PR[9] (combine PR-1-PR-8) feat: combine weeks 1-9 implementations into single branch by San1357 · Pull Request #245 · theochem/gbasis

San1357 · 2026-03-11T06:59:34Z

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!

…eline

…d.py

…rrays

…sion

…omputation

…version

…heochem#208)

San1357 · 2026-03-11T07:08:17Z

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 · 2026-03-11T11:17:48Z

tests/test_pyscf_comparison.py

+try:
+    from pyscf import gto
+    HAS_PYSCF = True
+except ImportError:
+    HAS_PYSCF = False
+


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.

@msricher Done! Added pyscf to [dev] dependencies in pyproject.toml and removed the conditional HAS_PYSCF imports from the test file.

@msricher I see the CI is failing because pyscf can't be built on Windows. I'll use pytest.importorskip instead and remove pyscf from dev dependencies. Will push the fix shortly.

@msricher Updated! Removed pyscf from dev dependencies (it fails to build on Windows) and used pytest.importorskip instead — tests will skip automatically if pyscf is not available.

Copilot

Pull request overview

This PR consolidates the Week 1–9 work into a single branch, delivering a new OS+HGP-based 2-electron integral pipeline (with screening and Boys function support) plus expanded validation/testing (including PySCF comparisons) and tighter libcint comparison tolerances.

Changes:

Added a full OS+HGP ERI implementation (VRR/ETR/HRR + contraction) and integrated it into gbasis.integrals.electron_repulsion, with optional Schwarz screening.
Added Boys function implementations (including erf/erfc variants) and extensive new tests/validation (unit + integration + PySCF).
Updated libcint tests to use the improved ERI implementation and tightened tolerances (with ERI-specific tolerances).

Reviewed changes

Copilot reviewed 11 out of 11 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
`gbasis/integrals/_two_elec_int_improved.py`	New OS+HGP ERI pipeline implementation (VRR/ETR/HRR + contraction + primitive screening hook).
`gbasis/integrals/_schwarz_screening.py`	New Schwarz screening utilities + screener class.
`gbasis/integrals/boys_functions.py`	New Boys function implementations (standard + erf/erfc + recursion + factory).
`gbasis/integrals/electron_repulsion.py`	Integrates OS+HGP into ERI construction; adds “improved” ERI API with optional Schwarz screening.
`tests/test_two_elec_int_improved.py`	New unit/integration tests for VRR/ETR/HRR, contraction, reordering, and screening integration.
`tests/test_schwarz_screening.py`	New tests validating bounds, screener behavior, and screening correctness.
`tests/test_pyscf_comparison.py`	New PySCF cross-validation tests for original vs improved ERIs and physical sanity checks.
`tests/test_boys_functions.py`	New unit tests for Boys functions (standard + erf/erfc + recursion + mpmath reference).
`tests/test_electron_repulsion.py`	Reworked tests focusing on improved ERI class/API integration and equivalence checks.
`tests/test_libcint.py`	Uses improved ERIs for libcint comparison and tightens tolerances with ERI-specific override.

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Copilot · 2026-03-12T13:53:57Z

gbasis/integrals/_two_elec_int_improved.py

+        prefactor = np.where(np.abs(prefactor) >= primitive_threshold, prefactor, 0.0)
+
+    orders = np.arange(m_max)[:, None, None, None, None]
+    integrals_m = boys_func(orders, weighted_dist[None, :, :, :, :]) * prefactor


boys_func is invoked as boys_func(orders, weighted_dist) here, but the new erf/erfc Boys functions require rho (harmonic mean) to compute the rescaling. As a result, passing get_boys_function('erf'/'erfc', ...) into this pipeline will raise at runtime and attenuated potentials can’t actually be used. Consider updating the pipeline to call boys_func(orders, weighted_dist, rho=harm_mean) (and documenting the expected callable signature accordingly).

Suggested change

integrals_m = boys_func(orders, weighted_dist[None, :, :, :, :]) * prefactor

integrals_m = boys_func(orders, weighted_dist[None, :, :, :, :], rho=harm_mean) * prefactor

@Copilot suggestion-1 Fixed!

