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 test_sqrt_second_order(self):
with lib.light_speed(10) as c:
nao = mol.nao_nr()
aoslices = mol.aoslice_by_atom()
p0, p1 = aoslices[0][2:]
s1p1 = mol1.intor('int1e_ipovlp', comp=3)
s1p2 = mol2.intor('int1e_ipovlp', comp=3)
s1_1 = numpy.zeros((3,nao,nao))
s1_1[:,p0:p1] = -s1p1[:,p0:p1]
s1_1 = s1_1 + s1_1.transpose(0,2,1)
s1_2 = numpy.zeros((3,nao,nao))
s1_2[:,p0:p1] = -s1p2[:,p0:p1]
s1_2 = s1_2 + s1_2.transpose(0,2,1)
s2sqrt_ref = (_sqrt1(mol1.intor('int1e_ovlp'), s1_1[2]) -
_sqrt1(mol2.intor('int1e_ovlp'), s1_2[2])) / 0.0002 * lib.param.BOHR
s2invsqrt_ref = (_invsqrt1(mol1.intor('int1e_ovlp'), s1_1[2]) -
_invsqrt1(mol2.intor('int1e_ovlp'), s1_2[2])) / 0.0002 * lib.param.BOHR
s1p = mol.intor('int1e_ipovlp', comp=3)
s1i = numpy.zeros((3,nao,nao))
s1i[:,p0:p1] = -s1p[:,p0:p1]
s1i = s1i + s1i.transpose(0,2,1)
s2aap = mol.intor('int1e_ipipovlp', comp=9).reshape(3,3,nao,nao)
s2abp = mol.intor('int1e_ipovlpip', comp=9).reshape(3,3,nao,nao)
s2 = numpy.zeros((3,3,nao,nao))
s2[:,:,p0:p1] = s2aap[:,:,p0:p1]
s2[:,:,p0:p1,p0:p1] += s2abp[:,:,p0:p1,p0:p1]
s2 = s2 + s2.transpose(0,1,3,2)
s2sqrt = _sqrt2(mol.intor('int1e_ovlp'), s1i[2], s1i[2], s2[2,2])
s2invsqrt = _invsqrt2(mol.intor('int1e_ovlp'), s1i[2], s1i[2], s2[2,2])
self.assertAlmostEqual(abs(s2sqrt-s2sqrt_ref).max(), 0, 7)
self.assertAlmostEqual(abs(s2invsqrt-s2invsqrt_ref).max(), 0, 7)
p0, p1 = aoslices[1][2:]
s1_1 = numpy.zeros((3,nao,nao))
s1_1[:,p0:p1] = -s1p1[:,p0:p1]
s1_1 = s1_1 + s1_1.transpose(0,2,1)
s1_2 = numpy.zeros((3,nao,nao))
s1_2[:,p0:p1] = -s1p2[:,p0:p1]
s1_2 = s1_2 + s1_2.transpose(0,2,1)
s2sqrt_ref = (_sqrt1(mol1.intor('int1e_ovlp'), s1_1[2]) -
_sqrt1(mol2.intor('int1e_ovlp'), s1_2[2])) / 0.0002 * lib.param.BOHR
s2invsqrt_ref = (_invsqrt1(mol1.intor('int1e_ovlp'), s1_1[2]) -
_invsqrt1(mol2.intor('int1e_ovlp'), s1_2[2])) / 0.0002 * lib.param.BOHR
q0, q1 = aoslices[0][2:]
s1i = numpy.zeros((3,nao,nao))
s1i[:,p0:p1] = -s1p[:,p0:p1]
s1i = s1i + s1i.transpose(0,2,1)
s1j = numpy.zeros((3,nao,nao))
s1j[:,q0:q1] = -s1p[:,q0:q1]
s1j = s1j + s1j.transpose(0,2,1)
s2 = numpy.zeros((3,3,nao,nao))
s2[:,:,p0:p1,q0:q1] = s2abp[:,:,p0:p1,q0:q1]
s2 = s2 + s2.transpose(0,1,3,2)
s2sqrt = _sqrt2(mol.intor('int1e_ovlp'), s1i[2], s1j[2], s2[2,2])
s2invsqrt = _invsqrt2(mol.intor('int1e_ovlp'), s1i[2], s1j[2], s2[2,2])
self.assertAlmostEqual(abs(s2sqrt-s2sqrt_ref).max(), 0, 7)
self.assertAlmostEqual(abs(s2invsqrt-s2invsqrt_ref).max(), 0, 7)
def test_khf(self):
with lib.light_speed(2) as c:
mf = scf.KRHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
mf.kpts = cell.make_kpts([3,1,1])
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[0], h1[0]),6/8.98384358326*-0.47578184212352159+0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[1], h1[1]),6/8.98384358326*-0.09637799091491725+0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[2], h1[2]),6/8.98384358326*-0.09637799091491725+0j, 8)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
mcs = mcscf.CASCI(mf, 4, 4).as_scanner().x2c()
gscan = mcs.nuc_grad_method().as_scanner()
