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Make use of ERI redundancies #55

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awf opened this issue Aug 30, 2023 · 0 comments
Open

Make use of ERI redundancies #55

awf opened this issue Aug 30, 2023 · 0 comments
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awf commented Aug 30, 2023 •
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The ERI tensor has numerous redundancies:

  1. permutation invariances: E_ijkl = E_jikl etc
  2. orthogonalities: E_ijkl = 0 for some combinations of (i,j) in some basis sets
  3. sparsity: E_ijkl \approx 0 when atoms (ijkl) are far from each other

The electron repulsion integrals are stored in ERI and most of the entries are zero. Furthermore, ERI satisfies an 8x symmetry:

  • E_ij.. = E_ji.. # E is a symmetric matrix of ...
  • E_..kl = E_..lk # ... symmetric matrices
  • E_[ij][kl] = E_[kl][ij] # .. and one more symmetry

This file computes the ERI einsum using a sparse matrix vector multiplication.
@awf awf added the epic label Aug 30, 2023
@awf awf changed the title Make use of ERI redundancies to save memory Make use of ERI redundancies Aug 30, 2023
@awf awf mentioned this issue Aug 30, 2023
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@AlexanderMath AlexanderMath mentioned this issue Sep 1, 2023
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@mihaipgc mihaipgc mentioned this issue Sep 27, 2023
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