Locating Transition States

Locating transition state geometries is different from optimizing ground states, where general all-purpose methods can be used.  Locating a transition state geometry involves deciding on which of several different strategy should be used. Several options are available. These range from simple one-step optimizations to quite complicated processes.  The choice of which option to use depends on the type of reaction that is being studied.  In general, the simplest method that will locate the transition state should be used.  Be aware that sometimes none of the techniques described below will work.  When that happens, the possibility that there is a fault in the model of the chemical system must be considered, and that a re-examination of the project might be necessary. 

Techniques for locating transition states

In order of complexity, these are:

Narcissistic reactions

In narcissistic reactions the reactants and products look the same.  Reactions of this type are also called fluxional and degenerate rearrangement reactions; all three names reflect the fact that the product(s) of reaction are essentially the same as the reactant(s), the only difference being that the order of the atoms has changed.  If this option can be used - use it!  It's simple, fast, and reliable.

More complicated methods

All the following methods involve two steps.  The first step depends on the method used, and produces a geometry that is near to the transition state.  This approximate transition state geometry is then optimized to produce the refined transition state.  For this, any of the standard transition state refinement methods can be used: TS, SIGMA or NLLSQ.

Almost narcissistic reactions

For convenience, reactions that are similar, but not the same as, narcissistic reactions can be modeled using a method similar to that used for narcissistic reactions.  The only difference is the addition of a step to optimize the transition state geometry. As with true narcissistic reactions, if this option can be used - use it!  It's almost as simple, fast, and reliable as the narcissistic reactions.

Use of reaction path

In some reactions, one specific atomic parameter, either an interatomic distance, bond angle, or dihedral, can be identified as being related to the reaction path.  In this type of reaction, simply increasing or decreasing the atomic parameter will allow the path to be mapped out.  The transition state geometry is then the highest point on the reaction path. 

Use of reaction path, starting near the transition state

This option is new in the sense that it has not been used before.  However, it is not new in that it uses tools that have existed in MOPAC for a long time.


In reactions where an atom, A, moves from being bonded to another atom, B, to being bonded to a third atom, C, can be assumed to have a transition state somewhere between B and C.  Using symmetry, a dummy atom is placed at a point equidistant from B and C, and a reaction path for atom A is then constructed.  Atom A is moved in a straight line from atom B to the dummy atom, and then in a line away from atom B, still in a straight line away from atom B.  At each point on this line the positions of all atoms, and, most important, the position of the dummy atom are optimized.   Setting up this type of reaction path requires a significant effort, but as with the first few methods, when it can be used it is very reliable.


CPU intensive methods SADDLE and LOCATE-TS

If at all possible, avoid using these methods.  They are very CPU intensive, and quite often require the user to make value judgments. They are, however, often the only techniques that are successful when working with enzymes.

Both methods use two data-sets, one that represents the reactants and one for the products.  Both methods work by reducing the distance, RRP, between the systems representing the reactants and products, in a systematic manner. 

SADDLE works by moving whichever system has the lower energy in the direction of the other system, that is, it reduces RRP by moving one system towards the other while holding the other system fixed.  The geometry of the moving system is then optimized, subject to the constraint that RRP is held constant.  If the optimized heat of formation rises above that of the system that was held fixed, then the roles are reversed.  That is, the system that was held fixed is now optimized subject to the RRP constraint, and the system that was being optimized is now held fixed.  This procedure slowly moves both systems up the reaction barrier while simultaneously keeping the heats of the two systems roughly the same. Eventually RRP becomes small enough that gradient minimization methods can be used for refining the transition state.

LOCATE-TS works in a different way.  It uses a bias to move both systems towards each other.  The bias can be regarded as a force pulling the reactants towards the products, and pulling the products towards the reactants.  Both pulls are equal and opposite in direction.  At each step, the geometries of both systems are optimized, subject to the bias; at the end of each step both systems will be in equilibrium with the bias.  This means that the slope of the reaction barrier for one system is equal and opposite to the slope of the other system.  Put another way, the gradients due to the bias acting on both systems are equal and opposite.  Motion up the reaction barrier is achieved by increasing the bias.  Near the top of the barrier, the slope decreases as the transition state is approached, and gradient minimization methods can then be used for refining the transition state. 

So SADDLE works by moving up the barrier by moving whichever system has the lower energy in the direction of the other system, and LOCATE-TS works by moving both systems up the barrier simultaneously, while keeping the slope of the barrier the same by using a bias.  In practice, the LOCATE-TS method is more efficient than the SADDLE method.

Use of the SADDLE technique

For more complicated reactions, the fact that the transition-state geometry is the highest point on the lowest-energy path between reactants and products can be used for locating it.  The SADDLE technique uses as data both the optimized reactant geometry and the optimized product geometry.  It calculates the distance in Ångstroms between the two, and whichever system has the lower heat of formation is moved a small distance towards the other geometry, thus shortening the distance between them.  If the new ΔHf is still lower than that of the other geometry, another step is taken.  When the ΔHf rises above that of the other geometry, the stationary and moving geometries are swapped around. This procedure results in the distance between the two geometries getting steadily shorter, and both geometries have roughly the same heat of formation, and the transition state geometry is somewhere between the two geometries. Eventually the distance becomes very small, and the average of the two geometries is then a good approximation to the transition state.

Use of LOCATE-TS technique

This technique is particularly suitable for modeling complicated systems such as transition states for individual steps in enzyme-catalyzed reactions.

An alternative to the SADDLE technique is to replace the ΔHf criterion with the gradient criterion.  In the LOCATE-TS method, the starting point is the same as in the SADDLE technique.  A bias or force is then applied to both the reactants and products, pulling them towards each other.  This force is steadily increased until the approximate transition state is located.  The transition state is then refined in a set of two-step operations.  One operation involves gradient minimization of only those atoms that are directly involved in the reaction, the other operation is an unconstrained geometry optimization of all the other atoms.

Once an acceptable transition state geometry is obtained, it should be further refined by running the geometry optimization with a tighter criterion, for proteins GNORM=5 would be appropriate.  Monitor the job to watch the heat of formation.  When it stops decreasing (it does not decrease over say 50 - 100 cycles) the geometry can be considered as being at an energy minimum.

Caveat: The LOCATE-TS technique uses the MOZYME LMO method, and will not work for systems that cannot be run using MOZYME.

Use of a two-dimensional grid

Use this technique only for demonstration purposes.  It produces a two-dimensional contour map for a reaction.  The X and Y dimensions are two geometric variables, and the third dimension is the energy at that point.  Visual inspection should show the approximate location of the transition state.  Re-running the job, focusing on the region around the transition state, should produce a more refined geometry.

Although this technique can be used with proteins it is very CPU intensive.  A better alternative is to use a mixture of LOCATE-TS and SADDLE.  Use LOCATE-TS with a small bias, for example LOCATE-TS(C:3,3,3,5,5;), to quickly minimize the distance between the reactants and products, then switch to SADDLE to ascend the barrier.