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Coordinate Scan

A Coordinate Scan (or Potential Energy Surface Scan) steps a single internal coordinate — a bond length, a bond angle, or a dihedral angle — through a series of fixed values and records the energy at each one. Unlike a Geometry Optimization or Transition State Search, which locate a single stationary point, a scan builds up a one-dimensional slice through the full multidimensional Potential Energy Surface (PES).

Gaussian supports two flavors of scan:

  • A rigid scan, where only the chosen coordinate changes and every other coordinate is frozen at its starting value.
  • A relaxed scan, where the chosen coordinate is held fixed at each step while every other coordinate is fully re-optimized — a full geometry optimization performed at each scan point.

This tutorial focuses on the relaxed scan, the far more common and chemically meaningful choice, using a bond-length scan of the acidic O–H bond in the hydrogen-bonded formic acid dimer as the worked example.

What Is a Relaxed Scan?

At each of the requested scan points, Gaussian:

  • fixes the scanned coordinate at a specified value,
  • optimizes every remaining internal coordinate to convergence,
  • records the resulting energy and geometry,
  • then moves the scanned coordinate to its next value and repeats, using the previous step's optimized geometry as the starting guess.

The result is a curve — energy versus the scanned coordinate — where every point already has the surrounding strain relaxed away, making it a much better approximation of a real reaction or deformation pathway than a rigid scan.

The Three Coordinate Types

Any of the three basic internal coordinate types can be scanned:

  • Bond length (B) — stretching or compressing a bond; used for bond-dissociation curves, proton-transfer profiles, and hydrogen-bond studies (the example used here).
  • Bond angle (A) — bending a three-atom angle; used for inversion barriers and in-plane bending profiles.
  • Dihedral angle (D) — rotating around a bond; used for torsional/rotational barriers and conformational searches.

The input syntax is identical for all three — only the coordinate being marked for scanning changes. This is covered in detail in Input File.

Why Perform a Coordinate Scan?

A relaxed scan is typically used to

  • map out a bond-stretching or bond-breaking energy profile,
  • explore a proton-transfer or hydrogen-bond coordinate, as in the formic acid dimer example,
  • locate an approximate transition-state geometry (the highest point along the scan) to use as a starting guess for a full Transition State Search,
  • study torsional or conformational energy profiles,
  • generate a quick, low-cost preview of a reaction path before committing to a full IRC calculation.

How Does Gaussian Perform a Scan?

Read Scan Specification
 (coordinate, start value, steps, step size)
        │
        ▼
Fix Scanned Coordinate at Step n
        │
        ▼
Optimize All Remaining Coordinates
   (Berny Optimization)
        │
        ▼
Converged? ── No ──▶ Continue Optimizing
        │
       Yes
        │
        ▼
Record Energy & Geometry for Step n
        │
        ▼
 More Steps Remaining? ── Yes ──▶ Advance Coordinate,
        │                          Repeat from Step n+1
        No
        │
        ▼
Summary of Optimized Potential
      Surface Scan

Typical Applications

  • Bond dissociation and proton-transfer energy profiles.
  • Hydrogen-bond strength and geometry studies (this tutorial's example).
  • Locating approximate transition states before a full TS search.
  • Torsional and conformational energy profiles.
  • Ring-puckering and inversion-barrier studies.

Prerequisites

A relaxed scan requires

  • a reasonable starting geometry (ideally already close to equilibrium),
  • a clearly identified coordinate to scan, expressed either as a Z-matrix variable or as an atom-index specification,
  • a sensible step size and step count — too coarse a step can miss important features; too fine a step multiplies the number of optimizations required.

What You Will Learn

This section demonstrates how to perform a relaxed Coordinate Scan in Gaussian, using an 11-point bond-length scan of the formic acid dimer. It covers:

  • Preparing the Z-matrix-based scan input file.
  • How to scan a bond angle or a dihedral angle instead of a bond length.
  • Running the scan and reading the per-step optimization output.
  • Interpreting the final Summary of Optimized Potential Surface Scan table and its energy profile.
  • The mathematics of a relaxed scan as a constrained optimization problem.