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 realvalued 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
Typename 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.
Nondistinct 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.