Structure-Preserving Full Approximation Scheme for Real-Space Hartree-Fock Equations

Abstract

We develop a structure-preserving full approximation scheme (FAS) for the real-space restricted Hartree-Fock equations. The method treats the orbital equations, Coulomb and exchange pair potentials, and orthonormality constraints as a coupled nonlinear system on a hierarchy of finite-element spaces. Forced Gram targets, occupied-frame alignment, and auxiliary-variable reconstruction provide constraint compatibility and occupied-rotation equivariance under suitable assumptions. Analysis of the full self-consistent response identifies an elliptic kinetic principal part, motivating the multilevel treatment. The resulting solver, FAS-H, combines FAS cycles with a residual-triggered horizontal Newton correction on the finest grid. Numerical experiments on eight closed-shell systems show convergence in 4-11 cycles across three grid levels. Across 24 system-grid comparisons, FAS-H is 1.60-5.02 times faster than SCF and uses 68-91% less weighted FFT work, while standalone horizontal Newton is faster in some cases.

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BibTeX RIS

BibTeX

@misc{zhang2026structurepreserving,
  title = {{Structure-Preserving Full Approximation Scheme for Real-Space Hartree-Fock Equations}},
  author = {Yuejia Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00880},
  eprint = {2611.00880},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00880},
}

RIS

TY  - UNPB
TI  - Structure-Preserving Full Approximation Scheme for Real-Space Hartree-Fock Equations
AU  - Yuejia Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00880
UR  - https://arxiv.org/abs/2611.00880
AB  - We develop a structure-preserving full approximation scheme (FAS) for the real-space restricted Hartree-Fock equations. The method treats the orbital equations, Coulomb and exchange pair potentials, and orthonormality constraints as a coupled nonlinear system on a hierarchy of finite-element spaces. Forced Gram targets, occupied-frame alignment, and auxiliary-variable reconstruction provide constraint compatibility and occupied-rotation equivariance under suitable assumptions. Analysis of the full self-consistent response identifies an elliptic kinetic principal part, motivating the multilevel treatment. The resulting solver, FAS-H, combines FAS cycles with a residual-triggered horizontal Newton correction on the finest grid. Numerical experiments on eight closed-shell systems show convergence in 4-11 cycles across three grid levels. Across 24 system-grid comparisons, FAS-H is 1.60-5.02 times faster than SCF and uses 68-91% less weighted FFT work, while standalone horizontal Newton is faster in some cases.
ER  -

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