QMCPACK / QMCPACK/qmcpack

Backflow revival roadmap

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Description

> First, please note what would be needed to restore backflow optimization? What is the specific functionality we were using in the old classes that is not present in the modern ones? This note is needed for future revisiting, and perhaps if it can be readily described we might be able to fix it sooner.

High order partial derivatives of SPOSet are needed to be called by determinants with backflow. Those implementations need to be added back.

_Originally posted by @ye-luo in https://github.com/QMCPACK/qmcpack/issues/4688#issuecomment-1661159101_

Could anyone with more experience with backflow provide a more detailed roadmap for bringing backflow back? Maybe a checklist of tasks..
- What specific classes need these higher order partial derivatives? What are the functions that need a derivative (and wrt what input parameters?)
- Once these derivatives are implemented will backflow just work? or is there additional plumbing required?

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