[Octopus-users] integration

[Miguel Marques]

  Dear Emily,

  The density in octopus is normalized in the grid. This means that

sum_i n(i) * vol_pp

  must integrate exactly to the number of electrons. Maybe in your test
you did not include all significant digits (or a conversion from Ang to
Hartree with a factor different from the one used internally)?

  cheers,
  Miguel

Emily wrote:
> Hello Octopus Users,
> 
> I would like to know how Octopus normalizes the wavefunctions...is it on
> a grid or are there some underlying functions (existant or created by
> the numbers on the grid) that are numerically integrated?
> 
> I ask because I added up the density on every point in my grid and
> multiplied by a volume element (grid spacing in x,y,z directions
> multiplied by each other), and this number nearly matched the total
> number of electrons in my system, but was very slightly over (error in
> the 5th significant digit).  Then I did a spline interpolation to
> octuple the number of points in my grid and repeated the process and got
> slightly fewer electrons (error in the 3rd significant digit).  And if
> Octopus normalizes by summing on the grid, I would expect an
> interpolation to reduce the agreement between its number of electrons
> and mine, but if you are normalizing some underlying function, then by
> getting closer to that underlying function with an interpolation I'd
> expect to improve my agreement.
> 
> Can anybody comment?
> 
> Thanks very much,
> Emily 
> 
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> Octopus-users at tddft.org
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> 


-- 
Dr. Miguel A. L. Marques
marques at tddft.org

Laboratoire de Physique de la Matière Condensée et Nanostructures
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