def e2n(N, tmpdir='/tmp', hfx=1, Sg=1, Sv=1):
"""
E[2]*N linear transformation:
[k,F] = [k(pq)E(Sv)(pq), F(rs)E(rs)]
= k(pq)F(rs) (E(ps)d(rq) - E(rq)d(ps))
= k(pq)F(ps)E(ps) - k(pq)F(rp)E(rq)
= [k,F](pq)E(pq)
= kF
<[q,kF]> = <[E_{pq}, kF(rs)E(rs)]>
= kF(rs) <E(ps)d(rq) - E(rq)d(ps)>
= kF(qs)D(ps) - kF(rp)D(rq)
= [D, kF.T](pq)
kD = <[k, E(pq)]>
= <[k(rs) E(rs), E(pq)]>
= k(rs) (E(rq)d(ps) - E(ps)d(rq))
= k(rp)D(rq) - k(qs)D(ps)
= [k.T, D](p,q)
Fk = F[kD]
"""
SIRIFC = os.path.join(tmpdir, 'SIRIFC')
AOONEINT = os.path.join(tmpdir, 'AOONEINT')
AOTWOINT = os.path.join(tmpdir, 'AOTWOINT')
LUINDF = os.path.join(tmpdir, 'LUINDF')
ifc = sirifc.sirifc(SIRIFC)
cmo = get_cmo(AOONEINT, SIRIFC)
h = one.read('ONEHAMIL', filename=AOONEINT).unblock().unpack()
S = one.read('OVERLAP', filename=AOONEINT).unblock().unpack().view(util.full.matrix)
da, db = get_densities(SIRIFC)
kN = rspvec.tomat(N, ifc, tmpdir=tmpdir).view(util.full.matrix).T
kn = (cmo*kN*cmo.T).view(util.full.matrix)
dak = (kn.T*S*da - da*S*kn.T)
dbk = (kn.T*S*db - db*S*kn.T)*Sv
(fa, fb), = two.fockab((da, db), filename=AOTWOINT, hfx=hfx)
fa += h; fb += h
(fak, fbk), = two.fockab((dak, dbk), filename=AOTWOINT, hfx=hfx)
kfa = (S*kn*fa - fa*kn*S)
kfb = (S*kn*fb - fb*kn*S)*Sv
fa = fak + kfa
fb = fbk + kfb
gao = S*(da*fa.T + Sg*db*fb.T) - (fa.T*da + Sg*fb.T*db)*S
gm = cmo.T*gao*cmo
# sign convention <[q,[k,F]]> = -E[2]*N
gv = - rspvec.tovec(gm, ifc)
return gv
def test_h1diag_initial_energy(self):
Da, Db = self.dab()
(Fa, Fb), = two.fockab((Da, Db), filename=self.aotwoint)
E = self.EN + rohf.energy(Da, Db, self.h1, Fa, Fb)
Eref = -73.4538472272
assert E == approx(Eref)
def test_fab_f(self):
"""Test alpha and beta Fock matrix, Fortran version"""
d_a = Matrix((6, 6))
d_b = Matrix((6, 6))
d_a[0, 0] = 1
d_a[1, 1] = 1
d_b[0, 0] = 1
(f_a, f_b), = fockab((d_a, d_b), filename=os.path.join(self.suppdir, "AOTWOINT"), f2py=True)
np.testing.assert_allclose(f_a, self.faref)
np.testing.assert_allclose(f_b, self.fbref)
def E3(pB, pC, ifc, **kwargs):
""" Emulate the so called E3 contribution to a quadratic response function
<<A; B, C>> = NA E3 (NB NC + NC NB) + A2 (NB NC + NC NB) + NA (B2 NC + C2 NB)
Emulation of current Dalton implementation in terms of high spin fock matrices
Closed and open shell matrices
Dc = inactive
