def dumpAct(fname, info, actlst, base=1):
actlst2 = [i - base for i in actlst]
mol, ova, fav, pT, nb, nalpha, nbeta, nc, na, nv, lmo, enorb, occ = info
corb = set(range(nc))
aorb = set(range(nc, nc + na))
vorb = set(range(nc + na, nc + na + nv))
print '[dumpAct]'
print ' corb=', corb
print ' aorb=', aorb
print ' vorb=', vorb
sorb = set(actlst2)
rcorb = corb.difference(corb.intersection(sorb))
#assuming act in actlst
#raorb = aorb.difference(aorb.intersection(sorb))
rvorb = vorb.difference(vorb.intersection(sorb))
corb = list(rcorb)
aorb = list(sorb)
vorb = list(rvorb)
print ' corb=', corb
print ' aorb=', aorb
print ' vorb=', vorb
clmo = lmo[:, corb].copy()
almo = lmo[:, aorb].copy()
vlmo = lmo[:, vorb].copy()
ierr, ua = pmloc.loc(mol, almo)
almo = almo.dot(ua)
#>>> DUMP <<<#
# P-SORT
mo_c = clmo
mo_v = vlmo
e_c = enorb[corb].copy()
e_v = enorb[vorb].copy()
n_c = occ[corb].copy()
n_v = occ[vorb].copy()
mo_o, n_o, e_o = ulocal.psort(ova, fav, pT, almo)
lmo2 = numpy.hstack((mo_c, mo_o, mo_v))
enorb = numpy.hstack([e_c, e_o, e_v])
occ = numpy.hstack([n_c, n_o, n_v])
assert len(enorb) == nb
assert len(occ) == nb
# CHECK
diff = reduce(numpy.dot, (lmo2.T, ova, lmo2)) - numpy.identity(nb)
print 'diff=', numpy.linalg.norm(diff)
ulocal.lowdinPop(mol, lmo, ova, enorb, occ)
ulocal.dumpLMO(mol, fname + '_new', lmo2)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
print 'diff(LMO2-LMO)=', numpy.linalg.norm(lmo2 - lmo)
nc = len(e_c)
na = len(e_o)
nv = len(e_v)
assert na == len(actlst)
assert nc + na + nv == nb
print 'nc,na,nv,nb=', nc, na, nv, nb
return lmo2, nc, na, nv
def dumpAct(fname,info,actlst,base=1):
actlst2 = [i-base for i in actlst]
mol,ova,fav,pT,nb,nalpha,nbeta,nc,na,nv,lmo,enorb,occ = info
corb = set(range(nc))
aorb = set(range(nc,nc+na))
vorb = set(range(nc+na,nc+na+nv))
print '[dumpAct]'
print ' corb=',corb
print ' aorb=',aorb
print ' vorb=',vorb
sorb = set(actlst2)
rcorb = corb.difference(corb.intersection(sorb))
#assuming act in actlst
#raorb = aorb.difference(aorb.intersection(sorb))
rvorb = vorb.difference(vorb.intersection(sorb))
corb = list(rcorb)
aorb = list(sorb)
vorb = list(rvorb)
print ' corb=',corb
print ' aorb=',aorb
print ' vorb=',vorb
clmo = lmo[:,corb].copy()
almo = lmo[:,aorb].copy()
vlmo = lmo[:,vorb].copy()
ierr,ua = pmloc.loc(mol,almo)
almo = almo.dot(ua)
#>>> DUMP <<<#
# P-SORT
mo_c = clmo
mo_v = vlmo
e_c = enorb[corb].copy()
e_v = enorb[vorb].copy()
n_c = occ[corb].copy()
n_v = occ[vorb].copy()
mo_o,n_o,e_o = ulocal.psort(ova,fav,pT,almo)
lmo2 = numpy.hstack((mo_c,mo_o,mo_v))
enorb = numpy.hstack([e_c,e_o,e_v])
occ = numpy.hstack([n_c,n_o,n_v])
assert len(enorb)==nb
assert len(occ)==nb
# CHECK
diff = reduce(numpy.dot,(lmo2.T,ova,lmo2)) - numpy.identity(nb)
