def __init__(self, bee, xcoefs, ldac, ggac):
"""BEEVDW kernel.
parameters:
bee : str
choose BEE1 or BEE2 exchange basis expansion.
xcoefs : array
coefficients for exchange.
ldac : float
coefficient for LDA correlation.
pbec : float
coefficient for PBE correlation.
"""
if bee == 'BEE2':
self.BEE = BEE2(xcoefs)
self.GGAc = LibXC('GGA_C_PBE')
self.xtype = 'GGA'
self.type = 'GGA'
elif bee == 'BEE3':
self.BEE = LibXC('MGGA_X_MBEEFVDW')
self.GGAc = LibXC('GGA_C_PBE_SOL')
self.xtype = 'MGGA'
self.type = 'MGGA'
else:
raise ValueError('Unknown BEE exchange: %s', bee)
self.LDAc = LibXC('LDA_C_PW')
self.ldac = ldac
self.ggac = ggac
if bee in ['BEE1', 'BEE2']:
self.ggac -= 1.0
self.name = 'BEEVDW'
def VDWFunctional(name, fft=True, **kwargs):
if name == 'vdW-DF':
kernel = LibXC('GGA_X_PBE_R+LDA_C_PW')
elif name == 'vdW-DF2':
kernel = LibXC('GGA_X_RPW86+LDA_C_PW')
kwargs['Zab'] = -1.887
elif name == 'optPBE-vdW':
kernel = LibXC('GGA_X_OPTPBE_VDW+LDA_C_PW')
elif name == 'optB88-vdW':
kernel = LibXC('GGA_X_OPTB88_VDW+LDA_C_PW')
elif name == 'C09-vdW':
kernel = LibXC('GGA_X_C09X+LDA_C_PW')
elif name == 'BEEF-vdW':
from gpaw.xc.bee import BEEVDWKernel
kernel = BEEVDWKernel('BEE2', None, 0.600166476948828631066,
0.399833523051171368934)
kwargs['Zab'] = -1.887
kwargs['setup_name'] = 'PBE'
elif name == 'mBEEF-vdW':
from gpaw.xc.bee import BEEVDWKernel
kernel = BEEVDWKernel('BEE3', None, 0.405258352, 0.356642240)
kwargs['Zab'] = -1.887
kwargs['vdwcoef'] = 0.886774972
kwargs['Nr'] = 4096
kwargs['setup_name'] = 'PBEsol'
assert fft
return MGGAFFTVDWFunctional(name, kernel, **kwargs)
else:
2 / 0
if fft:
return GGAFFTVDWFunctional(name, kernel, **kwargs)
return GGARealSpaceVDWFunctional(name, kernel, **kwargs)
def __init__(self, just_kidding=False):
self.just_kidding = just_kidding
self.type = 'GGA'
self.lda_c = LibXC('LDA_C_PW')
if self.just_kidding:
self.name = 'purepython rPW86_with_%s' % self.lda_c.name
else:
self.name = 'purepython cx'
def __init__(self, c=None):
self.tb09 = LibXC('MGGA_X_TB09').xc.tb09
self.ldac = LibXC('LDA_C_PW')
self.fixedc = c is not None # calculate c or use fixed value
self.c = c # amount of "exact exchange"
self.n = 0 # Lebedev quadrature point number (0-49)
self.sign = 1.0 # sign of PAW correction: +1 for AE and -1 for PS
self.I = None # integral from Eq. (3)
def __init__(self, xcoefs, ldac, pbec, lyp):
self.BEE1 = BEE1(xcoefs)
self.LDAc = LibXC('LDA_C_PW')
self.PBEc = LibXC('GGA_C_PBE')
self.LYP = LibXC('GGA_C_LYP')
self.ldac = ldac
self.pbec = pbec
self.lyp = lyp
self.type = 'GGA'
self.name = 'BEEVDW'
def __init__(self, bee, xcoefs, ldac, ggac):
"""BEEVDW kernel.
parameters:
bee : str
choose BEE1 or BEE2 exchange basis expansion.
xcoefs : array
coefficients for exchange.
ldac : float
coefficient for LDA correlation.
pbec : float
coefficient for PBE correlation.
"""
if bee == 'BEE2':
self.BEE = BEE2(xcoefs)
self.GGAc = LibXC('GGA_C_PBE')
self.xtype = 'GGA'
self.type = 'GGA'
elif bee == 'BEE3':
self.BEE = LibXC('MGGA_X_MBEEFVDW')
self.GGAc = LibXC('GGA_C_PBE_SOL')
self.xtype = 'MGGA'
self.type = 'MGGA'
else:
raise ValueError('Unknown BEE exchange: %s', bee)
self.LDAc = LibXC('LDA_C_PW')
self.ldac = ldac
self.ggac = ggac
if bee in ['BEE1', 'BEE2']:
self.ggac -= 1.0
self.name = 'BEEVDW'
def vdw_df2(**kwargs):
kwargs1 = dict(name='vdW-DF2',
setup_name='PBE',
semilocal_xc=GGA(LibXC('GGA_X_RPW86+LDA_C_PW'),
stencil=kwargs.pop('stencil', 2)))
kwargs1.update(kwargs)
return VDWXC(**kwargs1)
def create_xc(func, mode):
isinstance(func, str)
isinstance(mode, int)
if mode == 0:
xc = LibXC(func)
else:
xc = XCKernel(func)
return xc
def calculate(self, e_g, n_sg, dedn_sg,
sigma_xg=None, dedsigma_xg=None,
tau_sg=None, dedtau_sg=None):
n_g = n_sg[0]
m_vg = n_sg[1:4]
m_g = (m_vg**2).sum(0)**0.5
nnew_sg = np.empty((2,) + n_g.shape)
nnew_sg[:] = n_g
nnew_sg[0] += m_g
nnew_sg[1] -= m_g
nnew_sg *= 0.5
vnew_sg = np.zeros_like(nnew_sg)
LibXC.calculate(self, e_g, nnew_sg, vnew_sg)
dedn_sg[0] += 0.5 * vnew_sg.sum(0)
vnew_sg /= np.where(m_g < 1e-15, 1, m_g)
dedn_sg[1:4] += 0.5 * vnew_sg[0] * m_vg
dedn_sg[1:4] -= 0.5 * vnew_sg[1] * m_vg
def vdw_C09(**kwargs):
kwargs1 = dict(name='vdW-C09',
libvdwxc_name='vdW-DF',
setup_name='PBE',
semilocal_xc=GGA(LibXC('GGA_X_C09X+LDA_C_PW'),
stencil=kwargs.pop('stencil', 2)))
kwargs1.update(kwargs)
return VDWXC(**kwargs1)
def test_selfconsistent():
from gpaw import GPAW
from ase.build import molecule
from gpaw.xc.gga import GGA
system = molecule('H2O')
system.center(vacuum=3.)
def test(xc):
calc = GPAW(
mode='lcao',
xc=xc,
setups='sg15',
txt='gpaw.%s.txt' % str(xc) # .kernel.name
)
system.set_calculator(calc)
return system.get_potential_energy()
libxc_results = {}
for name in ['GGA_X_PBE_R+LDA_C_PW', 'GGA_X_RPW86+LDA_C_PW']:
xc = GGA(LibXC(name))
e = test(xc)
libxc_results[name] = e
cx_gga_results = {}
cx_gga_results['rpw86'] = test(GGA(CXGGAKernel(just_kidding=True)))
cx_gga_results['lv_rpw86'] = test(GGA(CXGGAKernel(just_kidding=False)))
vdw_results = {}
vdw_coef0_results = {}
for vdw in [vdw_df(), vdw_df2(), vdw_df_cx()]:
vdw.vdwcoef = 0.0
vdw_coef0_results[vdw.__class__.__name__] = test(vdw)
vdw.vdwcoef = 1.0 # Leave nicest text file by running real calc last
vdw_results[vdw.__class__.__name__] = test(vdw)
from gpaw.mpi import world
# These tests basically verify that the LDA/GGA parts of vdwdf
# work correctly.
if world.rank == 0:
print('Now comparing...')
err1 = cx_gga_results['rpw86'] - libxc_results['GGA_X_RPW86+LDA_C_PW']
print('Our rpw86 must be identical to that of libxc. Err=%e' % err1)
print('RPW86 interpolated with Langreth-Vosko stuff differs by %f' %
(cx_gga_results['lv_rpw86'] - cx_gga_results['rpw86']))
print('Each vdwdf with vdwcoef zero must yield same result as gga'
'kernel')
err_df1 = vdw_coef0_results['VDWDF'] - libxc_results['GGA_X_PBE_R+'
'LDA_C_PW']
print(' df1 err=%e' % err_df1)
err_df2 = vdw_coef0_results['VDWDF2'] - libxc_results['GGA_X_RPW86+'
'LDA_C_PW']
print(' df2 err=%e' % err_df2)
err_cx = vdw_coef0_results['VDWDFCX'] - cx_gga_results['lv_rpw86']
print(' cx err=%e' % err_cx)
def XC(kernel, parameters=None):
"""Create XCFunctional object.
kernel: XCKernel object or str
Kernel object or name of functional.
parameters: ndarray
Parameters for BEE functional.
