Is the ccECP Br.upf correct?

The reason for having different non-local components in the quantum chemistry formats vs *.upf files is that the former is a semi-local (SL) potential while the latter is a transformed Kleinman-Bylander (KB) potential. The transformation is carried out for efficiency purposes, it reduces the number of integrals from O(NM²) to O(NM) (M=number of basis functions, N=number of atoms). Therefore, these two potentials are actually slightly different except for the atomic configuration which was used to construct the KB potential in which case they produce numerically the same results.

In the KB transformation, one has the freedom to choose the local channel to be any l <= l_max + 1 number. So choosing l <= l_max will effectively reduce the number of non-local channels by 1. Of course, one can choose l_max + 1 to be local, then the number of non-local channels remains the same. The reason for not doing this is to achieve the best transferability (going from SL to KB) and to avoid the ghost states (i.e, in KB form, for a given l, eigenfunctions with more radial nodes can have lower energies than the nodeless ground state eigenfunctions, which is not physical). In addition, in this case, choosing local = l_max + 1 would require f-occupations which increases difficulties with DFT convergences for the reference configuration.

So actually this reduction is there for all semi-local ccECPs. So far, we didn't observe problems due this SL->KB transformation, especially given that in QMC we use the original semi-local potential (*.xml) with the correct number of non-local channels and without transformation biases.

This is my understanding, others can correct me if something looks off.

QMCPACK / pseudopotentiallibrary

Is the ccECP Br.upf correct? #74