CAS-CI

ferric runs complete-active-space configuration interaction (CAS-CI) from a closed-shell RHF reference. It is a Rust library routine only: the CLI and the Python bindings do not expose it.

The Hamiltonian, the determinant phase convention and the Slater-Condon rules are derived in crates/ferric-ci/theory.md. The phase conventions are checked by scripts/casci_slater_condon_phases_sympy.py.

Scope

With no inactive orbitals the method is FCI in the basis. A call that fails the bookkeeping check, 2 * active_start + n_alpha + n_beta == nelec, returns an error. So does a non-restricted reference, n_active == 0, or n_active > 63 (the u64 string limit).

Energy

$$ E_\text{CASCI} = E_\text{core} + \lambda_\text{min}(H_\text{act}), $$

where $E_\text{core}$ is the nuclear repulsion plus the energy of the active_start doubly occupied inactive orbitals, and $H_\text{act}$ carries the inactive-core Fock potential in its one-electron part. e_active is e_total - e_core, the quantity PySCF reports as CASCI.e_cas.

Library use

use ferric_ci::{run_cas_ci, CasCiConfig};

// `mol`, `prep` and `rhf` come from a converged restricted solve_rhf
// with exact J/K (no density fitting), as in the validation tests.
let cfg = CasCiConfig {
    n_active: 6,
    n_elec_active: (3, 3),
    active_start: 4,          // MOs 0..4 are doubly occupied and inactive
    ..Default::default()
};
let res = run_cas_ci(&mol, &prep, &rhf, cfg)?;
println!("{res}");            // energy, determinant count, iterations

CasCiResult holds e_total, e_active, e_core, n_determinants, ci_vector (index ia * n_beta + ib), converged and iterations. Defaults: conv_thresh = 1e-9, max_subspace = 50, max_iter = 200.

Limits

• The active-space integrals come from a dense AO ERI tensor, O(nbasis⁴) memory. Use it on minimal and double-zeta basis sets.
• The sigma build is an O(N_det²) loop over determinant pairs. It does not use the string-based Knowles-Handy/Olsen algorithm.
• The Davidson subspace needs 2 * max_subspace * N_det * 8 bytes. memory_budget_bytes bounds the integral transform and the subspace; None resolves through FERRIC_MEM_BUDGET_GB, then 0.8 of available RAM, then a 2 GiB floor.

Validation

Compared with PySCF mcscf.CASCI on an exact-integral RHF with the same orbital window, and with a dense diagonalization of the full active-space Hamiltonian:

Each system is also run with the window moved down one orbital. The test tolerance is 3e-9 Ha. The stretched N2 reference is the symmetric RHF, which is internally unstable toward a symmetry-broken RHF 0.19 Ha lower; both codes use the symmetric state.

The sign convention is checked three ways, because energy comparisons cannot detect a diagonal $\pm1$ similarity of $H$:

1. tests/slater_condon_brute_force.rs compares general_element, sigma and the diagonal with an independent bit-loop second-quantized $H$ on random asymmetric integrals, CAS(4,4) to CAS(6,6), odd and even $N_\alpha$. The largest difference is 8.9e-15.
2. scripts/casci_slater_condon_phases_sympy.py builds the Jordan-Wigner operators symbolically, verifies the anticommutation relations, and shows that a line-for-line port of general_element equals the explicit $H$ as an exact linear form in $h_{pq}$ and $(pq|rs)$ for four $(n, N_\alpha, N_\beta)$ sectors. Four sign mutations and the interleaved orbital order each fail.
3. The PySCF energies above fix the spectrum.

The grade is on Capabilities and validation. Sources: crates/ferric-ci/tests/validation_casci.rs and scripts/validation/gen_casci.py.