Recognized names are: LDA, PW91, PBE, revPBE, RPBE, BLYP, HCTH407,
TPSS, M06L, revTPSS, vdW-DF, vdW-DF2, EXX, PBE0, B3LYP, BEE,
GLLBSC. One can also use equivalent libxc names, for example
GGA_X_PBE+GGA_C_PBE is equivalent to PBE, and LDA_X to the LDA exchange.
In this way one has access to all the functionals defined in libxc.
See gpaw.xc.libxc_functionals.py for the complete list. """
if isinstance(kernel, str):
name = kernel
if name in ['vdW-DF', 'vdW-DF2']:
from gpaw.xc.vdw import FFTVDWFunctional
return FFTVDWFunctional(name)
elif name in ['EXX', 'PBE0', 'B3LYP']:
from gpaw.xc.hybrid import HybridXC
return HybridXC(name)
elif name == 'BEE1':
from gpaw.xc.bee import BEE1
kernel = BEE1(parameters)
elif name.startswith('GLLB'):
from gpaw.xc.gllb.nonlocalfunctionalfactory import \
NonLocalFunctionalFactory
xc = NonLocalFunctionalFactory().get_functional_by_name(name)
xc.print_functional()
return xc
elif name == 'LB94':
from gpaw.xc.lb94 import LB94
kernel = LB94()
elif name.startswith('ODD_'):
from ODD import ODDFunctional
return ODDFunctional(name[4:])
elif name.endswith('PZ-SIC'):
try:
from ODD import PerdewZungerSIC as SIC
return SIC(xc=name[:-7])
except:
from gpaw.xc.sic import SIC
return SIC(xc=name[:-7])
elif name.startswith('old'):
from gpaw.xc.kernel import XCKernel
kernel = XCKernel(name[3:])
else:
kernel = LibXC(kernel)
if kernel.type == 'LDA':
return LDA(kernel)
elif kernel.type == 'GGA':
return GGA(kernel)
else:
return MGGA(kernel)
def __init__(self, name):
self.name = name
self.kernels = []
self.coefs = []
self.type = 'LDA'
for x in name.split('+'):
c, n = x.split('_', 1)
self.coefs.append(float(c))
kernel = LibXC(n)
self.kernels.append(kernel)
if kernel.type == 'GGA':
self.type = 'GGA'
def vdw_df_cx(**kwargs):
# cx semilocal exchange is in libxc 2.2.2 or newer (or maybe from older)
kernel = kwargs.get('kernel')
if kernel is None:
kernel = LibXC('GGA_X_LV_RPW86+LDA_C_PW')
kwargs1 = dict(
name='vdW-DF-cx',
setup_name='PBE',
# PBEsol is most correct but not distributed by default.
semilocal_xc=GGA(kernel, stencil=kwargs.pop('stencil', 2)))
kwargs1.update(kwargs)
return VDWXC(**kwargs1)
def calculate(self,
e_g,
n_sg,
dedn_sg,
sigma_xg=None,
dedsigma_xg=None,
tau_sg=None,
dedtau_sg=None):
n_g = n_sg[0]
m_vg = n_sg[1:4]
m_g = (m_vg**2).sum(0)**0.5
nnew_sg = np.empty((2, ) + n_g.shape)
nnew_sg[:] = n_g
nnew_sg[0] += m_g
nnew_sg[1] -= m_g
nnew_sg *= 0.5
vnew_sg = np.zeros_like(nnew_sg)
LibXC.calculate(self, e_g, nnew_sg, vnew_sg)
dedn_sg[0] += 0.5 * vnew_sg.sum(0)
vnew_sg /= np.where(m_g < 1e-15, 1, m_g)
dedn_sg[1:4] += 0.5 * vnew_sg[0] * m_vg
dedn_sg[1:4] -= 0.5 * vnew_sg[1] * m_vg
def vdw_df_cx(*args, **kwargs):
try:
# Exists in libxc 2.2.2 or newer (or maybe from older)
kernel = LibXC('GGA_X_LV_RPW86+LDA_C_PW')
except NameError:
kernel = CXGGAKernel()
# Hidden debug feature
if kwargs.get('gga_backend') == 'purepython':
kernel = CXGGAKernel()
kwargs.pop('gga_backend')
assert 'gga_backend' not in kwargs
return VDWXC(semilocal_xc=GGA(kernel), name='vdW-DF-CX', *args, **kwargs)
def test_derivatives():
gen = np.random.RandomState(1)
shape = (1, 20, 20, 20)
ngpts = np.product(shape)
n_sg = gen.rand(*shape)
sigma_xg = np.zeros(shape)
sigma_xg[:] = gen.rand(*shape)
qe_kernel = CXGGAKernel(just_kidding=True)
libxc_kernel = LibXC('GGA_X_RPW86+LDA_C_PW')
cx_kernel = CXGGAKernel(just_kidding=False)
def check(kernel, n_sg, sigma_xg):
e_g = np.zeros(shape[1:])
dedn_sg = np.zeros(shape)
dedsigma_xg = np.zeros(shape)
kernel.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg)
return e_g, dedn_sg, dedsigma_xg
def check_and_write(kernel):
n1_sg = n_sg.copy()
e_g, dedn_sg, dedsigma_xg = check(kernel, n_sg, sigma_xg)
dedn = dedn_sg[0, 0, 0, 0]
dedsigma = dedsigma_xg[0, 0, 0, 0]
dn = 1e-6
n1_sg = n_sg.copy()
n1_sg[0, 0, 0, 0] -= dn / 2.
e1_g, _, _ = check(kernel, n1_sg, sigma_xg)
n1_sg[0, 0, 0, 0] += dn
e2_g, _, _ = check(kernel, n1_sg, sigma_xg)
dedn_fd = (e2_g[0, 0, 0] - e1_g[0, 0, 0]) / dn
dedn_err = abs(dedn - dedn_fd)
print('e', e_g.sum() / ngpts)
print('dedn', dedn, 'fd', dedn_fd, 'err %e' % dedn_err)
sigma1_xg = sigma_xg.copy()
sigma1_xg[0, 0, 0, 0] -= dn / 2.
e1s_g, _, _ = check(kernel, n_sg, sigma1_xg)
sigma1_xg[0, 0, 0, 0] += dn
e2s_g, _, _ = check(kernel, n_sg, sigma1_xg)
dedsigma_fd = (e2s_g[0, 0, 0] - e1s_g[0, 0, 0]) / dn
dedsigma_err = dedsigma - dedsigma_fd
print('dedsigma', dedsigma, 'fd', dedsigma_fd, 'err %e' % dedsigma_err)
return e_g, dedn_sg, dedsigma_xg
print('pw86r libxc')
e_lxc_g, dedn_lxc_g, dedsigma_lxc_g = check_and_write(libxc_kernel)
print()
print('pw86r ours')
e_qe_g, dedn_qe_g, dedsigma_qe_g = check_and_write(qe_kernel)
print()
print('cx')
check_and_write(cx_kernel)
print()
print('lxc vs qe discrepancies')
print('=======================')
e_err = np.abs(e_lxc_g - e_qe_g).max()
print('e', e_err)
dedn_err = np.abs(dedn_qe_g - dedn_lxc_g).max()
dedsigma_err = np.abs(dedsigma_lxc_g - dedsigma_qe_g).max()
print('dedn', dedn_err)
print('dedsigma', dedsigma_err)
class CXGGAKernel:
def __init__(self, just_kidding=False):
self.just_kidding = just_kidding
self.type = 'GGA'
self.lda_c = LibXC('LDA_C_PW')
if self.just_kidding:
self.name = 'purepython rPW86_with_%s' % self.lda_c.name
else:
self.name = 'purepython cx'
def calculate(self, e_g, n_sg, v_sg, sigma_xg, dedsigma_xg):
e_g[:] = 0.0
dedsigma_xg[:] = 0.0
self.lda_c.calculate(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
for arr in [n_sg, v_sg, sigma_xg, dedsigma_xg]:
assert len(arr) == 1
self._exchange(n_sg[0], sigma_xg[0], e_g, v_sg[0], dedsigma_xg[0])
def _exchange(self, rho, grho, sx, v1x, v2x):
"""Calculate cx local exchange.
