def s2n(N, tmpdir='/tmp', Sg=1, Sv=1):
"""
S[2]*N linear transformation:
<[q,k]> = <[E(Sg)_{ij}, k_{kl}, E(Sv)_{kl}]> =
= k_{kl} [E_{il}d(kj) - E(kj)d(il)]
= k(jl)E(SgSv)(il) - k(ki)E(SgSv)(kj)
= D(SgSv)k.T(ij) - k.TD(SgSv)(ij)
= [D(SgSv), k.T](ij)
"""
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 = ifc.cmo.unblock()
S = one.read('OVERLAP', filename=AOONEINT).unblock().unpack()
da, db = dens.Dab(SIRIFC)
kN = rspvec.tomat(N, ifc, tmpdir=tmpdir).T
kn = cmo*kN*cmo.T
dak = (kn.T*S*da - da*S*kn.T)
dbk = (kn.T*S*db - db*S*kn.T)*Sv
gv = -rspvec.tovec(cmo.T*S*(dak+Sg*dbk)*S*cmo, ifc)
return gv
def test_tovec(self):
Nx = rspvec.read("XDIPLEN", propfile=self.RSPVEC)["XDIPLEN"]
kx = rspvec.tomat(Nx, self.ifc, tmpdir=self.tmpdir)
Nx = rspvec.tovec(kx, self.ifc, tmpdir=self.tmpdir)
this = Nx[44]
ref = 0.75732690
assert this == approx(ref)
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 A2B(*args, **kwargs):
pA, pB, ifc = args
tmpdir = kwargs.get("tmpdir", ".")
AOONEINT = os.path.join(tmpdir, "AOONEINT")
S = one.read(label = "OVERLAP", filename = AOONEINT).unblock().unpack()
cmo = ifc.cmo.unblock()
mA = pA["matrix"]
kB = cmo*pB["kappa"]*cmo.T
BA = S*kB*mA - mA*kB*S
da, db = dens.Dab(ifc_=ifc)
G = cmo.T*(S*(da*BA.T + db*BA.T) - (BA.T*da + BA.T*db)*S)*cmo
Gv = rspvec.tovec(G, ifc)
return Gv
def B2C(*args, **kwargs):
pB, pC, ifc = args
tmpdir = kwargs.get("tmpdir", ".")
AOONEINT = os.path.join(tmpdir, "AOONEINT")
S = one.read(label = "OVERLAP", filename = AOONEINT).unblock().unpack()
cmo = ifc.cmo.unblock()
mB = pB["matrix"]
mC = pC["matrix"]
kB = cmo*pB["kappa"]*cmo.T
kC = cmo*pC["kappa"]*cmo.T
kBmC = S*kB*mC - mC*kB*S
kCmB = S*kC*mB - mB*kC*S
BC = kBmC + kCmB
da, db = dens.Dab(ifc_=ifc)
G = cmo.T*(S*(da*BC.T + db*BC.T) - (BC.T*da + BC.T*db)*S)*cmo
Gv = rspvec.tovec(G, ifc)
return Gv
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 mat2vec(self, mat):
ifc = self._sirifc()
mat = rspvec.tovec(np.array(mat), ifc)
return mat
def test_tovec(self):
ref = rspvec.read("XDIPLEN", propfile=self.RSPVEC)["XDIPLEN"]
kx = rspvec.tomat(ref, self.ifc, tmpdir=self.tmpdir)
this = rspvec.tovec(kx, self.ifc, tmpdir=self.tmpdir)
np.testing.assert_almost_equal(this, ref)