toxa81
commented
3 years ago For SIRIUS we should change the way Hubbard orbitals are loaded. We either set the atomic orbital for a particular ℓ-channel (allow multiple ℓ-channels) or we set plane-wave coefficients of the Wannier orbital. In the former case we give either a scalar orbital and provide ℓ or spinor orbital and provide j. The m-index will be expanded later by SIRIUS. In the later case we should set ℓ and then provide 2ℓ+1 sets of plane-wave coefficients for each k-point.
The averaging of the Hubbard radial functions should happen on the QE side.
Possible API:
! assume that atomic orbitals psi is already prepared by QE
! loop over atom types
do iat=1,nat
! loop over Hubbard orbitals of a given atom type
do iorb=1,norb(iat)
! get orbital quantum number
l = l_of_orbital(iorb, iat)
! get principal quantum number
n = n_of_orbital(iorb, iat)
! get occupancy
occ = o_of_orbital(iorb, iat)
! add Hubbard orbital and specify radial atomic part
call sirius_add_hubbard_orbital(sim_ctx, label(iat), n, l, occ, U(iorb, iat), J(irob, iat), f=psi(:, iorb, iat))
enddo
enddo
! for Wannier orbitals
call sirius_add_hubbard_orbital(sim_ctx, 'Ni', n=3, l=2, occupancy, U, J)
! and then later for k-points
do ik=1,nk
i = 0
do ia=1,nat
do orb=1,norb
l = l_of_psi(orb, ia)
do m = -l, l
i = i + 1
call sirius_add_hubbard_orbital_k(ks_handler, ik, ia, l,
enddo 
mtaillefumier
timrov
haampie
This is a placeholder to discuss the indexing of Hubbard orbitals. In QE Hubbard orbitals can be generated either from pseudo-atomic radial wave-functions (stored in the UPF) or from the Wannier functions.
Atomic orbitals
UPF files can be of two kinds: "normal" and "relativistic". In the first case pseudo-atomic orbitals are labeled by orbital quantum number ℓ={s,p,d,f}. In the second case pseudo-atomic wave functions should be 2-component spinors with "major" and "minor" components (in reality they are not, only one components is stored. which? "major"?) and are labeled by the total orbital quantum number j. For example, for d-shell one will find j=3/2 and j=5/2 radial wave-functions. Later, the QE code will create an average radial wave-function out of two (supposedly "major") 3/2 and 5/2 components. So basically, in SO case the code still deals with scalar {s,p,d,f}-like orbitals.
For non-magnetic calculation the Hubbard orbital basis is just |nℓm> localized pseudo-atomic functions. For magnetic collinear it is basically the same, just transformed into pure spinors (|nℓm>, 0) and (0, |nℓm>) but we can think of them as of scalar functions without a spin index. The non-collinear case is not clear. Are localized functions the same as in collinear case?
Wannier orbitals Wannier orbitals are created from the unitary transformation of Bloch KS wave-functions. They look similar to the atomic orbitals (let's think of them as 2ℓ+1 orthogonal functions). In magnetic collinear case the wave-functions have spin-up and spin-down channels and correspondingly, Wannier functions become spin-dependent. In the non-collinear case the KS wave-functions are two-component spinors. The Wannier functions, in principle, should also be two-component spinors. The number of such functions should be (2ℓ+1)
To summarize: in the case of atomic orbitals the number of independent Hubbard orbitals is 2ℓ+1 because, basically, this the only information about pseudo-atomic wave-functions, obtained from the UPF files. In case of Wannier orbitals the number of independent Hubbard orbitals is N_spin * (2ℓ+1) and in case of non-collinear magnetism each of the 2(2ℓ+1) Wannier functions has two components.
When we index Hubbard orbitals, we can stay in "spin-up", "spin-down" notation only if Hubbard orbitals are the pure spinors of (|phi>, 0) (0, |phi>) kind. Is it the case in current LDA+U implementation of QE?