Output File¶
Normal Termination¶
Orbital Optimization: Macro-Iterations¶
CASSCF alternates between solving the CI problem within the active space and optimizing the orbitals themselves — a macro-iteration cycle (see Orbital Optimization). This calculation converged after 26 such cycles:
Initial CI Check vs. Final Converged States¶
ORCA first diagonalizes the CI problem using the input RHF orbitals as-is, before any orbital optimization, as a sanity check:
<<<<<<<<<<<<<<<<<<INITIAL CI STATE CHECK>>>>>>>>>>>>>>>>>>
ROOT 0: E= -2042.3277166206 Eh
ROOT 1: E= -2042.1676129466 Eh 4.357 eV 35138.7 cm**-1
ROOT 2: E= -2042.1140409482 Eh 5.814 eV 46896.4 cm**-1
After the full 26 macro-iterations, the final, converged CASSCF state energies are lower and shifted:
CAS-SCF STATES FOR BLOCK 0 MULT= 1 NROOTS= 3
---------------------------------------------
ROOT 0: E= -2042.3470259034 Eh
ROOT 1: E= -2042.1679107518 Eh 4.874 eV 39311.2 cm**-1
ROOT 2: E= -2042.1618097383 Eh 5.040 eV 40650.2 cm**-1
| State | Energy (Eh) | ΔE vs. S₀ | ΔE vs. S₀ |
|---|---|---|---|
| S₀ (ROOT 0) | −2042.3470259034 | — | — |
| S₁ (ROOT 1) | −2042.1679107518 | 4.874 eV | 39311.2 cm⁻¹ |
| S₂ (ROOT 2) | −2042.1618097383 | 5.040 eV | 40650.2 cm⁻¹ |
The ground state (S₀) energy drops and the excitation energies shift noticeably between the initial guess and the final result — this is exactly what orbital optimization is for: the RHF orbitals were a good starting point, but CASSCF re-optimizes them specifically for the multi-state, multi-configurational problem at hand, not just for the ground state RHF describes well.
Configuration State Function (CSF) Weights¶
Each state is reported as a weighted sum over configuration state functions — the coefficients showing how multi-configurational (or not) each state actually is:
ROOT 0: E= -2042.3470259034 Eh
0.91933 [ 0]: 2200
0.03086 [ 3]: 2020
0.02884 [ 9]: 1111
...
ROOT 1: E= -2042.1679107518 Eh 4.874 eV 39311.2 cm**-1
0.41147 [ 1]: 2110
0.28149 [ 3]: 2020
0.09592 [ 6]: 1210
0.08801 [ 2]: 2101
...
ROOT 2: E= -2042.1618097383 Eh 5.040 eV 40650.2 cm**-1
0.52643 [ 1]: 2110
0.21929 [ 3]: 2020
0.08399 [ 2]: 2101
...
The 2200/2020/1111-style labels are occupation strings across the 4 active orbitals (2 = doubly occupied, 1 = singly occupied, 0 = empty). Reading these:
- S₀ is well described by a single configuration (
2200, 91.9% weight) — close to what a single-determinant method would already capture, which is why RHF gives a reasonable ground-state geometry and orbitals even though it can't describe the excited states at all. - S₁ and S₂ are genuinely multiconfigurational — no single CSF exceeds 53% weight, and both states mix the same handful of configurations (
2110,2020,2101,1210) in different proportions. This is precisely the situation Why Hartree–Fock Fails describes: a single Slater determinant simply cannot represent either excited state well, which is why CASSCF — not RHF — is needed to describe them at all.
Comparing With the GAMESS CASSCF Tutorial¶
The GAMESS CASSCF tutorial runs the same molecule, the same CAS(4,4) active space, and the same 3 states — the only differences are the basis set (CCD there vs. def2-SVP here) and the software. That makes the two directly comparable: the state ordering and the qualitative CSF character (a well-behaved S₀ against two strongly mixed excited states) should match; the absolute energies and excitation gaps will differ somewhat with the change of basis set. Working through both tutorials side by side is a useful check that the physics — not just the software — is being understood correctly.