Use minimum image of particles in EwaldRef

[ye-luo]

Proposed changes

The reference calculation went wrong this time.
When particles don't start within the unit cell, the grid summation of EwardRef doesn't work well. See first commit.
The QMCPACK value is OK. #2105 (comment) passes with this fix.

Closes #2105

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

• Bugfix

Does this introduce a breaking change?

• No

What systems has this change been tested on?

epyc-server

Checklist

• Yes. This PR is up to date with current the current state of 'develop'

[ye-luo]

Test this please

[jtkrogel]

Is the underlying issue a premature truncation of the real space sum?

If r_i-r_j is outside the cell, then the first term in the sum (centered at zero lattice vector shift) could be rather small, perhaps smaller than the tolerance for the sum overall.

[ye-luo]

Is the underlying issue a premature truncation of the real space sum?

Yes

If r_i-r_j is outside the cell, then the first term in the sum (centered at zero lattice vector shift) could be rather small, perhaps smaller than the tolerance for the sum overall.

The tolerance check is on the sum of the absolute values contributed by grid points on the surface shell.
This first term (all 0 offset) is always excluded from the tolerance check. Instead some later shell went under tolerance before reaching the shells which contributes significant values when the initial coordinate delta are very far from the center.

[prckent]

I also thought about testing for several shells in a row being below tolerance, but I think once the particles are minimum imaged that is no longer necessary. Also, if a particle ever wandered "far enough" there could still be an issue with not testing enough shells.

Since this fixes the reported problem, adds a test for it, and doesn't require any changes to the values used in other tests, can we consider this safe to merge?

[ye-luo]

Test this please

[jtkrogel]

Yes, let's merge this.

[ye-luo]

Test this please