print 'diff=',numpy.linalg.norm(diff)
ulocal.lowdinPop(mol,lmo,ova,enorb,occ)
ulocal.dumpLMO(mol,fname+'_new',lmo2)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
print 'diff(LMO2-LMO)=',numpy.linalg.norm(lmo2-lmo)
nc = len(e_c)
na = len(e_o)
nv = len(e_v)
assert na == len(actlst)
assert nc+na+nv == nb
print 'nc,na,nv,nb=',nc,na,nv,nb
return lmo2,nc,na,nv
def dumpLocal(fname):
chkfile = fname+'.chk'
outfile = fname+'_cmo.molden'
tools.molden.from_chkfile(outfile, chkfile)
mol,mf = scf.chkfile.load_scf(chkfile)
mo_coeff = mf["mo_coeff"]
ova=mol.intor_symmetric("cint1e_ovlp_sph")
nb = mo_coeff.shape[1]
nalpha = (mol.nelectron+mol.spin)/2
nbeta = (mol.nelectron-mol.spin)/2
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
# UHF-alpha/beta
ma = mo_coeff[0]
mb = mo_coeff[1]
#=============================
# Localization
#=============================
ma_c = ma[:,:nalpha].copy()
ma_v = ma[:,nalpha:].copy()
#--------------------
# Occupied space: PM
#--------------------
import pmloc
ierr,uc = pmloc.loc(mol,ma_c)
mc = numpy.dot(ma_c,uc)
#--------------------
# Virtual space: PAO
#--------------------
aux = lowdin(ova)
mv = scdm(ma_v,ova,aux)
# P[dm]
pa = numpy.dot(ma[:,:nalpha],ma[:,:nalpha].T)
pb = numpy.dot(mb[:,:nbeta],mb[:,:nbeta].T)
pT = 0.5*(pa+pb)
# E-SORT
enorb = mf["mo_energy"]
fa = reduce(numpy.dot,(ma,numpy.diag(enorb[0]),ma.T))
fb = reduce(numpy.dot,(mb,numpy.diag(enorb[1]),mb.T))
fav = 0.5*(fa+fb)
mc,occ_c,ec = psort(ova,fav,pT,mc)
mv,occ_v,ev = psort(ova,fav,pT,mv)
#---Check---
tij = reduce(numpy.dot,(mc.T,ova,ma_c))
sig = scipy.linalg.svd(tij,compute_uv=False)
print 'nc=',nalpha,numpy.sum(sig**2)
assert abs(nalpha-numpy.sum(sig**2))<1.e-8
tij = reduce(numpy.dot,(mv.T,ova,ma_v))
sig = scipy.linalg.svd(tij,compute_uv=False)
print 'nv=',nb-nalpha,numpy.sum(sig**2)
assert abs(nb-nalpha-numpy.sum(sig**2))<1.e-8
lmo = numpy.hstack([mc,mv])
enorb = numpy.hstack([ec,ev])
occ = numpy.hstack([occ_c,occ_v])
lowdinPop(mol,lmo,ova,enorb,occ)
dumpLMO(mol,fname,lmo)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
return 0
def dumpLUNO(fname, thresh=0.01):
chkfile = fname + '.chk'
outfile = fname + '_cmo.molden'
tools.molden.from_chkfile(outfile, chkfile)
#=============================
# Natural orbitals
# Lowdin basis X=S{-1/2}
# psi = chi * C
# = chi' * C'
# = chi*X*(X{-1}C')
#=============================
mol, mf = scf.chkfile.load_scf(chkfile)
mo_coeff = mf["mo_coeff"]
ova = mol.intor_symmetric("cint1e_ovlp_sph")
nb = mo_coeff.shape[1]
# Check overlap
diff = reduce(numpy.dot,
(mo_coeff[0].T, ova, mo_coeff[0])) - numpy.identity(nb)
print numpy.linalg.norm(diff)
diff = reduce(numpy.dot,
