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.