Added rho=None to PointChargeIntegral.boys_func and all custom boys_func definitions in tests, and now passing rho=harm_mean at the call site in _two_elec_int_improved.py. erf/erfc potentials will now work correctly at runtime.

Copilot · 2026-03-12T13:53:57Z

gbasis/integrals/_two_elec_int_improved.py

+    # Initialize output array with contiguous memory
+    # axis 0: m, axis 1: a_x, axis 2: a_y, axis 3: a_z
+    integrals_vert = np.zeros((m_max, m_max, m_max, m_max, *integrals_m.shape[1:]), order="C")
+


integrals_vert is allocated with shape (m_max, m_max, m_max, m_max, ...), where m_max = angmom_a + angmom_b + angmom_c + angmom_d + 1. Only the A-side angular momentum range is needed for VRR (and later code slices down to m_max_a = angmom_a + angmom_b + 1 in HRR), so this over-allocates memory/work by potentially large factors for higher angular momentum cases. Consider sizing the a_x/a_y/a_z axes to m_max_a (or the maximum needed for the bra side) instead of m_max.

Copilot · 2026-03-12T13:53:58Z

gbasis/integrals/_two_elec_int_improved.py

+    # Initialize ETR output with contiguous memory
+    integrals_etransf = np.zeros(
+        (m_max_c, m_max_c, m_max_c, m_max, m_max, m_max, *n_primitives), order="C"
+    )


integrals_etransf is allocated with (m_max_c, m_max_c, m_max_c, m_max, m_max, m_max, ...), but downstream HRR only uses the A-side axes up to m_max_a = angmom_a + angmom_b + 1. Using m_max (which includes C/D angular momentum) for the a_x/a_y/a_z dimensions can significantly increase memory and runtime for mixed high-angular-momentum cases. Consider allocating the A-side axes to m_max_a and threading that size through ETR/contract/HRR.

gbasis/integrals/electron_repulsion.py

Copilot · 2026-03-12T13:53:58Z

tests/test_schwarz_screening.py

+        # The loose threshold should be at least as permissive
+        if not sig_strict:
+            assert sig_loose or not sig_loose  # may or may not be significant
+        if sig_loose:
+            assert True  # loose is at least as permissive


test_threshold_sensitivity currently contains assertions that are tautologies (e.g., assert sig_loose or not sig_loose / assert True) and therefore won’t catch regressions in shell_pair_significant. Since the predicate is monotonic in threshold (smaller threshold should be at least as permissive), this test should assert something like sig_strict <= sig_loose (i.e., if sig_strict is True then sig_loose must be True), or assert explicit expected outcomes for this geometry/exponent setup.

Suggested change

# The loose threshold should be at least as permissive

if not sig_strict:

assert sig_loose or not sig_loose # may or may not be significant

if sig_loose:

assert True # loose is at least as permissive

# The loose threshold should be at least as permissive:

# any pair significant under the strict threshold must also be

# significant under the loose threshold (monotonicity in threshold).

assert (not sig_strict) or sig_loose

@Copilot suggestion-5 Fixed!

Replaced the tautological assertions with a proper monotonicity check — if a pair is significant under the strict threshold, it must also be significant under the loose threshold.

Copilot · 2026-03-12T13:53:58Z

gbasis/integrals/electron_repulsion.py

+    if schwarz_threshold > 0:
+        index_map = {id(shell): i for i, shell in enumerate(basis)}
+        screener = SchwarzScreener(
+            list(basis),
+            ElectronRepulsionIntegralImproved.boys_func,
+            compute_two_electron_integrals_os_hgp,
+            schwarz_threshold,
+        )


When schwarz_threshold > 0, a new SchwarzScreener (and full bounds matrix) is recomputed on every call. Since compute_schwarz_bounds() evaluates (ab|ab) via the full OS+HGP ERI routine for each shell pair, this setup cost can be substantial and may dominate for repeated ERI builds with the same basis. Consider caching the screener/bounds keyed by the basis (or exposing a way to reuse a precomputed screener) to avoid repeated O(n_shell^2) bound evaluations.

