=r5[23,18]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r5[0,5]=r5[5,0]=1
r5[1,6]=r5[6,1]=1
r5[3,8]=r5[8,3]=1
r5[14,19]=r5[19,14]=1
r5[15,20]=r5[20,15]=1
r5[17,22]=r5[22,17]=1
#Swapping 1s of hydrogen
r5[10,12]=r5[12,10]=1
r5[24,26]=r5[26,24]=1
r5[11,13]=r5[13,11]=1
r5[25,27]=r5[27,25]=1
# R-matrix for axis of symmetry C_2 around z axis.
r6=np.zeros([28,28])
#Swapping px picks up a negative sign
r6[2,7]=r6[7,2]=-1
r6[3,8]=r6[8,3]=-1
r6[16,21]=r6[21,16]=-1
r6[17,22]=r6[22,17]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r6[0,5]=r6[5,0]=1
r6[1,6]=r6[6,1]=1
r6[4,9]=r6[9,4]=1
r6[14,19]=r6[19,14]=1
r6[15,20]=r6[20,15]=1
r6[18,23]=r6[23,18]=1
#Swapping 1s of hydrogen
r6[10,13]=r6[13,10]=1
r6[24,27]=r6[27,24]=1
r6[11,12]=r6[12,11]=1
r6[25,26]=r6[26,25]=1
# # R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
r7=np.eye(28)
r7[3,3]=-1
r7[4,4]=-1
r7[8,8]=-1
r7[9,9]=-1
r7[17,17]=-1
r7[18,18]=-1
r7[22,22]=-1
r7[23,23]=-1
r7[10,10]=r7[11,11]=r7[12,12]=r7[13,13]=0
r7[24,24]=r7[25,25]=r7[26,26]=r7[27,27]=0
r7[10,11]=r7[11,10]=r7[12,13]=r7[13,12]=1
r7[24,25]=r7[25,24]=r7[26,27]=r7[27,26]=1
r_matrices.append(r1)
r_matrices.append(r2)
r_matrices.append(r3)
r_matrices.append(r4)
r_matrices.append(r5)
r_matrices.append(r6)
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Boron trifluoride molecule
#=================================
elif MoleculeFlag == 'BF3':
r_matrices = []
try:
data = np.load(MoleculeFlag+'.npz')
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['B',(0.0000 ,0.0000 ,0.000000 )],
['F',(0.0000 ,1.3070 ,0.00000 )],
['F',(1.1319 ,-0.6535, 0.000 )],
['F',(-1.1319 ,-0.6535, 0.00)]]
mol.basis = 'sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
fer_op = FermionicOperator(h1=one_b, h2=two_b)
# Spin symmetry:
r1=np.zeros([40,40])
for i in range(40):
if i<20:
r1[i+20,i]=1.
else:
r1[i-20,i]=1.
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}.
r2=np.eye(40)
r2[4,4]=-1
r2[9,9]=-1
r2[14,14]=-1
r2[19,19]=-1
r2[24,24]=-1
r2[29,29]=-1
r2[34,34]=-1
r2[39,39]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}.
r3=np.eye(40)
r3[2,2]=-1
r3[7,7]=-1
r3[22,22]=-1
r3[27,27]=-1
for i in range(5):
r3[10+i,10+i]=0
r3[15+i,15+i]=0
r3[30+i,30+i]=0
r3[35+i,35+i]=0
r3[10+i,15+i]=1
r3[15+i,10+i]=1
r3[30+i,35+i]=1
r3[35+i,30+i]=1
r3[12,17]=-1
r3[17,12]=-1
r3[32,37]=-1
r3[37,32]=-1
r_matrices.append(r3)
# R-matrix for axis of symmetry C_2 around y axis.
r4=np.eye(40)
r4[2,2]=-1
r4[4,4]=-1
r4[7,7]=-1
r4[9,9]=-1
r4[22,22]=-1
r4[24,24]=-1
r4[29,29]=-1
r4[27,27]=-1
for i in range(5):
r4[10+i,10+i]=0
r4[15+i,15+i]=0
r4[30+i,30+i]=0
r4[35+i,35+i]=0
r4[10+i,15+i]=1
r4[15+i,10+i]=1
r4[30+i,35+i]=1
r4[35+i,30+i]=1
r4[12,17]=-1
r4[17,12]=-1
r4[14,19]=-1
r4[19,14]=-1
r4[32,37]=-1
r4[37,32]=-1
r4[34,39]=-1
r4[39,34]=-1
r_matrices.append(r4)
