def __iter__(self):
"""
Initial setup for SCF iterations
"""
self.na = (self.nel + 2 * self.ms) // 2
self.nb = (self.nel - 2 * self.ms) // 2
AOONEINT = os.path.join(self.tmpdir, 'AOONEINT')
self.Z = one.readhead(AOONEINT)['potnuc']
self.h1 = one.read(label='ONEHAMIL',
filename=AOONEINT).unpack().unblock()
self.S = one.read(label='OVERLAP',
filename=AOONEINT).unpack().unblock()
if self.C is None:
self.Ca = dens.cmo(self.h1, self.S)
self.Cb = self.Ca
self.C = (self.Ca, self.Cb)
return self
def udiis(
Ca,
Cb,
na,
nb,
iters=10,
fock=jensen,
hfx=1,
threshold=1e-6,
maxerr=2,
unrest=False,
wrkdir="/tmp",
):
print(Ca, Cb)
saveD = 1
saveC = 0
E = 0
aooneint = os.path.join(wrkdir, "AOONEINT")
aotwoint = os.path.join(wrkdir, "AOTWOINT")
potnuc = one.readhead(aooneint)["potnuc"]
vecs = []
vecsa = []
vecsb = []
evecsa = []
evecsb = []
Eit = []
S = one.read("OVERLAP", aooneint).unpack().unblock()
h = S.I @ one.read("ONEHAMIL", aooneint).unpack().unblock()
Da = dens.C1D(Ca, na) @ S
Db = dens.C1D(Cb, nb) @ S
try:
for i in range(iters):
Da = dens.C1D(Ca, na) @ S
Db = dens.C1D(Cb, nb) @ S
print("D", (Da + Db) @ S.I)
(Fa, Fb), = two.fockab((Da, Db), hfx=hfx, filename=aotwoint)
Fa = h + S.I @ Fa
Fb = h + S.I @ Fb
E0 = E
E = ((Da @ (h + Fa)) + (Db @ (h + Fb))).tr() / 2 + potnuc
D = Da + Db
print("hd", (h @ D).tr(), h & D, h & D.T)
print("FD", Fa & Da)
Eit.append(E)
ga = Da @ Fa - Fa @ Da
gb = Db @ Fb - Fb @ Db
if unrest:
g2 = -(ga @ ga + gb @ gb)
else:
g2 = -(ga + gb) @ (ga + gb)
gn = math.sqrt(g2.tr())
print("%2d:E = %16.12f %16.5e %16.2e" % (i + 1, E, gn, E - E0))
if gn < threshold:
raise Converged(gn)
# if E > E0:
# raise Exception("Energy increase")
if unrest:
Ca = dens.cmo(Fa)
Cb = dens.cmo(Fb)
# Ca = Ca*Ua
# Cb = Cb*Ub
else:
Ca = dens.cmo(Feff(Da, Db, Fa, Fb), S)
Cb = Ca[:, :]
Da = dens.C1D(Ca, na) @ S
Db = dens.C1D(Cb, nb) @ S
if saveD:
vecsa.append(Da)
vecsb.append(Db)
evecsa.append(ga @ Da - Da @ ga)
evecsb.append(gb @ Db - Db @ gb)
elif saveC:
vecsa.append(Ca)
vecsb.append(Cb)
evecsa.append(ga)
evecsb.append(gb)
else:
vecsa.append(Fa)
vecsb.append(Fb)
evecsa.append(ga)
evecsb.append(gb)
edim = min(len(evecsa), maxerr)
eva = evecsa[-edim:]
evb = evecsb[-edim:]
fva = vecsa[-edim:]
fvb = vecsb[-edim:]
B = mkB3(eva, evb, unrest)
rhs = full.matrix((edim + 1, 1))
rhs[-1, 0] = -1
c = rhs / B
subvecsa = full.matrix(Fa.shape)
subvecsb = full.matrix(Fb.shape)
for j in range(edim):
subvecsa += c[j, 0] * fva[j]
subvecsb += c[j, 0] * fvb[j]
if saveD:
Da = subvecsa
Db = subvecsb
