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How Does a Coordinate Scan Work?

A full Potential Energy Surface has one dimension for every internal coordinate of the molecule — far too many to visualize directly. A coordinate scan takes a one-dimensional cut through that surface, along a single bond length, bond angle, or dihedral angle, so the energy profile along that one coordinate can be plotted and understood directly.

Rigid vs. Relaxed Scans

There are two ways to take that cut:

  • Rigid scan — only the scanned coordinate changes; every other coordinate stays frozen at its starting value at every step. This is fast (no optimization needed), but it ignores how the rest of the molecule would naturally respond to the change, so the resulting energies are almost always too high and can distort the shape of the profile.
  • Relaxed scan (used in this tutorial) — the scanned coordinate is held fixed while every other coordinate is fully optimized at each step. This is effectively a constrained geometry optimization performed once per scan point, so each energy already has the surrounding structural strain relaxed away.

A relaxed scan costs roughly (number of scan points) × (cost of one geometry optimization), but produces a far more chemically realistic curve — this is why it is the default choice for bond-dissociation curves, torsional profiles, and reaction-path previews.

The Scan Workflow

Read Scan Specification
        │
        ▼
Fix Scanned Coordinate at Current Value
        │
        ▼
Optimize Remaining Coordinates
   (Berny Algorithm)
        │
        ▼
   Converged?
    │      │
   No      Yes
    │      │
 Keep    Record Energy
 Optimizing  & Geometry
              │
              ▼
     More Scan Points?
        │        │
       Yes        No
        │        │
  Step Coordinate  Build Summary
  (warm-start from   Table / PES
   previous geometry)   Curve
        │
        ▼
   (repeat)

Because each scan point reuses the previous point's optimized geometry as its starting guess, the optimizations after the first one are usually quick — the geometry only needs to adjust slightly for the small change in the scanned coordinate.

The Same Idea for Angles and Dihedrals

Nothing about this workflow changes if a bond angle or a dihedral angle is scanned instead of a bond length — only the coordinate being frozen at each step is different:

  • A bond-length scan probes stretching, compression, dissociation, and proton-transfer coordinates.
  • A bond-angle scan probes bending and inversion barriers.
  • A dihedral-angle scan probes torsional barriers and conformational interconversion.

What a Scan Is — and Isn't

The maximum-energy point along a relaxed scan is often used as a starting guess for a full Transition State Search, since it sits near the top of the barrier along that coordinate. It is only an approximation, however: a relaxed scan follows the scanned coordinate exactly, whereas a true reaction path (found with an Intrinsic Reaction Coordinate calculation) follows the steepest-descent direction in the full coordinate space, which may curve away from any single, hand-picked coordinate. When the scanned coordinate is a good proxy for the reaction coordinate — as with a simple bond-length scan of a proton being transferred — the two agree closely; when it isn't, the scan can only be trusted as a rough preview.