def extract_basis_functions(self, basis_name='atompaw.sz'):
"""Create BasisFunctions object with pseudo wave functions."""
from gpaw.basis_data import Basis, BasisFunction
assert self.wfs.nspins == 1
basis = Basis(self.symbol, basis_name, readxml=False)
basis.d = self.wfs.gd.h
basis.ng = self.wfs.gd.ng + 1
basis.generatorattrs = {} # attrs of the setup maybe
basis.generatordata = 'AtomPAW' # version info too?
bf_j = basis.bf_j
for l, n, f, eps, psit_G in self.state_iter():
phit_g = np.empty(basis.ng)
phit_g[0] = 0.0
phit_g[1:] = psit_G
phit_g *= np.sign(psit_G[-1])
# If there's no node at zero, we shouldn't set phit_g to zero
# We'll make an ugly hack
if abs(phit_g[1]) > 3.0 * abs(phit_g[2] - phit_g[1]):
phit_g[0] = phit_g[1]
bf = BasisFunction(l, self.wfs.gd.rcut, phit_g,
'%s%d e=%.3f f=%.3f' % ('spdfgh'[l], n, eps, f))
bf_j.append(bf)
return basis
def extract_basis_functions(self, basis_name='atompaw.sz'):
"""Create BasisFunctions object with pseudo wave functions."""
from gpaw.basis_data import Basis, BasisFunction
assert self.wfs.nspins == 1
basis = Basis(self.symbol, basis_name, readxml=False)
basis.d = self.wfs.gd.r_g[0]
basis.ng = self.wfs.gd.N + 1
basis.generatorattrs = {} # attrs of the setup maybe
basis.generatordata = 'AtomPAW' # version info too?
bf_j = basis.bf_j
for l, n, f, eps, psit_G in self.state_iter():
phit_g = np.empty(basis.ng)
phit_g[0] = 0.0
phit_g[1:] = psit_G
phit_g *= np.sign(psit_G[-1])
# If there's no node at zero, we shouldn't set phit_g to zero
# We'll make an ugly hack
if abs(phit_g[1]) > 3.0 * abs(phit_g[2] - phit_g[1]):
phit_g[0] = phit_g[1]
bf = BasisFunction(l, self.wfs.gd.r_g[-1], phit_g,
'%s%d e=%.3f f=%.3f' % ('spdfgh'[l], n, eps, f))
bf_j.append(bf)
return basis
def generate(self, zetacount=2, polarizationcount=1,
tailnorm=(0.16, 0.3, 0.6), energysplit=0.1, tolerance=1.0e-3,
referencefile=None, referenceindex=None, rcutpol_rel=1.0,
rcutmax=20.0, #ngaussians=None,
rcharpol_rel=None,
vconf_args=(12.0, 0.6), txt='-',
include_energy_derivatives=False,
lvalues=None):
"""Generate an entire basis set.
This is a high-level method which will return a basis set
consisting of several different basis vector types.
Parameters:
===================== =================================================
``zetacount`` Number of basis functions per occupied orbital
``polarizationcount`` Number of polarization functions
``tailnorm`` List of tail norms for split-valence scheme
``energysplit`` Energy increase defining confinement radius (eV)
``tolerance`` Tolerance of energy split (eV)
``referencefile`` gpw-file used to generate polarization function
``referenceindex`` Index in reference system of relevant atom
``rcutpol_rel`` Polarization rcut relative to largest other rcut
``rcutmax`` No cutoff will be greater than this value
``vconf_args`` Parameters (alpha, ri/rc) for conf. potential
``txt`` Log filename or '-' for stdout
===================== =================================================
Returns a fully initialized Basis object.
"""
if txt == '-':
txt = sys.stdout
elif txt is None:
txt = devnull
if isinstance(tailnorm, float):
tailnorm = (tailnorm,)
assert 1 + len(tailnorm) >= max(polarizationcount, zetacount), \
'Needs %d tail norm values, but only %d are specified' % \
(max(polarizationcount, zetacount) - 1, len(tailnorm))
textbuffer = StringIO()
class TeeStream: # Quick hack to both write and save output
def __init__(self, out1, out2):
self.out1 = out1
self.out2 = out2
def write(self, string):
self.out1.write(string)
self.out2.write(string)
txt = TeeStream(txt, textbuffer)
if vconf_args is not None:
amplitude, ri_rel = vconf_args
g = self.generator
rgd = self.rgd
# Find out all relevant orbitals
# We'll probably need: s, p and d.
# The orbitals we want are stored in u_j.
# Thus we must find the j corresponding to the highest energy of
# each orbital-type.
#
# However not all orbitals in l_j are actually occupied, so we
# will check the occupations in the generator object's lists
#
# ASSUMPTION: The last index of a given value in l_j corresponds
# exactly to the orbital we want, except those which are not occupied
#
# Get (only) one occupied valence state for each l
# Not including polarization in this list
if lvalues is None:
lvalues = np.unique([l for l, f in zip(g.l_j[g.njcore:],
g.f_j[g.njcore:])
if f > 0])
if lvalues[0] != 0: # Always include s-orbital !