(Fa, Fb), = two.fockab((Da, Db), hfx=hfx, filename=aotwoint)
Fa = h + S.I @ Fa
Fb = h + S.I @ Fb
vecsa[i] = Da
vecsb[i] = Db
elif saveC:
Ca = subvecsa
Cb = subvecsb
Da = dens.C1D(Ca, na) @ S
Db = dens.C1D(Cb, nb) @ S
else:
Fa = subvecsa
Fb = subvecsb
Da = dens.C1D(Ca, na) @ S
Db = dens.C1D(Cb, nb) @ S
except Converged:
print("Converged after %d iterations\n" % (i + 1, ))
except Increase:
print("Ca Cb", Ca, Cb)
print("Da Db", Da, Db)
print("Na Nb", Da.tr(), Db.tr())
print("Fa Fb", Fa, Fb)
print("E1", (h * (Da + Db)).tr())
print("E2", (Fa * Da + Fb * Db).tr() / 2 - (h * (Da + Db)).tr() / 2)
print("E", E - potnuc)
def diis(
C,
nisht,
nasht,
iters=10,
fock=jensen,
hfx=1,
threshold=1e-6,
maxerr=2,
wrkdir="/tmp",
):
C1 = C
E = 0
aooneint = pathlib.Path(wrkdir) / "AOONEINT"
aotwoint = pathlib.Path(wrkdir) / "AOTWOINT"
potnuc = one.readhead(aooneint)["potnuc"]
vecs = []
evecs = []
h = one.read("ONEHAMIL", aooneint).unpack().unblock()
S = one.read("OVERLAP", aooneint).unpack().unblock()
try:
for i in range(iters):
Di, Da = dens.C2D(C, nisht, nasht)
D = Di + Da
Fc = h + two.fock(D, filename=aotwoint, hfx=hfx)
Fo = two.fock(Da, hfc=0, filename=aotwoint) + Fc
F = fock(S, Di, Da, Fc, Fo, C, h)
E0 = E
E = ((h + Fc) & D) / 2 + ((Fo - Fc) & Da) / 2 + potnuc
g = grad(S, C1, Di, Da, Fc, Fo)
# gao = gradao(S, C, Di, Da, Fc, Fo)
gn = gradvec(S, C, Di, Da, Fc, Fo, nisht, nasht).norm2()
gn /= math.sqrt(2)
print("%2d:E = %16.12f %16.5e %16.2e" % (i + 1, E, gn, E - E0))
if gn < threshold:
raise Converged(gn)
vecs.append(F)
evecs.append(g)
edim = min(len(evecs), maxerr)
ev = evecs[-edim:]
fv = vecs[-edim:]
B = mkB(ev)
rhs = full.matrix((edim + 1, 1))
rhs[-1, 0] = 1
c = rhs / B
subevecs = full.matrix(g.shape)
subvecs = full.matrix(F.shape)
for i in range(edim):
subevecs += c[i, 0] * ev[i]
subvecs += c[i, 0] * fv[i]
update = -subevecs
upd = update.lower()
upd.anti = 0
update = upd.unpack()
F = subvecs # +update
C = dens.cmo(F, S)
except Converged:
print("-Converged-")
except Stop:
print("-STOP-")
def uroothan(Ca,
Cb,
na,
nb,
hfx=1,
iters=10,
threshold=1e-6,
unrest=False,
wrkdir="/tmp"):
"""
Open-shell Roothan iterations, restricted or unrestricted
"""
if unrest:
print("Unrestricted HF Na=%d Nb=%d\n" % (na, nb))
else:
print("Restricted RHF Na=%d Nb=%d\n" % (na, nb))
E0 = 0.0
aooneint = os.path.join(wrkdir, "AOONEINT")
aotwoint = os.path.join(wrkdir, "AOTWOINT")
h = one.read("ONEHAMIL", aooneint).unpack().unblock()
S = one.read("OVERLAP", aooneint).unpack().unblock()
potnuc = one.readhead(aooneint)["potnuc"]
