def rpa_dt(axes, rs, nx=32):
""" calculate kinetic finite size error assuming RPA U(k) and S(k)
Args:
raxes (np.array): reciprocal space lattice
rs (float): Wigner-Seitz radius i.e. density parameter
Return:
float: kinetic finite size correction
"""
from qharv.inspect import axes_pos
density = (4 * np.pi / 3 * rs**3.)**(-1)
# get RPA U(k) and S(k)
kf = heg_kfermi(rs)
fuk = lambda k: gaskell_rpa_uk(k, rs, kf)
fsk = effective_fsk_from_fuk(fuk, rs)
# setup integration grid
raxes = axes_pos.raxes(axes)
qgrid = mp_grid(raxes, nx)
# perform quadrature
# weights
rvol = axes_pos.volume(raxes)
intnorm = 1. / (2 * np.pi)**3 * rvol / nx**3 * density
# sum
qmags = np.linalg.norm(qgrid, axis=1)
integrand = lambda k: 0.5 * k**2 * fuk(k)**2 * fsk(k)
dtlr = intnorm * integrand(qmags).sum()
return dtlr
def heg_jas(rs, axes, nr, nsh0=5, kc=None, zoom=1e10):
# note zoom of 1e10 keeps 10 digits when grouping kshells
# probably too high of a resolution, but this is QMCPACK default
kf = heg_kfermi(rs) # assume unpolarized
if kc is None:
kc = kf
from qharv.inspect import axes_pos
rcut = axes_pos.rwsc(axes)
# step 1: build short-range Jastrow
uuc, udc = get_rpa_coeff(rs, rcut, nr)
j2sr = fusr(rcut, uuc, udc)
# step 2: find unique kmags
raxes = axes_pos.raxes(axes)
kvecs = get_kshells(nsh0, raxes)
kmags = np.linalg.norm(kvecs, axis=-1)
sel = (0 < kmags) & (kmags < kc)
import static_correlation as sc
#ukmags = np.unique(kmags[sel]) # no tolerance option
kmags1 = kmags[sel]
sels = sc.kshell_sels(kmags1, zoom)
ukmags = np.array([kmags1[s].mean() for s in sels])
# step 3: get Ulr
urpa = gaskell_rpa_uk(ukmags, rs, kf)
usrk = evaluate_ft(ukmags, j2sr, rcut)
ulrk = usrk - urpa
return ukmags, ulrk, uuc, udc
def sofk_snapshot(axes, pos, nkmax=5, legal_kvecs=None):
""" calculate the structure factor of a snapshot of a crystal structure given 'axes' and 'pos' of atoms.
'nkmax' is the number of kvectors to include in each of x,y,z directions.
return 2 lists: legal kvectors, and S(k) of each kvector
Args:
axes (np.array): crystal lattice vectors.
pos (np.array): positions of atoms.
nkmax (int,optional): maximum number of kvectors in each spatial dimension, default is 5. Used only if legal_kvecs is not give.
leagal_kvecs (np.array,optional): kvectors upon which S(k) is defined, default is to recalculate up to nkmax.