(mo_coeff[1].T, ova, mo_coeff[1])) - numpy.identity(nb)
print numpy.linalg.norm(diff)
# UHF-alpha/beta
ma = mo_coeff[0]
mb = mo_coeff[1]
nalpha = (mol.nelectron + mol.spin) / 2
nbeta = (mol.nelectron - mol.spin) / 2
# Spin-averaged DM
pTa = numpy.dot(ma[:, :nalpha], ma[:, :nalpha].T)
pTb = numpy.dot(mb[:, :nbeta], mb[:, :nbeta].T)
pT = 0.5 * (pTa + pTb)
# Lowdin basis
s12 = sqrtm(ova)
s12inv = lowdin(ova)
pTOAO = reduce(numpy.dot, (s12, pT, s12))
eig, coeff = scipy.linalg.eigh(-pTOAO)
eig = -2.0 * eig
eig[eig < 0.0] = 0.0
eig[abs(eig) < 1.e-14] = 0.0
ifplot = False #True
if ifplot:
import matplotlib.pyplot as plt
plt.plot(range(nb), eig, 'ro')
plt.show()
# Back to AO basis
coeff = numpy.dot(s12inv, coeff)
diff = reduce(numpy.dot, (coeff.T, ova, coeff)) - numpy.identity(nb)
print 'CtSC-I', numpy.linalg.norm(diff)
#
# Averaged Fock
#
enorb = mf["mo_energy"]
fa = reduce(numpy.dot, (ma, numpy.diag(enorb[0]), ma.T))
fb = reduce(numpy.dot, (mb, numpy.diag(enorb[1]), mb.T))
# Non-orthogonal cases: FC=SCE
# Fao = SC*e*C{-1} = S*C*e*Ct*S
fav = 0.5 * (fa + fb)
# Expectation value of natural orbitals <i|F|i>
fexpt = reduce(numpy.dot, (coeff.T, ova, fav, ova, coeff))
enorb = numpy.diag(fexpt)
nocc = eig.copy()
#
# Reordering and define active space according to thresh
#
idx = 0
active = []
for i in range(nb):
if nocc[i] <= 2.0 - thresh and nocc[i] >= thresh:
active.append(True)
else:
active.append(False)
print '\nNatural orbitals:'
for i in range(nb):
print 'orb:', i, active[i], nocc[i], enorb[i]
active = numpy.array(active)
actIndices = list(numpy.argwhere(active == True).flatten())
cOrbs = coeff[:, :actIndices[0]]
aOrbs = coeff[:, actIndices]
vOrbs = coeff[:, actIndices[-1] + 1:]
nb = cOrbs.shape[0]
nc = cOrbs.shape[1]
na = aOrbs.shape[1]
nv = vOrbs.shape[1]
print 'core orbs:', cOrbs.shape
print 'act orbs:', aOrbs.shape
print 'vir orbs:', vOrbs.shape
assert nc + na + nv == nb
# dump UNO
with open(fname + '_uno.molden', 'w') as thefile:
molden.header(mol, thefile)
molden.orbital_coeff(mol, thefile, coeff)
#=====================
# Population analysis
#=====================
from pyscf import lo
aux = lo.orth_ao(mol, method='meta_lowdin')
#clmo = ulocal.scdm(cOrbs,ova,aux)
#almo = ulocal.scdm(aOrbs,ova,aux)
clmo = cOrbs
almo = aOrbs
ierr, uc = pmloc.loc(mol, clmo)
ierr, ua = pmloc.loc(mol, almo)
clmo = clmo.dot(uc)
almo = almo.dot(ua)
vlmo = ulocal.scdm(vOrbs, ova, aux)
# P-SORT
mo_c, n_c, e_c = ulocal.psort(ova, fav, pT, clmo)
mo_o, n_o, e_o = ulocal.psort(ova, fav, pT, almo)
mo_v, n_v, e_v = ulocal.psort(ova, fav, pT, vlmo)
lmo = numpy.hstack((mo_c, mo_o, mo_v)).copy()
enorb = numpy.hstack([e_c, e_o, e_v])
occ = numpy.hstack([n_c, n_o, n_v])
# CHECK
diff = reduce(numpy.dot, (lmo.T, ova, lmo)) - numpy.identity(nb)
