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The Complete Relaxed Scan Algorithm

Putting every piece together, a relaxed coordinate scan in Gaussian proceeds as:

  1. Parse the scan specification. Identify the coordinate to scan (a Z-matrix variable, or a bond/angle/dihedral atom-index specification under modredundant), its starting value \(q_0\), step size \(\Delta q\), and number of steps \(N\).
  2. Set the scan coordinate to \(q_0\) for the first scan point.
  3. Freeze the scanned coordinate and run a full Berny geometry optimization over every remaining internal coordinate, starting from the current structure.
  4. Converge to a constrained stationary point. Confirm convergence, record the energy and geometry, and note the residual force (-DE/DX) along the frozen coordinate — the Lagrange multiplier of the constraint.
  5. Advance the scan coordinate to \(q_0 + \Delta q\) (and so on for subsequent points), using the just-optimized geometry as a warm-start guess for the next optimization.
  6. Repeat steps 3–5 for all \(N+1\) scan points.
  7. Assemble the results into the Summary of Optimized Potential Surface Scan table — the full \((q_n, E_n)\) profile — which can then be plotted directly as the reconstructed energy curve.

The result is a relaxed, one-dimensional cut through the full Potential Energy Surface: cheaper than a true reaction-path calculation, and — for a well-chosen scan coordinate — a close approximation to it.