Atomic PAW setups¶
Calculating matrix elements of nabla¶
This integral is needed for LrTDDFT and response function related quantities:
where \(|\phi_i\rangle = \phi_i(\mathbf r) = \phi_j(r)Y_{\ell m}(\hat{\mathbf r})\), and \(|\tilde\phi_i\rangle = \tilde\phi_i(\mathbf r) = \tilde\phi_j(r)Y_{\ell m}(\hat{\mathbf r})\).
Since we use real-valued spherical harmonics, we have:
Splitting the integral in radial and angular parts, we get:
where \(G_{\ell m,\ell'm'}^{\ell''m''}\) are Gaunt coefficents and the
last angular integral has been calculated as Y_LLv
in the
gaunt.py module.
More stuff¶
- class gpaw.setup.Setup(data, xc, lmax=0, basis=None, filter=None)[source]¶
Attributes:
Name
Description
Z
Charge
type
Type-name of setup (eg. ‘paw’)
symbol
Chemical element label (eg. ‘Mg’)
xcname
Name of xc
data
Container class for information on the the atom, eg. Nc, Nv, n_j, l_j, f_j, eps_j, rcut_j. It defines the radial grid by ng and beta, from which r_g = beta * arange(ng) / (ng - arange(ng)). It stores pt_jg, phit_jg, phi_jg, vbar_g
Attributes for making PAW corrections
Name
Description
Delta0
Constant in compensation charge expansion coeff.
Delta_iiL
Linear term in compensation charge expansion coeff.
Delta_pL
Packed version of
Delta_iiL
.dO_ii
Overlap coefficients
B_ii
Projector function overlaps B_ii = <pt_i | pt_i>
dC_ii
Inverse overlap coefficients
E
Reference total energy of atom
M
Constant correction to Coulomb energy
M_p
Linear correction to Coulomb energy
M_pp
2nd order correction to Coulomb energy and Exx energy
Kc
Core kinetic energy
K_p
Linear correction to kinetic energy
ExxC
Core Exx energy
X_p
Linear correction to Exx energy
MB
Constant correction due to vbar potential
MB_p
Linear correction due to vbar potential
dEH0
Constant correction due to average electrostatic potential
dEH_p
Linear correction due to average electrostatic potential
I4_iip
Correction to integrals over 4 all electron wave functions
Nct
Analytical integral of the pseudo core density
nct
It also has the attribute
xc_correction
which is an XCCorrection class instance capable of calculating the corrections due to the xc functional.Splines:
Name
Description
pt_j
Projector functions
phit_j
Pseudo partial waves
vbar
vbar potential
nct
Pseudo core density
ghat_l
Compensation charge expansion functions
tauct
Pseudo core kinetic energy density
- calculate_projector_overlaps(pt_jg)[source]¶
Compute projector function overlaps B_ii = <pt_i | pt_i>.
- class gpaw.setup.Setups(Z_a, setup_types, basis_sets, xc, filter=None, world=None)[source]¶
Collection of Setup objects. One for each distinct atom.
Non-distinct atoms are those with the same atomic number, setup, and basis.
Class attributes:
nvalence
Number of valence electrons.nao
Number of atomic orbitals.Eref
Reference energy.core_charge
Core hole charge.