print 'diff=', numpy.linalg.norm(diff)
ulocal.lowdinPop(mol, lmo, ova, enorb, occ)
ulocal.dumpLMO(mol, fname, lmo)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
return mol, ova, fav, pT, nb, nalpha, nbeta, nc, na, nv, lmo, enorb, occ
def dumpLocal(fname):
chkfile = fname+'.chk'
outfile = fname+'_cmo.molden'
tools.molden.from_chkfile(outfile, chkfile)
mol,mf = scf.chkfile.load_scf(chkfile)
mo_coeff = mf["mo_coeff"]
ova=mol.intor_symmetric("cint1e_ovlp_sph")
nb = mo_coeff.shape[1]
nalpha = (mol.nelectron+mol.spin)/2
nbeta = (mol.nelectron-mol.spin)/2
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
# UHF-alpha/beta
ma = mo_coeff[0]
mb = mo_coeff[1]
#=============================
# Localization
#=============================
ma_c = ma[:,:nalpha].copy()
ma_v = ma[:,nalpha:].copy()
#--------------------
# Occupied space: PM
#--------------------
import pmloc
ierr,uc = pmloc.loc(mol,ma_c)
mc = numpy.dot(ma_c,uc)
#--------------------
# Virtual space: PAO
#--------------------
from pyscf import lo
aux = lo.orth_ao(mol,method='meta_lowdin')
mv = scdm(ma_v,ova,aux)
# P[dm]
pa = numpy.dot(ma[:,:nalpha],ma[:,:nalpha].T)
pb = numpy.dot(mb[:,:nbeta],mb[:,:nbeta].T)
pT = 0.5*(pa+pb)
# E-SORT
enorb = mf["mo_energy"]
fa = reduce(numpy.dot,(ma,numpy.diag(enorb[0]),ma.T))
fb = reduce(numpy.dot,(mb,numpy.diag(enorb[1]),mb.T))
fav = 0.5*(fa+fb)
mc,occ_c,ec = psort(ova,fav,pT,mc)
mv,occ_v,ev = psort(ova,fav,pT,mv)
#---Check---
tij = reduce(numpy.dot,(mc.T,ova,ma_c))
sig = scipy.linalg.svd(tij,compute_uv=False)
print 'nc=',nalpha,numpy.sum(sig**2)
assert abs(nalpha-numpy.sum(sig**2))<1.e-8
tij = reduce(numpy.dot,(mv.T,ova,ma_v))
sig = scipy.linalg.svd(tij,compute_uv=False)
print 'nv=',nb-nalpha,numpy.sum(sig**2)
assert abs(nb-nalpha-numpy.sum(sig**2))<1.e-8
lmo = numpy.hstack([mc,mv])
enorb = numpy.hstack([ec,ev])
occ = numpy.hstack([occ_c,occ_v])
lowdinPop(mol,lmo,ova,enorb,occ)
dumpLMO(mol,fname,lmo)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
return 0
def dumpLUNO(fname,thresh=0.01):
chkfile = fname+'.chk'
outfile = fname+'_cmo.molden'
tools.molden.from_chkfile(outfile, chkfile)
#=============================
# Natural orbitals
# Lowdin basis X=S{-1/2}
# psi = chi * C
# = chi' * C'
# = chi*X*(X{-1}C')
#=============================
mol,mf = scf.chkfile.load_scf(chkfile)
mo_coeff = mf["mo_coeff"]
ova=mol.intor_symmetric("cint1e_ovlp_sph")
nb = mo_coeff.shape[1]
# Check overlap
diff = reduce(numpy.dot,(mo_coeff[0].T,ova,mo_coeff[0])) - numpy.identity(nb)
print numpy.linalg.norm(diff)
diff = reduce(numpy.dot,(mo_coeff[1].T,ova,mo_coeff[1])) - numpy.identity(nb)
print numpy.linalg.norm(diff)
# UHF-alpha/beta
ma = mo_coeff[0]
