[Octopus-users] integration

[Emily]

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