@Copilot suggestion-6 Fixed!

Fixed! Added a module-level cache _schwarz_screener_cache keyed by (basis_ids, threshold). Now the SchwarzScreener and its bounds matrix are only computed once per unique basis+threshold combination — subsequent calls reuse the cached screener directly.

San1357 · 2026-03-12T14:26:53Z

Thanks for the review @marco-2023! Some really good catches here.

Going through all 6 fixes now:

The missing rho in boys_func is a real bug — erf/erfc would silently fail at runtime. Will pass rho=harm_mean.
integrals_vert over-allocation makes sense to fix, A-side only needs m_max_a.
Same for integrals_etransf, will resize the A-side axes.
Thread-safety issue noted — will refactor Schwarz screener to pass via kwargs instead of class-level state.
Yeah the tautological assertions are a bad miss on my part, will replace with a proper monotonicity check.
Will add screener caching so bounds aren't recomputed on every call.

Will push the fixes shortly!

…otentials

…threshold_sensitivity

…-safety

San1357 · 2026-03-12T15:18:23Z

@marco-2023 Fixed @Copilot suggestion 1, 4, 5, and 6! For @copilot suggestion 2 and 3 — the memory over-allocation in integrals_vert and integrals_etransf is a valid point, but resizing the A-side axes to m_max_a would require changes deeper in the VRR/ETR logic. I'd rather not rush that and risk breaking things. Happy to tackle it as a follow-up once the current fixes are reviewed.

San1357 · 2026-03-12T15:38:57Z

@msricher, @marco-2023 , @Copilot
Re: Comments 2 & 3 (VRR/ETR A-side over-allocation)

Thanks for the review! After careful analysis, the A-side axes in both integrals_vert and integrals_etransf must be sized m_max, not m_max_a.

The ETR uses the recursion:

[a|c+1] = ... − (ζ/η)[a+1|c] + ...
To build C angular momentum from scratch (c=0 → c=angmom_c+angmom_d), the first ETR step reads [a+1 | c=0] — i.e., the VRR output — where a ranges up to angmom_a + angmom_b + angmom_c + angmom_d. Capping the VRR at m_max_a = angmom_a + angmom_b + 1 would leave those higher-a slots as zero, silently corrupting results for any shell quartet with non-zero CD angular momentum (e.g. (ss|pp), (pp|dd)).

This is a known characteristic of the OS/HGP algorithm: the VRR must "over-build" A-side angular momentum to provide the ETR with enough input. A triangular indexing scheme could reduce memory usage here, but that's a more involved restructuring.

Happy to discuss further if I've misread the intent of the comment!

marco-2023

Overall, the code is clean, nice work. I added some comments that I would like to get feedback on before this is merged.

marco-2023 · 2026-03-12T02:56:35Z

gbasis/integrals/electron_repulsion.py

-                cont_four.angmom_components_cart,
-                cont_four.exps,
-                cont_four.coeffs,
-            )


I thought the idea was adding the new class ElectronRepulsionIntegralImproved, which is going to ultimately substitute this one. Why the modifications to the original class?

You're right @marco-2023 — this was an unintentional change. The original ElectronRepulsionIntegral class got modified in a commit that was meant to be a style/formatting fix, but it accidentally replaced the old _compute_two_elec_integrals implementation with compute_two_electron_integrals_os_hgp.

The original class should remain as-is (using the old algorithm as reference), and only ElectronRepulsionIntegralImproved should use the new OS+HGP pipeline. As a side effect, this also means the comparison tests in test_electron_repulsion.py (result_old vs result_new) will be meaningful again — right now both classes call the same function so the tests can't catch regressions.

Will revert this in the next push.

marco-2023 · 2026-03-12T13:54:46Z

gbasis/integrals/_schwarz_screening.py

+        self.n_computed = 0
+
+        # Precompute Schwarz bounds
+        self.bounds = compute_schwarz_bounds(contractions, boys_func, compute_integral_func)


Here, compute_schwarz_bounds calls compute_schwarz_bound_shell_pair for each pair of shells. Then compute_schwarz_bound_shell_pair computes the integrals for each shell pair. Isn't this the same as computing all the integrals unscreened?