mb = mo_coeff[1]
nalpha = (mol.nelectron+mol.spin)/2
nbeta = (mol.nelectron-mol.spin)/2
# Spin-averaged DM
pTa = numpy.dot(ma[:,:nalpha],ma[:,:nalpha].T)
pTb = numpy.dot(mb[:,:nbeta],mb[:,:nbeta].T)
pT = 0.5*(pTa+pTb)
# Lowdin basis
s12 = sqrtm(ova)
s12inv = lowdin(ova)
pTOAO = reduce(numpy.dot,(s12,pT,s12))
eig,coeff = scipy.linalg.eigh(-pTOAO)
eig = -2.0*eig
eig[eig<0.0]=0.0
eig[abs(eig)<1.e-14]=0.0
ifplot = False #True
if ifplot:
import matplotlib.pyplot as plt
plt.plot(range(nb),eig,'ro')
plt.show()
# Back to AO basis
coeff = numpy.dot(s12inv,coeff)
diff = reduce(numpy.dot,(coeff.T,ova,coeff)) - numpy.identity(nb)
print 'CtSC-I',numpy.linalg.norm(diff)
#
# Averaged Fock
#
enorb = mf["mo_energy"]
fa = reduce(numpy.dot,(ma,numpy.diag(enorb[0]),ma.T))
fb = reduce(numpy.dot,(mb,numpy.diag(enorb[1]),mb.T))
# Non-orthogonal cases: FC=SCE
# Fao = SC*e*C{-1} = S*C*e*Ct*S
fav = 0.5*(fa+fb)
# Expectation value of natural orbitals <i|F|i>
fexpt = reduce(numpy.dot,(coeff.T,ova,fav,ova,coeff))
enorb = numpy.diag(fexpt)
nocc = eig.copy()
#
# Reordering and define active space according to thresh
#
idx = 0
active=[]
for i in range(nb):
if nocc[i]<=2.0-thresh and nocc[i]>=thresh:
active.append(True)
else:
active.append(False)
print '\nNatural orbitals:'
for i in range(nb):
print 'orb:',i,active[i],nocc[i],enorb[i]
active = numpy.array(active)
actIndices = list(numpy.argwhere(active==True).flatten())
cOrbs = coeff[:,:actIndices[0]]
aOrbs = coeff[:,actIndices]
vOrbs = coeff[:,actIndices[-1]+1:]
nb = cOrbs.shape[0]
nc = cOrbs.shape[1]
na = aOrbs.shape[1]
nv = vOrbs.shape[1]
print 'core orbs:',cOrbs.shape
print 'act orbs:',aOrbs.shape
print 'vir orbs:',vOrbs.shape
assert nc+na+nv == nb
# dump UNO
with open(fname+'_uno.molden','w') as thefile:
molden.header(mol,thefile)
molden.orbital_coeff(mol,thefile,coeff)
#=====================
# Population analysis
#=====================
aux = s12inv
#clmo = ulocal.scdm(cOrbs,ova,aux)
#almo = ulocal.scdm(aOrbs,ova,aux)
clmo = cOrbs
almo = aOrbs
ierr,uc = pmloc.loc(mol,clmo)
ierr,ua = pmloc.loc(mol,almo)
clmo = clmo.dot(uc)
almo = almo.dot(ua)
vlmo = ulocal.scdm(vOrbs,ova,aux)
# P-SORT
mo_c,n_c,e_c = ulocal.psort(ova,fav,pT,clmo)
mo_o,n_o,e_o = ulocal.psort(ova,fav,pT,almo)
mo_v,n_v,e_v = ulocal.psort(ova,fav,pT,vlmo)
lmo = numpy.hstack((mo_c,mo_o,mo_v)).copy()
enorb = numpy.hstack([e_c,e_o,e_v])
occ = numpy.hstack([n_c,n_o,n_v])
# CHECK
diff = reduce(numpy.dot,(lmo.T,ova,lmo)) - numpy.identity(nb)
print 'diff=',numpy.linalg.norm(diff)
ulocal.lowdinPop(mol,lmo,ova,enorb,occ)
ulocal.dumpLMO(mol,fname,lmo)
print 'nalpha,nbeta,mol.spin,nb:',\
nalpha,nbeta,mol.spin,nb
return mol,ova,fav,pT,nb,nalpha,nbeta,nc,na,nv,lmo,enorb,occ