lvalues = np.array([0] + list(lvalues))
#print energysplit
if isinstance(energysplit,float):
energysplit=[energysplit]*(max(lvalues)+1)
#print energysplit,'~~~~~~~~'
title = '%s Basis functions for %s' % (g.xcname, g.symbol)
print >> txt, title
print >> txt, '=' * len(title)
j_l = {} # index j by l rather than the other way around
reversed_l_j = list(g.l_j)
reversed_l_j.reverse() # the values we want are stored last
for l in lvalues:
j = len(reversed_l_j) - reversed_l_j.index(l) - 1
j_l[l] = j
singlezetas = []
energy_derivative_functions = []
multizetas = [[] for i in range(zetacount - 1)]
polarization_functions = []
splitvalencedescr = 'split-valence wave, fixed tail norm'
derivativedescr = 'derivative of sz wrt. (ri/rc) of potential'
for l in lvalues:
# Get one unmodified pseudo-orbital basis vector for each l
j = j_l[l]
n = g.n_j[j]
orbitaltype = str(n) + 'spdf'[l]
msg = 'Basis functions for l=%d, n=%d' % (l, n)
print >> txt
print >> txt, msg + '\n', '-' * len(msg)
print >> txt
if vconf_args is None:
adverb = 'sharply'
else:
adverb = 'softly'
print >> txt, 'Zeta 1: %s confined pseudo wave,' % adverb,
u, e, de, vconf, rc = self.rcut_by_energy(j, energysplit[l],
tolerance,
vconf_args=vconf_args)
if rc > rcutmax:
rc = rcutmax # scale things down
if vconf is not None:
vconf = g.get_confinement_potential(amplitude, ri_rel * rc,
rc)
u, e = g.solve_confined(j, rc, vconf)
print >> txt, 'using maximum cutoff'
print >> txt, 'rc=%.02f Bohr' % rc
else:
print >> txt, 'fixed energy shift'
print >> txt, 'DE=%.03f eV :: rc=%.02f Bohr' % (de * Hartree,
rc)
if vconf is not None:
print >> txt, ('Potential amp=%.02f :: ri/rc=%.02f' %
(amplitude, ri_rel))
phit_g = self.smoothify(u, l)
bf = BasisFunction(l, rc, phit_g,
'%s-sz confined orbital' % orbitaltype)
norm = np.dot(g.dr, phit_g * phit_g)**.5
print >> txt, 'Norm=%.03f' % norm
singlezetas.append(bf)
zetacounter = iter(xrange(2, zetacount + 1))
if include_energy_derivatives:
assert zetacount > 1
zeta = zetacounter.next()
print >> txt, '\nZeta %d: %s' % (zeta, derivativedescr)
vconf2 = g.get_confinement_potential(amplitude,
ri_rel * rc * .99, rc)
u2, e2 = g.solve_confined(j, rc, vconf2)
phit2_g = self.smoothify(u2, l)
dphit_g = phit2_g - phit_g
dphit_norm = np.dot(rgd.dr_g, dphit_g * dphit_g) ** .5
dphit_g /= dphit_norm
descr = '%s-dz E-derivative of sz' % orbitaltype
bf = BasisFunction(l, rc, dphit_g, descr)
energy_derivative_functions.append(bf)
for i, zeta in enumerate(zetacounter): # range(zetacount - 1):
print >> txt, '\nZeta %d: %s' % (zeta, splitvalencedescr)
# Unresolved issue: how does the lack of normalization
# of the first function impact the tail norm scheme?
# Presumably not much, since most interesting stuff happens
# close to the core.
rsplit, norm, splitwave = rsplit_by_norm(rgd, l, phit_g,
tailnorm[i]**2.0,
txt)
descr = '%s-%sz split-valence wave' % (orbitaltype,
'0sdtq56789'[zeta])
bf = BasisFunction(l, rsplit, phit_g - splitwave, descr)
multizetas[i].append(bf)
if polarizationcount > 0:
# Now make up some properties for the polarization orbital
# We just use the cutoffs from the previous one times a factor
rcut = max([bf.rc for bf in singlezetas]) * rcutpol_rel
rcut = min(rcut, rcutmax)
# Find 'missing' values in lvalues
for i, l in enumerate(lvalues):
if i != l:
l_pol = i
break
else:
l_pol = lvalues[-1] + 1
msg = 'Polarization function: l=%d, rc=%.02f' % (l_pol, rcut)
print >> txt, '\n' + msg
print >> txt, '-' * len(msg)
# Make a single Gaussian for polarization function.
#
# It is known that for given l, the sz cutoff defined
# by some fixed energy is strongly correlated to the
# value of the characteristic radius which best reproduces
# the wave function found by interpolation.
#
# We know that for e.g. d orbitals:
# rchar ~= .37 rcut[sz](.3eV)
# Since we don't want to spend a lot of time finding
# these value for other energies, we just find the energy
# shift at .3 eV now
j = max(j_l.values())
u, e, de, vconf, rc_fixed = self.rcut_by_energy(j, .3, 1e-2,
6., (12., .6))
default_rchar_rel = .25
# Defaults for each l. Actually we don't care right now
rchar_rels = {}
if rcharpol_rel is None:
rcharpol_rel = rchar_rels.get(l_pol, default_rchar_rel)
rchar = rcharpol_rel * rc_fixed
gaussian = QuasiGaussian(1./rchar**2, rcut)
psi_pol = gaussian(rgd.r_g) * rgd.r_g**(l_pol + 1)
norm = np.dot(rgd.dr_g, psi_pol * psi_pol) ** .5
psi_pol /= norm
print >> txt, 'Single quasi Gaussian'
msg = 'Rchar = %.03f*rcut = %.03f Bohr' % (rcharpol_rel, rchar)
adjective = 'Gaussian'
print >> txt, msg
#else:
# psi_pol = self.make_polarization_function(rcut, l_pol,
# referencefile,
# referenceindex,
# ngaussians, txt)
# adjective = 'interpolated'
type = '%s-type %s polarization' % ('spdfg'[l_pol], adjective)
bf_pol = BasisFunction(l_pol, rcut, psi_pol, type)
polarization_functions.append(bf_pol)
for i in range(polarizationcount - 1):
npol = i + 2
msg = '\n%s: %s' % (['Secondary', 'Tertiary', 'Quaternary', \
'Quintary', 'Sextary', 'Septenary'][i],
splitvalencedescr)
print >> txt, msg
rsplit, norm, splitwave = rsplit_by_norm(rgd, l_pol, psi_pol,
tailnorm[i],
txt)
descr = ('%s-type split-valence polarization %d'
% ('spdfg'[l_pol], npol))
bf_pol = BasisFunction(l_pol, rsplit, psi_pol - splitwave,
descr)
polarization_functions.append(bf_pol)
bf_j = []
bf_j.extend(singlezetas)
bf_j.extend(energy_derivative_functions)
for multizeta_list in multizetas:
bf_j.extend(multizeta_list)
bf_j.extend(polarization_functions)
rcmax = max([bf.rc for bf in bf_j])
# The non-equidistant grids are really only suited for AE WFs
d = 1./64.