Note that this *adds* to the energy density sx so that it can
be called after LDA correlation part without ruining anything.
Also it adds to v1x and v2x as is normal in GPAW."""
tol = 1e-20
rho[rho < tol] = tol
grho[grho < tol] = tol
alp = 0.021789
beta = 1.15
a = 1.851
b = 17.33
c = 0.163
mu_LM = 0.09434
s_prefactor = 6.18733545256027
Ax = -0.738558766382022 # = -3./4. * (3./pi)**(1./3)
four_thirds = 4. / 3.
grad_rho = np.sqrt(grho)
# eventually we need s to power 12. Clip to avoid overflow
# (We have individual tolerances on both rho and grho, but
# they are not sufficient to guarantee this)
s_1 = (grad_rho / (s_prefactor * rho**four_thirds)).clip(0.0, 1e20)
s_2 = s_1 * s_1
s_3 = s_2 * s_1
s_4 = s_3 * s_1
s_5 = s_4 * s_1
s_6 = s_5 * s_1
fs_rPW86 = (1.0 + a * s_2 + b * s_4 + c * s_6)**(1. / 15.)
if self.just_kidding:
fs = fs_rPW86
else:
fs = (1.0 + mu_LM * s_2) / (1.0 + alp * s_6) \
+ alp * s_6 / (beta + alp * s_6) * fs_rPW86
# the energy density for the exchange.
sx[:] += Ax * rho**four_thirds * fs
df_rPW86_ds = (1. / (15. * fs_rPW86**14.0)) * \
(2 * a * s_1 + 4 * b * s_3 + 6 * c * s_5)
if self.just_kidding:
df_ds = df_rPW86_ds # XXXXXXXXXXXXXXXXXXXX
else:
df_ds = 1. / (1. + alp * s_6)**2 \
* (2.0 * mu_LM * s_1 * (1. + alp * s_6) -
6.0 * alp * s_5 * (1. + mu_LM * s_2)) \
+ alp * s_6 / (beta + alp * s_6) * df_rPW86_ds \
+ 6.0 * alp * s_5 * fs_rPW86 / (beta + alp * s_6) \
* (1. - alp * s_6 / (beta + alp * s_6))
# de/dn. This is the partial derivative of sx wrt. n, for s constant
v1x[:] += Ax * four_thirds * (rho**(1. / 3.) * fs - grad_rho /
(s_prefactor * rho) * df_ds)
# de/d(nabla n). The other partial derivative
v2x[:] += 0.5 * Ax * df_ds / (s_prefactor * grad_rho)
def __init__(self, world=None, Zab=-0.8491, vdwcoef=1.0, q0cut=5.0,
phi0=0.5, ds=1.0, Dmax=20.0, nD=201, ndelta=21,
soft_correction=False, setup_name='revPBE',
verbose=False, energy_only=False):
"""vdW-DF.
parameters:
name: str
Name of functional.
world: MPI communicator
Communicator to parallelize over. Defaults to gpaw.mpi.world.
q0cut: float
Maximum value for q0.
phi0: float
Smooth value for phi(0,0).
ds: float
Cutoff for smooth kernel.
Dmax: float
Maximum value for D.
nD: int
Number of values for D in kernel-table.
ndelta: int
Number of values for delta in kernel-table.
soft_correction: bool
Correct for soft kernel.
kernel:
Which kernel to use.
Zab:
parameter in nonlocal kernel.
vdwcoef: float
Scaling of vdW energy.
verbose: bool
Print useful information.
"""
if world is None:
self.world = mpi.world
else:
self.world = world
self.Zab = Zab
self.vdwcoef = vdwcoef
self.q0cut = q0cut
self.phi0 = phi0
self.ds = ds
self.delta_i = np.linspace(0, 1.0, ndelta)
self.D_j = np.linspace(0, Dmax, nD)
self.verbose = verbose
self.read_table()
self.soft_correction = soft_correction
if soft_correction:
dD = self.D_j[1]
self.C_soft = np.dot(self.D_j**2, self.phi_ij[0]) * 4 * pi * dD
self.gd = None
self.energy_only = energy_only
self.timer = nulltimer
self.LDAc = LibXC('LDA_C_PW')
self.setup_name = setup_name
def __init__(self):
LibXC.__init__(self, 'LDA')
class TB09Kernel:
name = 'TB09'
type = 'MGGA'
alpha = -0.012
beta = 1.023
def __init__(self, c=None):
self.tb09 = LibXC('MGGA_X_TB09').xc.tb09
self.ldac = LibXC('LDA_C_PW')
self.fixedc = c is not None # calculate c or use fixed value
self.c = c # amount of "exact exchange"
self.n = 0 # Lebedev quadrature point number (0-49)
self.sign = 1.0 # sign of PAW correction: +1 for AE and -1 for PS
self.I = None # integral from Eq. (3)
def calculate(self, e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg, tau_sg,
dedtau_sg):
ns = len(n_sg)
n_sg[n_sg < 1e-6] = 1e-6
if n_sg.ndim == 4:
if not self.fixedc:
if self.c is None:
# We don't have the integral yet - just use 1.0:
self.c = 1.0
else:
self.I = self.world.sum(self.I)
self.c = (self.alpha + self.beta *
(self.I / self.gd.volume)**0.5)
# Start calculation of c for use in the next SCF step:
if ns == 1:
gradn_g = sigma_xg[0]**0.5
else:
gradn_g = (sigma_xg[0] + 2 * sigma_xg[1] +
sigma_xg[2])**0.5
self.I = self.gd.integrate(gradn_g / n_sg.sum(0))
# The domain is not distributed like the PAW corrections:
self.I /= self.world.size
lapl_sg = self.gd.empty(ns)
for n_g, lapl_g in zip(n_sg, lapl_sg):
self.lapl.apply(n_g, lapl_g)
else:
rgd = self.rgd
lapl_sg = []
for n_Lg in self.n_sLg:
lapl_g = rgd.laplace(np.dot(self.Y_L, n_Lg))
l = 0
L1 = 0
while L1 < len(self.Y_L):
L2 = L1 + 2 * l + 1
n_g = np.dot(self.Y_L[L1:L2], n_Lg[L1:L2])
with seterr(divide='ignore', invalid='ignore'):
lapl_g -= l * (l + 1) * n_g / rgd.r_g**2
lapl_g[0] = 0.0
L1 = L2
l += 1
lapl_sg.append(lapl_g)
if not self.fixedc:
# PAW corrections to integral:
w = self.sign * weight_n[self.n]
if ns == 1:
gradn_g = sigma_xg[0]**0.5
else:
gradn_g = (sigma_xg[0] + 2 * sigma_xg[1] +
sigma_xg[2])**0.5
self.I += w * rgd.integrate(gradn_g / n_sg.sum(0))
self.n += 1
if self.n == len(weight_n):
self.n = 0
self.sign = -self.sign
# dedn_sg[:] = 0.0
sigma_xg[sigma_xg < 1e-10] = 1e-10
tau_sg[tau_sg < 1e-10] = 1e-10
for n_g, sigma_g, lapl_g, tau_g, v_g in zip(n_sg, sigma_xg[::2],
lapl_sg, tau_sg, dedn_sg):
self.tb09(self.c, n_g.ravel(), sigma_g, lapl_g, tau_g, v_g,
dedsigma_xg)
self.ldac.calculate(e_g, n_sg, dedn_sg)
e_g[:] = 0.0
dedsigma_xg[:] = 0.0
dedtau_sg[:] = 0.0
def vdw_C09(*args, **kwargs):
return VDWXC(semilocal_xc=GGA(LibXC('GGA_X_C09X+LDA_C_PW')),
name='vdW-C09',
libvdwxc_name='vdW-DF',
*args,
**kwargs)
def XC(kernel, parameters=None, atoms=None, collinear=True):
"""Create XCFunctional object.
kernel: XCKernel object, dict or str
Kernel object or name of functional.
parameters: ndarray
Parameters for BEE functional.