I think I get this, you run a $O(n^2)$ screening to screen the $O(n^4)$ integrals.

Exactly, @marco-2023 — compute_schwarz_bounds runs in O(n²) over shell pairs, computing (ab|ab) type integrals. This upfront cost then screens out negligible shell quartets from the O(n⁴) ERI computation, which is where the real savings come from for larger basis sets.

gbasis/integrals/electron_repulsion.py

marco-2023 · 2026-03-12T17:28:41Z

gbasis/integrals/electron_repulsion.py

+
+    """
+
+    boys_func = PointChargeIntegral.boys_func


Why not use the new boys_function_standard?

Makes sense. Updated ElectronRepulsionIntegralImproved.boys_func to use get_boys_function("coulomb") from boys_functions.py — no reason to borrow from PointChargeIntegral when we have a dedicated module for this.

marco-2023 · 2026-03-12T17:49:22Z

gbasis/integrals/electron_repulsion.py

+        if cache_key not in _schwarz_screener_cache:
+            _schwarz_screener_cache[cache_key] = SchwarzScreener(
+                list(basis),
+                ElectronRepulsionIntegralImproved.boys_func,


I would import and use the boys' function from the new module. Maybe I am wrong, but adding the function as a member of a class to then pass the method unbounded as an argument seems overcomplicated. Your thoughts @San1357

passing get_boys_function("coulomb") directly to SchwarzScreener is cleaner. Going through ElectronRepulsionIntegralImproved.boys_func was an unnecessary indirection, especially since get_boys_function is already imported. Fixed in the latest commit.

gbasis/integrals/point_charge.py

…lsionIntegralImproved

…ralImproved.boys_func

…lass reference

San1357 · 2026-03-13T20:40:00Z

Hi @marco-2023, addressed all your comments:

Reverted ElectronRepulsionIntegral to use the original _compute_two_elec_integrals — the unintentional change is fixed.
Confirmed — compute_schwarz_bounds runs O(n²) to screen O(n⁴), which is the intended design.
Opened follow-up issue Add cache management for _schwarz_screener_cache (unbounded memory growth) #247 for cache management.
Updated ElectronRepulsionIntegralImproved.boys_func to use get_boys_function("coulomb") from boys_functions.py.
Passing get_boys_function("coulomb") directly to SchwarzScreener instead of going through the class.
Replaced inline hyp1f1 in PointChargeIntegral.boys_func with boys_function_standard.

All changes are in the latest push. Let me know if anything needs further revision.

marco-2023

I think it is ready to merge

San1357 · 2026-03-14T05:39:49Z

Thanks for the review and approval @marco-2023! Does this need another maintainer's sign-off before merging?

San1357 added 25 commits February 12, 2026 15:25

feat: add Boys function APIs and validation tests

2d3fe98

fix: move qc-dev-env/ from.gitignore to .git/info/exclude

db5045e

refactor: vectorize boys_function_all_orders with NumPy broadcasting

4824a2a

fix: add raise-from in mpmath ImportError (ruff B904)

