New (Local) Atom Properties: Electrostatic Potential, Gaussian Basis Set Expansion

[PaulWAyers]

Electrostatic Potential Tabulation

Motivated by the need to compute interactions between promolecules, it would be useful to tabulate the electrostatic potential (the electronic part only) for the atoms/ions in the database,

$$ \Phi_e(r) = \int frac{\rho(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|} d \mathbf{r}' $$

If I am correct, this is easy to achieve, because we have the atomic densities and we can solve the (radial) Poisson equation using Grid, specifically see the example.

Atomic Density BFits

The BFit package provides the capability to fit atomic densities to a sum of (s-type) Gaussians. There is already an interface to AtomDB, though the example may be out of date. It would be good to store the Gaussian coefficients/exponents for the atoms/ions in the databases.

It would also be nice if we could then produce a promolecule as a series of centers/Gaussian-exponents/Gaussian-coefficients but this is easy to do, I think, by using make_promolecule and then using the coeffs attribute of the promolecule class. I.e., making a Gaussian approximation to a promolecule is really a topic for a Jupyter notebook tutorial.