Recognized names are: LDA, PW91, PBE, revPBE, RPBE, BLYP, HCTH407,
TPSS, M06-L, revTPSS, vdW-DF, vdW-DF2, EXX, PBE0, B3LYP, BEE,
GLLBSC. One can also use equivalent libxc names, for example
GGA_X_PBE+GGA_C_PBE is equivalent to PBE, and LDA_X to the LDA exchange.
In this way one has access to all the functionals defined in libxc.
See xc_funcs.h for the complete list. """
if isinstance(kernel, basestring):
kernel = xc_string_to_dict(kernel)
kwargs = {}
if isinstance(kernel, dict):
kwargs = kernel.copy()
name = kwargs.pop('name')
backend = kwargs.pop('backend', None)
if backend == 'libvdwxc' or name == 'vdW-DF-cx':
# Must handle libvdwxc before old vdw implementation to override
# behaviour for 'name'. Also, cx is not implemented by the old
# vdW module, so that always refers to libvdwxc.
from gpaw.xc.libvdwxc import get_libvdwxc_functional
return get_libvdwxc_functional(name=name, **kwargs)
elif backend:
error_msg = "A special backend for the XC functional was given, "\
"but not understood. Please check if there's a typo."
raise ValueError(error_msg)
if name in ['vdW-DF', 'vdW-DF2', 'optPBE-vdW', 'optB88-vdW',
'C09-vdW', 'mBEEF-vdW', 'BEEF-vdW']:
from gpaw.xc.vdw import VDWFunctional
return VDWFunctional(name, **kwargs)
elif name in ['EXX', 'PBE0', 'B3LYP',
'CAMY-BLYP', 'CAMY-B3LYP', 'LCY-BLYP', 'LCY-PBE']:
from gpaw.xc.hybrid import HybridXC
return HybridXC(name, **kwargs)
elif name.startswith('LCY-') or name.startswith('CAMY-'):
parts = name.split('(')
from gpaw.xc.hybrid import HybridXC
return HybridXC(parts[0], omega=float(parts[1][:-1]))
elif name in ['HSE03', 'HSE06']:
from gpaw.xc.exx import EXX
return EXX(name, **kwargs)
elif name == 'BEE1':
from gpaw.xc.bee import BEE1
kernel = BEE1(parameters)
elif name == 'BEE2':
from gpaw.xc.bee import BEE2
kernel = BEE2(parameters)
elif name.startswith('GLLB'):
from gpaw.xc.gllb.nonlocalfunctionalfactory import \
NonLocalFunctionalFactory
# Pass kwargs somewhere?
xc = NonLocalFunctionalFactory().get_functional_by_name(name)
xc.print_functional()
return xc
elif name == 'LB94':
from gpaw.xc.lb94 import LB94
kernel = LB94()
elif name == 'TB09':
from gpaw.xc.tb09 import TB09
return TB09(**kwargs)
elif name.endswith('PZ-SIC'):
from gpaw.xc.sic import SIC
return SIC(xc=name[:-7], **kwargs)
elif name in ['TPSS', 'M06-L', 'M06L', 'revTPSS']:
if name == 'M06L':
name = 'M06-L'
warnings.warn('Please use M06-L instead of M06L')
from gpaw.xc.kernel import XCKernel
kernel = XCKernel(name)
elif name.startswith('old'):
from gpaw.xc.kernel import XCKernel
kernel = XCKernel(name[3:])
elif name == 'PPLDA':
from gpaw.xc.lda import PurePythonLDAKernel
kernel = PurePythonLDAKernel()
elif name in ['pyPBE', 'pyPBEsol', 'pyRPBE', 'pyzvPBEsol']:
from gpaw.xc.gga import PurePythonGGAKernel
kernel = PurePythonGGAKernel(name)
elif name == '2D-MGGA':
from gpaw.xc.mgga import PurePython2DMGGAKernel
kernel = PurePython2DMGGAKernel(name, parameters)
elif name[0].isdigit():
from gpaw.xc.parametrizedxc import ParametrizedKernel
kernel = ParametrizedKernel(name)
elif name == 'null':
from gpaw.xc.kernel import XCNull
kernel = XCNull()
elif name == 'QNA':
from gpaw.xc.qna import QNA
return QNA(atoms, kernel['parameters'], kernel['setup_name'],
alpha=kernel['alpha'], stencil=kwargs.get('stencil', 2))
else:
kernel = LibXC(name)
if kernel.type == 'LDA':
if not collinear:
kernel = NonCollinearLDAKernel(kernel)
xc = LDA(kernel, **kwargs)
return xc
elif kernel.type == 'GGA':
return GGA(kernel, **kwargs)
else:
return MGGA(kernel, **kwargs)
def __init__(self,
world=None,
Zab=-0.8491,
vdwcoef=1.0,
q0cut=5.0,
phi0=0.5,
ds=1.0,
Dmax=20.0,
nD=201,
ndelta=21,
soft_correction=False,
setup_name='revPBE',
verbose=False,
energy_only=False):
"""vdW-DF.
parameters:
name: str
Name of functional.
world: MPI communicator
Communicator to parallelize over. Defaults to gpaw.mpi.world.
q0cut: float
Maximum value for q0.
phi0: float
Smooth value for phi(0,0).
ds: float
Cutoff for smooth kernel.
Dmax: float
Maximum value for D.
nD: int
Number of values for D in kernel-table.
ndelta: int
Number of values for delta in kernel-table.
soft_correction: bool
Correct for soft kernel.
kernel:
Which kernel to use.
Zab:
parameter in nonlocal kernel.
vdwcoef: float
Scaling of vdW energy.
verbose: bool
Print useful information.
"""
if world is None:
self.world = mpi.world
else:
self.world = world
self.Zab = Zab
self.vdwcoef = vdwcoef
self.q0cut = q0cut
self.phi0 = phi0
self.ds = ds
self.delta_i = np.linspace(0, 1.0, ndelta)
self.D_j = np.linspace(0, Dmax, nD)
self.verbose = verbose
self.read_table()
self.soft_correction = soft_correction
if soft_correction:
dD = self.D_j[1]
self.C_soft = np.dot(self.D_j**2, self.phi_ij[0]) * 4 * pi * dD
self.gd = None
self.energy_only = energy_only
self.timer = nulltimer
self.LDAc = LibXC('LDA_C_PW')
self.setup_name = setup_name
def vdw_optB88(*args, **kwargs):
return VDWXC(semilocal_xc=GGA(LibXC('GGA_X_OPTB88_VDW+LDA_C_PW')),
name='optB88',
libvdwxc_name='vdW-DF',
*args,
**kwargs)
class BEEVDWKernel(XCKernel):
"""Kernel for BEEVDW functionals."""
def __init__(self, bee, xcoefs, ldac, ggac):
"""BEEVDW kernel.
parameters:
bee : str
choose BEE1 or BEE2 exchange basis expansion.
xcoefs : array
coefficients for exchange.
ldac : float
coefficient for LDA correlation.
pbec : float
coefficient for PBE correlation.
