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 __init__(self, symbol, l_j):
rgd = EquidistantRadialGridDescriptor(0.02, 160)
Basis.__init__(self, symbol, 'simple', readxml=False, rgd=rgd)
self.generatordata = 'simple'
bf_j = self.bf_j
rcgauss = rgd.r_g[-1] / 3.0
gauss_g = np.exp(-(rgd.r_g / rcgauss)**2.0)
for l in l_j:
phit_g = rgd.r_g**l * gauss_g
norm = (rgd.integrate(phit_g**2) / (4 * np.pi))**0.5
phit_g /= norm
bf = BasisFunction(None, l, rgd.r_g[-1], phit_g, 'gaussian')
bf_j.append(bf)
def __init__(self, symbol, l_j):
Basis.__init__(self, symbol, 'simple', readxml=False)
self.generatordata = 'simple'
self.d = 0.02
self.ng = 160
rgd = self.get_grid_descriptor()
bf_j = self.bf_j
rcgauss = rgd.r_g[-1] / 3.0
gauss_g = np.exp(-(rgd.r_g / rcgauss)**2.0)
for l in l_j:
phit_g = rgd.r_g**l * gauss_g
norm = (rgd.integrate(phit_g**2) / (4 * np.pi))**0.5
phit_g /= norm
bf = BasisFunction(l, rgd.r_g[-1], phit_g, 'gaussian')
bf_j.append(bf)
def __init__(self, symbol, l_j):
Basis.__init__(self, symbol, 'simple', readxml=False)
self.generatordata = 'simple'
self.d = 0.02
self.ng = 160
rgd = self.get_grid_descriptor()
bf_j = self.bf_j
rcgauss = rgd.rcut / 3.0
gauss_g = np.exp(-(rgd.r_g / rcgauss)**2.0)
for l in l_j:
phit_g = rgd.r_g**l * gauss_g
norm = np.dot((rgd.r_g * phit_g)**2, rgd.dr_g)**.5
phit_g /= norm
bf = BasisFunction(l, rgd.rcut, phit_g, 'gaussian')
bf_j.append(bf)
def add_ngto(basis, l, alpha, tol, label):
rgd = basis.get_grid_descriptor()
rmax = rgd.r_g[-1]
# Get NGTO with the initial (large) rcut=rmax
psiref_g = get_ngto(rgd, l, alpha, rmax)
# Make rcut smaller
# Guess initial rcut where we are close to the tolerance
i = np.where(psiref_g > tol)[0][-1]
rcut = rgd.r_g[i]
psi_g = get_ngto(rgd, l, alpha, rcut)
err = np.max(np.absolute(psi_g - psiref_g))
# Increase/decrease rcut to find the smallest rcut
# that yields error within the tolerance
if err > tol:
# Increase rcut -> decrease err
for i in range(i, basis.ng):
rcut = rgd.r_g[i]
psi_g = get_ngto(rgd, l, alpha, rcut)
err = np.max(np.absolute(psi_g - psiref_g))
if err < tol:
break
else:
# Decrease rcut -> increase err
for i in range(i, 0, -1):
rcut = rgd.r_g[i]
psi_g = get_ngto(rgd, l, alpha, rcut)
err = np.max(np.absolute(psi_g - psiref_g))
if err > tol:
i += 1
break
# Construct NGTO with the found rcut
rcut = rgd.r_g[i]
psi_g = get_ngto(rgd, l, alpha, rcut)
# Change norm (maybe unnecessary)
psi_g = psi_g[:(i + 1)] * 0.5
# Create associated basis function
bf = BasisFunction(None, l, rcut, psi_g, label)
basis.bf_j.append(bf)
def get_stored_basis_functions(self, ):
b = Basis(self.symbol, 'upf', readxml=False)
b.generatordata = 'upf-pregenerated'
states = self.data['states']
maxlen = max([len(state.values) for state in states])
orig_r = self.data['r']
rcut = min(orig_r[maxlen - 1], 12.0) # XXX hardcoded 12 max radius
b.d = 0.02
b.ng = int(1 + rcut / b.d)
rgd = b.get_grid_descriptor()
for j, state in enumerate(states):
val = state.values
phit_g = np.interp(rgd.r_g, orig_r, val)
phit_g = divrl(phit_g, 1, rgd.r_g)
icut = len(phit_g) - 1 # XXX correct or off-by-one?