equidistant_grid = np.arange(0., rcmax + d, d)
ng = len(equidistant_grid)
for bf in bf_j:
# We have been storing phit_g * r, but we just want phit_g
bf.phit_g = divrl(bf.phit_g, 1, rgd.r_g)
gcut = min(int(1 + bf.rc / d), ng - 1)
assert equidistant_grid[gcut] >= bf.rc
assert equidistant_grid[gcut - 1] <= bf.rc
bf.rc = equidistant_grid[gcut]
# Note: bf.rc *must* correspond to a grid point (spline issues)
bf.ng = gcut + 1
# XXX all this should be done while building the basis vectors,
# not here
# Quick hack to change to equidistant coordinates
spline = Spline(bf.l, rgd.r_g[rgd.r2g_floor(bf.rc)],
bf.phit_g,
rgd.r_g, beta=rgd.beta, points=100)
bf.phit_g = np.array([spline(r) * r**bf.l
for r in equidistant_grid[:bf.ng]])
bf.phit_g[-1] = 0.
basis = Basis(g.symbol, self.name, False)
basis.ng = ng
basis.d = d
basis.bf_j = bf_j
basis.generatordata = textbuffer.getvalue().strip()
basis.generatorattrs = {'version' : version}
textbuffer.close()
return basis
def generate(
self,
zetacount=2,
polarizationcount=1,
tailnorm=(0.16, 0.3, 0.6),
energysplit=0.1,
tolerance=1.0e-3,
referencefile=None,
referenceindex=None,
rcutpol_rel=1.0,
rcutmax=20.0,
rcharpol_rel=None,
vconf_args=(12.0, 0.6),
txt='-',
include_energy_derivatives=False,
# lvalues=None, # XXX clean up some of these!
jvalues=None,
l_pol=None):
"""Generate an entire basis set.
This is a high-level method which will return a basis set
consisting of several different basis vector types.
Parameters:
===================== =================================================
``zetacount`` Number of basis functions per occupied orbital
``polarizationcount`` Number of polarization functions
``tailnorm`` List of tail norms for split-valence scheme
``energysplit`` Energy increase defining confinement radius (eV)
``tolerance`` Tolerance of energy split (eV)
``referencefile`` gpw-file used to generate polarization function
``referenceindex`` Index in reference system of relevant atom
``rcutpol_rel`` Polarization rcut relative to largest other rcut
``rcutmax`` No cutoff will be greater than this value
``vconf_args`` Parameters (alpha, ri/rc) for conf. potential
``txt`` Log filename or '-' for stdout
===================== =================================================
Returns a fully initialized Basis object.
"""
if txt == '-':
txt = sys.stdout
elif txt is None:
txt = devnull
if isinstance(tailnorm, float):
tailnorm = (tailnorm, )
if 1 + len(tailnorm) < max(polarizationcount, zetacount):
raise ValueError(
'Needs %d tail norm values, but only %d are specified' %
(max(polarizationcount, zetacount) - 1, len(tailnorm)))
textbuffer = StringIO()
class TeeStream: # quick hack to both write and save output
def __init__(self, out1, out2):
self.out1 = out1
self.out2 = out2
def write(self, string):
self.out1.write(string)
self.out2.write(string)
txt = TeeStream(txt, textbuffer)
if vconf_args is not None:
amplitude, ri_rel = vconf_args
g = self.generator
rgd = self.rgd
njcore = g.njcore
n_j = g.n_j[njcore:]
l_j = g.l_j[njcore:]
f_j = g.f_j[njcore:]
if jvalues is None:
jvalues = []
sortkeys = []
for j in range(len(n_j)):
if f_j[j] == 0 and l_j[j] != 0:
continue
jvalues.append(j)
sortkeys.append(l_j[j])
# Now order jvalues by l
#
# Use a stable sort so the energy ordering within each
# angular momentum is guaranteed to be preserved
args = np.argsort(sortkeys, kind='mergesort')
jvalues = np.array(jvalues)[args]
fulljvalues = [njcore + j for j in jvalues]
if isinstance(energysplit, float):
energysplit = [energysplit] * len(jvalues)
title = '%s Basis functions for %s' % (g.xcname, g.symbol)
print(title, file=txt)
print('=' * len(title), file=txt)
singlezetas = []
energy_derivative_functions = []
multizetas = [[] for i in range(zetacount - 1)]
polarization_functions = []
splitvalencedescr = 'split-valence wave, fixed tail norm'
derivativedescr = 'derivative of sz wrt. (ri/rc) of potential'
for vj, fullj, esplit in zip(jvalues, fulljvalues, energysplit):
l = l_j[vj]
n = n_j[vj]
assert n > 0
orbitaltype = str(n) + 'spdf'[l]
msg = 'Basis functions for l=%d, n=%d' % (l, n)
print(file=txt)
print(msg + '\n', '-' * len(msg), file=txt)
print(file=txt)
if vconf_args is None:
adverb = 'sharply'
else:
adverb = 'softly'
print('Zeta 1: %s confined pseudo wave,' % adverb,
end=' ',
file=txt)
u, e, de, vconf, rc = self.rcut_by_energy(fullj,
esplit,
tolerance,
vconf_args=vconf_args)
if rc > rcutmax:
rc = rcutmax # scale things down
if vconf is not None:
vconf = g.get_confinement_potential(
amplitude, ri_rel * rc, rc)
u, e = g.solve_confined(fullj, rc, vconf)
print('using maximum cutoff', file=txt)
print('rc=%.02f Bohr' % rc, file=txt)
else:
print('fixed energy shift', file=txt)
print('DE=%.03f eV :: rc=%.02f Bohr' % (de * Hartree, rc),
file=txt)
if vconf is not None:
print('Potential amp=%.02f :: ri/rc=%.02f' %
(amplitude, ri_rel),
file=txt)
phit_g = self.smoothify(u, l)
bf = BasisFunction(n, l, rc, phit_g,
'%s-sz confined orbital' % orbitaltype)
norm = np.dot(g.dr, phit_g * phit_g)**.5
print('Norm=%.03f' % norm, file=txt)
singlezetas.append(bf)
zetacounter = iter(range(2, zetacount + 1))
if include_energy_derivatives:
assert zetacount > 1
zeta = next(zetacounter)
print('\nZeta %d: %s' % (zeta, derivativedescr), file=txt)
vconf2 = g.get_confinement_potential(amplitude,
ri_rel * rc * .99, rc)
u2, e2 = g.solve_confined(fullj, rc, vconf2)
phit2_g = self.smoothify(u2, l)
dphit_g = phit2_g - phit_g
dphit_norm = np.dot(rgd.dr_g, dphit_g * dphit_g)**.5
dphit_g /= dphit_norm
descr = '%s-dz E-derivative of sz' % orbitaltype
bf = BasisFunction(None, l, rc, dphit_g, descr)
energy_derivative_functions.append(bf)
for i, zeta in enumerate(zetacounter):
print('\nZeta %d: %s' % (zeta, splitvalencedescr), file=txt)