5278ebf

feat: implement VRR (Eq. 65) for OS+HGP two-electron integral pipeline

c19cb89

feat: implement ETR (Eq. 66) and primitive contraction for OS+HGP pip…

2ec8140

…eline

feat: implement HRR (Eq. 67) and complete OS+HGP pipeline

6e40ec7

add test files for two elect int improved.py

bf6e727

test: add erf/erfc attenuated Boys function tests and update docstring

8ab104e

style: apply black/ruff formatting to test_boys_functions.py

4347444

style: apply black/ruff formatting fixes to test_two_elec_int_improve…

d96fd22

…d.py

style: move imports to top-level, fix ruff PLC0415 in test file

7ec98dd

style: fix black formatting

f0f57fa

refactor: vectorize norm computation over all 4 centers using NumPy a…

2cea131

…rrays

test: add tests for _optimized_contraction

60ddebb

fix: handle different K per center in _optimized_contraction

e1612a7

style: fix black formatting and import sorting in test_electron_repul…

3411d23

…sion

feat: implement Schwarz screening to optimize two-electron integral c…

6314d78

…omputation

feat: add PySCF comparison tests and OS+HGP tutorial notebook

cdf9bd4

Merge branch 'feat/VRR-two-electron-integral' into local-test-all

84c7511

merge: resolve add/add conflicts keeping electron-repulsion-improved …

4ee3247

…version

Merge branch 'feat/schwarz-screening' into local-test-all

b6ff02c

Merge branch 'feat/pyscf-tests-tutorial' into local-test-all

7c85807

fix: tighten libcint ERI tolerance and use improved implementation (t…

f630272

…heochem#208)

Merge branch 'feat/libcint-tolerance-fix' into local-test-all

4e2994e

San1357 requested a review from msricher March 11, 2026 07:09

msricher reviewed Mar 11, 2026

View reviewed changes

San1357 added 2 commits March 11, 2026 22:09

fix: add pyscf to dev deps and remove conditional imports in test

b351377

fix: use pytest.importorskip for pyscf instead of dev dependency

6e3a73e

This was referenced Mar 11, 2026

[PR-7] feat: add PySCF validation tests and interactive tutorial notebook #241

Closed

[PR-8] fix: tighten libcint ERI tolerance and use improved implementation (#208) #242

Closed

marco-2023 self-requested a review March 11, 2026 20:27

San1357 requested a review from msricher March 12, 2026 13:41

marco-2023 requested review from Copilot and removed request for msricher March 12, 2026 13:46

Copilot started reviewing on behalf of marco-2023 March 12, 2026 13:46 View session

Copilot AI reviewed Mar 12, 2026

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San1357 added 4 commits March 12, 2026 20:13

fix: pass rho=harm_mean to boys_func to support erf/erfc attenuated p…

0c215e6

…otentials

fix: replace tautological assertions with monotonicity check in test_…

874c15b

…threshold_sensitivity

fix: pass screener via kwargs instead of class-level state for thread…

65879ad

…-safety

perf: cache SchwarzScreener to avoid recomputing bounds on every call

fb9e1a6

marco-2023 requested changes Mar 13, 2026

View reviewed changes

revert: restore original ElectronRepulsionIntegral to use old algorithm

bfac8b0

San1357 mentioned this pull request Mar 13, 2026

Add cache management for _schwarz_screener_cache (unbounded memory growth) #247

Open

San1357 added 3 commits March 14, 2026 01:23

fix: use get_boys_function from boys_functions module in ElectronRepu…

f2f0e0d

…lsionIntegralImproved

fix: use get_boys_function directly instead of ElectronRepulsionInteg…

76107ea

…ralImproved.boys_func

fix: use boys_functions module directly instead of inline hyp1f1 or c…

104446c

…lass reference

marco-2023 marked this pull request as ready for review March 14, 2026 01:34

marco-2023 self-requested a review March 14, 2026 01:34

marco-2023 approved these changes Mar 14, 2026

View reviewed changes

marco-2023 merged commit 8c8f69c into theochem:master Mar 16, 2026
9 checks passed

marco-2023 mentioned this pull request Mar 16, 2026

Add Boys function utility for 2-electron integral evaluation #248

Closed

5 tasks

This was referenced Mar 24, 2026

GSoC 2026: Better linking between Libcint and GBasis #229

Open

GSoC 2026: Improve performance of 2-electron integrals using screening #230

Open

	integrals_m = boys_func(orders, weighted_dist[None, :, :, :, :]) * prefactor
	integrals_m = boys_func(orders, weighted_dist[None, :, :, :, :], rho=harm_mean) * prefactor

Conversation

San1357 commented Mar 11, 2026

Summary

Changes

Test Results

Related PRs

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!

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San1357 commented Mar 11, 2026

Summary (Final Completion Of WOC #221 )

Request :

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Pull request overview

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@Copilot suggestion-1 Fixed!

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@Copilot suggestion-5 Fixed!

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@Copilot suggestion-6 Fixed!

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