Returns:
(np.array,np.array): (kvecs,S(k))
"""
from qharv.inspect.axes_pos import raxes
rho = lambda kvec: np.exp(1j * np.dot(pos, kvec)).sum()
reclat = raxes(axes)
if legal_kvecs is None:
import chiesa_correction as chc
cube_pts = chc.cubic_pos(nkmax)
legal_kvecs = np.dot(cube_pts[1:], reclat)
sk_arr = np.array([(rho(kvec) * rho(-kvec)).real / len(pos)
for kvec in legal_kvecs])
return legal_kvecs, sk_arr
def detect_p21c_layers(mols, kfracs=None):
from qharv.inspect import axes_pos
# setup S(k) calculation
from qharv_db import grsk
if kfracs is None:
kfracs = np.array([
[0, -8, 16],
[0, 8, 16],
])
axes = mols.get_cell()
raxes = axes_pos.raxes(axes)
kvecs = np.dot(kfracs, raxes)
# detect layers
layers = find_layers(mols)
groups = extract_layers(layers, [mols])
grps = [g[0] for g in groups]
# loop through 3 layers at a time
nlayer = len(grps)
layer_desc = []
for ilayer in range(1, nlayer-1):
pos0 = grps[ilayer-1]
pos1 = grps[ilayer]
pos2 = grps[ilayer+1]
pos = np.concatenate([pos0, pos1, pos2], axis=0)
sk1 = grsk.Sk(kvecs, pos)
layer_desc.append(sk1.sum())
return layer_desc
def get_all_rhok(fwf, kbrags, norb=None, ispin=0, show_progress=True):
from qharv.seed import wf_h5
from qharv.inspect import axes_pos
from rsgub.grids.forlib.find_gvecs import calc_rhok
fp = wf_h5.read(fwf)
axes = wf_h5.get(fp, 'axes')
# calculate ukbrags
raxes = axes_pos.raxes(axes)
kcand = np.dot(kbrags, np.linalg.inv(raxes))
ukbrags = np.round(kcand).astype(int)
# check ukbrags
kbrags1 = np.dot(ukbrags, raxes)
assert np.allclose(kbrags, kbrags1)
# calculate rhok
gvecs = wf_h5.get(fp, 'gvectors')
ntwist = wf_h5.get(fp, 'nkpt')[ispin]
# store complex numbers in real view
data = np.zeros([ntwist, 2*len(ukbrags)])
if show_progress:
from progressbar import ProgressBar
bar = ProgressBar(maxval=ntwist)
for itwist in range(ntwist):
cmat = wf_h5.get_cmat(fp, itwist, ispin, norb=norb)
val = 2*calc_rhok(ukbrags, gvecs, cmat)
data[itwist, :] = val.view(float)
if show_progress:
bar.update(itwist)
fp.close()
return data
def legal_kvecs(axes, nsh, eps=1e-8): from qharv.inspect import axes_pos raxes = axes_pos.raxes(axes) gvecs = axes_pos.cubic_pos(2*nsh+1)-nsh kvecs = np.dot(gvecs, raxes) kmags = np.linalg.norm(kvecs, axis=-1) sel = (kmags>eps) & (kvecs[:, 2]>=0) return kvecs[sel]
def get_qvecs_and_intnorm(axes, mx): from qharv.inspect import axes_pos # get qvectors raxes = axes_pos.raxes(axes) fvecs = 1./mx*axes_pos.cubic_pos(mx) qvecs = np.dot(fvecs, raxes) qvecs -= qvecs.mean(axis=0) # calculate integration norm intnorm = axes_pos.volume(raxes)/mx**3/(2*np.pi)**3 return qvecs, intnorm
def calc_nk1d_fsc(uk, unkm, nelec, rs=3.25, mx=8):
from qharv.inspect import axes_pos
from solith.li_nofk.expt_jofp import flip_and_clamp
from solith.dft_calc.bcc_crystal import get_cubic_axes
from chiesa_correction import IsotropicMomentumDistributionFSC
axes = get_cubic_axes(rs, nelec)
raxes = axes_pos.raxes(axes)
fsc = IsotropicMomentumDistributionFSC(rs)
fsc.init_missing_qvecs(raxes, mx)
fnk = flip_and_clamp(uk, unkm, kind='linear')
kvs = np.array([[k, 0, 0] for k in uk])
dnk_fsc = fsc.evaluate_fsc(fnk, kvs)
return np.array(dnk_fsc)
def get_momenta_and_weights(fp, ispin, ikpt, kmax, ecore, efermi):
""" Histogram psig^2 for a single determinant of Kohn-Sham orbitals at a
single twist. Select states with momenta k<kmax and energy ecore<e<efermi.