# Unresolved issue: how does the lack of normalization
# of the first function impact the tail norm scheme?
# Presumably not much, since most interesting stuff happens
# close to the core.
rsplit, norm, splitwave = rsplit_by_norm(
rgd, l, phit_g, tailnorm[i]**2.0, txt)
descr = '%s-%sz split-valence wave' % (orbitaltype,
'0sdtq56789'[zeta])
bf = BasisFunction(None, l, rsplit, phit_g - splitwave, descr)
multizetas[i].append(bf)
if polarizationcount > 0 or l_pol is not None:
if l_pol is None:
# Now make up some properties for the polarization orbital
# We just use the cutoffs from the previous one times a factor
# Find 'missing' values in lvalues
lvalues = [l_j[vj] for vj in jvalues]
for i in range(max(lvalues) + 1):
if list(lvalues).count(i) == 0:
l_pol = i
break
else:
l_pol = max(lvalues) + 1
# Find the last state with l=l_pol - 1, which will be the state we
# base the polarization function on
for vj, fullj, bf in zip(jvalues[::-1], fulljvalues[::-1],
singlezetas[::-1]):
if bf.l == l_pol - 1:
fullj_pol = fullj
rcut = bf.rc * rcutpol_rel
break
else:
raise ValueError('The requested value l_pol=%d requires l=%d '
'among valence states' % (l_pol, l_pol - 1))
rcut = min(rcut, rcutmax)
msg = 'Polarization function: l=%d, rc=%.02f' % (l_pol, rcut)
print('\n' + msg, file=txt)
print('-' * len(msg), file=txt)
# Make a single Gaussian for polarization function.
#
# It is known that for given l, the sz cutoff defined
# by some fixed energy is strongly correlated to the
# value of the characteristic radius which best reproduces
# the wave function found by interpolation.
#
# We know that for e.g. d orbitals:
# rchar ~= .37 rcut[sz](.3eV)
# Since we don't want to spend a lot of time finding
# these value for other energies, we just find the energy
# shift at .3 eV now
u, e, de, vconf, rc_fixed = self.rcut_by_energy(
fullj_pol, .3, 1e-2, 6., (12., .6))
default_rchar_rel = .25
# Defaults for each l. Actually we don't care right now
rchar_rels = {}
if rcharpol_rel is None:
rcharpol_rel = rchar_rels.get(l_pol, default_rchar_rel)
rchar = rcharpol_rel * rc_fixed
gaussian = QuasiGaussian(1.0 / rchar**2, rcut)
psi_pol = gaussian(rgd.r_g) * rgd.r_g**(l_pol + 1)
norm = np.dot(rgd.dr_g, psi_pol * psi_pol)**.5
psi_pol /= norm
print('Single quasi Gaussian', file=txt)
msg = 'Rchar = %.03f*rcut = %.03f Bohr' % (rcharpol_rel, rchar)
adjective = 'Gaussian'
print(msg, file=txt)
type = '%s-type %s polarization' % ('spdfg'[l_pol], adjective)
bf_pol = BasisFunction(None, l_pol, rcut, psi_pol, type)
polarization_functions.append(bf_pol)
for i in range(polarizationcount - 1):
npol = i + 2
msg = '\n%s: %s' % ([
'Secondary', 'Tertiary', 'Quaternary', 'Quintary',
'Sextary', 'Septenary'
][i], splitvalencedescr)
print(msg, file=txt)
rsplit, norm, splitwave = rsplit_by_norm(
rgd, l_pol, psi_pol, tailnorm[i], txt)
descr = ('%s-type split-valence polarization %d' %
('spdfg'[l_pol], npol))
bf_pol = BasisFunction(None, l_pol, rsplit,
psi_pol - splitwave, descr)
polarization_functions.append(bf_pol)
bf_j = []
bf_j.extend(singlezetas)
bf_j.extend(energy_derivative_functions)
for multizeta_list in multizetas:
bf_j.extend(multizeta_list)
bf_j.extend(polarization_functions)
rcmax = max([bf.rc for bf in bf_j])
# The non-equidistant grids are really only suited for AE WFs
d = 1.0 / 64
equidistant_grid = np.arange(0.0, rcmax + d, d)
ng = len(equidistant_grid)
for bf in bf_j:
# We have been storing phit_g * r, but we just want phit_g
bf.phit_g = divrl(bf.phit_g, 1, rgd.r_g)
gcut = min(int(1 + bf.rc / d), ng - 1)
assert equidistant_grid[gcut] >= bf.rc
assert equidistant_grid[gcut - 1] <= bf.rc
bf.rc = equidistant_grid[gcut]
# Note: bf.rc *must* correspond to a grid point (spline issues)
bf.ng = gcut + 1
# XXX all this should be done while building the basis vectors,
# not here
# Quick hack to change to equidistant coordinates
spline = rgd.spline(bf.phit_g,
rgd.r_g[rgd.floor(bf.rc)],
bf.l,
points=100)
bf.phit_g = np.array(
[spline(r) * r**bf.l for r in equidistant_grid[:bf.ng]])
bf.phit_g[-1] = 0.
