Transition States (TS)
Transition states are of high chemical interest but computationally often hard to pinpoint. Moreover, the accuracy of the results may be very critical when, for instance, the energy barrier between reactants and products is required at kcal precision. At first sight, the determination of a transition state (TS) is very similar to a minimization. A stationary point is searched where the gradient vector vanishes. The Hessian is updated in an iterative procedure, after some kind of initial estimate. The difference between a TS search and a minimization is only that at the TS the Hessian has a negative eigenvalue.
Transition state search methods, described in the ADF User Documentation:
When we are close enough to the TS, the standard procedure used for minimization will produce the TS. However, the energy surface around the TS often displays sizeable anharmonicity. Neglecting third- and higher-order terms, as inherent to the Newton approach, is therefore likely to be less accurate. Moreover, taking wrong or too large steps in a minimization usually keeps us in the local bowl containing the minimum so that the gradients at any new geometry still point more or less towards the minimum. With transition states, however, it is much more common that a too-large step brings us to a location where the energy surface has little resemblance anymore to the surface close to the TS, and the procedure easily loses sight completely of where the TS might be. The aspects that discriminate TS search implementations from a simple minimization are largely related to these considerations. In the first place, a different Hessian update scheme is applied: obviously we have no reason to apply a method that favors a positive definite Hessian. Second, control by the program of, for instance, a maximum step length to take at each optimization step is tighter. Third, checks are performed to verify that the Hessian has the right structure (one negative eigenvalue) and, if it is found otherwise, adjustments are applied, all this to avoid that the procedure wanders away from the TS and loses track. Despite such precautions, a successful search for a TS often requires that the initial Hessian is fairly accurate. A force field-based estimate may then be inadequate, and one has to perform a calculation of frequencies first and feed the result into the TS run, which makes the whole procedure more cumbersome and time-consuming.
A reasonable first estimate of the TS, crucial for the successful application of the TS search algorithm, can, in many cases, be identified by a linear transit procedure.
Links
ADF User Documentation: TS,
NEB
ADF-GUI: structure and reactivity,
Tutorial:
reactivity
Examples: reactivity
References: TS,
NEB
Related: linear transit, IRC
