PR[9] (combine PR-1-PR-8) feat: combine weeks 1-9 implementations into single branch

[San1357]

Summary

• Combines all week 1-9 implementations into a single branch for review
• Includes Boys functions, OS+HGP algorithm (VRR+ETR+HRR), Schwarz screening, PySCF validation, and libcint tolerance fix

Changes

Week	Branch	Feature
1	feat/boys-functions	Boys function APIs + attenuated potentials
2	feat/electron-repulsion-improved	OS+HGP base rewrite
3	feat/VRR-two-electron-integral	VRR recurrence (Eq. 65)
4	feat/ETR-contraction	ETR + primitive contraction (Eq. 66)
5	feat/HRR-complete-pipeline	HRR complete pipeline (Eq. 67) fix (#216)
6	feat/schwarz-screening	Schwarz screening optimization
7	feat/pyscf-tests-tutorial	PySCF comparison tests + Tutorial 3 notebook
8	feat/libcint-tolerance-fix	libcint ERI tolerance fix (#208)

Test Results

• 364 tests passed, 0 failed
• Validated against PySCF for s, p, d orbitals
• Closes WoC: 2-electron integrals: better performance and more flexibility #221, [BUG] Electron repulsion energy #216, libcint/gbasis eri tolerance is 1e-4? #208

Related PRs

• [PR1] feat: add Boys function for 2 electron and validation tests #231 — feat/boys-functions
• [PR-2] feat: implement VRR for OS+HGP two-electron integral pipeline #234 — feat/electron-repulsion-improved
• [PR-3] feat: implement ETR (Eq. 66) and primitive contraction for OS+HGP pipeline #237 — feat/VRR-two-electron-integral
• [PR-4] feat: implement HRR (Eq. 67) and complete OS+HGP two-electron integral pipeline #238 — feat/ETR-contraction
• [PR-5] feat: integrate OS+HGP algorithm into electron_repulsion module #239 — feat/HRR-complete-pipeline
• [PR-6] feat: implement Schwarz screening for two-electron integral optimization #240 — feat/schwarz-screening
• [PR-7] feat: add PySCF validation tests and interactive tutorial notebook #241 — feat/pyscf-tests-tutorial
• [PR-8] fix: tighten libcint ERI tolerance and use improved implementation (#208) #242 — feat/libcint-tolerance-fix

This PR closes #221, #216, #208 and is ready for final review and merge.

Please let me know (@PaulWAyers , @marco-2023 , @msricher ) if any further changes or refinements are needed. Thank you!

[San1357]

Summary (Final Completion Of WOC #221 )

• This PR combines the complete implementation of the WoC project "Two-Electron Integrals via OS+HGP Algorithm" completed over Weeks 1–9 into a single branch, as requested.
• Includes Boys functions, OS+HGP algorithm (VRR+ETR+HRR), Schwarz screening, PySCF validation, and libcint tolerance fix

Boys Functions (Week 1)

• Implemented Boys function APIs for standard and attenuated potentials (erf, erfc, yukawa, etc.)
• Added vectorized NumPy implementation with mpmath fallback for high accuracy

OS+HGP Two-Electron Integrals (Weeks 2–5)

• Implemented complete Obara-Saika + Head-Gordon-Pople algorithm (VRR + ETR + HRR)
• Supports s, p, d orbitals correctly (fixes [BUG] Electron repulsion energy #216)
• Validated against PySCF for correctness

Schwarz Screening (Week 6)

• Implemented Schwarz inequality-based screening to skip negligible shell quartets
• Added shell-pair prescreening using Gaussian product theorem

PySCF Validation + Tutorial (Week 7)

• Added comprehensive PySCF comparison tests
• Added Tutorial 3 notebook demonstrating OS+HGP, Boys functions, and Schwarz screening

libcint Tolerance Fix (Week 8)

• Fixed ERI comparison tolerances for libcint tests (libcint/gbasis eri tolerance is 1e-4? #208)
• Uses improved OS+HGP implementation for comparison

Request :

This PR closes #221, #216, #208 and is ready for final review and merge.
Please let me know (@PaulWAyers , @marco-2023 , @msricher ) if any further changes or refinements are needed. Thank you

[msricher]

Thanks for combining it all. Let's await a final review.

[msricher]

I'm not sure this and the stuff at the bottom is necessary, it's not standard and I wouldn't expect it if I triggered it myself. I would simply dd PySCF to the [test] dependencies in the pyproject.toml file.