Args:
fp (h5py.File): pwscf.pwscf.h5 file pointer
ispin (int): determinant index (0: unpolarized, 0/1: polarized)
ikpt (int): twist vector index
kmax (float): maximum momentum to record
ecore (float): Core state energy bound. States below ecore are excluded
efermi (float): Fermi energy
Return:
(np.array, np.array): (momenta, weights)
"""
# get reciprocal lattice vectors to do lattice transformation
axes = wf_h5.get(fp, 'axes')
raxes = axes_pos.raxes(axes)
# Bloch function momenta (kvecs)
gvecs = wf_h5.get(fp, 'gvectors')
kvecs = np.dot(gvecs, raxes)
# crystal momentum (tvec)
kpath = wf_h5.kpoint_path(ikpt)
utvec = fp[os.path.join(kpath, 'reduced_k')].value
tvec = np.dot(utvec, raxes)
# true momentum = crystal + Bloch momentum
mykvecs = kvecs + tvec[np.newaxis, :]
# keep kvectors below kmax
mykmags = np.linalg.norm(mykvecs, axis=1)
sel = mykmags < kmax
momenta = mykvecs[sel]
# accumulate occupation
weights = np.zeros(len(momenta))
# keep states below the Fermi level and outside the core
nstate = fp[os.path.join(kpath, 'spin_%d' % ispin,
'number_of_states')].value[0]
evals = fp[os.path.join(kpath, 'spin_%d' % ispin, 'eigenvalues')].value
esel = (evals > ecore) & (evals < efermi)
states = np.arange(nstate)
for istate in states[esel]:
psig = wf_h5.get_orb_in_pw(fp, ikpt, ispin, istate)
pg2 = psig.conj() * psig
if not np.allclose(pg2.imag, 0): raise RuntimeError('dot not zero')
pg2 = pg2.real[sel]
weights += pg2
return momenta, weights
def get_explicit_kpaths(seek_json, dk=0.025):
""" convert implicit kpath info to explicit list of kpoints
make simple edits to the JSON file returned from the seeK-path website
so that it would be accepted by seekpath.getpaths.get_explicit_from_implicit
example of implicit kpath:
'path':[
['GAMMA', 'H'],
['H', 'N'],
['N', 'GAMMA'],
['GAMMA', 'P'],
['P', 'H'],
['P', 'N']
],
'kpoints_rel':[
'GAMMA':[0.0,0.0,0.0],
'H':[0.5,-0.5,0.5],
'N':[0.0,0.0,0.5],
'P':[0.25,0.25,0.25]
]
example of explicity kpath:
'kpoints_labels':['Gamma','',...,'N'],
'kpoints_abs': array([
[0.,0.,0.]
[0.018,0.,0.018],
...,
[1.618,1.618,3.236]
])
Args:
seek_json (str): JSON file pasted from seeK-path website
dk (float, optional): spacing in reciprocal space in Hartree a.u.
Return:
dict: return value of seekpath.getpaths.get_explicit_from_implicit
"""
from qharv.inspect import axes_pos # need raxes
with open(seek_json, 'r') as f:
data = json.load(f)
# end with
data['point_coords'] = data['kpoints']
data['reciprocal_primitive_lattice'] = axes_pos.raxes(
data['primitive_lattice'])
kpaths = seekpath.getpaths.get_explicit_from_implicit(data, dk)
return kpaths
def write_detsk(h5file, ikpt, fwf, ispin, nsh0, kc):
"""Calculate determinant S(k) at given twist
Args:
h5file (tables.file.File): hdf5 file handle
ikpt (int): twist index
fwf (str): wf h5 file e.g. pwscf.pwscf.h5
ispin (int): spin index, use 0 for unpolarized
nsh0 (int): number of shells to use
kc (float): PW cutoff
"""
from qharv.seed import wf_h5
from qharv.inspect.axes_pos import raxes
from qharv.reel.config_h5 import save_dict
from solith.li_nofk.forlib.det import calc_detsk
from chiesa_correction import mirror_xyz, cubic_pos
# creat slab for twist
gname = 'twist%s' % str(ikpt).zfill(3)
slab = h5file.create_group('/', gname, '')
# read wf file
fp = wf_h5.read(fwf)
gvecs = wf_h5.get(fp, 'gvectors')
cmat = wf_h5.get_cmat(fp, ikpt, ispin)
wf_h5.normalize_cmat(cmat)
axes = wf_h5.get(fp, 'axes')
fp.close()
raxes = raxes(axes)
# decide which qvectors to calculate S(q)
qvecs = mirror_xyz(cubic_pos(nsh0))
