def make_h1_soc(hfcobj, dm0):
'''1-electron and 2-electron spin-orbit coupling integrals.
1-electron SOC integral is the imaginary part of [i sigma dot pV x p],
ie [sigma dot pV x p].
Note sigma_z is considered in the SOC integrals (the (-) sign for beta-beta
block is included in the integral). The factor 1/2 in the spin operator
s=sigma/2 is not included.
'''
# JCP, 122, 034107 Eq (2) = 1/4c^2 hso1e
mol = hfcobj.mol
assert(not mol.has_ecp())
if hfcobj.so_eff_charge:
hso1e = 0
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = koseki_charge(mol.atom_charge(ia))
hso1e += -Z * mol.intor('int1e_prinvxp', 3)
else:
hso1e = mol.intor('int1e_pnucxp', 3)
hso = [hso1e, -hso1e]
if hfcobj.para_soc2e:
hso2e = hfcobj.make_h1_soc2e(dm0)
hso[0] += hso2e[0]
hso[1] += hso2e[1]
return hso
def make_h1_soc(hfcobj, dm0):
'''1-electron and 2-electron spin-orbit coupling integrals.
1-electron SOC integral is the imaginary part of [i sigma dot pV x p],
ie [sigma dot pV x p].
Note sigma_z is considered in the SOC integrals (the (-) sign for beta-beta
block is included in the integral). The factor 1/2 in the spin operator
s=sigma/2 is not included.
'''
# JCP, 122, 034107 Eq (2) = 1/4c^2 hso1e
mol = hfcobj.mol
assert(not mol.has_ecp())
if hfcobj.so_eff_charge:
hso1e = 0
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = koseki_charge(mol.atom_charge(ia))
hso1e += -Z * mol.intor('int1e_prinvxp', 3)
else:
hso1e = mol.intor('int1e_pnucxp', 3)
hso = [hso1e, -hso1e]
if hfcobj.para_soc2e:
hso2e = hfcobj.make_h1_soc2e(dm0)
hso[0] += hso2e[0]
hso[1] += hso2e[1]
return hso
def make_h01_soc1e(obj, mo_coeff, mo_occ, qed_fac=1):
mol = obj.mol
assert (not mol.has_ecp())
alpha2 = nist.ALPHA**2
#qed_fac = (nist.G_ELECTRON - 1)
if obj.so_eff_charge:
hso1e = 0
for ia in range(mol.natm):
Z = koseki_charge(mol.atom_charge(ia))
mol.set_rinv_origin(mol.atom_coord(ia))
hso1e += -Z * mol.intor_asymmetric('int1e_prinvxp', 3)
else:
hso1e = mol.intor_asymmetric('int1e_pnucxp', 3)
hso1e *= qed_fac * (alpha2 / 4)
return hso1e
def make_h01_soc1e(gobj, mo_coeff, mo_occ, qed_fac=1):
mol = gobj.mol
assert(not mol.has_ecp())
alpha2 = nist.ALPHA ** 2
#qed_fac = (nist.G_ELECTRON - 1)
# hso1e is the imaginary part of [i sigma dot pV x p]
# JCP, 122, 034107 Eq (2) = 1/4c^2 hso1e
if gobj.so_eff_charge:
hso1e = 0
for ia in range(mol.natm):
Z = koseki_charge(mol.atom_charge(ia))
mol.set_rinv_origin(mol.atom_coord(ia))
hso1e += -Z * mol.intor_asymmetric('int1e_prinvxp', 3)
else:
hso1e = mol.intor_asymmetric('int1e_pnucxp', 3)
hso1e *= qed_fac * (alpha2/4)
return hso1e
def make_h01_soc1e(gobj, mo_coeff, mo_occ, qed_fac=1):
mol = gobj.mol
assert(not mol.has_ecp())
alpha2 = nist.ALPHA ** 2
#qed_fac = (nist.G_ELECTRON - 1)
# hso1e is the imaginary part of [i sigma dot pV x p]
# JCP, 122, 034107 Eq (2) = 1/4c^2 hso1e
if gobj.so_eff_charge:
hso1e = 0
for ia in range(mol.natm):
Z = koseki_charge(mol.atom_charge(ia))
mol.set_rinv_origin(mol.atom_coord(ia))
hso1e += -Z * mol.intor_asymmetric('int1e_prinvxp', 3)
else:
hso1e = mol.intor_asymmetric('int1e_pnucxp', 3)
hso1e *= qed_fac * (alpha2/4)
return hso1e
def dia(gobj, dm0, gauge_orig=None):
'''Note the side effects of set_common_origin'''
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3, 3))
mol = gobj.mol
effspin = mol.spin * .5
muB = .5 # Bohr magneton
dma, dmb = dm0
totdm = dma + dmb
spindm = dma - dmb
alpha2 = nist.ALPHA**2
#Many choices of qed_fac, see JPC, 101, 3388
#qed_fac = (nist.G_ELECTRON - 1)
#qed_fac = nist.G_ELECTRON / 2
qed_fac = 1
assert (not mol.has_ecp())
if gauge_orig is not None:
mol.set_common_origin(gauge_orig)
e11 = numpy.zeros((3, 3))
im, mass_center = rhf_rotg.inertia_tensor(mol)
for ia in range(mol.natm):
Z = koseki_charge(mol.atom_charge(ia))
R = mol.atom_coord(ia) - mass_center
with mol.with_rinv_origin(R):
h11 = mol.intor('int1e_drinv', comp=3) * Z # * mol.atom_charge(ia)
t1 = numpy.einsum('xij,ij->x', h11, spindm)
e11 += numpy.dot(R, t1) * numpy.eye(3) - numpy.kron(R, t1).reshape(
3, 3)
#GIAO part of dia-magnetic constribution
#print('kron', numpy.kron(R, t1).reshape(3,3))
#h22 = mol.intor('int1e_a01gp', comp=9)
#e11 -= Z * numpy.einsum('xij,ij->x', h22, spindm).reshape(3,3)
gdia = e11 * alpha2 / effspin / 4.