print(potnuc)
iterinf = []
try:
for i in range(iters):
Da = dens.C1D(Ca, na)
Db = dens.C1D(Cb, nb)
(Fa, Fb), = fockab((Da, Db), hfx=hfx, filename=aotwoint)
Fa += h
Fb += h
E = 0.5 * ((Da & (h + Fa)) + (Db & (h + Fb))) + potnuc
ga = S @ Da @ Fa - Fa @ Da @ S
gb = S @ Db @ Fb - Fb @ Db @ S
g = ga + gb
if unrest:
g2 = -(ga @ ga + gb @ gb)
else:
g2 = (ga + gb) @ (S.I @ (ga + gb) @ S.I).T
gn = sqrt(g2.tr())
gn = sqrt(2 * (ga + gb) & (S.I @ (ga + gb) @ S.I))
iterinf.append((E, gn))
print("%2d:E=%16.10f %16.5e %16.2e" % (i + 1, E, gn, E - E0))
if gn < threshold:
raise Converged(gn)
if unrest:
Ca = dens.cmo(Fa, S)
Cb = dens.cmo(Fb, S)
else:
D = Da + Db
Ds = Da - Db
Fs = Fa - Fb
ID = S.I - D
F0 = (Fa + Fb) / 2
V = sum(S @ P @ (g - F0) @ Q @ S
for P, Q in combinations((Db, Da - Db, S.I - Da), 2))
V += V.T
V = jensen(S, 2 * Db, Da - Db, F0, Fa)
# F = ((Fa + Fb) + Ds @ Fs @ ID + ID @ Fs @ Ds) / 2
F = F0 + V
F = S @ Feff(Da @ S, Db @ S, S.I @ Fa, S.I @ Fb)
Ca = dens.cmo(F, S)
Cb = Ca
except Converged:
print("-Converged-")
if unrest:
return (Ca, Cb)
else:
return Ca
print("Na Nb", Da.tr(), Db.tr())
print("Fa Fb", Fa, Fb)
print("E1", (h * (Da + Db)).tr())
print("E2", (Fa * Da + Fb * Db).tr() / 2 - (h * (Da + Db)).tr() / 2)
print("E", E - potnuc)
if __name__ == "__main__":
if 1:
wrkdir = "tests/test_heh.d"
aooneint = os.path.join(wrkdir, "AOONEINT")
aotwoint = os.path.join(wrkdir, "AOTWOINT")
potnuc = one.readhead(aooneint)["potnuc"]
h = one.read("ONEHAMIL", aooneint).unpack().unblock()
S = one.read("OVERLAP", aooneint).unpack().unblock()
Ca = dens.cmo(h, S)
Cb = Ca
kwargs = dict(wrkdir=wrkdir, iters=20, threshold=1e-5)
uroothan(Ca, Cb, 2, 1, unrest=False, **kwargs)
diis(Ca, 2, 1, **kwargs)
#udiis(Ca, Cb, 1, 1, **kwargs)
if 0:
wrkdir = "tests/test_h2.d"
aooneint = os.path.join(wrkdir, "AOONEINT")
aotwoint = os.path.join(wrkdir, "AOTWOINT")
potnuc = one.readhead(aooneint)["potnuc"]
h = one.read("ONEHAMIL", aooneint).unpack().unblock()
S = one.read("OVERLAP", aooneint).unpack().unblock()
Ca = dens.cmo(h, S)
def _update_mo(self):
F = self.Feff()
Ca = dens.cmo(F, self.S)
Cb = Ca
self.C = Ca, Cb
def update_mo(self):
F = self.Fopt()
Ca = dens.cmo(F, self.S)
Cb = Ca
self.C = Ca, Cb
def update_mo(self):
Ca = dens.cmo(self.h1 + self.Fa, self.S)[:, :self.na]
Cb = dens.cmo(self.h1 + self.Fb, self.S)[:, :self.nb]
self.C = Ca, Cb
def test_h1diag_initial_mo(self):
cmo = dens.cmo(self.h1, self.S)
cmo = self.cmo()
npt.assert_allclose(cmo, ref.C1)
def cmo(self):
return dens.cmo(self.h1, self.S)