rcut = rgd.r_g[icut]
bf = BasisFunction(state.l, rcut, phit_g, 'pregenerated')
b.bf_j.append(bf)
return b
def create_basis_set(self, tailnorm=0.0005, scale=200.0, splitnorm=0.16):
rgd = self.rgd
self.basis = Basis(self.aea.symbol, 'dzp', readxml=False, rgd=rgd)
# We print text to sdtout and put it in the basis-set file
txt = 'Basis functions:\n'
# Bound states:
for l, waves in enumerate(self.waves_l):
for i, n in enumerate(waves.n_n):
if n > 0:
tn = tailnorm
if waves.f_n[i] == 0:
tn = min(0.05, tn * 20) # no need for long tail
phit_g, ronset, rc, de = self.create_basis_function(
l, i, tn, scale)
bf = BasisFunction(n, l, rc, phit_g, 'bound state')
self.basis.append(bf)
txt += '%d%s bound state:\n' % (n, 'spdf'[l])
txt += (' cutoff: %.3f to %.3f Bohr (tail-norm=%f)\n' %
(ronset, rc, tn))
txt += ' eigenvalue shift: %.3f eV\n' % (de * Hartree)
# Split valence:
for l, waves in enumerate(self.waves_l):
# Find the largest n that is occupied:
n0 = None
for f, n in zip(waves.f_n, waves.n_n):
if n > 0 and f > 0:
n0 = n
if n0 is None:
continue
for bf in self.basis.bf_j:
if bf.l == l and bf.n == n0:
break
# Radius and l-value used for polarization function below:
rcpol = bf.rc
lpol = l + 1
phit_g = bf.phit_g
# Find cutoff radius:
n_g = np.add.accumulate(phit_g**2 * rgd.r_g**2 * rgd.dr_g)
norm = n_g[-1]
gc = (norm - n_g > splitnorm * norm).sum()
rc = rgd.r_g[gc]
phit2_g = rgd.pseudize(phit_g, gc, l, 2)[0] # "split valence"
bf = BasisFunction(n, l, rc, phit_g - phit2_g, 'split valence')
self.basis.append(bf)
txt += '%d%s split valence:\n' % (n0, 'spdf'[l])
txt += ' cutoff: %.3f Bohr (tail-norm=%f)\n' % (rc, splitnorm)
# Polarization:
gcpol = rgd.round(rcpol)
alpha = 1 / (0.25 * rcpol)**2
# Gaussian that is continuous and has a continuous derivative at rcpol:
phit_g = np.exp(-alpha * rgd.r_g**2) * rgd.r_g**lpol
phit_g -= rgd.pseudize(phit_g, gcpol, lpol, 2)[0]
phit_g[gcpol:] = 0.0
bf = BasisFunction(None, lpol, rcpol, phit_g, 'polarization')
self.basis.append(bf)
txt += 'l=%d polarization functions:\n' % lpol
txt += ' cutoff: %.3f Bohr (r^%d exp(-%.3f*r^2))\n' % (rcpol, lpol,
alpha)
self.log(txt)
# Write basis-set file:
self.basis.generatordata = txt
self.basis.generatorattrs.update(
dict(tailnorm=tailnorm, scale=scale, splitnorm=splitnorm))
self.basis.name = '%de.dzp' % self.nvalence
return self.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 get_orbitals_by_energy_shift(opts, setup, **kwargs):
h = opts.grid
try:
f_ln = setup.f_ln
except AttributeError:
f_ln = []
for n, l, f in zip(setup.n_j, setup.l_j, setup.f_j):
if n < 0:
continue
if l == len(f_ln):
f_ln.append([])
if f > 0 and n > 0:
f_ln[l].append(f)
def calculate(rcut, h=h, txt='-'):
return atompaw(setup, f_ln, rcut, h=h, txt=txt, **kwargs)
def get_orbital_energy(l0, n0, rcut):
calc = calculate(rcut, 0.15, txt=None)
for l, n, f, eps, psit_G in calc.state_iter():
if l == l0 and n + 1 == n0: # XXX
return eps
raise ValueError('No such valence state: l=%d, n=%d' % (l0, n0))
calc0 = calculate(2.0, 0.2, txt=None) # XXX
def valence_states():
for l, n, f, eps, psit_G in calc0.state_iter():
yield l, n + 1 # XXX
bf_j = []
for i, (l, n) in enumerate(valence_states()):
e0 = get_orbital_energy(l, n, 15.0) * 27.211 # 15Ang == infinity
print('e0', e0)
def obj(rcut):
