def test_hfw(self):
with lib.light_speed(10) as c:
x2c_1 = sfx2c1e.SpinFreeX2C(mol1)
x2c_2 = sfx2c1e.SpinFreeX2C(mol2)
x2cobj = sfx2c1e.SpinFreeX2C(mol)
fh_ref = (x2c_1.get_hcore() -
x2c_2.get_hcore()) / 0.0002 * lib.param.BOHR
fh = x2cobj.hcore_deriv_generator(deriv=1)
self.assertAlmostEqual(abs(fh(0)[2] - fh_ref).max(), 0, 7)
x2c_1.xuncontract = 0
x2c_2.xuncontract = 0
x2cobj.xuncontract = 0
fh_ref = (x2c_1.get_hcore() -
x2c_2.get_hcore()) / 0.0002 * lib.param.BOHR
fh = x2cobj.hcore_deriv_generator(deriv=1)
self.assertAlmostEqual(abs(fh(0)[2] - fh_ref).max(), 0, 7)
x2c_1.xuncontract = 1
x2c_2.xuncontract = 1
x2cobj.xuncontract = 1
x2c_1.approx = 'ATOM1E'
x2c_2.approx = 'ATOM1E'
x2cobj.approx = 'ATOM1E'
fh_ref = (x2c_1.get_hcore() -
x2c_2.get_hcore()) / 0.0002 * lib.param.BOHR
fh = x2cobj.hcore_deriv_generator(deriv=1)
self.assertAlmostEqual(abs(fh(0)[2] - fh_ref).max(), 0, 7)
def writeSOCIntegrals(mc,
ncasorbs=None,
rdm1=None,
pictureChange1e="bp",
pictureChange2e="bp",
uncontract=True):
from pyscf.x2c import x2c, sfx2c1e
from pyscf.lib.parameters import LIGHT_SPEED
LIGHT_SPEED = 137.0359895000
alpha = 1.0 / LIGHT_SPEED
if (uncontract):
xmol, contr_coeff = x2c.X2C().get_xmol(mc.mol)
else:
xmol, contr_coeff = mc.mol, numpy.eye(mc.mo_coeff.shape[0])
rdm1ao = rdm1
if (rdm1 is None):
rdm1ao = 1. * mc.make_rdm1()
if len(rdm1ao.shape) > 2: rdm1ao = (rdm1ao[0] + rdm1ao[1])
if (uncontract):
dm = reduce(numpy.dot, (contr_coeff, rdm1ao, contr_coeff.T))
else:
dm = 1. * rdm1ao
np, nc = contr_coeff.shape[0], contr_coeff.shape[1]
hso1e = numpy.zeros((3, np, np))
h1e_1c, x, rp = sfx2c1e.SpinFreeX2C(mc.mol).get_hxr(mc.mol,
uncontract=uncontract)
#two electron terms
if (pictureChange2e == "bp"):
h2ao = -(alpha)**2 * 0.5 * xmol.intor(
'cint2e_p1vxp1_sph', comp=3, aosym='s1')
h2ao = h2ao.reshape(3, np, np, np, np)
hso1e += 1. * (numpy.einsum('ijklm,lm->ijk', h2ao, dm) - 1.5 *
(numpy.einsum('ijklm, kl->ijm', h2ao, dm) +
numpy.einsum('ijklm,mj->ilk', h2ao, dm)))
elif (pictureChange2e == "x2c"):
dm1 = dm / 2.
pLL, pLS, pSS = get_p(dm1, x, rp)
#kint = get_kint(xmol)
#hso1e += -(alpha)**2*0.5*get_fso2e_withkint(kint,x,rp,pLL,pLS,pSS)
hso1e += -(alpha)**2 * 0.5 * get_fso2e(xmol, x, rp, pLL, pLS, pSS)
elif (pictureChange2e == "none"):
hso1e *= 0.0
else:
print(pictureChane2e, "not a valid option")
exit(0)
#MF 1 electron term
if (pictureChange1e == "bp"):
hso1e += (alpha)**2 * 0.5 * get_wso(xmol)
elif (pictureChange1e == "x2c1"):
dm /= 2.
pLL, pLS, pSS = get_p(dm, x, rp)
wso = (alpha)**2 * 0.5 * get_wso(xmol)
hso1e += get_hso1e(wso, x, rp)
elif (pictureChange1e == "x2cn"):
h1e_2c = x2c.get_hcore(xmol)
for i in range(np):
for j in range(np):
if (abs(h1e_2c[2 * i, 2 * j + 1].imag) > 1.e-8):
hso1e[0][i, j] -= h1e_2c[2 * i, 2 * j + 1].imag * 2.
if (abs(h1e_2c[2 * i, 2 * j + 1].real) > 1.e-8):
hso1e[1][i, j] -= h1e_2c[2 * i, 2 * j + 1].real * 2.
if (abs(h1e_2c[2 * i, 2 * j].imag) > 1.e-8):
hso1e[2][i, j] -= h1e_2c[2 * i, 2 * j].imag * 2.
else:
print(pictureChane1e, "not a valid option")
exit(0)
h1ao = numpy.zeros((3, nc, nc))
if (uncontract):
for ic in range(3):
h1ao[ic] = reduce(numpy.dot,
(contr_coeff.T, hso1e[ic], contr_coeff))
else:
h1ao = 1. * hso1e
ncore, ncas = mc.ncore, mc.ncas
if (ncasorbs is not None):
ncas = ncasorbs
mo_coeff = mc.mo_coeff
h1 = numpy.einsum('xpq,pi,qj->xij', h1ao, mo_coeff,
mo_coeff)[:, ncore:ncore + ncas, ncore:ncore + ncas]
print1Int(h1, 'SOC')
print(v.shape)
# Transform dipole operator r
x2cobj = x2c.X2C(mol)
with mol.with_common_orig((0., 0., 0.)):
# Function picture_change also supports operators in matrix representation
c = lib.param.LIGHT_SPEED
xmol = x2cobj.get_xmol()[0]
rLL = xmol.intor('int1e_r_spinor')
rSS = xmol.intor('int1e_sprsp_spinor') * (.5 / c)**2
even_operator = (rLL, rSS)
v = x2cobj.picture_change(even_operator)
print(v.shape)
# Transform operator 1/|r-R_O| under spin-free X2c framework
x2cobj = sfx2c1e.SpinFreeX2C(mol)
with mol.with_rinv_origin((0., 0., 0.)):
v = x2cobj.picture_change(('int1e_rinv', 'int1e_prinvp'))
print(v.shape)
# Transform the Hamiltonian using the picture_change function
x2cobj = sfx2c1e.SpinFreeX2C(mol)
c = lib.param.LIGHT_SPEED
xmol = x2cobj.get_xmol()[0]
t = xmol.intor_symmetric('int1e_kin')
w = xmol.intor_symmetric('int1e_pnucp')
v = 'int1e_nuc'
h1 = x2cobj.picture_change(even_operator=(v, w * (.5 / c)**2 - t),
odd_operator=t)
print(abs(h1 - x2cobj.get_hcore()).max())