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PreprintCC BY-NC-NDChemRxiv

Semiempirical Quantum Chemistry in the Age of ab initio Data and Differentiable Programming: III. Differentiable Complete Active Space Configuration Interaction

  • Martin Stöhr1,2,3
  • Todd J. Martínez1,2,3
  1. 1Department of Chemistry and The PULSE Institute
  2. 2Stanford University
  3. 3SLAC National Accelerator Laboratory
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Abstract

We present an efficient, differentiable complete-active-space configuration-interaction (CASCI) framework for GPU-accelerated electronic-structure calculations. The approach is integrated into the PyTorch-based PYSEQM package together with orthogonalization-corrected OM2 and OM3 semiempirical Hamiltonians and floating-occupation molecular orbitals. By combining determinant-based direct CI with matrix-free eigensolution and custom reverse-mode differentiation, the method retains the memory efficiency of the forward calculation while providing derivatives with respect to continuous model parameters and molecular coordinates. Its modular formulation separates the CASCI treatment from the underlying one-and two-electron quantities, facilitating use with different electronic-structure backends. The resulting framework provides state energies, density and transition density matrices, transition properties, and analytic response information for multiconfigurational electronic states. In combination with semiempirical effective Hamiltonians, it offers a computationally economical route to differentiable multireference electronic structure for bondbreaking processes and electronically excited systems. We illustrate this formalism studying minimum-energy conical intersections, solvent effects on the intersection seam energetics, and a proof-of-concept inverse design problem of excitation energies in an external electric field.

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Cite

BibTeXRIS
BibTeX
@misc{stohr2026semiempirical,
  title = {{Semiempirical Quantum Chemistry in the Age of ab initio Data and Differentiable Programming: III. Differentiable Complete Active Space Configuration Interaction}},
  author = {Martin Stöhr and Todd J. Martínez},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010422/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010422/v1},
  note = {CC BY-NC-ND},
}
RIS
TY  - UNPB
TI  - Semiempirical Quantum Chemistry in the Age of ab initio Data and Differentiable Programming: III. Differentiable Complete Active Space Configuration Interaction
AU  - Martin Stöhr
AU  - Todd J. Martínez
PY  - 2026
DA  - 2026/10/13
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010422/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010422/v1
AB  - We present an efficient, differentiable complete-active-space configuration-interaction (CASCI) framework for GPU-accelerated electronic-structure calculations. The approach is integrated into the PyTorch-based PYSEQM package together with orthogonalization-corrected OM2 and OM3 semiempirical Hamiltonians and floating-occupation molecular orbitals. By combining determinant-based direct CI with matrix-free eigensolution and custom reverse-mode differentiation, the method retains the memory efficiency of the forward calculation while providing derivatives with respect to continuous model parameters and molecular coordinates. Its modular formulation separates the CASCI treatment from the underlying one-and two-electron quantities, facilitating use with different electronic-structure backends. The resulting framework provides state energies, density and transition density matrices, transition properties, and analytic response information for multiconfigurational electronic states. In combination with semiempirical effective Hamiltonians, it offers a computationally economical route to differentiable multireference electronic structure for bondbreaking processes and electronically excited systems. We illustrate this formalism studying minimum-energy conical intersections, solvent effects on the intersection seam energetics, and a proof-of-concept inverse design problem of excitation energies in an external electric field.
ER  -