"""
if bee == 'BEE2':
self.BEE = BEE2(xcoefs)
self.GGAc = LibXC('GGA_C_PBE')
self.xtype = 'GGA'
self.type = 'GGA'
elif bee == 'BEE3':
self.BEE = LibXC('MGGA_X_MBEEFVDW')
self.GGAc = LibXC('GGA_C_PBE_SOL')
self.xtype = 'MGGA'
self.type = 'MGGA'
else:
raise ValueError('Unknown BEE exchange: %s', bee)
self.LDAc = LibXC('LDA_C_PW')
self.ldac = ldac
self.ggac = ggac
if bee in ['BEE1', 'BEE2']:
self.ggac -= 1.0
self.name = 'BEEVDW'
def calculate(self,
e_g,
n_sg,
dedn_sg,
sigma_xg=None,
dedsigma_xg=None,
tau_sg=None,
dedtau_sg=None):
if debug:
self.check_arguments(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg,
tau_sg, dedtau_sg)
if self.xtype == 'GGA':
self.BEE.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg)
elif self.xtype == 'MGGA':
self.BEE.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg,
tau_sg, dedtau_sg)
else:
raise ValueError('Unexpected value of xtype:', self.xtype)
e0_g = np.empty_like(e_g)
dedn0_sg = np.empty_like(dedn_sg)
dedsigma0_xg = np.empty_like(dedsigma_xg)
for coef, kernel in [(self.ldac, self.LDAc), (self.ggac, self.GGAc)]:
dedn0_sg[:] = 0.0
kernel.calculate(e0_g, n_sg, dedn0_sg, sigma_xg, dedsigma0_xg)
e_g += coef * e0_g
dedn_sg += coef * dedn0_sg
if kernel.type == 'GGA':
dedsigma_xg += coef * dedsigma0_xg
def XC(kernel, parameters=None):
"""Create XCFunctional object.
kernel: XCKernel object or str
Kernel object or name of functional.
parameters: ndarray
Parameters for BEE functional.
Recognized names are: LDA, PW91, PBE, revPBE, RPBE, BLYP, HCTH407,
TPSS, M06-L, revTPSS, vdW-DF, vdW-DF2, EXX, PBE0, B3LYP, BEE,
GLLBSC. One can also use equivalent libxc names, for example
GGA_X_PBE+GGA_C_PBE is equivalent to PBE, and LDA_X to the LDA exchange.
In this way one has access to all the functionals defined in libxc.
See xc_funcs.h for the complete list. """
if isinstance(kernel, basestring):
name = kernel
if name in [
'vdW-DF', 'vdW-DF2', 'optPBE-vdW', 'optB88-vdW', 'C09-vdW',
'mBEEF-vdW', 'BEEF-vdW'
]:
from gpaw.xc.vdw import VDWFunctional
return VDWFunctional(name)
elif name in ['EXX', 'PBE0', 'B3LYP']:
from gpaw.xc.hybrid import HybridXC
return HybridXC(name)
elif name in ['HSE03', 'HSE06']:
from gpaw.xc.exx import EXX
return EXX(name)
elif name == 'BEE1':
from gpaw.xc.bee import BEE1
kernel = BEE1(parameters)
elif name == 'BEE2':
from gpaw.xc.bee import BEE2
kernel = BEE2(parameters)
elif name.startswith('GLLB'):
from gpaw.xc.gllb.nonlocalfunctionalfactory import \
NonLocalFunctionalFactory
xc = NonLocalFunctionalFactory().get_functional_by_name(name)
xc.print_functional()
return xc
elif name == 'LB94':
from gpaw.xc.lb94 import LB94
kernel = LB94()
elif name == 'TB09':
from gpaw.xc.tb09 import TB09
return TB09()
elif name.startswith('ODD_'):
from ODD import ODDFunctional
return ODDFunctional(name[4:])
elif name.endswith('PZ-SIC'):
try:
from ODD import PerdewZungerSIC as SIC
return SIC(xc=name[:-7])
except:
from gpaw.xc.sic import SIC
return SIC(xc=name[:-7])
elif name in ['TPSS', 'M06-L', 'M06L', 'revTPSS']:
if name == 'M06L':
name = 'M06-L'
warnings.warn('Please use M06-L instead of M06L')
from gpaw.xc.kernel import XCKernel
kernel = XCKernel(name)
elif name.startswith('old'):
from gpaw.xc.kernel import XCKernel
kernel = XCKernel(name[3:])
elif name == 'PPLDA':
from gpaw.xc.lda import PurePythonLDAKernel
kernel = PurePythonLDAKernel()
elif name in ['pyPBE', 'pyPBEsol', 'pyRPBE', 'pyzvPBEsol']:
from gpaw.xc.gga import PurePythonGGAKernel
kernel = PurePythonGGAKernel(name)
elif name == '2D-MGGA':
from gpaw.xc.mgga import PurePython2DMGGAKernel
kernel = PurePython2DMGGAKernel(name, parameters)
elif name[0].isdigit():
from gpaw.xc.parametrizedxc import ParametrizedKernel
kernel = ParametrizedKernel(name)
else:
kernel = LibXC(kernel)
if kernel.type == 'LDA':
return LDA(kernel)
elif kernel.type == 'GGA':
return GGA(kernel)
else:
return MGGA(kernel)
class VDWFunctional(GGA):
"""Base class for vdW-DF."""
def __init__(
self,
name,
world=None,
q0cut=5.0,
phi0=0.5,
ds=1.0,
Dmax=20.0,
nD=201,
ndelta=21,
soft_correction=False,
kernel=None,
Zab=None,
vdwcoef=1.0,
verbose=False,
energy_only=False,
):
"""vdW-DF.
parameters:
name: str
Name of functional.
world: MPI communicator
Communicator to parallelize over. Defaults to gpaw.mpi.world.
q0cut: float
Maximum value for q0.
phi0: float
Smooth value for phi(0,0).
ds: float
Cutoff for smooth kernel.
Dmax: float
Maximum value for D.
nD: int
Number of values for D in kernel-table.
ndelta: int
Number of values for delta in kernel-table.
soft_correction: bool
Correct for soft kernel.
kernel:
Which kernel to use.
Zab:
parameter in nonlocal kernel.
vdwcoef: float
Scaling of vdW energy.
verbose: bool
Print useful information.
"""
if world is None:
self.world = mpi.world
else:
self.world = world
self.q0cut = q0cut
self.phi0 = phi0
self.ds = ds
self.delta_i = np.linspace(0, 1.0, ndelta)
self.D_j = np.linspace(0, Dmax, nD)
self.verbose = verbose
self.read_table()
self.soft_correction = soft_correction
if soft_correction:
dD = self.D_j[1]
self.C_soft = np.dot(self.D_j ** 2, self.phi_ij[0]) * 4 * pi * dD
self.gd = None
self.energy_only = energy_only
self.timer = nulltimer
if name == "vdW-DF":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_PBE_R+LDA_C_PW")
Zab = -0.8491
elif name == "vdW-DF2":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_RPW86+LDA_C_PW")
Zab = -1.887
elif name == "optPBE-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_OPTPBE_VDW+LDA_C_PW")
Zab = -0.8491
elif name == "optB88-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_OPTB88_VDW+LDA_C_PW")
Zab = -0.8491
elif name == "C09-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_C09X+LDA_C_PW")
Zab = -0.8491
else:
assert kernel is not None and Zab is not None
self.Zab = Zab
GGA.__init__(self, kernel)
self.vdwcoef = vdwcoef
self.name = name
self.LDAc = LibXC("LDA_C_PW")
def get_setup_name(self):
return "revPBE"
def initialize(self, density, hamiltonian, wfs, occupations):
self.timer = wfs.timer
def get_Ecnl(self):
return self.Ecnl
def calculate_gga(self, e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg):
GGA.calculate_gga(self, e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg)
eLDAc_g = self.gd.empty()
vLDAc_sg = self.gd.zeros(1)
if self.vdwcoef == 0.0:
return
if len(n_sg) == 1:
self.LDAc.calculate(eLDAc_g, n_sg, vLDAc_sg)
e = self.get_non_local_energy(n_sg[0], sigma_xg[0], eLDAc_g, vLDAc_sg[0], dedn_sg[0], dedsigma_xg[0])
else:
n_sg = n_sg.sum(0)
n_sg.shape = (1,) + n_sg.shape
self.LDAc.calculate(eLDAc_g, n_sg, vLDAc_sg)
v_g = np.zeros_like(e_g)
deda2nl_g = np.zeros_like(e_g)
a2_g = sigma_xg[0] + 2 * sigma_xg[1] + sigma_xg[2]
e = self.get_non_local_energy(n_sg[0], a2_g, eLDAc_g, vLDAc_sg[0], v_g, deda2nl_g)
dedsigma_xg[0] += self.vdwcoef * deda2nl_g
dedsigma_xg[1] += self.vdwcoef * 2 * deda2nl_g
dedsigma_xg[2] += self.vdwcoef * deda2nl_g
dedn_sg += self.vdwcoef * v_g
if self.gd.comm.rank == 0:
e_g[0, 0, 0] += self.vdwcoef * e / self.gd.dv
def get_non_local_energy(self, n_g=None, a2_g=None, e_LDAc_g=None, v_LDAc_g=None, v_g=None, deda2_g=None):
"""Calculate non-local correlation energy.
parameters:
n_g: ndarray
Density.
a2_g: ndarray
Absolute value of the gradient of the density - squared.
e_LDAc_g: ndarray
LDA correlation energy density.
