Harmonic transition state theory HTST

Transition state theory is very often used in its harmonic approximation. The harmonic approximation is applicable under the normal assumptions of transition state theory, but further demands that the potential energy surface is smooth enough for a harmonic expansion of the potential energy to make sense. Since the harmonic expansion is performed in the initial state and in a first-order saddle point on the 

By performing a normal mode analysis in the initial state and in the saddle point, it is then possible to obtain the harmonic expansion of the potential in the reactant region  

Since in eq. (23) there is one frequency more in the numerator than in the denominator it is often interpreted as an attempt frequency of the reactant system multiplied by a Boltzmann factor corresponding to the energy barrier between the initial state and the saddle point in the transition state. The transition state theory result is often written in the form (see page 110 of [3])  

Some important systems, which certainly do not fulfill the assumptions of harmonic transition state theory are gas phase reactions. In the gas phase, there are zero-modes such as translation and rotation, and these lead to totally different configuration integrals than those obtained from a normal mode analysis. For these species one can in a simple manner modify the terms going into the HTST rate by incorporating the molecular partition functions [3,119]. 

---

In TAD, which assumes that harmonic transition state theory (HTST) holds, the simulation is carried out at elevated temperature in order to collect a sequence of escape times from the local energy minimum in which the system... 

Figure 6.5 Hopping rate for an Ag atom on Cu(100) as predicted with one dimensional harmonic transition state theory (ID HTST). The other two solid lines show the predicted rate using the DFT calculated activation energy, AE = 0.36 eV, and estimating the TST prefac tor as either 1012 or 1013 s 1. The two dashed lines show the prediction from using the ID HTST prefactor from DFT (v — 1.94 x 1012 s 1) and varying the DFT calculated activation energy by + 0.05 eV.

Fortunately, the reaction rates of many important processes can be obtained without a full molecular dynamics simulation. Most reaction rate theories for elementary processes build upon the ideas introduced in the so-called transition state theory [88-90]. We shall focus on this theory here, particularly because it (and its harmonic approximation, HTST) has been shown to yield reliable results for elementary processes at surfaces. 

---