g1 = gscan(mol)[1]
self.assertAlmostEqual(lib.finger(g1), -0.070708933966346407, 7)
e1 = mcs('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2')
e2 = mcs('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2')
self.assertAlmostEqual(g1[1,2], (e1-e2)/0.002*lib.param.BOHR, 5)
def test_khf(self):
with lib.light_speed(2) as c:
mf = scf.KRHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
mf.kpts = cell.make_kpts([3,1,1])
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[0], h1[0]),-0.47578184212352159+0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[1], h1[1]),-0.09637799091491725+0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[2], h1[2]),-0.09637799091491725+0j, 8)
def test_hf(self):
with lib.light_speed(2) as c:
mf = scf.RHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(numpy.einsum('ij,ji', dm, h1), 2/3.7865300454631*-0.47578184212352159+0j, 8)
kpts = cell.make_kpts([3,1,1])
h1 = mf.get_hcore(kpt=kpts[1])
self.assertAlmostEqual(numpy.einsum('ij,ji', dm, h1), 2/3.7865300454631*-0.09637799091491725+0j, 8)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
mc = mcscf.CASSCF(mf, 4, 4).x2c().run()
gscan = mc.nuc_grad_method().as_scanner()
g1 = gscan(mol)[1]
self.assertAlmostEqual(lib.finger(g1), -0.070281684620797591, 7)
mcs = mcscf.CASSCF(mf, 4, 4).as_scanner().x2c()
e1 = mcs('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2')
e2 = mcs('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2')
self.assertAlmostEqual(g1[1,2], (e1-e2)/0.002*lib.param.BOHR, 5)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
mcs = mcscf.CASCI(mf, 4, 4).as_scanner().x2c()
gscan = mcs.nuc_grad_method().as_scanner()
g1 = gscan(mol)[1]
self.assertAlmostEqual(lib.finger(g1), -0.070708933966346407, 7)
e1 = mcs('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2')
e2 = mcs('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2')
self.assertAlmostEqual(g1[1, 2],
(e1 - e2) / 0.002 * lib.param.BOHR, 5)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
mc = mcscf.CASSCF(mf.x2c(), 4, 4).run()
gscan = mc.nuc_grad_method().as_scanner()
g1 = gscan(mol)[1]
self.assertAlmostEqual(lib.finger(g1), -0.07027493570511917, 7)
mcs = mcscf.CASSCF(mf, 4, 4).as_scanner().x2c()
e1 = mcs('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2')
e2 = mcs('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2')
self.assertAlmostEqual(g1[1,2], (e1-e2)/0.002*lib.param.BOHR, 5)
def test_hf(self):
with lib.light_speed(2) as c:
mf = scf.RHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(numpy.einsum('ij,ji', dm, h1),
-0.2458227312351979 + 0j, 8)
kpts = cell.make_kpts([3, 1, 1])
h1 = mf.get_hcore(kpt=kpts[1])
self.assertAlmostEqual(numpy.einsum('ij,ji', dm, h1),
-0.04113247191600125 + 0j, 8)
def test_r2(self):
with lib.light_speed(10) as c:
r1_1 = get_r1(mol1, 0, 2)
r1_2 = get_r1(mol2, 0, 2)
r2_ref = (r1_1 - r1_2) / 0.0002 * lib.param.BOHR
r2 = get_r2(mol, 0, 0, 2, 2)
self.assertAlmostEqual(abs(r2 - r2_ref).max(), 0, 7)
r1_1 = get_r1(mol1, 1, 2)
r1_2 = get_r1(mol2, 1, 2)
r2_ref = (r1_1 - r1_2) / 0.0002 * lib.param.BOHR