"""
gd = self.gd
n_g = n_g.clip(1e-7, np.inf)
# Calculate q0 and cut it off smoothly at q0cut:
kF_g = (3 * pi ** 2 * n_g) ** (1.0 / 3.0)
q0_g, dhdx_g = hRPS(kF_g - 4 * pi / 3 * e_LDAc_g / n_g - self.Zab / 36 / kF_g * a2_g / n_g ** 2, self.q0cut)
if self.verbose:
print ("VDW: q0 (min, mean, max): (%f, %f, %f)" % (q0_g.min(), q0_g.mean(), q0_g.max()))
if self.soft_correction:
dEcnl = gd.integrate(n_g ** 2 / q0_g ** 3) * 0.5 * self.C_soft
else:
dEcnl = 0.0
# Distribute density and q0 to all processors:
n_g = gd.collect(n_g, broadcast=True)
q0_g = gd.collect(q0_g, broadcast=True)
if not self.energy_only:
self.dhdx_g = gd.collect(dhdx_g, broadcast=True)
Ecnl = self.calculate_6d_integral(n_g, q0_g, a2_g, e_LDAc_g, v_LDAc_g, v_g, deda2_g)
Ecnl += dEcnl
self.Ecnl = Ecnl
return Ecnl
def read_table(self):
name = "phi-%.3f-%.3f-%.3f-%d-%d.pckl" % (self.phi0, self.ds, self.D_j[-1], len(self.delta_i), len(self.D_j))
if "GPAW_VDW" in os.environ:
print "Use of GPAW_VDW is deprecated."
print "Put", name, "in your GPAW_SETUP_PATH directory."
dirs = [os.environ["GPAW_VDW"]]
else:
dirs = setup_paths + ["."]
for dir in dirs:
filename = os.path.join(dir, name)
if os.path.isfile(filename):
self.phi_ij = pickle.load(open(filename))
if self.verbose:
print "VDW: using", filename
return
print "VDW: Could not find table file:", name
self.make_table(name)
def make_table(self, name):
print "VDW: Generating vdW-DF kernel ..."
print "VDW:",
ndelta = len(self.delta_i)
nD = len(self.D_j)
self.phi_ij = np.zeros((ndelta, nD))
for i in range(self.world.rank, ndelta, self.world.size):
print ndelta - i,
sys.stdout.flush()
delta = self.delta_i[i]
for j in range(nD - 1, -1, -1):
D = self.D_j[j]
d = D * (1.0 + delta)
dp = D * (1.0 - delta)
if d ** 2 + dp ** 2 > self.ds ** 2:
self.phi_ij[i, j] = phi(d, dp)
else:
P = np.polyfit(
[0, self.D_j[j + 1] ** 2, self.D_j[j + 2] ** 2],
[self.phi0, self.phi_ij[i, j + 1], self.phi_ij[i, j + 2]],
2,
)
self.phi_ij[i, : j + 3] = np.polyval(P, self.D_j[: j + 3] ** 2)
break
self.world.sum(self.phi_ij)
print
print "VDW: Done!"
if self.world.rank == 0:
pickle.dump(self.phi_ij, open(name, "w"), pickle.HIGHEST_PROTOCOL)
def make_prl_plot(self, multiply_by_4_pi_D_squared=True):
import pylab as plt
x = np.linspace(0, 8.0, 100)
for delta in [0, 0.5, 0.9]:
y = [self.phi(D * (1.0 + delta), D * (1.0 - delta)) for D in x]
if multiply_by_4_pi_D_squared:
y *= 4 * pi * x ** 2
plt.plot(x, y, label=r"$\delta=%.1f$" % delta)
plt.legend(loc="best")
plt.plot(x, np.zeros(len(x)), "k-")
plt.xlabel("D")
plt.ylabel(r"$4\pi D^2 \phi(\rm{Hartree})$")
plt.show()
def phi(self, d, dp):
"""Kernel function.
Uses bi-linear interpolation and returns zero for D > Dmax.
"""
P = self.phi_ij
D = (d + dp) / 2.0
if D < 1e-14:
return P[0, 0]
if D >= self.D_j[-1]:
return 0.0
delta = abs((d - dp) / (2 * D))
ddelta = self.delta_i[1]
x = delta / ddelta
i = int(x)
if i == len(self.delta_i) - 1:
i -= 1
x = 1.0
else:
x -= i
dD = self.D_j[1]
y = D / dD
j = int(y)
y -= j
return x * (y * P[i + 1, j + 1] + (1 - y) * P[i + 1, j]) + (1 - x) * (y * P[i, j + 1] + (1 - y) * P[i, j])
from gpaw.xc.libxc import LibXC
from math import pi
import numpy as np
nspins = 1
for name in [
'LDA',
'PBE',
'revPBE',
'RPBE',
'LDA_X',
'GGA_X_PBE_R',
'GGA_X_RPBE',
'LDA_C_PW',
]:
xc = LibXC(name)
xc.initialize(nspins)
libxc = xc.xc
lxc_fxc = libxc.calculate_fxc_spinpaired
lxc_fxc_fd = libxc.calculate_fxc_fd_spinpaired
na = 2.0
if nspins == 2:
nb = 1.0
else:
nb = 0.0
print na, nb
if (nb > 0.0): assert (nspins == 2)
if nspins == 2:
sigma0 = 2.0 # (0.0, 1.0, 1.0)
sigma1 = 2.0
sigma2 = 5.0 # (1.0, 2.0, 0.0)
import numpy as np
from gpaw.xc.libxc import LibXC, short_names
from gpaw.xc.kernel import XCKernel, codes
from gpaw.xc.bee import BEE1
functionals = [LibXC(name) for name in short_names]
functionals += [XCKernel(name) for name in codes]
functionals += [BEE1()]
#name = 'LDA'
#name = 'PBE'
#functionals = [LibXC('MGGA_X_TPSS')]
# XCKernel(name)]
#functionals = [f for f in functionals if f.type=='MGGA']
def f1(n_xg, xc):
e_g = np.empty_like(n_xg[0])
n_sg = n_xg[:1]
sigma_xg = n_xg[1:2]
tau_sg = n_xg[2:]
dedn_sg = np.zeros_like(n_sg)
dedsigma_xg = np.zeros_like(sigma_xg)
dedtau_sg = np.zeros_like(tau_sg)
xc.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg, tau_sg, dedtau_sg)
return e_g, np.concatenate((dedn_sg, dedsigma_xg, dedtau_sg))
def f2(n_xg, xc):
e_g = np.empty_like(n_xg[0])
n_sg = n_xg[:2]
sigma_xg = n_xg[2:5]
tau_sg = n_xg[5:]
dedn_sg = np.zeros_like(n_sg)
from gpaw.xc.libxc import LibXC
from math import pi
import numpy as np
nspins = 1
for name in [
'LDA', 'PBE', 'revPBE', 'RPBE',
'LDA_X', 'GGA_X_PBE_R', 'GGA_X_RPBE',
'LDA_C_PW',
]:
xc = LibXC(name)
xc.initialize(nspins)
libxc = xc.xc
lxc_fxc = libxc.calculate_fxc_spinpaired
lxc_fxc_fd = libxc.calculate_fxc_fd_spinpaired
na = 2.0
if nspins == 2:
nb = 1.0
else:
nb = 0.0
print na, nb
if (nb > 0.0): assert (nspins == 2)
if nspins == 2:
sigma0 = 2.0 # (0.0, 1.0, 1.0)
sigma1 = 2.0
sigma2 = 5.0 # (1.0, 2.0, 0.0)
else:
sigma0 = 2.0 # (0.0, 1.0, 1.0)
sigma1 = 0.0
sigma2 = 0.0
taua=(3.*pi**2)**(2./3.)*na**(5./3.)/2.*sigma0
def vdw_df2(*args, **kwargs):
return VDWXC(semilocal_xc=GGA(LibXC('GGA_X_RPW86+LDA_C_PW')),
name='vdW-DF2',
*args,
**kwargs)
import numpy as np
from gpaw.xc.libxc import LibXC, short_names
from gpaw.xc.kernel import XCKernel, codes
from gpaw.test import equal
funcs = []
modes = []
for name in short_names:
try:
LibXC(name)
except NameError:
continue
funcs.append(name)
modes.append(0)
for name in codes:
funcs.append(name)
modes.append(1)
def create_xc(func, mode):
isinstance(func, str)
isinstance(mode, int)
if mode == 0:
xc = LibXC(func)
else:
xc = XCKernel(func)
return xc
def f1(n_xg, xc):
e_g = np.empty_like(n_xg[0])
class VDWFunctionalBase:
"""Base class for vdW-DF."""
