Nexus: Extend excitations to allow 'lowest' gap

[mcbennet]

Proposed changes

This PR allows the user to specify 'lowest' for the excitation, e.g.,

generate_qmcpack(
...,
excitation = ['up','lowest'], # 'up' can be replaced with 'down', 'singlet', or 'triplet'
...,
)

where nexus will then generate the lowest excitation for the given type (up,down,singlet,triplet) based on the energy index (electron count). The resulting qmcpack input will contain the corresponding excitation in energy format.

This PR also fixes a couple minor bugs in the previous 'singlet' and 'triplet' types.

In addition, post analysis checks for the various excitation input types have been added -- the user's input is checked against qmcpack's generated einspline files to verify that the user's requested excitation is consistent with the change to the einspline file.

What type(s) of changes does this code introduce?

• Bugfix
• New feature

Does this introduce a breaking change?

• No. nxs-tests pass in ubuntu desktop (with the exception of simulation_module)

What systems has this change been tested on?

Ubuntu desktop

Checklist

• Yes. This PR is up to date with current the current state of 'develop'
• N/A. Code added or changed in the PR has been clang-formatted
• No. This PR adds tests to cover any new code, or to catch a bug that is being fixed
• No. Documentation has been added (if appropriate)

[qmc-robot]

Can one of the admins verify this patch?

[mcbennet]

Changing to draft PR. There are a few additional tests I would like to look at before this goes in.

[mcbennet]

Okay, IMO this PR is ready to go in -- removing draft state. For diamond (primitive with 4 up and 4 down electrons), I tested that the VMC-NoJ kinetic energies from various excitation (gamma-to-gamma) specifications agree with the total kinetic energy from the eshdf tool. That plot is attached. This test was necessary because ['*','lowest'] will produce a qmcpack input that is equivalent to excitation = ['*','-4 +5'], and we want to verify that this agrees with the 'band' excitation type.

Ground: ground state WF
Up-Band: excitation = ['up','0 3 0 4']
Dn-Band: excitation = ['down','0 3 0 4']
Up-Energy: excitation = ['up','-4 +5']
Up-Binary: excitation = ['singlet','-4 +5'] -> Before running, CSF coefficients are changed by hand to make excitation consistent with others above, i.e., (0.707,0.707) -> (1.000,0.000)

All the VMC KEs appear to be in really good agreement here and also in good agreement with eshdf.

[jtkrogel]

Looking good overall. Just needs some hardening.

[mcbennet]

This PR should now be ready for review.

[ye-luo]

Test this please

[jtkrogel]

See comments below.

[mcbennet]

@jtkrogel I think everything in your review is either addressed or outdated

[jtkrogel]

Still needs lowercase comparison ('vb' in b.lower()). And similar for any other cases.

[jtkrogel]

LGTM

[ye-luo]

Test this please