Locating Transition States

Unlike optimizing ground states, locating transition states involves deciding on an efficient strategy. In general, there are three stages in locating transition states:

1. Generating a geometry in the region of the transition state.

2. Refining the transition state geometry.

3. Characterizing the transition state.

Of these three, the first is by far the most difficult. The following approaches are suggested as potential strategies for generating a geometry in the region of the transition state.

General strategy (works for almost all reactions, but is slower than the special cases below, when they are applicable).

 The SADDLE calculation will work for most systems.  This uses the following sequence:

• Optimize the reactant geometry.
• Using the same atoms in the same sequence, optimize the product geometry.
• Do a geometry optimization of the product geometry using the reactant geometry as reference, this uses GEO_REF. This gives rise to a geometry on the product side of the transition state that is between the true product geometry and the transition state, that is, it is in the slope that leads up to the transition state.
• Do a geometry optimization of the reactant geometry using the new product geometry as reference, again using GEO_REF. This gives rise to a geometry on the reactant side nearer to the transition state than the true reactant geometry. 
• Using these two geometries, one on the reactant side of the transition state and one on the product side, run the SADDLE calculation.  For most calculations, this will terminate in a point near to the transition state.
• If the calculation ends because "both reactants and products are on the same side of the transition state," use two of the geometries to set up a new SADDLE calculation. Use a smaller BAR=n.nn, e.g., BAR=0.03, and re-run the calculation. If CPU time is not important, run the original data set with BAR=0.03.
• Use the final geometry, or the highest energy geometry, if the SADDLE does not run to completion, as the starting point for a TS calculation.

For  worked examples, see:
 Ester hydrolysis Saddle calculation
 1,5 Hexadiene Cope re-arrangement
 Acetone ene-ol - keto tautomerization
 Retro-ene eliminination of isochorismic acid to give pyruvic plus salicylic acids
 Prototype of aspartate protease catalyzed hydrolysis of peptide

Transition states for some special types of reaction can be located more easily using different computational techniques.  The more important of these are:

For narcissistic reactions (reactions in which the reactants and products are the same, e.g. the inversion of ammonia.

• Use geometric constrains, e.g. SYMMETRY, to lock the geometry in the symmetry of the potential transition state.
• Minimize the DH_f.
• Verify that the system is a transition state. If it has more than one negative force constant, use another method.

(For the Cope rearrangement of 1,5 hexadiene, even though the transition state is symmetric, it is faster to use the general SADDLE method described above.)

For a bond making-bond breaking reaction (e.g., an S_N² reaction)

• Use SYMMETRY to set the two bonds equal. If does not matter that the bonds are of different type. For example, to locate the transition state for Br^- reacting with CH₄ to give CH₃Br, the C-Br and C-H bonds would be set equal.
• Optimize the geometry, to minimize the DH_f. Any geometry optimizer could be used, but of course the default optimizer should be tried first.
• Remove the symmetry constraint, and locate the transition state using TS. At this point, the main geometric change is to adjust the two bond lengths involved in the reaction.
• For a worked example, see SN2

For barriers to rotation, inversion, or other simple reaction that does not involve making or breaking bonds

• Optimize the starting geometry.
• Optimize the final geometry.
• Identify the coordinate that corresponds to the reaction. This is likely to be an angle or a dihedral.
• Starting with the higher energy geometry, use a path option to drive the reaction in the direction of the other geometry. Use about 20 points, and go about half way to the other geometry--the transition state is likely to be between the higher energy geometry and the half-way point.
• From the output, locate the highest energy point--this will be near to the transition state.
• Starting with the geometry of the highest energy point, repeat the path calculation. Use smaller steps (0.1 times the previous step is usually OK), and again do 20 points.
• Inspect the reaction gradient. It should drop as the transition state is approached. If it does, then use TS to refine the transition state.
• For a worked example involving the rotation of the C2-C3 bond in butane, see Barriers.

For bond making or bond breaking reactions involving exactly one change in covalent bonding

• Identify the reaction coordinate (the bond that makes or breaks)
• Use a path calculation to drive the reaction.
• The geometry of the highest point on the reaction path should then be used to start a TS calculation.
• For a worked example (CH3-Br + F(-) => CH3-F + Br(-)) see SN2_Path

For bond making or bond breaking reactions involving exactly one bond being made and one bond being broken

 The  GRID calculation can be used.  In this, two coordinates that are important in the reaction are chosen, and the Potential Energy Surface for the optimized geometry is generated for all reasonable values of these coordinates.  Visual inspection of the resulting map can usually provide a guide to the transition state.  Once the approximate transition state is determined, it can be further refined using TS.