Include hydrogenic basis sets

[susilehtola]

These are the hydrogenic basis sets from J. Chem. Phys. 152, 134108 (2020); https://doi.org/10.1063/1.5144964

hgbs-9.gbs are optimized basis sets for Z=1-118 without polarization functions hgbsp1-9.gbs are optimized basis sets for Z=1-118 with 1 polarization shell hgbsp2-9.gbs are optimized basis sets for Z=1-118 with 2 polarization shells hgbsp3-9.gbs are optimized basis sets for Z=1-118 with 3 polarization shells

ahgbs-9.gbs are augmented optimized basis sets for Z=1-118 without polarization functions ahgbsp1-9.gbs are augmented optimized basis sets for Z=1-118 with 1 polarization shell ahgbsp2-9.gbs are augmented optimized basis sets for Z=1-118 with 2 polarization shells ahgbsp3-9.gbs are augmented optimized basis sets for Z=1-118 with 3 polarization shells

hgbs.zip

[susilehtola]

Forgot to mention that the sets are for \epsilon=10^{-9}... the paper also has sets for other thresholds.

[bennybp]

Would you be willing to write a short description or notes for these (and the sets in #110)? You certainly understand the details more than I do. What they should be used for, etc.

[susilehtola]

Sure. Note I also added the augmented sets that I forgot in the initial ticket. Description as follows:

The hydrogenic basis sets are formed on one-electron model systems that imitate the behavior of real atoms and molecules, where the full nuclear charge is seen at the nucleus while far away the effective nuclear charge goes to one for the optimized effective potential, and zero for density functional approximations. The basis set for atom Z is obtained by optimizing even-tempered exponents for the ground state of Z^{(Z-1)+} for every angular momentum, and by adding more functions until all the one-electron ions from H to Z^{(Z-1)+} are reproduced within the wanted tolerance. Augmented basis sets are obtained by requiring the basis to be accurate also for the Z=1/2 one-electron ion. For details on the formation of the basis sets, see S. Lehtola, J. Chem. Phys. 152, 134108 (2020). DOI: 10.1063/1.5144964.

Since the basis sets don't assume the atoms to be in a specific configuration, they turn out to be widely transferable and accurate. Not all atoms are accurately described by the non-augmented sets, since the potential therein is weaker than -1/r, but the augmented sets afford excellent in these cases. I recommend that you check whether augmentation affects your results.

A practical issue in the use of these basis sets is their high number of diffuse functions of high angular momentum that arise from the use of a constant effective charge model Zeff(r) = Zeff: in reality, Zeff(r) goes to zero rapidly away from the nucleus. These diffuse functions cause significant linear dependencies in molecular calculations, but they are not a problem in practice since even pathological linear dependencies can be cured with a simple Cholesky procedure that can be easily included in any pre-existing implementation of the canonical orthogonalization procedure [S. Lehtola, J. Chem. Phys. 151, 241102 (2019); DOI: 10.1063/1.5139948 and S. Lehtola, Phys. Rev. A 101, 032504 (2020). DOI: 10.1103/PhysRevA.101.032504].

[susilehtola]

These are now on the repo.