basistype = get_basis_name(zetacount, polarizationcount)
if self.name is None:
compound_name = basistype
else:
compound_name = '%s.%s' % (self.name, basistype)
basis = Basis(g.symbol, compound_name, False,
EquidistantRadialGridDescriptor(d, ng))
basis.bf_j = bf_j
basis.generatordata = textbuffer.getvalue().strip()
basis.generatorattrs = {'version': version}
textbuffer.close()
return basis
def generate(self, zetacount=2, polarizationcount=1,
tailnorm=(0.16, 0.3, 0.6), energysplit=0.1, tolerance=1.0e-3,
referencefile=None, referenceindex=None, rcutpol_rel=1.0,
rcutmax=20.0, #ngaussians=None,
rcharpol_rel=None,
vconf_args=(12.0, 0.6), txt='-',
include_energy_derivatives=False,
#lvalues=None, # XXX clean up some of these!
jvalues=None,
l_pol=None
):
"""Generate an entire basis set.
This is a high-level method which will return a basis set
consisting of several different basis vector types.
Parameters:
===================== =================================================
``zetacount`` Number of basis functions per occupied orbital
``polarizationcount`` Number of polarization functions
``tailnorm`` List of tail norms for split-valence scheme
``energysplit`` Energy increase defining confinement radius (eV)
``tolerance`` Tolerance of energy split (eV)
``referencefile`` gpw-file used to generate polarization function
``referenceindex`` Index in reference system of relevant atom
``rcutpol_rel`` Polarization rcut relative to largest other rcut
``rcutmax`` No cutoff will be greater than this value
``vconf_args`` Parameters (alpha, ri/rc) for conf. potential
``txt`` Log filename or '-' for stdout
===================== =================================================
Returns a fully initialized Basis object.
"""
if txt == '-':
txt = sys.stdout
elif txt is None:
txt = devnull
if isinstance(tailnorm, float):
tailnorm = (tailnorm,)
assert 1 + len(tailnorm) >= max(polarizationcount, zetacount), \
'Needs %d tail norm values, but only %d are specified' % \
(max(polarizationcount, zetacount) - 1, len(tailnorm))
textbuffer = StringIO()
class TeeStream: # Quick hack to both write and save output
def __init__(self, out1, out2):
self.out1 = out1
self.out2 = out2
def write(self, string):
self.out1.write(string)
self.out2.write(string)
txt = TeeStream(txt, textbuffer)
if vconf_args is not None:
amplitude, ri_rel = vconf_args
g = self.generator
rgd = self.rgd
njcore = g.njcore
n_j = g.n_j[njcore:]
l_j = g.l_j[njcore:]
f_j = g.f_j[njcore:]
if jvalues is None:
jvalues = []
sortkeys = []
for j in range(len(n_j)):
if f_j[j] == 0 and l_j[j] != 0:
continue
jvalues.append(j)
sortkeys.append(l_j[j])
# Now order jvalues by l
#
# Use a stable sort so the energy ordering within each
# angular momentum is guaranteed to be preserved
args = np.argsort(sortkeys, kind='mergesort')
jvalues = np.array(jvalues)[args]
fulljvalues = [njcore + j for j in jvalues]
if isinstance(energysplit, float):
energysplit = [energysplit] * len(jvalues)
title = '%s Basis functions for %s' % (g.xcname, g.symbol)
print >> txt, title
print >> txt, '=' * len(title)
singlezetas = []
energy_derivative_functions = []
multizetas = [[] for i in range(zetacount - 1)]
polarization_functions = []
splitvalencedescr = 'split-valence wave, fixed tail norm'
derivativedescr = 'derivative of sz wrt. (ri/rc) of potential'
for vj, fullj, esplit in zip(jvalues, fulljvalues, energysplit):
l = l_j[vj]
n = n_j[vj]
assert n > 0
orbitaltype = str(n) + 'spdf'[l]
msg = 'Basis functions for l=%d, n=%d' % (l, n)
print >> txt
print >> txt, msg + '\n', '-' * len(msg)
print >> txt
if vconf_args is None:
adverb = 'sharply'
else:
adverb = 'softly'
print >> txt, 'Zeta 1: %s confined pseudo wave,' % adverb,
u, e, de, vconf, rc = self.rcut_by_energy(fullj, esplit,
tolerance,
vconf_args=vconf_args)
if rc > rcutmax:
rc = rcutmax # scale things down
if vconf is not None:
vconf = g.get_confinement_potential(amplitude, ri_rel * rc,
rc)
u, e = g.solve_confined(fullj, rc, vconf)
print >> txt, 'using maximum cutoff'
print >> txt, 'rc=%.02f Bohr' % rc
else:
print >> txt, 'fixed energy shift'
print >> txt, 'DE=%.03f eV :: rc=%.02f Bohr' % (de * Hartree,
rc)
if vconf is not None:
print >> txt, ('Potential amp=%.02f :: ri/rc=%.02f' %
(amplitude, ri_rel))
phit_g = self.smoothify(u, l)
bf = BasisFunction(l, rc, phit_g,
'%s-sz confined orbital' % orbitaltype)
norm = np.dot(g.dr, phit_g * phit_g)**.5
print >> txt, 'Norm=%.03f' % norm
singlezetas.append(bf)
zetacounter = iter(xrange(2, zetacount + 1))
if include_energy_derivatives:
assert zetacount > 1
zeta = zetacounter.next()
print >> txt, '\nZeta %d: %s' % (zeta, derivativedescr)
vconf2 = g.get_confinement_potential(amplitude,
ri_rel * rc * .99, rc)
u2, e2 = g.solve_confined(fullj, rc, vconf2)
phit2_g = self.smoothify(u2, l)
dphit_g = phit2_g - phit_g
dphit_norm = np.dot(rgd.dr_g, dphit_g * dphit_g) ** .5
dphit_g /= dphit_norm
descr = '%s-dz E-derivative of sz' % orbitaltype
bf = BasisFunction(l, rc, dphit_g, descr)
energy_derivative_functions.append(bf)
for i, zeta in enumerate(zetacounter): # range(zetacount - 1):
print >> txt, '\nZeta %d: %s' % (zeta, splitvalencedescr)
