def udft_fixed_occ(atoms,occa, occb, **kwargs):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose',False)
ConvCriteria = kwargs.get('ConvCriteria',1e-4)
MaxIter = kwargs.get('MaxIter',20)
DoAveraging = kwargs.get('DoAveraging',True)
averaging = kwargs.get('averaging',0.5)
ETemp = kwargs.get('ETemp',False)
functional = kwargs.get('functional','LDA')
#default to LDA which has no correlation since that is easier
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = kwargs.get('bfs',None)
if not bfs:
basis_data = kwargs.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = kwargs.get('integrals',None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',32)
grid_fineness = kwargs.get('grid_fineness',1)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs',None)
if not orbs: orbe,orbs = geigh(h,S)
orbsa = orbsb = orbs
nalpha,nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" % (
atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mk_auger_dens(orbsa, occa)
Db = mk_auger_dens(orbsb, occb)
Dab = Da + Db
if DoAveraging:
if i:
Da = averaging*Da + (1-averaging)*Da0
Db = averaging*Db + (1-averaging)*Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
#remember we must use a functional that has no correlation energy
gr.setdens(Da,Db)
exca,XCa,XCb = getXC(gr,nel,**kwargs)
Fa = h+Ja+Jb+XCa
Fb = h+Ja+Jb+XCb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
Eone = trace2(Dab,h)
Ej = 0.5*trace2(Dab,Ja+Jb)
Exc = 0.5*exca + 0.5*excb
energy = Eone + Ej + Exc + enuke
print i+1," ",energy," ",Ej," ",Exc
if verbose:
print "%d %10.4f %10.4f %10.4f" % (i,energy,Ej,Exc)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (
functional,atoms.name,energy)
return energy,(orbea,orbeb),(orbsa,orbsb)
def dft_fixed_occ(atoms,occs,**kwargs):
"""\
dft(atoms,**kwargs) - DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
spin_type A Average occupation method for open shell (default)
R Restricted open shell (not implemented yet)
U Unrestricted open shell (aka spin-polarized dft)
Only A works now. Stay tuned.
"""
verbose = kwargs.get('verbose',False)
ConvCriteria = kwargs.get('ConvCriteria',1e-4)
MaxIter = kwargs.get('MaxIter',20)
DoAveraging = kwargs.get('DoAveraging',True)
ETemp = kwargs.get('ETemp',False)
functional = kwargs.get('functional','SVWN')
kwargs['do_grad_dens'] = need_gradients[functional]
bfs = kwargs.get('bfs',None)
if not bfs:
basis_data = kwargs.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = kwargs.get('integrals',None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',32)
grid_fineness = kwargs.get('grid_fineness',1)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs',None)
if orbs is None: orbe,orbs = geigh(h,S)
nclosed,nopen = atoms.get_closedopen()
if verbose:
print "DFT calculation on %s using functional %s" % (
atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nclosed = %d" % nclosed
print "Nopen = %d" % nclosed
if nopen: print "Using spin-averaged dft for open shell calculation"
eold = 0.