def __init__(self,
world=None,
Zab=-0.8491,
vdwcoef=1.0,
q0cut=5.0,
phi0=0.5,
ds=1.0,
Dmax=20.0,
nD=201,
ndelta=21,
soft_correction=False,
setup_name='revPBE',
verbose=False,
energy_only=False):
"""vdW-DF.
parameters:
name: str
Name of functional.
world: MPI communicator
Communicator to parallelize over. Defaults to gpaw.mpi.world.
q0cut: float
Maximum value for q0.
phi0: float
Smooth value for phi(0,0).
ds: float
Cutoff for smooth kernel.
Dmax: float
Maximum value for D.
nD: int
Number of values for D in kernel-table.
ndelta: int
Number of values for delta in kernel-table.
soft_correction: bool
Correct for soft kernel.
kernel:
Which kernel to use.
Zab:
parameter in nonlocal kernel.
vdwcoef: float
Scaling of vdW energy.
verbose: bool
Print useful information.
"""
if world is None:
self.world = mpi.world
else:
self.world = world
self.Zab = Zab
self.vdwcoef = vdwcoef
self.q0cut = q0cut
self.phi0 = phi0
self.ds = ds
self.delta_i = np.linspace(0, 1.0, ndelta)
self.D_j = np.linspace(0, Dmax, nD)
self.verbose = verbose
self.read_table()
self.soft_correction = soft_correction
if soft_correction:
dD = self.D_j[1]
self.C_soft = np.dot(self.D_j**2, self.phi_ij[0]) * 4 * pi * dD
self.gd = None
self.energy_only = energy_only
self.timer = nulltimer
self.LDAc = LibXC('LDA_C_PW')
self.setup_name = setup_name
def get_setup_name(self):
return self.setup_name
def get_Ecnl(self):
return self.Ecnl
def calculate_impl(self, gd, n_sg, v_sg, e_g):
sigma_xg, dedsigma_xg, gradn_svg = gga_vars(gd, self.grad_v, n_sg)
self.calculate_exchange(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
self.calculate_correlation(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
add_gradient_correction(self.grad_v, gradn_svg, sigma_xg, dedsigma_xg,
v_sg)
def calculate_exchange(self, e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg):
raise NotImplementedError
def calculate_correlation(self, e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg):
eLDAc_g = self.gd.empty()
vLDAc_sg = self.gd.zeros(1)
if self.vdwcoef == 0.0:
return
if len(n_sg) == 1:
self.LDAc.calculate(eLDAc_g, n_sg, vLDAc_sg)
e = self.get_non_local_energy(n_sg[0], sigma_xg[0], eLDAc_g,
vLDAc_sg[0], dedn_sg[0],
dedsigma_xg[0])
else:
n_sg = n_sg.sum(0)
n_sg.shape = (1, ) + n_sg.shape
self.LDAc.calculate(eLDAc_g, n_sg, vLDAc_sg)
v_g = np.zeros_like(e_g)
deda2nl_g = np.zeros_like(e_g)
a2_g = sigma_xg[0] + 2 * sigma_xg[1] + sigma_xg[2]
e = self.get_non_local_energy(n_sg[0], a2_g, eLDAc_g, vLDAc_sg[0],
v_g, deda2nl_g)
dedsigma_xg[0] += self.vdwcoef * deda2nl_g
dedsigma_xg[1] += self.vdwcoef * 2 * deda2nl_g
dedsigma_xg[2] += self.vdwcoef * deda2nl_g
dedn_sg += self.vdwcoef * v_g
if self.gd.comm.rank == 0:
e_g[0, 0, 0] += self.vdwcoef * e / self.gd.dv
def get_non_local_energy(self,
n_g=None,
a2_g=None,
e_LDAc_g=None,
v_LDAc_g=None,
v_g=None,
deda2_g=None):
"""Calculate non-local correlation energy.
parameters:
n_g: ndarray
Density.
a2_g: ndarray
Absolute value of the gradient of the density - squared.
e_LDAc_g: ndarray
LDA correlation energy density.
"""
gd = self.gd
n_g = n_g.clip(1e-7, np.inf)
# Calculate q0 and cut it off smoothly at q0cut:
kF_g = (3 * pi**2 * n_g)**(1.0 / 3.0)
q0_g, dhdx_g = hRPS(
kF_g - 4 * pi / 3 * e_LDAc_g / n_g -
self.Zab / 36 / kF_g * a2_g / n_g**2, self.q0cut)
if self.verbose:
print(('VDW: q0 (min, mean, max): (%f, %f, %f)' %
(q0_g.min(), q0_g.mean(), q0_g.max())))
if self.soft_correction:
dEcnl = -gd.integrate(n_g**2 / q0_g**3) * 0.5 * self.C_soft
else:
dEcnl = 0.0
# Distribute density and q0 to all processors:
n_g = gd.collect(n_g, broadcast=True)
q0_g = gd.collect(q0_g, broadcast=True)
if not self.energy_only:
self.dhdx_g = gd.collect(dhdx_g, broadcast=True)
Ecnl = self.calculate_6d_integral(n_g, q0_g, a2_g, e_LDAc_g, v_LDAc_g,
v_g, deda2_g)
Ecnl += dEcnl
self.Ecnl = Ecnl
return Ecnl
def read_table(self):
name = ('phi-%.3f-%.3f-%.3f-%d-%d.txt' %
(self.phi0, self.ds, self.D_j[-1], len(
self.delta_i), len(self.D_j)))
dirs = setup_paths + ['.']
for dir in dirs:
filename = os.path.join(dir, name)
if os.path.isfile(filename):
self.phi_ij = np.loadtxt(filename)
if self.verbose:
print('VDW: using', filename)
return
if sys.version_info[0] == 2:
oldname = name[:-3] + 'pckl'
for dir in dirs:
filename = os.path.join(dir, oldname)
if os.path.isfile(filename):
self.phi_ij = pickle.load(open(filename, 'rb'))
if self.verbose:
print('VDW: using', filename)
return
print('VDW: Could not find table file:', name)
self.make_table(name)
def make_table(self, name):
print('VDW: Generating vdW-DF kernel ...')
