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Add RI and THC-ISDF two-electron integral factorizations#66

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rubber-duck-debug wants to merge 2 commits intohatemhelal:mainfrom
rubber-duck-debug:feature/coulomb
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Add RI and THC-ISDF two-electron integral factorizations#66
rubber-duck-debug wants to merge 2 commits intohatemhelal:mainfrom
rubber-duck-debug:feature/coulomb

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Summary

  • Add TwoElectronRI, TwoElectronTHC, and TwoElectronTHCRI factorizations in mess/two_electron.py, each with Coulomb (J) and exchange (K) builds
  • RI uses Cholesky-contracted three-center integrals from PySCF; THC-ISDF selects interpolation points via QRCP on AO pair products and fits a compact core tensor Z
  • TwoElectronTHCRI combines exact RI Coulomb with approximate THC exchange — per-iteration cost drops from O(N^4) to O(N^2*M + NM^2) while keeping J exact
  • Integrate into Hamiltonian via coulomb= parameter ("full", "ri", "thc-ri")
  • THC exchange supports MO-form build (O(N_occ) scaling) when C_occ is provided
  • Cap interpolation points at 20*N to prevent pathological M from oversized auxiliary bases
  • QRCP and pseudoinverse run through JAX for GPU readiness

Consolidate into mess/two_electron.py with string-based coulomb=    parameter on Hamiltonian. THC-K follows arXiv:1911.00470 Eq. 38.
THC-ISDF approximates the O(N^4) ERI tensor as a product of collocation matrices X (N, M) and a small core Z (M, M), reducing per-iteration Coulomb to O(NM + M^2) and exchange to O(N^2*M + NM^2). The hybrid RI-J/THC-K variant uses exact RI for Coulomb and cheap THC for exchange. Interpolation points are selected via QRCP on AO pair products, with CVT prescreening for large grids. Z is fit by pseudoinverse against either the full ERI (isdf_thc) or RI three-center integrals (isdf_thc_ri), avoiding the full ERI entirely in the latter case.
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