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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.

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