Transition state computational approaches

Reaction rates are macroscopic averages of the number of microscopical molecules that pass from the reactant to the product valley in the potential hypersurface. An estimation of this rate can be obtained from the energy of the highest point in the reaction path, the transition state. This approach will however fail when the reaction proceeds without an enthalpic barrier or when there are many low frequency modes. The study of these cases will require the analysis of the trajectory of the molecule on the potential hypersurface. This idea constitutes the basis of molecular dynamics (MD) [96]. Molecular dynamics were traditionally too computationally demanding for transition metal complexes, but things seem now to be changing with the use of the Car-Parrinello (CP) method [97]. This approach has in fact been already succesfully applied to the study of the catalyzed polymerization of olefins [98]. 

Even if a system is not in chemical equilibrium it is possible to calculate the rate at which it is approaching equilibrium if we have sufficiently detailed knowledge of the energies involved in the transition state (so that it is possible to calculate the partition functions - the crucial step). However, computational chemistry has advanced to a level that good estimates of reaction rates can almost be obtained routinely. We will discuss examples in Chapter 6. 

Today a good understanding of transition state structure can be obtained through a combination of experimental measurements of kinetic isotope effects (KIE) and computational chemistry methods (Schramm, 1998). The basis for the KIE approach is that incorporation of a heavy isotope, at a specific atom in a substrate molecule, will affect the enzymatic reaction rate to an extent that is correlated with the change in bond vibrational environment for that atom, in going from the ground state to the... 

The HCN exchange itself proceeds through a trigonal bipyr-amidal intermediate [Li(NCH)5]+ reached via a late transition state. The entering HCN molecule approaches the lithium cation directly, and pushes three coordinated solvent molecules away toward the equatorial positions. In line with the experimental observation of a very fast exchange process, the computed... 

In the computed transition state (Fig. 23b) the azide and formyloxyl groups are approaching colinearity (N2-N1-09 = 158.6°) and the Sn2 displacement is... 

Quantum mechanics provide many approaches to the description of molecular structure, namely valence bond (VB) theory (8-10), molecular orbital (MO) theory (11,12), and density functional theory (DFT) (13). The former two theories were developed at about the same time, but diverged as competing methods for describing the electronic structure of chemical systems (14). The MO-based methods of calculation have enjoyed great popularity, mainly due to the availability of efficient computer codes. Together with geometry optimization routines for minima and transition states, the MO methods (DFT included) have become prevalent in applications to molecular structure and reactivity. 

Besides the experimental studies, the theoretical approaches have also been developed to study the details of state-to-state chemistry to probing the transition-state. Polanyi and coworkers computed classical trajectories to follow the dynamics of... 

Two newer approaches offer the promise of more detailed information about the transition states, or structures the crystallographic approach under discussion, and calculation. It is an everyday observation that the rapid pace of developments in computing technology has revolutionized the scope of calculational chemistry. High level calculations on molecules with... 

Since the situation about the height of the insertion barrier is not so clear, we performed a systematic comparison of the performances of different computational approaches in determining insertion barriers and geometries, with the aim to offer a further contribution to the discussion. The insertion transition state was located with different pure and hybrid DFT functional, and at the HF and MP2 level of theory. The main geometrical parameters of the transition state for the insertion reaction of ethene into the Zr-C bond of the H2Si(Cp)2ZrCH3+ species are reported in Table 4. 

---