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cleaned the procedure for locating maxR #575

Merged
merged 4 commits into from
Jun 7, 2023
Merged

cleaned the procedure for locating maxR #575

merged 4 commits into from
Jun 7, 2023

Commits on Jun 7, 2023

  1. cleaned the procedure for locating maxR 

    Instead of searching for a 0 in the radial function
we now search for an integration that contians 99.99% of the
radial function.
The integration uses the trapezoid integration mechanism
with f(r)**2*r**3 as that should be normalized for a
radial function.

This should make it much more stable against different radial
function arguments and produce more accurate ranges for the
orbitals.

Now a warning will be issued when the routine cannot determine
a correct R (based on inputs).

Ensured that all orbitals with radial functions
can pre-calculate the R in case user did not supply it.
One can always forcefully set it by supplying it.

Signed-off-by: Nick Papior <[email protected]>
    @zerothi
    zerothi committed Jun 7, 2023
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  2. handed control of R discovery to the end-user 

    This way we can converge faster to a better approach than
the current absolute value of the functional integral.

Tried functions:
1. f(r)  ->  problematic when f turns negative
2. f(r) ** 2 -> yields somewhat short R
3. f(r) * r -> problematic when f turns negative
4. (f(r) * r)**2 -> yields too short R
5. f(r)**2 * r**3 -> much better
6. abs(f(r)) -> yields a pretty long tail, but should be fine

With the current approach users can manually control
the behaviour by supplying a dictionary which passed
the arguments to the radial_minimize_range method.

Signed-off-by: Nick Papior <[email protected]>
    @zerothi
    zerothi committed Jun 7, 2023
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  3. amended typing and added dr argument 

    dr argument controls the precision of the integrals.

Signed-off-by: Nick Papior <[email protected]>
    @zerothi
    zerothi committed Jun 7, 2023
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  4. Ensured orbital copy passes over the R value 

    This ensures that copying does not destroy the R value.
Added tests for all orbital classes to ensure
it is copied over correctly.

Signed-off-by: Nick Papior <[email protected]>
    @zerothi
    zerothi committed Jun 7, 2023
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