def para(gobj, mo10, mo_coeff, mo_occ, qed_fac=1):
mol = gobj.mol
effspin = mol.spin * .5
muB = .5 # Bohr magneton
#qed_fac = (nist.G_ELECTRON - 1)
orboa = mo_coeff[0][:,mo_occ[0]>0]
orbob = mo_coeff[1][:,mo_occ[1]>0]
dm0a = numpy.dot(orboa, orboa.T)
dm0b = numpy.dot(orbob, orbob.T)
dm10a = [reduce(numpy.dot, (mo_coeff[0], x, orboa.T)) for x in mo10[0]]
dm10b = [reduce(numpy.dot, (mo_coeff[1], x, orbob.T)) for x in mo10[1]]
dm10a = numpy.asarray([x-x.T for x in dm10a])
dm10b = numpy.asarray([x-x.T for x in dm10b])
hso1e = uhf_g.make_h01_soc1e(gobj, mo_coeff, mo_occ, qed_fac)
gpara1e =-numpy.einsum('xji,yij->xy', dm10a, hso1e)
gpara1e+= numpy.einsum('xji,yij->xy', dm10b, hso1e)
gpara1e *= 1./effspin / muB
_write(gobj, align(gpara1e)[0], 'SOC(1e)/OZ')
if gobj.para_soc2e:
gpara2e = gobj.make_para_soc2e((dm0a,dm0b), (dm10a,dm10b), qed_fac)
_write(gobj, align(gpara2e)[0], 'SOC(2e)/OZ')
else:
gpara2e = 0
gpara = gpara1e + gpara2e
return gpara
def para(gobj, mo10, mo_coeff, mo_occ, qed_fac=1):
mol = gobj.mol
effspin = mol.spin * .5
muB = .5 # Bohr magneton
#qed_fac = (nist.G_ELECTRON - 1)
orboa = mo_coeff[0][:,mo_occ[0]>0]
orbob = mo_coeff[1][:,mo_occ[1]>0]
dm0a = numpy.dot(orboa, orboa.T)
dm0b = numpy.dot(orbob, orbob.T)
dm10a = [reduce(numpy.dot, (mo_coeff[0], x, orboa.T)) for x in mo10[0]]
dm10b = [reduce(numpy.dot, (mo_coeff[1], x, orbob.T)) for x in mo10[1]]
dm10a = numpy.asarray([x-x.T for x in dm10a])
dm10b = numpy.asarray([x-x.T for x in dm10b])
hso1e = uhf_g.make_h01_soc1e(gobj, mo_coeff, mo_occ, qed_fac)
gpara1e =-numpy.einsum('xji,yij->xy', dm10a, hso1e)
gpara1e+= numpy.einsum('xji,yij->xy', dm10b, hso1e)
gpara1e *= 1./effspin / muB
_write(gobj, align(gpara1e)[0], 'SOC(1e)/OZ')
if gobj.para_soc2e:
gpara2e = gobj.make_para_soc2e((dm0a,dm0b), (dm10a,dm10b), qed_fac)
_write(gobj, align(gpara2e)[0], 'SOC(2e)/OZ')
else:
gpara2e = 0
gpara = gpara1e + gpara2e
return gpara
def make_para_soc2e(gobj, dm0, dm10, sso_qed_fac=1):
if isinstance(gobj.para_soc2e, str):
with_sso = 'SSO' in gobj.para_soc2e.upper()
with_soo = 'SOO' in gobj.para_soc2e.upper()
with_somf = 'SOMF' in gobj.para_soc2e.upper()
with_amfi = 'AMFI' in gobj.para_soc2e.upper()
assert(not (with_somf and (with_sso or with_soo)))
elif gobj.para_soc2e:
with_sso = with_soo = True
with_somf = with_amfi = False
else:
with_sso = with_soo = with_somf = False
with_amfi = True
mol = gobj.mol
alpha2 = nist.ALPHA ** 2
effspin = mol.spin * .5
muB = .5 # Bohr magneton
#sso_qed_fac = (nist.G_ELECTRON - 1)
mf = gobj._scf
ni = mf._numint
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
if abs(omega) > 1e-10:
raise NotImplementedError
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
v1 = get_vxc_soc(ni, mol, mf.grids, mf.xc, dm0,
max_memory=max_memory, verbose=gobj.verbose)
dm10a, dm10b = dm10
if with_somf:
ej = numpy.einsum('yil,xli->xy', v1[0]+v1[1], dm10a-dm10b)
else:
ej = numpy.einsum('yil,xli->xy', v1[0], dm10a)
ej -= numpy.einsum('yil,xli->xy', v1[1], dm10b)
#ej *= -2 #Veff(-2X) approximation of JCP 122 034107
gpara2e = 0
if abs(hyb) > 1e-10:
if with_amfi:
vj, vk = uhf_g.get_jk_amfi(mol, dm0)
else:
vj, vk = uhf_g.get_jk(mol, dm0)
if with_sso or with_soo:
ek = numpy.einsum('yil,xli->xy', vk[0], dm10a)