print('VDW:', end=' ')
ndelta = len(self.delta_i)
nD = len(self.D_j)
self.phi_ij = np.zeros((ndelta, nD))
for i in range(self.world.rank, ndelta, self.world.size):
print(ndelta - i, end=' ')
sys.stdout.flush()
delta = self.delta_i[i]
for j in range(nD - 1, -1, -1):
D = self.D_j[j]
d = D * (1.0 + delta)
dp = D * (1.0 - delta)
if d**2 + dp**2 > self.ds**2:
with seterr(divide='ignore'):
self.phi_ij[i, j] = phi(d, dp)
else:
P = np.polyfit([0, self.D_j[j + 1]**2, self.D_j[j + 2]**2],
[
self.phi0, self.phi_ij[i, j + 1],
self.phi_ij[i, j + 2]
], 2)
self.phi_ij[i, :j + 3] = np.polyval(P, self.D_j[:j + 3]**2)
break
self.world.sum(self.phi_ij)
print()
print('VDW: Done!')
header = ('phi0={0:.3f}, ds={1:.3f}, Dmax={2:.3f}, nD={3}, ndelta={4}'.
format(self.phi0, self.ds, self.D_j[-1], len(self.delta_i),
len(self.D_j)))
if self.world.rank == 0:
np.savetxt(name, self.phi_ij, header=header)
def make_prl_plot(self, multiply_by_4_pi_D_squared=True):
import pylab as plt
x = np.linspace(0, 8.0, 100)
for delta in [0, 0.5, 0.9]:
y = [self.phi(D * (1.0 + delta), D * (1.0 - delta)) for D in x]
if multiply_by_4_pi_D_squared:
y *= 4 * pi * x**2
plt.plot(x, y, label=r'$\delta=%.1f$' % delta)
plt.legend(loc='best')
plt.plot(x, np.zeros(len(x)), 'k-')
plt.xlabel('D')
plt.ylabel(r'$4\pi D^2 \phi(\rm{Hartree})$')
plt.show()
def phi(self, d, dp):
"""Kernel function.
Uses bi-linear interpolation and returns zero for D > Dmax.
"""
P = self.phi_ij
D = (d + dp) / 2.0
if D < 1e-14:
return P[0, 0]
if D >= self.D_j[-1]:
return 0.0
delta = abs((d - dp) / (2 * D))
ddelta = self.delta_i[1]
x = delta / ddelta
i = int(x)
if i == len(self.delta_i) - 1:
i -= 1
x = 1.0
else:
x -= i
dD = self.D_j[1]
y = D / dD
j = int(y)
y -= j
return (x * (y * P[i + 1, j + 1] + (1 - y) * P[i + 1, j]) + (1 - x) *
(y * P[i, j + 1] + (1 - y) * P[i, j]))
from math import pi
import numpy as np
from gpaw.xc.libxc import LibXC
x0 = LibXC('LDA_X')
def f0(xc, rs, s):
n = 3 / (4 * pi * rs**3)
third = 1.0 / 3.0
kF = (3 * pi**2 * n)**third
a2 = (2 * kF * n * s)**2
e = np.zeros(1)
xc.calculate(e,
np.array([[n]]), np.zeros((1, 1)),
np.array([[a2]]), np.zeros((1, 1)))
exc = n * e[0]
x0.calculate(e, np.array([[n]]), np.zeros((1, 1)))
ex0 = n * e[0]
return exc / ex0
def f1(xc, rs, s):
n = 3 / (4 * pi * rs**3)
# na = 2 * n
third = 1.0 / 3.0
kF = (3 * pi**2 * n)**third
a2 = (2 * kF * n * s)**2
e = np.zeros(1)
xc.calculate(e,
np.array([[n], [0]]), np.zeros((2, 1)),
np.array([[a2], [0], [0]]), np.zeros((3, 1)))
exc = n * e[0]
def vdw_df(*args, **kwargs):
return VDWXC(semilocal_xc=GGA(LibXC('GGA_X_PBE_R+LDA_C_PW')),
name='vdW-DF',
*args,
**kwargs)
def __init__(
self,
name,
world=None,
q0cut=5.0,
phi0=0.5,
ds=1.0,
Dmax=20.0,
nD=201,
ndelta=21,
soft_correction=False,
kernel=None,
Zab=None,
vdwcoef=1.0,
verbose=False,
energy_only=False,
):
"""vdW-DF.
parameters:
name: str
Name of functional.
world: MPI communicator
Communicator to parallelize over. Defaults to gpaw.mpi.world.
q0cut: float
Maximum value for q0.
phi0: float
Smooth value for phi(0,0).
ds: float
Cutoff for smooth kernel.
Dmax: float
Maximum value for D.
nD: int
Number of values for D in kernel-table.
ndelta: int
Number of values for delta in kernel-table.
soft_correction: bool
Correct for soft kernel.
kernel:
Which kernel to use.
Zab:
parameter in nonlocal kernel.
vdwcoef: float
Scaling of vdW energy.
verbose: bool
Print useful information.
"""
if world is None:
self.world = mpi.world
else:
self.world = world
self.q0cut = q0cut
self.phi0 = phi0
self.ds = ds
self.delta_i = np.linspace(0, 1.0, ndelta)
self.D_j = np.linspace(0, Dmax, nD)
self.verbose = verbose
self.read_table()
self.soft_correction = soft_correction
if soft_correction:
dD = self.D_j[1]
self.C_soft = np.dot(self.D_j ** 2, self.phi_ij[0]) * 4 * pi * dD
self.gd = None
self.energy_only = energy_only
self.timer = nulltimer
if name == "vdW-DF":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_PBE_R+LDA_C_PW")
Zab = -0.8491
elif name == "vdW-DF2":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_RPW86+LDA_C_PW")
Zab = -1.887
elif name == "optPBE-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_OPTPBE_VDW+LDA_C_PW")
Zab = -0.8491
elif name == "optB88-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_OPTB88_VDW+LDA_C_PW")
Zab = -0.8491
elif name == "C09-vdW":
assert kernel is None and Zab is None
kernel = LibXC("GGA_X_C09X+LDA_C_PW")
Zab = -0.8491
else:
assert kernel is not None and Zab is not None
self.Zab = Zab
GGA.__init__(self, kernel)
self.vdwcoef = vdwcoef
self.name = name
self.LDAc = LibXC("LDA_C_PW")
class BEEVDWKernel(XCKernel):
"""Kernel for BEEVDW functionals."""
def __init__(self, bee, xcoefs, ldac, ggac):
"""BEEVDW kernel.
parameters:
bee : str
choose BEE1 or BEE2 exchange basis expansion.
xcoefs : array
coefficients for exchange.
ldac : float
coefficient for LDA correlation.
pbec : float
coefficient for PBE correlation.
"""
if bee == 'BEE2':
self.BEE = BEE2(xcoefs)
self.GGAc = LibXC('GGA_C_PBE')
self.xtype = 'GGA'
self.type = 'GGA'
elif bee == 'BEE3':
self.BEE = LibXC('MGGA_X_MBEEFVDW')
self.GGAc = LibXC('GGA_C_PBE_SOL')
self.xtype = 'MGGA'
self.type = 'MGGA'
else:
raise ValueError('Unknown BEE exchange: %s', bee)
self.LDAc = LibXC('LDA_C_PW')
self.ldac = ldac
self.ggac = ggac
if bee in ['BEE1', 'BEE2']:
self.ggac -= 1.0
self.name = 'BEEVDW'
def calculate(self, e_g, n_sg, dedn_sg,
sigma_xg=None, dedsigma_xg=None,
tau_sg=None, dedtau_sg=None):
if debug:
self.check_arguments(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg,
tau_sg, dedtau_sg)
if self.xtype == 'GGA':
self.BEE.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg)
elif self.xtype == 'MGGA':
self.BEE.calculate(e_g, n_sg, dedn_sg, sigma_xg, dedsigma_xg,
tau_sg, dedtau_sg)
else:
raise ValueError('Unexpected value of xtype:', self.xtype)
e0_g = np.empty_like(e_g)
dedn0_sg = np.empty_like(dedn_sg)
dedsigma0_xg = np.empty_like(dedsigma_xg)
for coef, kernel in [(self.ldac, self.LDAc),
(self.ggac, self.GGAc)]:
dedn0_sg[:] = 0.0
kernel.calculate(e0_g, n_sg, dedn0_sg, sigma_xg, dedsigma0_xg)
e_g += coef * e0_g
dedn_sg += coef * dedn0_sg
if kernel.type == 'GGA':
dedsigma_xg += coef * dedsigma0_xg