kvecs = np.dot(qvecs, raxes)
kmags = np.linalg.norm(kvecs, axis=-1)
qsel = (1e-8 < kmags) & (kmags < kc)
# calculate S(k)
sk0 = calc_detsk(qvecs[qsel], gvecs, cmat)
# save
arr_dict = {
'raxes': raxes,
'gvecs': qvecs[qsel],
'sk0': sk0
}
save_dict(arr_dict, h5file, slab)
def get_det_nk(fp, efermi, ecore=-np.inf, kmax=np.inf, ispin=0):
"""Calculate momentum distribution from Kohn-Sham determinant
same as get_momentum_distribution, but faster
Args:
fp (h5py.File): pwscf.pwscf.h5 file pointer
efermi (float): Fermi energy
ecore (float, optional): core energy, default -np.inf
kmax (float, optional): maximum k magnitude to record, default np.inf
ispin (int, optiona): default 0
Return:
(np.array, np.array): (kvecs, nkm), kvectors and n(k) mean (no error)
"""
from solith.li_nofk.forlib.det import nofk
# need Kohn-Sham eigenvalues to decide which states to use
bands = wf_h5.get_bands(fp, ispin=ispin)
nt, nstate = bands.shape
# need kgrid info: basis (raxes), unshifted (kvecs0), twists (tvecs)
axes = wf_h5.get(fp, 'axes')
raxes = axes_pos.raxes(axes)
gvecs = wf_h5.get(fp, 'gvectors')
utvecs = wf_h5.get_twists(fp)
tvecs = np.dot(utvecs, raxes)
kvecs0 = np.dot(gvecs, raxes)
# calculate n(k) at each twist
kvecsl = []
nkml = []
for it in range(nt):
kvecs = kvecs0 + tvecs[it] # current twist
# histogram orb^2
cmat = wf_h5.get_cmat(fp, it, ispin, nstate)
nocc, npw = cmat.shape
weights = nofk(kvecs, cmat, bands[it], kmax, ecore, efermi)
# save within a cutoff
kmags = np.linalg.norm(kvecs, axis=-1)
sel = kmags < kmax
kvecsl.append(kvecs[sel])
nkml.append(weights[sel])
kvecs = np.concatenate(kvecsl, axis=0)
nkm = np.concatenate(nkml)
return kvecs, nkm
def get_rhok(fwf, kbrags, norb=None, itwist=0, ispin=0): from qharv.seed import wf_h5 from qharv.inspect import axes_pos from rsgub.grids.forlib.find_gvecs import calc_rhok fp = wf_h5.read(fwf) axes = wf_h5.get(fp, 'axes') gvecs = wf_h5.get(fp, 'gvectors') cmat = wf_h5.get_cmat(fp, itwist, ispin, norb=norb) fp.close() # calculate ukbrags raxes = axes_pos.raxes(axes) kcand = np.dot(kbrags, np.linalg.inv(raxes)) ukbrags = np.round(kcand).astype(int) # check ukbrags kbrags1 = np.dot(ukbrags, raxes) assert np.allclose(kbrags, kbrags1) # calculate rhok val = 2*calc_rhok(ukbrags, gvecs, cmat) return val
def get_bands(nscf_out, tgrid0):
"""Get bands and kgrid info from nscf output
data contains: kvecs, bands, tgrid, raxes, gvecs
kvecs (nk, ndim) are reciprocal points possible in the irreducible wedge
kvecs are in 2\pi/alat units
bands (nk, nstate) are the Kohn-Sham eigenvalues
bands are in eV units
tgrid (ndim) is grid size in each dimension
!!!! currently assumed to be the same as x
raxes (ndim, ndim) is the reciprocal lattice
gvecs (nk, ndim) are reciprocal lattice points (kvecs) converted to integers
Args:
nscf_out (str): output file
tgrid0 (int): grid along x
Return:
dict: data
"""
from qharv.inspect import axes_pos
import qe_reader as qer
# get bands
data = qer.parse_nscf_bands(nscf_out)
kvecs = data['kvecs']
# get raxes, gvecs
tgrid = np.array([tgrid0] * 3)
axes = qer.read_out_cell(nscf_out)
raxes = axes_pos.raxes(axes)
gcand = np.dot(kvecs, np.linalg.inv(raxes / tgrid))
gvecs = np.around(gcand).astype(int)
data['tgrid'] = tgrid
data['raxes'] = raxes
data['gvecs'] = gvecs
data.pop('nkpt')
return data
def get_tgrid_raxes(nscf_in, ndim=3):
from qharv.inspect import axes_pos
tgrid, tshift = get_tgrid_tshift(nscf_in)
axes = get_axes(nscf_in, ndim=ndim)
raxes = axes_pos.raxes(axes)
return tgrid, raxes