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Interpreting the Gaussian Output File

1. The Reference SCF Solution

Before any stability test can run, Gaussian must first converge the ordinary SCF/DFT wavefunction at the requested level of theory:

SCF Done:  E(RB3LYP) =  -379.409333527     A.U. after   13 cycles

This RB3LYP/6-31G energy of the formic acid dimer, -379.409333527 a.u., is the reference determinant that the stability analysis will now examine.

2. Building the Trial Space

24 initial guesses have been made.
Convergence on wavefunction:    0.001000000000000

Gaussian generates an initial set of trial orbital-rotation vectors (here, 24 — one per occupied/low-virtual pairing considered first) and sets the convergence threshold for the iterative solver to 0.001.

3. Iterative (Davidson-Type) Diagonalization

Iteration     1 Dimension    24 NMult    24
CISAX will form    24 AO SS matrices at one time.
...
Iteration     5 Dimension    61 NMult    61

The orbital Hessian ("singles matrix") is never built or diagonalized in full — it would be far too large. Instead, Gaussian's CISAX routine expands a small trial subspace iteration by iteration (Dimension grows from 24 to 61 across 5 iterations), diagonalizes the much smaller projected matrix at each step, and tracks which converged root corresponds to which trial vector (New state X was old state Y), until the lowest eigenvalues stop changing.

4. The Stability Analysis Header

***********************************************************************
 Stability analysis using <AA,BB:AA,BB> singles matrix:
***********************************************************************

<AA,BB:AA,BB> indicates that both the alpha-alpha and beta-beta orbital-rotation blocks are diagonalized together. In a single pass, this tests both of the common internal instability channels for a closed-shell reference: real RHF→RHF (singlet) instabilities and spin-symmetry-breaking RHF→UHF (triplet) instabilities.

5. The Eigenvectors

Eigenvector   1:      Triplet-A    Eigenvalue= 0.1473900  <S**2>=2.000
     17 -> 25        -0.11358
     18 -> 26        -0.11203
     21 -> 26         0.45484
     22 -> 25         0.51155

Each eigenvector of the stability matrix is reported with:

  • a spin label (Singlet or Triplet), read directly from the computed <S**2> expectation value (0 for singlet, 2 for triplet),
  • a spatial symmetry label (A or B, from the point-group irreducible representations),
  • an eigenvalue, in Hartree — the curvature of the energy along that orbital-rotation direction,
  • the dominant occupied → virtual orbital pairs that mix to form that rotation, with their expansion coefficients.

Six roots are reported for this system: two near-degenerate triplet pairs (≈0.147 and ≈0.175 Hartree) and one singlet pair (≈0.215–0.217 Hartree) — all positive.

6. The Verdict

The wavefunction is stable under the perturbations considered.

Because every eigenvalue found is positive, no lower-energy real or spin-unrestricted determinant exists nearby: the RB3LYP/6-31G solution for the formic acid dimer is a genuine local minimum in orbital-rotation space.

Had the lowest eigenvalue instead been negative, Gaussian would report an internal instability and — since Stable=Opt is the implicit default — automatically rotate the orbitals along that eigenvector, restart the SCF from the improved guess, and repeat the whole procedure.

7. Job Completion

Job cpu time:  0 days  0 hours  0 minutes 23.0 seconds.
Normal termination of Gaussian 09 at Mon Jul 27 10:15:43 2026.

The population analysis, orbital energies, and other standard SCF output that follow the stability block are the usual post-SCF summary and are unaffected by the stability test itself.