r2 = get_r2(mol, 1, 0, 2, 2)
self.assertAlmostEqual(abs(r2 - r2_ref).max(), 0, 7)
def test_x2(self):
with lib.light_speed(10) as c:
x1_1 = get_x1(mol1, 0)
x1_2 = get_x1(mol2, 0)
x2_ref = (x1_1[2] - x1_2[2]) / 0.0002 * lib.param.BOHR
x2 = get_x2(mol, 0, 0)
self.assertAlmostEqual(abs(x2[2, 2] - x2_ref).max(), 0, 7)
x1_1 = get_x1(mol1, 1)
x1_2 = get_x1(mol2, 1)
x2_ref = (x1_1[2] - x1_2[2]) / 0.0002 * lib.param.BOHR
x2 = get_x2(mol, 1, 0)
self.assertAlmostEqual(abs(x2[2, 2] - x2_ref).max(), 0, 7)
def test_khf(self):
with lib.light_speed(2) as c:
mf = scf.KRHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
mf.kpts = cell.make_kpts([3, 1, 1])
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[0], h1[0]),
-0.31082970748083477 + 0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[1], h1[1]),
-0.05200981271862468 + 0j, 8)
self.assertAlmostEqual(numpy.einsum('ij,ji', dm[2], h1[2]),
-0.05200981271862468 + 0j, 8)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
pt = mp.mp2.MP2(mf.x2c())
pt.frozen = [0, 1, 10, 11, 12]
gscan = pt.nuc_grad_method().as_scanner().as_scanner()
e, g1 = gscan(mol)
ps = pt.as_scanner()
e1 = ps([[8, (0., 0., 0.)], [1, (0., -0.757, 0.5871)],
[1, (0., 0.757, 0.587)]])
e2 = ps([[8, (0., 0., 0.)], [1, (0., -0.757, 0.5869)],
[1, (0., 0.757, 0.587)]])
self.assertAlmostEqual(g1[1, 2],
(e1 - e2) / 0.0002 * lib.param.BOHR, 5)
def test_hf(self):
with lib.light_speed(2) as c:
mf = scf.RHF(cell).sfx2c1e()
mf.with_df = df.AFTDF(cell)
dm = mf.get_init_guess()
h1 = mf.get_hcore()
self.assertAlmostEqual(
numpy.einsum('ij,ji', dm, h1),
2 / 3.7865300454631 * -0.47578184212352159 + 0j, 8)
kpts = cell.make_kpts([3, 1, 1])
h1 = mf.get_hcore(kpt=kpts[1])
self.assertAlmostEqual(
numpy.einsum('ij,ji', dm, h1),
2 / 3.7865300454631 * -0.09637799091491725 + 0j, 8)
def test_with_x2c_scanner(self):
with lib.light_speed(20.):
mycc = cc.ccsd.CCSD(mf.x2c())
mycc.frozen = [0, 1, 10, 11, 12]
gscan = mycc.nuc_grad_method().as_scanner().as_scanner()
e, g1 = gscan(mol)
cs = mycc.as_scanner()
e1 = cs([[8, (0., 0., 0.)], [1, (0., -0.757, 0.5871)],
[1, (0., 0.757, 0.587)]])
e2 = cs([[8, (0., 0., 0.)], [1, (0., -0.757, 0.5869)],
[1, (0., 0.757, 0.587)]])
self.assertAlmostEqual(g1[1, 2],
(e1 - e2) / 0.0002 * lib.param.BOHR, 5)
def test_R1(self):
with lib.light_speed(10) as c:
R_1 = get_R(mol1)
R_2 = get_R(mol2)
R1_ref = (R_1 - R_2) / 0.0002 * lib.param.BOHR
R1t = get_r1(mol, 0, 2)
self.assertAlmostEqual(abs(R1t - R1_ref).max(), 0, 7)
x0 = get_x0(mol)
h0, s0 = get_h0_s0(mol)
e0, c0 = scipy.linalg.eigh(h0, s0)
get_h1_etc = sfx2c1e_grad._gen_first_order_quantities(
mol, e0, c0, x0)
R1 = get_h1_etc(0)[6][2]
self.assertAlmostEqual(abs(R1 - R1t).max(), 0, 9)
def test_x1(self):
with lib.light_speed(10) as c:
x_1 = get_x0(mol1)
x_2 = get_x0(mol2)
x1_ref = (x_1 - x_2) / 0.0002 * lib.param.BOHR
x1t = get_x1(mol, 0)
self.assertAlmostEqual(abs(x1t[2] - x1_ref).max(), 0, 7)
x0 = get_x0(mol)
h0, s0 = get_h0_s0(mol)
e0, c0 = scipy.linalg.eigh(h0, s0)
get_h1_etc = sfx2c1e_grad._gen_first_order_quantities(
mol, e0, c0, x0)
x1 = get_h1_etc(0)[4]
