Replace J3 Finite Difference Ion Derivatives with Analytic

[rcclay]

Please review the developer documentation
on the wiki of this project that contains help and requirements.

Proposed changes

For ion gradient, ion gradient of electron gradients, and ion gradients of the Laplacians, all these were originally calculated using finite differences on the ion particle set. This is slow and adds complexity to porting force code to batch. This PR bites the bullet and replaces these with proper analytic gradients.

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

Delete the items that do not apply

• New feature
• Testing changes (e.g. new unit/integration/performance tests)

Does this introduce a breaking change?

• No

What systems has this change been tested on?

Intel with g++

Checklist

Update the following with a yes where the items apply. If you're unsure about any of them, don't hesitate to ask. This is
simply a reminder of what we are going to look for before merging your code.

• Yes. This PR is up to date with current the current state of 'develop'
• Yes. Code added or changed in the PR has been clang-formatted
• Yes. 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)

[prckent]

Test this please

[prckent]

Great to see this improvement. Q. Where did the reference values used in the test come from?

[rcclay]

Great to see this improvement. Q. Where did the reference values used in the test come from?

It always amazes me how slow finite differences are. Reference values are from finite difference of J3 values, gradients, and laplacians.

[ye-luo]

If we don't have any other finite difference code left
virtual function needs to be adjusted with const

const ParticleSet& P,
const ParticleSet& source,

In a separate PR.

[ye-luo]

Test this please