3D BackFlowLux

[CheukHinHoJerry]

Updates from this PR, a list copy from #17 :

• Normalisation Ylm and Rlm: Verify the normalized constant for both solid harmonics and spherical harmonics, document this in the Polynomials4ML docs, check if there are other ways to normalize them, including the sense of norm used. -- @DexuanZhou
• Unit tests for Rlm: verify they match the explicit expressions, check derivatives, follow test_cylm.jl -- @DexuanZhou
• Unit tests for atomic orbitals: for Gaussian, Slater, and STO-NG functions. Check the derivatives of these functions and also verify the consistency of the standard and batched evaluation methods. -- @DexuanZhou
• SparseProduct: implement a sparse product without pooling in Polynomials4ML from which we can build atomic orbital bases -- @cortner and @CheukHinHoJerry
• AtomicOrbitalsBasis: implement the atomic orbitals basis which will be evaluating the atomic orbitals on multiple nuclei and merging them into a single basis. -- TBD
• BackflowPooling: implement the custom backflow pooling as a separate operation from the AtomicOrbitalsBasis -- @cortner and @CheukHinHoJerry
• Reorganize atorbbasis.jl : once the AtomicOrbitalsBasis and BackflowPooling is done, we can reorganize this into a very simple flux layer or chain -- TBD
• Correlations: Here we should be able to just use the standard implementation. But we do need to implement some scripts that will give us different choices of which correlations to involve in the model. This is where the real modelling happens!! -- @DexuanZhou (??)
• Clearly document the API

Additional comment that I don't fully understand yet - to be discussed in our next meeting?

• Also, huajie mentioned that we should convert the coefficients used in the chemical basis set to a format we can use. I will take a look at it first. https://www.basissetexchange.org/ https://github.com/MolSSI-BSE/basis_set_exchange

Some additional features:

• HyperDuals for Laplacian evaluation
• Fully Lux integration
• optimization workflows, including VMC, multilevel
• SR method

[cortner]

to be tagged as 0.0.2