[Pw_forum] Occupation matrix in LDA+U

[Matteo Cococcioni]

Dear Luca and Fabio

here are my answers.

1) the diagonal elements of the occupation matrix are the projection on 
the atomic orbitals in the order
you wrote. Of course also non diagonal elements are associated with d 
orbitals. they are not projection strictly
speaking but you can see them as generalized overlap terms between d 
atomic orbitals in the subspace of occupied Kohn-Sham states.

2) yes. from Doc/INPUT_PW:

   +--------------------------------------------------------------------
   Variable:       starting_ns_eigenvalue(m,ispin,I)

   Type:           REAL
   Default:        -1.d0 that means NOT SET
   Description:    In the first iteration of an LDA+U run it overwrites
                   the m-th eigenvalue of the ns occupation matrix for the
                   ispin component of atomic species I. Leave unchanged
                   eigenvalues that are not set. This is useful to suggest
                   the desired orbital occupations when the default choice
                   takes another path.
   +--------------------------------------------------------------------

keep in mind that you are adjusting the eigenvalue of the matrix. So you 
better give a look at the occupation matrix
and its spectrum after the first iteration of a non constraint run.

hope this helps,

Matteo



elbuesta at icqmail.com wrote:
> Dear all,
>
> We have a fews questions/doubts concerning the ns occupation matrix 
> for LDA+U calculations (starting_ns_eigenvalue(m,ispin,I)). Following 
> the idea presented in example 25 of quantum espresso, we are trying to 
> fix the initial occupation of the "d" orbital of Ni in a monolayer of 
> NiO in an anti-ferromagnetic state. The questions we have are:
>
> 1) Are each of the diagonal elements of the occupation matrix 
> associated with the d orbitals? Something like,
> (1,1) -> dz2, (2,2) -> dzx, (3,3) -> dzy, (4,4) -> d(x2-y2) and  (5,5) 
> -> dxy   ?
> 2) If there is this correspondence, is it possible to specify an 
> initial occupation of each of the orbitals after the initial guess is 
> evaluated in the first iteration? For example, in the attached input, 
> how could we specify that only the dz2, dxz and dyz orbitals are 
> initially completely occupied with 2 electrons? In other words, how 
> can we change the "spin down occupation matrix" of the Ni atom from
> 0.6 0.0 0.0 0.0 0.0            1.0 0.0 0.0 0.0 0.0
> 0.0 0.6 0.0 0.0 0.0            0.0 1.0 0.0 0.0 0.0
> 0.0 0.0 0.6 0.0 0.0     ->    0.0 0.0 1.0 0.0 0.0
> 0.0 0.0 0.0 0.6 0.0            0.0 0.0 0.0 0.0 0.0
> 0.0 0.0 0.0 0.0 0.6            0.0 0.0 0.0 0.0 0.0
> ??
>
> Thanks very much for your time,
> With best regards,
>
> Luca Sementa, Fábio Negreiros
> Postdoc students,
> IPCF - CNR - Pisa, Italy
>
> =
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