Hamiltonian-Guided Autoregressive Selected-Configuration Interaction Achieves Chemical Accuracy in Strongly Correlated Systems

Strongly correlated molecules remain out of reach for most electronic-structure solvers because the exact wave function spans a determinant space that grows exponentially with the number of orbitals. State-of-the-art selected-CI (e.g., CIPSI and HCI) and ML-CI methods mitigate search by exploiting Hamiltonian sparsity and learned prescreening. Nonetheless, in strongly multireference regimes, the excitation-based candidate lists can grow rapidly, which may increase memory and screening costs. We present the Hamiltonian-guided autoregressive selected-configuration interaction (HAAR-SCI), a learn-sample-compress workflow that runs on a single GPU. A gated Transformer samples determinants autoregressively; Gumbel Top-K noise encourages exploration, and GPU min-heap kernels keep only configurations with the largest Hamiltonian couplings. The network is retrained after each expansion, and iterations stop when successive energies differ by ≤1 mHa. Across an 18-molecule benchmark set reaching 116 spin-orbitals, HAAR-SCI attains a mean absolute error of 0.51 mHa while using much fewer determinants than heat-bath CI. It traces the entire N₂ dissociation curve within 0.67 mHa and achieves HCI accuracy for the 40-spin-orbital [Fe₂S₂(SCH₃)₄]²⁻ cluster with a determinant reduction of 72%, demonstrating its power on systems considered intractable for conventional selected-CI solvers. A final probability-mass pruning compresses typical wave functions by a further 10-50×, retaining <0.01% of the Hilbert space yet still capturing >99.9% of the correlation energy. HAAR-SCI thus offers a compact and truly scalable route to chemical-accuracy quantum chemistry on commodity hardware.