self.assertAlmostEqual(abs(x1 - x1t).max(), 0, 9)
def test_dhf_grad_with_ssss_high_cost(self):
with lib.light_speed(30):
mf = scf.DHF(h2o).run(conv_tol=1e-12)
g = mf.nuc_grad_method().kernel()
self.assertAlmostEqual(lib.finger(g), 0.0074947016737157545, 7)
ms = mf.as_scanner()
pmol = h2o.copy()
e1 = ms(pmol.set_geom_([["O" , (0. , 0. ,-0.001)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]], unit='Ang'))
e2 = ms(pmol.set_geom_([["O" , (0. , 0. , 0.001)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]], unit='Ang'))
self.assertAlmostEqual(g[0,2], (e2-e1)/0.002*lib.param.BOHR, 5)
def test_h2(self):
with lib.light_speed(10) as c:
h1_1, s1_1 = get_h1_s1(mol1, 0)
h1_2, s1_2 = get_h1_s1(mol2, 0)
h2_ref = (h1_1[2] - h1_2[2]) / 0.0002 * lib.param.BOHR
s2_ref = (s1_1[2] - s1_2[2]) / 0.0002 * lib.param.BOHR
h2, s2 = get_h2_s2(mol, 0, 0)
self.assertAlmostEqual(abs(h2[2, 2] - h2_ref).max(), 0, 7)
self.assertAlmostEqual(abs(s2[2, 2] - s2_ref).max(), 0, 7)
h1_1, s1_1 = get_h1_s1(mol1, 1)
h1_2, s1_2 = get_h1_s1(mol2, 1)
h2_ref = (h1_1[2] - h1_2[2]) / 0.0002 * lib.param.BOHR
s2_ref = (s1_1[2] - s1_2[2]) / 0.0002 * lib.param.BOHR
h2, s2 = get_h2_s2(mol, 1, 0)
self.assertAlmostEqual(abs(h2[2, 2] - h2_ref).max(), 0, 7)
self.assertAlmostEqual(abs(s2[2, 2] - s2_ref).max(), 0, 7)
def test_dhf_grad_with_ssss_high_cost(self):
with lib.light_speed(30):
mf = scf.DHF(h2o).run()
g = mf.nuc_grad_method().kernel()
self.assertAlmostEqual(lib.finger(g), 0.0074940105486053926, 7)
ms = mf.as_scanner()
pmol = h2o.copy()
e1 = ms(
pmol.set_geom_([["O",
(0., 0., -0.001)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]],
unit='Ang'))
e2 = ms(
pmol.set_geom_([["O",
(0., 0., 0.001)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]],
unit='Ang'))
self.assertAlmostEqual(g[0, 2], (e2 - e1) / 0.002 * lib.param.BOHR,
6)
vj[:,n2c:,n2c:] += vx[0]
vk[:,n2c:,:n2c] += vx[1]
vx = _vhf.rdirect_bindm('int2e_ip1spsp2_spinor', 's2kl',
('lk->s1ij', 'jk->s1il'), (dmss, dmls), 3,
mol._atm, mol._bas, mol._env) * c1**2
vj[:,:n2c,:n2c] += vx[0]
vk[:,:n2c,n2c:] += vx[1]
return vj, vk
if __name__ == "__main__":
from pyscf import gto
from pyscf import scf
from pyscf import lib
with lib.light_speed(30):
h2o = gto.Mole()
h2o.verbose = 0
h2o.output = None#"out_h2o"
h2o.atom = [
["O" , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)] ]
h2o.basis = {"H": '6-31g',
"O": '6-31g',}
h2o.build()
method = scf.dhf.UHF(h2o).run()
g = method.Gradients().kernel()
print(g)
ms = method.as_scanner()
mol = gto.Mole()
mol.basis = 'dzp-dk'
mol.atom = '''
O 0.000000 0.000000 0.118351
H 0.000000 0.761187 -0.469725
H 0.000000 -0.761187 -0.469725
'''
mol.charge = 0
mol.spin = 0
mol.symmetry = 1
mol.verbose = 4
mol.nucmod = 1
mol.build()
#with lib.light_speed(lib.param.LIGHT_SPEED):
with lib.light_speed(5.0):
mf = dft.DUKS(mol)
mf.grids.level = 3
#mf.grids.prune = None
mf.with_ssss = True
mf.with_gaunt = False
mf.with_breit = False
mf.chkfile = name + '.chk'
mf.kernel()
cc = lib.param.LIGHT_SPEED
print mf.mo_occ
dm = mf.make_rdm1()
coords = mf.grids.coords
weights = mf.grids.weights
