The search for transition states is similar to searches for local minima in that an attempt is made to minimize the gradient of the energy with respect to structural coordinates. In contrast to minima, however, transition states are located on a hilltop with respect to one of the coordinates, while they are minima with respect to the others. Three different strategies exist to search for transition states, which will be discussed in the following:
1) scanning the potential energy surface (a global approach)
2) walking uphill to the transition state (a local approach)
3) automated global search algorithms
Before going into some more detail, a comment on the term transition state appears appropriate. States are typically defined through their thermodynamic properties and not through their structural characteristics. What will be described in the following is, strictly speaking, the search for a vibrationless structure corresponding to the idealized transition state at a temperature of 0K. Since "structures of transition states" is an awkward term to use, we will talk about transition states in the following.