Mathematical Background¶
CASSCF theory doesn't depend on which software solves it, so the full derivation already lives on the GAMESS CASSCF pages rather than being duplicated here — the same approach used in the ORCA RHF tutorial, which links out to the GAMESS RHF mathematics rather than repeating it.
- Why Hartree–Fock Fails — why a single Slater determinant can't describe the excited states seen in Output File.
- The Active Space Concept — what an active space is and how CAS(4,4) is chosen.
- Configuration State Functions (CSFs) — the building blocks behind the
2200/2110/2020-style weights in the output. - The CASSCF Wavefunction
- The CASSCF Hamiltonian
- Solving the Configuration Interaction Problem — what "CI-PROBLEM SOLVED" in each macro-iteration is actually doing.
- Orbital Optimization — the other half of each macro-iteration.
- State-Averaged CASSCF — the theory behind computing S₀, S₁, and S₂ together.
- Density Matrices
- Natural Orbitals
What's Different in ORCA¶
The theory above is identical regardless of software. What genuinely differs is the algorithmic path ORCA takes to reach a converged CASSCF wavefunction — its specific macro-iteration scheme, the moread/%moinp orbital-guess mechanism used in this tutorial, and how nroots/mult map onto the state-averaging theory above. That's covered separately in Complete CASSCF Algorithm, mirroring how the ORCA RHF mathematics section has its own Complete RHF Algorithm alongside the shared GAMESS theory.