return gdia
def dia(gobj, dm0, gauge_orig=None):
'''Note the side effects of set_common_origin'''
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
mol = gobj.mol
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
muB = .5 # Bohr magneton
alpha2 = nist.ALPHA ** 2
#Many choices of qed_fac, see JPC, 101, 3388
#qed_fac = (nist.G_ELECTRON - 1)
#qed_fac = nist.G_ELECTRON / 2
qed_fac = 1
# relativistic mass correction (RMC)
rmc = -numpy.einsum('ij,ji', mol.intor('int1e_kin'), spindm)
rmc *= qed_fac / effspin * alpha2
logger.info(gobj, 'RMC = %s', rmc)
assert(not mol.has_ecp())
# GC(1e)
if gauge_orig is not None:
mol.set_common_origin(gauge_orig)
h11 = 0
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = mol.atom_charge(ia)
if gobj.so_eff_charge or not gobj.dia_soc2e:
Z = koseki_charge(Z)
# GC(1e) = 1/4c^2 Z/(2r_N^3) [vec{r}_N dot r sigma dot B - B dot vec{r}_N r dot sigma]
# a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r (dot sigma)
if gauge_orig is None:
h11 += Z * mol.intor('int1e_giao_a11part', 9)
else:
h11 += Z * mol.intor('int1e_cg_a11part', 9)
trh11 = h11[0] + h11[4] + h11[8]
h11[0] -= trh11
h11[4] -= trh11
h11[8] -= trh11
if gauge_orig is None:
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = mol.atom_charge(ia)
if gobj.so_eff_charge or not gobj.dia_soc2e:
Z = koseki_charge(Z)
h11 += Z * mol.intor('int1e_a01gp', 9)
gc1e = numpy.einsum('xij,ji->x', h11, spindm).reshape(3,3)
if gobj.mb: # correction of order c^{-2} from MB basis
gc1e += numpy.einsum('ij,ji', mol.intor('int1e_nuc'), spindm) * numpy.eye(3)
gc1e *= (alpha2/4) / effspin / muB
if gobj.verbose >= logger.INFO:
_write(gobj, gobj.align(gc1e)[0], 'GC(1e)')
if gobj.dia_soc2e:
gc2e = gobj.make_dia_gc2e(dm0, gauge_orig, qed_fac)
if gobj.verbose >= logger.INFO:
_write(gobj, gobj.align(gc2e)[0], 'GC(2e)')
else:
gc2e = 0
gdia = gc1e + gc2e + rmc * numpy.eye(3)
return gdia
def dia(gobj, dm0, gauge_orig=None):
'''Note the side effects of set_common_origin'''
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
mol = gobj.mol
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
muB = .5 # Bohr magneton
alpha2 = nist.ALPHA ** 2
#Many choices of qed_fac, see JPC, 101, 3388
#qed_fac = (nist.G_ELECTRON - 1)
#qed_fac = nist.G_ELECTRON / 2
qed_fac = 1
# relativistic mass correction (RMC)
rmc = -numpy.einsum('ij,ji', mol.intor('int1e_kin'), spindm)
rmc *= qed_fac / effspin * alpha2
logger.info(gobj, 'RMC = %s', rmc)
assert(not mol.has_ecp())
# GC(1e)
if gauge_orig is not None:
mol.set_common_origin(gauge_orig)
h11 = 0
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = mol.atom_charge(ia)
if gobj.so_eff_charge or not gobj.dia_soc2e:
Z = koseki_charge(Z)
# GC(1e) = 1/4c^2 Z/(2r_N^3) [vec{r}_N dot r sigma dot B - B dot vec{r}_N r dot sigma]
# a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r (dot sigma)
if gauge_orig is None:
h11 += Z * mol.intor('int1e_giao_a11part', 9)
else:
h11 += Z * mol.intor('int1e_cg_a11part', 9)
trh11 = h11[0] + h11[4] + h11[8]
h11[0] -= trh11
h11[4] -= trh11
h11[8] -= trh11
if gauge_orig is None:
for ia in range(mol.natm):
mol.set_rinv_origin(mol.atom_coord(ia))
Z = mol.atom_charge(ia)
if gobj.so_eff_charge or not gobj.dia_soc2e:
Z = koseki_charge(Z)
h11 += Z * mol.intor('int1e_a01gp', 9)
gc1e = numpy.einsum('xij,ji->x', h11, spindm).reshape(3,3)
if gobj.mb: # correction of order c^{-2} from MB basis
gc1e += numpy.einsum('ij,ji', mol.intor('int1e_nuc'), spindm) * numpy.eye(3)
gc1e *= (alpha2/4) / effspin / muB
if gobj.verbose >= logger.INFO:
_write(gobj, gobj.align(gc1e)[0], 'GC(1e)')
if gobj.dia_soc2e:
gc2e = gobj.make_dia_gc2e(dm0, gauge_orig, qed_fac)
if gobj.verbose >= logger.INFO:
_write(gobj, gobj.align(gc2e)[0], 'GC(2e)')
else:
gc2e = 0
gdia = gc1e + gc2e + rmc * numpy.eye(3)
return gdia
