CASINO pseudopotential library

The core radii are the radii outside of which we demand that the pseudo-orbitals and all-electron orbitals agree for the initial pseudopotential. Pseudopotentials generated by inversion of the Schrödinger or Dirac-Fock equations have long ranged non-local tails which must be cutoff (as described in Refs. 1 and 2). The cutoff procedure forces the pseudopotentials to be local outside of the localisation radius r_loc whilst correcting the pseudopotentials inside of r_loc to conserve ground state properties^*. This pseudopotential is the "tabulated" pseudopotential given in the periodic table. Parameterising such a pseudopotential in terms of a Gaussian basis set normally increases r_loc.

The all-electron and pseudo-HF LS-coupling eigenvalues should agree to high precision for a Hartree-Fock pseudopotential, but not necessarily for an AREP pseudopotential that is generated within Dirac-Fock theory.

The terms in the energy for a pseudo-HF calculation of the ground state of the atom are given. These are useful for checking purposes, for example these energies should be reproduced by a variational Monte Carlo calculation using the pseudopotential and the atomic orbitals resulting from a Hartree-Fock calculation using the same pseudopotential.

Data for a few excitation energies are also included in the summary. It should be noted that a pseudo-HF calculation with an AREP pseudopotential will not reproduce the same relativistic effects as those present in the original all-electron DF atom, even if scalar relativistic corrections and spin-orbit coupling are included. This implies that excitation energies for the pseudo-HF atom would differ from those of the all-electron DF atom even if the pseudopotential were able to reproduce the influence of the core electrons exactly.

Please note that there is a seperate summary file for each representation of each type of pseudopotential. These give the energies resulting from pseudo-HF calculations carried out using the tabulated representation, the CRYSTAL/GAUSSIAN Gaussian expansion, and the GAMESS Gaussian expansion of the pseudopotential. Small differences between the energies resulting from the tabulated and parameterised representations reflect the accuracy of the Gaussian fits.

In addition please note that the atomic orbitals provided in the periodic table have been calculated from the tabulated pseudopotentials, not the parameterised pseudopotentials.