# R-matrix for plane of symmetry \sigma_{yz}.
# r4=np.zeros([24,24])
# #Swapping px picks up a negative sign
# r4[2,7]=r4[7,2]=-1
# r4[14,19]=r4[19,14]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
# r4[0,5]=r4[5,0]=1
# r4[1,6]=r4[6,1]=1
# r4[12,17]=r4[17,12]=1
# r4[13,18]=r4[18,13]=1
# r4[3,8]=r4[8,3]=1
# r4[15,20]=r4[20,15]=1
# r4[21,16]=r4[16,21]=1
# r4[9,4]=r4[4,9]=1
# #Swapping 1s of hydrogen
# r4[10,11]=r4[11,10]=1
# r4[22,23]=r4[23,22]=1
# # R-matrix for axis of symmetry C_2 around z axis.
# r6=np.zeros([24,24])
# #Swapping px picks up a negative sign
# r6[2,7]=r6[7,2]=-1
# r6[14,19]=r6[19,14]=-1
# r6[15,20]=r6[20,15]=-1
# r6[3,8]=r6[8,3]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
# r6[0,5]=r6[5,0]=1
# r6[1,6]=r6[6,1]=1
# r6[12,17]=r6[17,12]=1
# r6[13,18]=r6[18,13]=1
# r6[9,4]=r6[4,9]=1
# r6[21,16]=r6[16,21]=1
# #Swapping 1s of hydrogen
# r6[10,11]=r6[11,10]=1
# r6[22,23]=r6[23,22]=1
# # R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
# r7=np.eye(24)
# r7[3,3]=-1
# r7[4,4]=-1
# r7[8,8]=-1
# r7[9,9]=-1
# r7[16,16]=-1
# r7[15,15]=-1
# r7[20,20]=-1
# r7[21,21]=-1
# print(r4)
# print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# fer_op.transform(r4)
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]-_q_.one_body_integrals[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]-_q_.one_body_integrals[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]))
# print(MoleculeFlag)
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]))
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# print(np.all(np.abs(fer_op.h1-_q_.one_body_integrals)<1.e-14))
# print(np.all(np.abs(fer_op.h2-_q_.two_body_integrals)<1.e-14))
# print(np.linalg.norm(fer_op.h2-_q_.two_body_integrals))
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Lithium hydride
#=================================
elif MoleculeFlag == "LiH":
r_matrices =[]
print(MoleculeFlag)
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['Li',(0.000, 0.0000, 0.0000 )],
['H',(1.5949,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
print(_q_.one_body_integrals)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['Li',(0.000, 0.0000, 0.0000 )],
['H',(1.5949,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Spin symmetry:
r1=np.zeros([12,12])
for i in range(12):
if i<6:
r1[i+6,i]=1.
else:
r1[i-6,i]=1.
r_matrices.append(r1)
# sigma{xy}
r2 = np.eye(12)
r2[4,4]=-1
r2[10,10]=-1
r_matrices.append(r2)
#sigma(yz)
r3 = np.eye(12)
r3[3,3]=-1
r3[9,9]=-1
r_matrices.append(r3)
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Beryllium hydride
#=================================
elif MoleculeFlag == "BeH2":
num_particles = 6
r_matrices =[]
print(MoleculeFlag)
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# fer_op = FermionicOperator(h1=one_b, h2=two_b)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
# r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
# r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
# r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
r_matrices.append(r7)
if check_r_matrix_flag and is_atomic:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
elif MoleculeFlag == "test":
r_matrices =[]
num_particles = 6
print(MoleculeFlag)
# try:
# data = np.load(MoleculeFlag+'.npz')
# data.files
# one_b = data['one_b']
# two_b = data['two_b']
# except IOError:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.3264,0.0000, 0.000 )],
['H',(-1.3264,0.0000, 0.000 )]]
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.3,0.0000, 0.000 )],
['H',(-1.3,0.0000, 0.000 )]]
mol.basis = 'sto-6g'
# mol.symmetry=True
# mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
# is_atomic =
_q_ = qmol_func(mol, atomic=is_atomic)
if is_atomic:
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
# fer_op = FermionicOperator(h1=one_b, h2=two_b)
# print(fer_op.h1)
# exit()
# r_matrices.append(np.eye(14))
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
# r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
# r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
# r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
# r_matrices.append(r7)
r8=np.zeros([14,14])
r8[0,0]=1
r8[1,1]=1
r8[2,2]=-1
r8[3,3]=-1
r8[4,4]=-1
r8[5,6]=1
r8[6,5]=1
r8[7,7]=1
r8[8,8]=1
r8[9,9]=-1
r8[10,10]=-1
r8[11,11]=-1
r8[12,13]=1
r8[13,12]=1
# r_matrices.append(r8)
# r_matrices=[]
# r_matrices.append(np.eye(fer_op.modes))
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
if is_atomic:
return [r_matrices,fer_op,num_particles]
else:
r_matrices =[]
r_matrices.append(np.eye(fer_op.modes))
return [r_matrices,fer_op, num_particles]