# Unresolved issue: how does the lack of normalization
# of the first function impact the tail norm scheme?
# Presumably not much, since most interesting stuff happens
# close to the core.
rsplit, norm, splitwave = rsplit_by_norm(rgd, l, phit_g,
tailnorm[i]**2.0,
txt)
descr = '%s-%sz split-valence wave' % (orbitaltype,
'0sdtq56789'[zeta])
bf = BasisFunction(l, rsplit, phit_g - splitwave, descr)
multizetas[i].append(bf)
if polarizationcount > 0 or l_pol is not None:
if l_pol is None:
# Now make up some properties for the polarization orbital
# We just use the cutoffs from the previous one times a factor
# Find 'missing' values in lvalues
lvalues = [l_j[vj] for vj in jvalues]
for i in range(max(lvalues) + 1):
if list(lvalues).count(i) == 0:
l_pol = i
break
else:
l_pol = max(lvalues) + 1
# Find the last state with l=l_pol - 1, which will be the state we
# base the polarization function on
for vj, fullj, bf in zip(jvalues[::-1], fulljvalues[::-1],
singlezetas[::-1]):
if bf.l == l_pol - 1:
vj_pol = vj # index of the state *which* we polarize
fullj_pol = fullj
rcut = bf.rc * rcutpol_rel
break
else:
raise ValueError('The requested value l_pol=%d requires l=%d '
'among valence states' % (l_pol, l_pol - 1))
rcut = min(rcut, rcutmax)
msg = 'Polarization function: l=%d, rc=%.02f' % (l_pol, rcut)
print >> txt, '\n' + msg
print >> txt, '-' * len(msg)
# Make a single Gaussian for polarization function.
#
# It is known that for given l, the sz cutoff defined
# by some fixed energy is strongly correlated to the
# value of the characteristic radius which best reproduces
# the wave function found by interpolation.
#
# We know that for e.g. d orbitals:
# rchar ~= .37 rcut[sz](.3eV)
# Since we don't want to spend a lot of time finding
# these value for other energies, we just find the energy
# shift at .3 eV now
u, e, de, vconf, rc_fixed = self.rcut_by_energy(fullj_pol,
.3, 1e-2,
6., (12., .6))
default_rchar_rel = .25
# Defaults for each l. Actually we don't care right now
rchar_rels = {}
if rcharpol_rel is None:
rcharpol_rel = rchar_rels.get(l_pol, default_rchar_rel)
rchar = rcharpol_rel * rc_fixed
gaussian = QuasiGaussian(1./rchar**2, rcut)
psi_pol = gaussian(rgd.r_g) * rgd.r_g**(l_pol + 1)
norm = np.dot(rgd.dr_g, psi_pol * psi_pol) ** .5
psi_pol /= norm
print >> txt, 'Single quasi Gaussian'
msg = 'Rchar = %.03f*rcut = %.03f Bohr' % (rcharpol_rel, rchar)
adjective = 'Gaussian'
print >> txt, msg
type = '%s-type %s polarization' % ('spdfg'[l_pol], adjective)
bf_pol = BasisFunction(l_pol, rcut, psi_pol, type)
polarization_functions.append(bf_pol)
for i in range(polarizationcount - 1):
npol = i + 2
msg = '\n%s: %s' % (['Secondary', 'Tertiary', 'Quaternary', \
'Quintary', 'Sextary', 'Septenary'][i],
splitvalencedescr)
print >> txt, msg
rsplit, norm, splitwave = rsplit_by_norm(rgd, l_pol, psi_pol,
tailnorm[i],
txt)
descr = ('%s-type split-valence polarization %d'
% ('spdfg'[l_pol], npol))
bf_pol = BasisFunction(l_pol, rsplit, psi_pol - splitwave,
descr)
polarization_functions.append(bf_pol)
bf_j = []
bf_j.extend(singlezetas)
bf_j.extend(energy_derivative_functions)
for multizeta_list in multizetas:
bf_j.extend(multizeta_list)
bf_j.extend(polarization_functions)
rcmax = max([bf.rc for bf in bf_j])
# The non-equidistant grids are really only suited for AE WFs
d = 1./64.
equidistant_grid = np.arange(0., rcmax + d, d)
ng = len(equidistant_grid)
for bf in bf_j:
# We have been storing phit_g * r, but we just want phit_g
bf.phit_g = divrl(bf.phit_g, 1, rgd.r_g)
gcut = min(int(1 + bf.rc / d), ng - 1)
assert equidistant_grid[gcut] >= bf.rc
assert equidistant_grid[gcut - 1] <= bf.rc
bf.rc = equidistant_grid[gcut]
# Note: bf.rc *must* correspond to a grid point (spline issues)
bf.ng = gcut + 1
# XXX all this should be done while building the basis vectors,
# not here
# Quick hack to change to equidistant coordinates
spline = rgd.spline(bf.phit_g, rgd.r_g[rgd.floor(bf.rc)], bf.l,
points=100)
bf.phit_g = np.array([spline(r) * r**bf.l
for r in equidistant_grid[:bf.ng]])
bf.phit_g[-1] = 0.