eps = get_orbital_energy(l, n, rcut) * 27.211
de = eps - opts.energy_shift - e0
# print rcut, eps, de
return de
# Not exactly efficient...
rcut = bisect(obj, 1.0, 15.0, xtol=0.1)
calc = calculate(h=h, rcut=rcut, txt=None)
bfs = calc.extract_basis_functions()
bf_j.append(bfs.bf_j[i])
d = bfs.d
ng = max([bf.ng for bf in bf_j])
rgd = EquidistantRadialGridDescriptor(d, ng)
basis = Basis(setup.symbol, 'strange', readxml=False, rgd=rgd)
basis.bf_j = bf_j
return basis
# for (l, n), cutoff in zip(valence_states(), cutoffs):
# calculate(
# return
# calc = calculate(rcut)
bfs = calc.extract_basis_functions(basis_name=opts.name)
ldict = dict([(bf.l, bf) for bf in bfs.bf_j])
rgd = bfs.get_grid_descriptor()
def get_rsplit(bf, splitnorm):
if opts.s_approaches_zero and bf.l == 0:
l = 1 # create a function phi(r) = A * r + O(r^2)
else:
l = bf.l
return rsplit_by_norm(rgd, l, bf.phit_g * rgd.r_g, splitnorm**2,
sys.stdout)
splitvalence_bfs = []
for splitnorm in opts.splitnorm:
splitnorm = float(splitnorm)
for orbital_bf in bfs.bf_j:
rsplit, normsqr, phit_g = get_rsplit(orbital_bf, splitnorm)
phit_g[1:] /= rgd.r_g[1:]
gcut = rgd.ceil(rsplit)
#tailnorm = np.dot(rgd.dr_g[gcut:],
# (rgd.r_g[gcut:] * orbital_bf.phit_g[gcut:])**2)**0.5
#print 'tailnorm', tailnorm
dphit_g = orbital_bf.phit_g[:gcut + 1] - phit_g[:gcut + 1]
bf = BasisFunction(l=orbital_bf.l,
rc=rgd.r_g[gcut],
phit_g=dphit_g,
type='%s split-valence' % 'spd'[orbital_bf.l])
splitvalence_bfs.append(bf)
bfs.bf_j.extend(splitvalence_bfs)
#rpol = None
for l in range(3):
if l not in ldict:
lpol = l
source_bf = ldict[lpol - 1]
break
else:
raise NotImplementedError('f-type polarization not implemented')
for splitnorm in opts.polarization:
splitnorm = float(splitnorm)
rchar, normsqr, phit_g = get_rsplit(source_bf, splitnorm)
gcut = rgd.ceil(3.5 * rchar)
rcut = rgd.r_g[gcut]
phit_g = get_gaussianlike_basis_function(rgd, lpol, rchar, gcut)
N = len(phit_g)
x = np.dot(rgd.dr_g[:N], (phit_g * rgd.r_g[:N])**2)**0.5
print('x', x)
bf = BasisFunction(None,
lpol,
rc=rcut,
phit_g=phit_g,
type='%s polarization' % 'spd'[lpol])
bf.phit_g
bfs.bf_j.append(bf)
bfs.write_xml()
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