Do = -active
Fc = Fa+Q
Fo = ? CHECK
Formulas
1/2*[qa, [kb, [kc, H]]] + P(b,c)
[kc, H] = (p~q|rs)H(Sc, 0) + (pq|r~s) H(0, Sc)
[kb, [kc, H]]
= (p~~q|rs)H(SbSc, 0) + (p~q|r~s) H(Sb, Sc)
+ (p~q|r~s)H(Sc, Sb) + (pq|r~~s) H(0, SbSc)
and for
H(S1, S2) generates Fock from (D(S1) g D(S2) - Da g Da - Db g Db
F(S1, S2) = E(S1) g D(S2) - D(S1) g E(S2) - Ea g Da - Da g Ea - Eb g Db - Db g Eb
= Ea [ g D(S2) - D(S1) g - g Da - Da g ]
+ Eb [ S1 g D(S2) - D(S1) g S2 - g Db - Db g ]
"""
tmpdir = kwargs.get('tmpdir', '/tmp')
AOONEINT = os.path.join(tmpdir, "AOONEINT")
h = one.read(label='ONEHAMIL', filename=AOONEINT).unpack().unblock()
S = one.read(label='OVERLAP', filename=AOONEINT).unblock().unpack()
AOTWOINT = os.path.join(tmpdir, "AOTWOINT")
kwargs['filename'] = AOTWOINT
cmo = ifc.cmo.unblock()
kB = cmo*pB["kappa"]*cmo.T
kC = cmo*pC["kappa"]*cmo.T
kB_ = kB*S
_kB = S*kB
kC_ = kC*S
_kC = S*kC
sB = pB.get("spin", 1)
sC = pC.get("spin", 1)
#
# Fock matrices
#
da, db = dens.Dab(ifc_=ifc)
(fa, fb), = two.fockab((da, db), **kwargs)
fa += h
fb += h
Bfa, Bfb = [_kB*f - f*kB_ for f in (fa, sB*fb)]
Cfa, Cfb = [_kC*f - f*kC_ for f in (fa, sC*fb)]
BCfa, BCfb = [_kB*Cf - Cf*kB_ for Cf in (Cfa, sB*Cfb)]
CBfa, CBfb = [_kC*Bf - Bf*kC_ for Bf in (Bfa, sC*Bfb)]
daB, dbB = [_kB.T*d - d*kB_.T for d in (da, sB*db)]
(faB, fbB), = two.fockab((daB, dbB), **kwargs)
CfaB, CfbB = [_kC*fB - fB*kC_ for fB in (faB, sC*fbB)]
daC, dbC = [_kC.T*d - d*kC_.T for d in (da, sC*db)]
(faC, fbC), = two.fockab((daC, dbC), **kwargs)
BfaC, BfbC = [_kB*fC - fC*kB_ for fC in (faC, sB*fbC)]
daBC, dbBC = (_kB.T*dC - dC*kB_.T for dC in (daC, sB*dbC))
daCB, dbCB = (_kC.T*dB - dB*kC_.T for dB in (daB, sC*dbB))
daBC = 0.5*(daBC + daCB)
dbBC = 0.5*(dbBC + dbCB)
(faBC, fbBC), = two.fockab((daBC, dbBC), **kwargs)
#
# Add all focks
#
fa = faBC + BfaC + CfaB + .5*(BCfa + CBfa)
fb = fbBC + BfbC + CfbB + .5*(BCfb + CBfb)
G = cmo.T*(S*(da*fa.T + db*fb.T) - (fa.T*da + fb.T*db)*S)*cmo
#G = cmo.T*(S*da*fa.T - fa.T*da *S)*cmo + \
# cmo.T*(S*db*fb.T - fb.T*db *S)*cmo
Gv = rspvec.tovec(G, ifc)
#print Gv
return Gv
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 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
def fab(self):
da, db = self.dab()
(fa, fb), = two.fockab((da, db), filename=self.aotwoint)
return fa, fb