compas / grasp

General Relativistic Atomic Structure Package
https://compas.github.io/grasp/
MIT License
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Lagrange multipliers for closed shells #3

Open cffischer opened 5 years ago

cffischer commented 5 years ago

My recollection is that some time in the past, the GRASP code was such that peel orbitals for closed subshells resulted in Lagrange multipliers between subshells of the same symmetry that were in the list of Core subshells. Now Lagrange multipliers between these orbitals have been removed. This is OK when all orbitals are varied but is wrong when some orbitals are fixed.

When a pair of orbitals of the same symmetry are varied and both are associated with closed subshells, the variational equations do not have a unique solution, and the desired solution corresponds to a solution for which the Lagrange multiplier between the pair is zero (an hence can be ignored). But when one orbital is fixed the Lagrange multiplier for a stationary solution needs to be determined. So, in 3s(2) Mg, for example, if I want to compute the 3s orbital in fixed 1s(2)2s(2)2p(6) core, Lagrange multipliers will be needed for the 1s3s and 2s3s pairs of orbitals. The GRASP2018 core omits these orbitals and results may not have good accuracy. This error needs to be corrected.

jongrumer commented 5 years ago

@cffischer - in relation to the fixes you submitted in the pending pull request #19 - would you like to elaborate a bit more on the issue you outlined above, and how your fixes relate to it? If it is not necessary, then maybe we should close this issue.

cffischer commented 5 years ago

The pull request will solve this problem.