Transition State Search

Overview

A transition state (TS) is a first-order saddle point on the potential energy surface (PES). It is characterized by exactly one imaginary vibrational frequency, corresponding to the reaction coordinate that connects reactant and product basins. Finding accurate TS geometries is essential for computing activation energies, predicting reaction rates, and understanding reaction mechanisms.

Unlike local minima, a TS is a maximum along one direction (the reaction coordinate) and a minimum along all remaining degrees of freedom. The unique imaginary mode of the mass-weighted Hessian at the TS defines the direction of bond breaking and bond forming.

Available Methods

MAPLE provides five transition state search algorithms, each suited to different problem types:

Method	Keyword	Description
P-RFO	`prfo`	Partitioned Rational Function Optimization. Refines a guess geometry near the TS using trust-region steps that maximize along one Hessian mode while minimizing along all others.
NEB	`neb`	Nudged Elastic Band. Requires reactant and product structures. Builds a minimum energy path (MEP) using a chain of images connected by spring forces.
Dimer	`dimer`	Minimum-mode following method. No endpoint structures needed. Uses two images separated by a small distance to estimate and follow the lowest curvature mode.
String/GSM	`string`	Growing String Method. Adaptive path growth from both endpoints with CI-STRING refinement. More efficient than NEB for large systems.
AutoNEB	`autoneb`	Automated multi-step NEB workflow. Recursively subdivides the reaction path to discover all intermediates and transition states in complex multi-step reactions.

Choosing a Method

The best method depends on what information you have and the complexity of the reaction:

You have a good TS guess (e.g., from a previous NEB or chemical intuition) → Use P-RFO for fast local refinement.
You have both reactant and product structures → Use NEB or String/GSM to find the MEP and locate the TS along it.
You only have one structure and no product → Use the Dimer method to explore the PES landscape from a single starting point.
The reaction has multiple steps or intermediates → Use AutoNEB to automatically discover all stationary points along the pathway.
Large systems with many atoms → String/GSM is often more efficient than NEB due to adaptive path growth.

General Workflow

A typical transition state search workflow follows these steps:

Optimize endpoints. Ensure your reactant and product geometries are properly optimized local minima. Poorly optimized endpoints can cause path-based methods to fail or converge to spurious saddle points.
Run the TS search. Choose an appropriate method (neb, string, dimer, or prfo) and run the calculation. For path-based methods, the highest-energy image (HEI) provides an initial TS estimate.
Refine the TS. Optionally refine the HEI with P-RFO using refine=nebts to obtain an accurate saddle-point geometry.
Verify with a frequency calculation. Confirm the TS has exactly one imaginary frequency. If there are zero or more than one imaginary frequencies, the geometry is not a true first-order saddle point.
Run IRC. Perform an intrinsic reaction coordinate (IRC) calculation from the TS to confirm that it connects the expected reactant and product.