[QE-users] DFT+U and metastable states

[Mahmoud Payami Shabestari]

Dear QE-users/Developers,



Hi.

I am trying to do an SCF calculation on a system with AFM order in 
z-direction with a metallic impurity atom in the unit cell.

I am employing the simplest version of DFT+U (lda_plus_u_kind=0) and QE-6.7.

The values of Hubbard_U is set to some non-zero value for the spin-up and 
spin-down atoms.

It is seen from the eigenvalues after iteration #1:



------------------------------------------

atom    1   Tr[ns(na)] (up, down, total) =   0.67656  0.33866  1.01522
   spin  1
    eigenvalues:
  0.057  0.060  0.060  0.111  0.111  0.116  0.162

   spin  2
    eigenvalues:
  0.037  0.037  0.039  0.041  0.041  0.044  0.101


atom    2   Tr[ns(na)] (up, down, total) =   0.38044  2.32226  2.70270
   spin  1
    eigenvalues:
  0.033  0.033  0.035  0.053  0.058  0.077  0.093

   spin  2
    eigenvalues:
  0.091  0.121  0.126  0.191  0.372  0.656  0.766

------------------------------------------



that we should have (?)  total number of 3x5=15 metastable states.



To discover the properties of those states, I used the following 15 
different combinations of "starting_ns_eigenvalues":



----------------------------

    starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0
    starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0
    starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0
    starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0
    starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0
    starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0
    starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0
    starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0
    starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0
    starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0
    starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0
    starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0
    starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0
    starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0
    starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0

---------------------------------------

and performed the 15 scf calculations. 

Surprisingly, I got the same results for the total energies for all 15 
different inputs:



------------------------------

!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry
!    total energy              =    -879.68389676 Ry

-------------------------------------------

On the other hand, the convergency has been achieved with different numbers 
of iterations:



-----------------------------

     convergence has been achieved in  70 iterations
     convergence has been achieved in  58 iterations
     convergence has been achieved in  48 iterations
     convergence has been achieved in  67 iterations
     convergence has been achieved in  57 iterations
     convergence has been achieved in  65 iterations
     convergence has been achieved in  52 iterations
     convergence has been achieved in  72 iterations
     convergence has been achieved in  59 iterations
     convergence has been achieved in  48 iterations
     convergence has been achieved in  54 iterations
     convergence has been achieved in  57 iterations
     convergence has been achieved in  46 iterations
     convergence has been achieved in  70 iterations
     convergence has been achieved in  62 iterations
---------------------------------------



Now question arises:

1- If the total energies are the same, maybe the QE code, irrespective of 
the starting_ns_eigenvalues, leads the system to global-minimum (or specific 
state) state ?

2- Why the number of convergency iterations differ?



Any comments is highly appreciated. 



With kind regards,

Mahmoud Payami



AEOI, Tehran, Iran

Email: mpayami at aeoi.org.ir

Phone: +98 (0)21 82066504



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