Laplacian method for Species class

[gabrielasd]

This pull request adds support for computing the Laplacian of the electron density and fixes incorrectly assigned second derivative of density values in the numeric dataset compilation script.

Main changes:

• A method named dd_dens_lapl_func is added to the Species class which (similar to dens_func ) returns a callable function. The function is set to zero when evaluated at $r=0$ (with a tolerance of $1.e-10$).
• In the compilation script for the numeric HF dataset, the second derivative of the density was obtained taking the available gradient and Laplacian of the density values (i.e. the second derivative is equated from the formula for the Laplacian evaluated on a radial grid). Here also a tolerance value is used to handle division by zero cases.

[marco-2023]

why not def load_numerical_hf_data(data_path=DEFAULT_DATAPATH): ?

[marco-2023]

Even more, I think this function should not have a default value. The only place where it is used inside run (line 183), a value is passed to this argument. I think the function that could/should have a default value should be the run function (line 155).

[gabrielasd]

Good point!
I think I'll go along the lines of your first suggestion making the change to simply
def load_numerical_hf_data(data_path)

I wouldn't make the change to the run function to keep consistency across all compilation scripts, and since the default path gets defined as kwd argument in the load function from the species module:

AtomDB/atomdb/species.py

Lines 782 to 790 in 511a702

	def load(
	elem,
	charge,
	mult,
	nexc=0,
	dataset=DEFAULT_DATASET,
	datapath=DEFAULT_DATAPATH,
	remotepath=DEFAULT_REMOTE,
	):

The way I see it, the run functions will hardly ever get used directly by the user, so having the default value of datapath only in load (and compile) seems OK to me.

[PaulWAyers]

Looks OK to me. If @marco-2023 and @gabrielasd are happy with it's fine to merge IMHO.

[marco-2023]

I think it is good