if DoAveraging:
print "Using DIIS averaging"
avg=DIIS(S)
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
#print "SCF Iteration:",i,"Starting Energy:",eold
#save the starting orbitals
oldorbs=orbs
if ETemp:
efermi = get_efermi(nel,orbe,ETemp)
occs = get_fermi_occs(efermi,orbe,ETemp)
D = mkdens_occs(orbs,occs)
entropy = get_entropy(occs,ETemp)
else:
D = mk_auger_dens(orbs, occs)
#D = mkdens_spinavg(orbs,nclosed,nopen)
gr.setdens(D)
J = getJ(Ints,D)
Exc,XC = getXC(gr,nel,**kwargs)
F = h+2*J+XC
if DoAveraging: F = avg.getF(F,D)
orbe,orbs = geigh(F,S)
#pad_out(orbs)
#save the new eigenstates of the fock operator F
neworbs=orbs
#send oldorbs and neworbs to get biorthogonalized method
#orbs = biorthog(neworbs, oldorbs, S, nel)
Ej = 2*trace2(D,J)
Eone = 2*trace2(D,h)
energy = Eone + Ej + Exc + enuke
print i+1," ",energy," ",Ej," ",Exc," ",enuke
if ETemp: energy += entropy
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i,energy,Eone,Ej,Exc,enuke)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final %s energy for system %s is %f" % (functional,atoms.name,energy)
return energy,orbe,orbs
def udft(atoms,**kwargs):
"""\
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose')
ConvCriteria = kwargs.get('ConvCriteria',settings.DFTConvergenceCriteria)
MaxIter = kwargs.get('MaxIter',settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging',settings.DFTAveraging)
ETemp = kwargs.get('ETemp',settings.DFT.ElectronTemperature)
functional = kwargs.get('functional',settings.DFTFunctional)
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = getbasis(atoms,**kwargs)
S,h,Ints = getints(bfs,atoms,**kwargs)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',settings.DFTGridRadii)
grid_fineness = kwargs.get('grid_fineness',settings.DFTGridFineness)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs')
if not orbs: orbe,orbs = geigh(h,S)
orbsa = orbsb = orbs
nalpha,nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" \
% (atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
gr.setdens(Da,Db)
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Exc,XCa,XCb = getXC(gr,nel,**kwargs)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
Eja = trace2(D,Ja)
Ejb = trace2(D,Jb)
Eone = 2*trace2(D,h)
energy = Eone + Eja + Ejb + Exc + enuke
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i,energy,Eone,Eja+Ejb,Exc,enuke)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (
functional,atoms.name,energy)
return energy,orbe,orbs
def udft_fixed_occ(atoms, occa, occb, **kwargs):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose', False)
ConvCriteria = kwargs.get('ConvCriteria', 1e-4)
MaxIter = kwargs.get('MaxIter', 20)
DoAveraging = kwargs.get('DoAveraging', True)
averaging = kwargs.get('averaging', 0.5)
ETemp = kwargs.get('ETemp', False)
functional = kwargs.get('functional', 'LDA')
#default to LDA which has no correlation since that is easier
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = kwargs.get('bfs', None)
if not bfs:
basis_data = kwargs.get('basis_data', None)
bfs = getbasis(atoms, basis_data)
integrals = kwargs.get('integrals', None)
if integrals:
S, h, Ints = integrals
else:
S, h, Ints = getints(bfs, atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', 32)
grid_fineness = kwargs.get('grid_fineness', 1)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs', None)
if not orbs: orbe, orbs = geigh(h, S)
orbsa = orbsb = orbs
nalpha, nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" % (atoms.name,
functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mk_auger_dens(orbsa, occa)
Db = mk_auger_dens(orbsb, occb)
Dab = Da + Db
if DoAveraging:
if i:
Da = averaging * Da + (1 - averaging) * Da0
Db = averaging * Db + (1 - averaging) * Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
#remember we must use a functional that has no correlation energy
gr.setdens(Da, Db)
exca, XCa, XCb = getXC(gr, nel, **kwargs)
Fa = h + Ja + Jb + XCa
Fb = h + Ja + Jb + XCb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
Eone = trace2(Dab, h)
Ej = 0.5 * trace2(Dab, Ja + Jb)
Exc = 0.5 * exca + 0.5 * excb
energy = Eone + Ej + Exc + enuke
print i + 1, " ", energy, " ", Ej, " ", Exc
if verbose:
print "%d %10.4f %10.4f %10.4f" % (i, energy, Ej, Exc)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, (orbea, orbeb), (orbsa, orbsb)
def dft_fixed_occ(atoms, occs, **kwargs):
"""\
dft(atoms,**kwargs) - DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
spin_type A Average occupation method for open shell (default)
R Restricted open shell (not implemented yet)
U Unrestricted open shell (aka spin-polarized dft)
Only A works now. Stay tuned.