basis = Basis(g.symbol, self.name, False)
basis.ng = ng
basis.d = d
basis.bf_j = bf_j
basis.generatordata = textbuffer.getvalue().strip()
basis.generatorattrs = {'version': version}
textbuffer.close()
return basis
def generate(
self,
zetacount=2,
polarizationcount=1,
tailnorm=(0.16, 0.3, 0.6),
energysplit=0.1,
tolerance=1.0e-3,
referencefile=None,
referenceindex=None,
rcutpol_rel=1.0,
rcutmax=20.0, #ngaussians=None,
rcharpol_rel=None,
vconf_args=(12.0, 0.6),
txt='-',
include_energy_derivatives=False,
lvalues=None):
"""Generate an entire basis set.
This is a high-level method which will return a basis set
consisting of several different basis vector types.
Parameters:
===================== =================================================
``zetacount`` Number of basis functions per occupied orbital
``polarizationcount`` Number of polarization functions
``tailnorm`` List of tail norms for split-valence scheme
``energysplit`` Energy increase defining confinement radius (eV)
``tolerance`` Tolerance of energy split (eV)
``referencefile`` gpw-file used to generate polarization function
``referenceindex`` Index in reference system of relevant atom
``rcutpol_rel`` Polarization rcut relative to largest other rcut
``rcutmax`` No cutoff will be greater than this value
``vconf_args`` Parameters (alpha, ri/rc) for conf. potential
``txt`` Log filename or '-' for stdout
===================== =================================================
Returns a fully initialized Basis object.
"""
if txt == '-':
txt = sys.stdout
elif txt is None:
txt = devnull
if isinstance(tailnorm, float):
tailnorm = (tailnorm, )
assert 1 + len(tailnorm) >= max(polarizationcount, zetacount), \
'Needs %d tail norm values, but only %d are specified' % \
(max(polarizationcount, zetacount) - 1, len(tailnorm))
textbuffer = StringIO()
class TeeStream: # Quick hack to both write and save output
def __init__(self, out1, out2):
self.out1 = out1
self.out2 = out2
def write(self, string):
self.out1.write(string)
self.out2.write(string)
txt = TeeStream(txt, textbuffer)
if vconf_args is not None:
amplitude, ri_rel = vconf_args
g = self.generator
rgd = self.rgd
# Find out all relevant orbitals
# We'll probably need: s, p and d.
# The orbitals we want are stored in u_j.
# Thus we must find the j corresponding to the highest energy of
# each orbital-type.
#
# However not all orbitals in l_j are actually occupied, so we
# will check the occupations in the generator object's lists
#
# ASSUMPTION: The last index of a given value in l_j corresponds
# exactly to the orbital we want, except those which are not occupied
#
# Get (only) one occupied valence state for each l
# Not including polarization in this list
if lvalues is None:
lvalues = np.unique([
l for l, f in zip(g.l_j[g.njcore:], g.f_j[g.njcore:]) if f > 0
])
if lvalues[0] != 0: # Always include s-orbital !
lvalues = np.array([0] + list(lvalues))
#print energysplit
if isinstance(energysplit, float):
energysplit = [energysplit] * (max(lvalues) + 1)
#print energysplit,'~~~~~~~~'
title = '%s Basis functions for %s' % (g.xcname, g.symbol)
print >> txt, title
print >> txt, '=' * len(title)
j_l = {} # index j by l rather than the other way around
reversed_l_j = list(g.l_j)
reversed_l_j.reverse() # the values we want are stored last
for l in lvalues:
j = len(reversed_l_j) - reversed_l_j.index(l) - 1
j_l[l] = j
singlezetas = []
energy_derivative_functions = []
multizetas = [[] for i in range(zetacount - 1)]
polarization_functions = []
splitvalencedescr = 'split-valence wave, fixed tail norm'
derivativedescr = 'derivative of sz wrt. (ri/rc) of potential'
for l in lvalues:
# Get one unmodified pseudo-orbital basis vector for each l
j = j_l[l]
n = g.n_j[j]
orbitaltype = str(n) + 'spdf'[l]
msg = 'Basis functions for l=%d, n=%d' % (l, n)
print >> txt
print >> txt, msg + '\n', '-' * len(msg)
print >> txt
if vconf_args is None:
adverb = 'sharply'
else:
adverb = 'softly'
print >> txt, 'Zeta 1: %s confined pseudo wave,' % adverb,
u, e, de, vconf, rc = self.rcut_by_energy(j,
energysplit[l],
tolerance,
vconf_args=vconf_args)
if rc > rcutmax:
rc = rcutmax # scale things down
if vconf is not None:
vconf = g.get_confinement_potential(
amplitude, ri_rel * rc, rc)
u, e = g.solve_confined(j, rc, vconf)
print >> txt, 'using maximum cutoff'
print >> txt, 'rc=%.02f Bohr' % rc
else:
print >> txt, 'fixed energy shift'
print >> txt, 'DE=%.03f eV :: rc=%.02f Bohr' % (de * Hartree,
rc)
if vconf is not None:
print >> txt, ('Potential amp=%.02f :: ri/rc=%.02f' %
(amplitude, ri_rel))
phit_g = self.smoothify(u, l)
bf = BasisFunction(l, rc, phit_g,
'%s-sz confined orbital' % orbitaltype)
norm = np.dot(g.dr, phit_g * phit_g)**.5
print >> txt, 'Norm=%.03f' % norm
singlezetas.append(bf)
zetacounter = iter(xrange(2, zetacount + 1))
if include_energy_derivatives:
assert zetacount > 1
zeta = zetacounter.next()
print >> txt, '\nZeta %d: %s' % (zeta, derivativedescr)
vconf2 = g.get_confinement_potential(amplitude,
ri_rel * rc * .99, rc)
u2, e2 = g.solve_confined(j, rc, vconf2)
phit2_g = self.smoothify(u2, l)
dphit_g = phit2_g - phit_g
dphit_norm = np.dot(rgd.dr_g, dphit_g * dphit_g)**.5
dphit_g /= dphit_norm
descr = '%s-dz E-derivative of sz' % orbitaltype
bf = BasisFunction(l, rc, dphit_g, descr)
energy_derivative_functions.append(bf)
for i, zeta in enumerate(zetacounter): # range(zetacount - 1):
print >> txt, '\nZeta %d: %s' % (zeta, splitvalencedescr)
