3.2 Proving that an optimized water structure is a minimum

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

3.2.1 Model, units and provenance

Geometry in Å; electronic energy in hartree; vibrational wavenumbers in cm⁻¹. Check each printed field and keep thermal and standard-state terms distinct.

Shared inputs, conventions and evidence

Original schematic: Proving that an optimized water structure is a minimum. No numerical results are claimed.

3.2.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

3.2.2.1 Input block 1

%chk=case10_water_min.chk
%mem=4GB
%nprocshared=2
#p B3LYP/6-31G(d) Opt=(Tight,CalcFC) Freq
   SCF=Tight Integral=UltraFine

Water optimization and minimum verification

0 1
O   0.000000   0.000000   0.000000
H   0.758000   0.000000   0.586000
H  -0.758000   0.000000   0.586000

3.2.3 Worked investigation

3.2.3.1 Question and intuition

Does “optimization completed” prove that a structure is stable? It establishes that the optimizer's convergence tests were satisfied, but does not by itself determine whether the surrounding surface curves upward in every vibrational direction. A frequency calculation examines local curvature. A bowl has positive curvature in all directions; a mountain pass has at least one downhill direction. For an isolated, nonlinear three-atom water molecule, the relevant vibrational subspace has 3N−6 = 3 modes. Translation and rotation of the whole molecule are not additional internal vibrations.

Prerequisites are a readable Gaussian output and familiarity with Cartesian coordinates. This case deliberately computes geometry and Hessian with the same method, basis, DFT integration grid, and SCF threshold. A Hessian calculated with a different model at a geometry optimized elsewhere generally does not certify a stationary point of that new model. The example assumes a neutral, closed-shell water molecule, not a radical, ion, cluster, or liquid-water sample.

3.2.3.2 Complete input

See input block 1 above.

Opt Freq performs the Hessian calculation after the geometry optimization. The final checkpoint is named case10_water_min.chk and is the explicit prerequisite for Cases 11 and 12. Preserve it after confirming that both stages finished. A file merely named “min” or “freq” does not establish its contents. Store the corresponding log with it, since the log records the model, convergence, frequencies, and termination status used to validate the checkpoint.

3.2.3.3 Workflow

Inspect the starting molecule and run the complete input. Record the Gaussian revision, route section, total charge, multiplicity, and resource settings in a small job manifest.
Find the final optimization convergence table. Check maximum/RMS forces and maximum/RMS displacements, together with the optimizer's completion message. Do not use a low SCF energy as a substitute for geometry convergence.
Read the vibrational-frequency blocks, not just the first “Low frequencies” diagnostic line. Count the three internal modes, record frequencies in cm−1 and IR intensities in km mol−1, and note whether any vibrational frequency is negative.
Animate each mode in a viewer and identify bending, symmetric stretching, and antisymmetric stretching from the displacement vectors. Atomic motion is more reliable for assignment than memorizing an approximate frequency region.
Read the final termination line and confirm that thermochemical data were actually printed. Archive the checkpoint only after all checks pass. If a meaningful imaginary mode remains, displace slightly along it in both directions, reoptimize, and repeat the frequency calculation.

3.2.3.4 Outputs and acceptance criteria

Gaussian commonly displays an imaginary frequency as a negative number in the vibrational-frequency list. It corresponds to negative curvature, not to a physically oscillating vibration with a negative oscillation rate. A successful minimum in this example should have three real internal vibrational modes, negligible residual gradient, and normal completion. This establishes a local minimum at the chosen model chemistry, not the global minimum among every possible connectivity, charge state, or electronic state.

For a very small negative mode in a larger floppy molecule, investigate numerical accuracy, the displacement pattern, and whether the geometry is genuinely unconverged. Do not invent a universal cutoff that converts all small imaginary values into positive ones. Tightening the optimization and integration grid and recalculating provides evidence; manually deleting the sign does not. Water is comparatively rigid, so an unexpected negative internal mode here deserves immediate diagnosis rather than an automatic “low-frequency exception.”

Harmonic frequencies are model predictions around one equilibrium geometry. Comparison with experiment may require a documented frequency scaling factor, anharmonic treatment, and matching phase and isotopic composition. A frequency scaling factor should never be selected merely to make a chosen peak look correct, and a scaled spectrum does not fix an unstable geometry. Keep unscaled frequencies available for auditing.