How CASSCF Works¶
Why RHF Isn't Enough Here¶
Restricted Hartree–Fock describes the wavefunction with a single Slater determinant — one specific assignment of electrons to orbitals. That's a good approximation when one configuration genuinely dominates, which is exactly what's seen for the ground state of DAE in this tutorial: the 2200 configuration carries 91.9% of the S₀ wavefunction (see Output File).
It breaks down for the excited states. Neither S₁ nor S₂ is well-represented by any single configuration — the leading CSF weight is only 41–53%, with several other configurations contributing significantly. A single-determinant method has no mechanism to describe a state that is genuinely a mixture of configurations; this is the general problem covered in Why Hartree–Fock Fails.
What CASSCF Adds¶
CASSCF handles this by splitting the orbitals into three groups — inactive (always doubly occupied), active (partially occupied, allowed to mix), and virtual (always empty) — and building a full configuration interaction expansion within just the active space, while simultaneously optimizing all the orbitals (not just the active ones) to minimize the energy of the resulting states.
For this tutorial, the active space is 4 electrons in 4 orbitals — see The Active Space Concept for how such a space is chosen in general.
Why Start From RHF Orbitals¶
CASSCF's orbital optimization is a local procedure — it improves on whatever orbitals it's given, but it isn't guaranteed to find the best possible active space from an arbitrary starting point. Reading in converged RHF orbitals (dae-rhf.gbw, via %moinp — see Input File) gives the optimization a physically reasonable starting point, rather than ORCA's generic initial guess. The Output File shows this mattering directly: the initial CI check (using unrotated RHF orbitals) gives noticeably different state energies than the final result after 26 macro-iterations of orbital optimization.
Computing Multiple States at Once¶
This calculation requests nroots 3 — three states, computed state-averaged, meaning the orbitals are optimized to describe all three states well simultaneously (with equal weight here) rather than being optimized separately for each one. This is necessary because S₁ and S₂ share the same active space and the same underlying orbitals; optimizing orbitals for S₀ alone would give a poor description of the excited states, and vice versa. See State-Averaged CASSCF for the general treatment.
What This Calculation Doesn't Do¶
CASSCF recovers the static correlation associated with near-degenerate configurations within the active space — it's what makes S₁ and S₂ describable at all. It does not recover dynamic correlation (the correlation missing even within a well-chosen active space), which is why the Electronic Structure Theory workflow follows CASSCF with a perturbative correction (XMCQDPT) before treating the resulting numbers as quantitatively reliable vertical excitation energies.