# Unresolved issue: how does the lack of normalization
# of the first function impact the tail norm scheme?
# Presumably not much, since most interesting stuff happens
# close to the core.
rsplit, norm, splitwave = rsplit_by_norm(
rgd, l, phit_g, tailnorm[i]**2.0, txt)
descr = '%s-%sz split-valence wave' % (orbitaltype,
'0sdtq56789'[zeta])
bf = BasisFunction(l, rsplit, phit_g - splitwave, descr)
multizetas[i].append(bf)
if polarizationcount > 0:
# Now make up some properties for the polarization orbital
# We just use the cutoffs from the previous one times a factor
rcut = max([bf.rc for bf in singlezetas]) * rcutpol_rel
rcut = min(rcut, rcutmax)
# Find 'missing' values in lvalues
for i, l in enumerate(lvalues):
if i != l:
l_pol = i
break
else:
l_pol = lvalues[-1] + 1
msg = 'Polarization function: l=%d, rc=%.02f' % (l_pol, rcut)
print >> txt, '\n' + msg
print >> txt, '-' * len(msg)
# Make a single Gaussian for polarization function.
#
# It is known that for given l, the sz cutoff defined
# by some fixed energy is strongly correlated to the
# value of the characteristic radius which best reproduces
# the wave function found by interpolation.
#
# We know that for e.g. d orbitals:
# rchar ~= .37 rcut[sz](.3eV)
# Since we don't want to spend a lot of time finding
# these value for other energies, we just find the energy
# shift at .3 eV now
j = max(j_l.values())
u, e, de, vconf, rc_fixed = self.rcut_by_energy(
j, .3, 1e-2, 6., (12., .6))
default_rchar_rel = .25
# Defaults for each l. Actually we don't care right now
rchar_rels = {}
if rcharpol_rel is None:
rcharpol_rel = rchar_rels.get(l_pol, default_rchar_rel)
rchar = rcharpol_rel * rc_fixed
gaussian = QuasiGaussian(1. / rchar**2, rcut)
psi_pol = gaussian(rgd.r_g) * rgd.r_g**(l_pol + 1)
norm = np.dot(rgd.dr_g, psi_pol * psi_pol)**.5
psi_pol /= norm
print >> txt, 'Single quasi Gaussian'
msg = 'Rchar = %.03f*rcut = %.03f Bohr' % (rcharpol_rel, rchar)
adjective = 'Gaussian'
print >> txt, msg
#else:
# psi_pol = self.make_polarization_function(rcut, l_pol,
# referencefile,
# referenceindex,
# ngaussians, txt)
# adjective = 'interpolated'
type = '%s-type %s polarization' % ('spdfg'[l_pol], adjective)
bf_pol = BasisFunction(l_pol, rcut, psi_pol, type)
polarization_functions.append(bf_pol)
for i in range(polarizationcount - 1):
npol = i + 2
msg = '\n%s: %s' % (['Secondary', 'Tertiary', 'Quaternary', \
'Quintary', 'Sextary', 'Septenary'][i],
splitvalencedescr)
print >> txt, msg
rsplit, norm, splitwave = rsplit_by_norm(
rgd, l_pol, psi_pol, tailnorm[i], txt)
descr = ('%s-type split-valence polarization %d' %
('spdfg'[l_pol], npol))
bf_pol = BasisFunction(l_pol, rsplit, psi_pol - splitwave,
descr)
polarization_functions.append(bf_pol)
bf_j = []
bf_j.extend(singlezetas)
bf_j.extend(energy_derivative_functions)
for multizeta_list in multizetas:
bf_j.extend(multizeta_list)
bf_j.extend(polarization_functions)
rcmax = max([bf.rc for bf in bf_j])
# The non-equidistant grids are really only suited for AE WFs
d = 1. / 64.
equidistant_grid = np.arange(0., rcmax + d, d)
ng = len(equidistant_grid)
for bf in bf_j:
# We have been storing phit_g * r, but we just want phit_g
bf.phit_g = divrl(bf.phit_g, 1, rgd.r_g)
gcut = min(int(1 + bf.rc / d), ng - 1)
assert equidistant_grid[gcut] >= bf.rc
assert equidistant_grid[gcut - 1] <= bf.rc
bf.rc = equidistant_grid[gcut]
# Note: bf.rc *must* correspond to a grid point (spline issues)
bf.ng = gcut + 1
# XXX all this should be done while building the basis vectors,
# not here
# Quick hack to change to equidistant coordinates
spline = Spline(bf.l,
rgd.r_g[rgd.r2g_floor(bf.rc)],
bf.phit_g,
rgd.r_g,
beta=rgd.beta,
points=100)
bf.phit_g = np.array(
[spline(r) * r**bf.l for r in equidistant_grid[:bf.ng]])
bf.phit_g[-1] = 0.
basis = Basis(g.symbol, self.name, False)
basis.ng = ng
basis.d = d
basis.bf_j = bf_j
basis.generatordata = textbuffer.getvalue().strip()
basis.generatorattrs = {'version': version}
textbuffer.close()
return basis