ek -= numpy.einsum('yil,xli->xy', vk[1], dm10b)
if with_sso:
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= sso_qed_fac * (ej - hyb * ek)
if with_soo:
ej += numpy.einsum('yij,xji->xy', vj[0]-vj[1], dm10a+dm10b)
gpara2e -= 2 * (ej - hyb * ek)
else: # SOMF, see JCP 122, 034107 Eq (19)
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
ek = numpy.einsum('yil,xli->xy', vk[0]+vk[1], dm10a-dm10b)
gpara2e -= ej - 1.5 * hyb * ek
else:
if with_amfi:
vj = uhf_g.get_j_amfi(mol, dm0)
else:
vj = uhf_g.get_j(mol, dm0)
if with_sso or with_soo:
if with_sso:
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= sso_qed_fac * ej
if with_soo:
ej += numpy.einsum('yij,xji->xy', vj[0]-vj[1], dm10a+dm10b)
gpara2e -= 2 * ej
else: # SOMF, see JCP 122, 034107 Eq (19)
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= ej
gpara2e *= (alpha2/4) / effspin / muB
if gobj.verbose >= logger.INFO:
_write(gobj, align(gpara2e)[0], 'SOC(2e)/OZ')
return gpara2e
def make_para_soc2e(gobj, dm0, dm10, sso_qed_fac=1):
if isinstance(gobj.para_soc2e, str):
with_sso = 'SSO' in gobj.para_soc2e.upper()
with_soo = 'SOO' in gobj.para_soc2e.upper()
with_somf = 'SOMF' in gobj.para_soc2e.upper()
with_amfi = 'AMFI' in gobj.para_soc2e.upper()
assert(not (with_somf and (with_sso or with_soo)))
elif gobj.para_soc2e:
with_sso = with_soo = True
with_somf = with_amfi = False
else:
with_sso = with_soo = with_somf = False
with_amfi = True
mol = gobj.mol
alpha2 = nist.ALPHA ** 2
effspin = mol.spin * .5
muB = .5 # Bohr magneton
#sso_qed_fac = (nist.G_ELECTRON - 1)
mf = gobj._scf
ni = mf._numint
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
if abs(omega) > 1e-10:
raise NotImplementedError
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
v1 = get_vxc_soc(ni, mol, mf.grids, mf.xc, dm0,
max_memory=max_memory, verbose=gobj.verbose)
dm10a, dm10b = dm10
if with_somf:
ej = numpy.einsum('yil,xli->xy', v1[0]+v1[1], dm10a-dm10b)
else:
ej = numpy.einsum('yil,xli->xy', v1[0], dm10a)
ej -= numpy.einsum('yil,xli->xy', v1[1], dm10b)
#ej *= -2 #Veff(-2X) approximation of JCP 122 034107
gpara2e = 0
if abs(hyb) > 1e-10:
if with_amfi:
vj, vk = uhf_g.get_jk_amfi(mol, dm0)
else:
vj, vk = uhf_g.get_jk(mol, dm0)
if with_sso or with_soo:
ek = numpy.einsum('yil,xli->xy', vk[0], dm10a)
ek -= numpy.einsum('yil,xli->xy', vk[1], dm10b)
if with_sso:
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= sso_qed_fac * (ej - hyb * ek)
if with_soo:
ej += numpy.einsum('yij,xji->xy', vj[0]-vj[1], dm10a+dm10b)
gpara2e -= 2 * (ej - hyb * ek)
else: # SOMF, see JCP 122, 034107 Eq (19)
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
ek = numpy.einsum('yil,xli->xy', vk[0]+vk[1], dm10a-dm10b)
gpara2e -= ej - 1.5 * hyb * ek
else:
if with_amfi:
vj = uhf_g.get_j_amfi(mol, dm0)
else:
vj = uhf_g.get_j(mol, dm0)
if with_sso or with_soo:
if with_sso:
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= sso_qed_fac * ej
if with_soo:
ej += numpy.einsum('yij,xji->xy', vj[0]-vj[1], dm10a+dm10b)
gpara2e -= 2 * ej
else: # SOMF, see JCP 122, 034107 Eq (19)
ej += numpy.einsum('yij,xji->xy', vj[0]+vj[1], dm10a-dm10b)
gpara2e -= ej
gpara2e *= (alpha2/4) / effspin / muB
if gobj.verbose >= logger.INFO:
_write(gobj, align(gpara2e)[0], 'SOC(2e)/OZ')
return gpara2e