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.