"""
verbose = kwargs.get('verbose', False)
ConvCriteria = kwargs.get('ConvCriteria', 1e-4)
MaxIter = kwargs.get('MaxIter', 20)
DoAveraging = kwargs.get('DoAveraging', True)
ETemp = kwargs.get('ETemp', False)
functional = kwargs.get('functional', 'SVWN')
kwargs['do_grad_dens'] = need_gradients[functional]
bfs = kwargs.get('bfs', None)
if not bfs:
basis_data = kwargs.get('basis_data', None)
bfs = getbasis(atoms, basis_data)
integrals = kwargs.get('integrals', None)
if integrals:
S, h, Ints = integrals
else:
S, h, Ints = getints(bfs, atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', 32)
grid_fineness = kwargs.get('grid_fineness', 1)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs', None)
if orbs is None: orbe, orbs = geigh(h, S)
nclosed, nopen = atoms.get_closedopen()
if verbose:
print "DFT calculation on %s using functional %s" % (atoms.name,
functional)
print "Nbf = %d" % len(bfs)
print "Nclosed = %d" % nclosed
print "Nopen = %d" % nclosed
if nopen: print "Using spin-averaged dft for open shell calculation"
eold = 0.
if DoAveraging:
print "Using DIIS averaging"
avg = DIIS(S)
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
#print "SCF Iteration:",i,"Starting Energy:",eold
#save the starting orbitals
oldorbs = orbs
if ETemp:
efermi = get_efermi(nel, orbe, ETemp)
occs = get_fermi_occs(efermi, orbe, ETemp)
D = mkdens_occs(orbs, occs)
entropy = get_entropy(occs, ETemp)
else:
D = mk_auger_dens(orbs, occs)
#D = mkdens_spinavg(orbs,nclosed,nopen)
gr.setdens(D)
J = getJ(Ints, D)
Exc, XC = getXC(gr, nel, **kwargs)
F = h + 2 * J + XC
if DoAveraging: F = avg.getF(F, D)
orbe, orbs = geigh(F, S)
#pad_out(orbs)
#save the new eigenstates of the fock operator F
neworbs = orbs
#send oldorbs and neworbs to get biorthogonalized method
#orbs = biorthog(neworbs, oldorbs, S, nel)
Ej = 2 * trace2(D, J)
Eone = 2 * trace2(D, h)
energy = Eone + Ej + Exc + enuke
print i + 1, " ", energy, " ", Ej, " ", Exc, " ", enuke
if ETemp: energy += entropy
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (i, energy, Eone,
Ej, Exc, enuke)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final %s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, orbe, orbs
def udft(atoms, **kwargs):
"""\
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose')
ConvCriteria = kwargs.get('ConvCriteria', settings.DFTConvergenceCriteria)
MaxIter = kwargs.get('MaxIter', settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging', settings.DFTAveraging)
ETemp = kwargs.get('ETemp', settings.DFT.ElectronTemperature)
functional = kwargs.get('functional', settings.DFTFunctional)
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = getbasis(atoms, **kwargs)
S, h, Ints = getints(bfs, atoms, **kwargs)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', settings.DFTGridRadii)
grid_fineness = kwargs.get('grid_fineness', settings.DFTGridFineness)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs')
if not orbs: orbe, orbs = geigh(h, S)
orbsa = orbsb = orbs
nalpha, nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" \
% (atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
gr.setdens(Da, Db)
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
Exc, XCa, XCb = getXC(gr, nel, **kwargs)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
Eja = trace2(D, Ja)
Ejb = trace2(D, Jb)
Eone = 2 * trace2(D, h)
energy = Eone + Eja + Ejb + Exc + enuke
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i, energy, Eone, Eja + Ejb, Exc, enuke)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, orbe, orbs
