Transition structure algorithms

McDouall J J W, Robb M A and Bernard F 1986 An efficient algorithm for the approximate location of transition structures in a diabatic surface formalism Chem. Phys. Lett. 129 595... 

Transition stale search algorithms rather climb up the potential energy surface, unlike geometry optimi/.ation routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain et nilibrinm geometries for either reactant or product. 

A steepest descents minimisation algorithm produces a path that oscillates about the true reaction pathway Ihe transition structure to a minimum. 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

The optimization of a transition structure will be much faster using methods for which the Hessian can be analytically calculated. For methods that incrementally compute the Hessian (i.e., the Berny algorithm), it is fastest to start with a Hessian from some simpler calculation, such as a semiempirical calculation. Occasionally, dilficulties are encountered due to these simpler methods giving a poor description of the Hessian. An option to compute the initial Hessian at the desired level of theory is often available to circumvent this problem at the expense of additional CPU time. 

An algorithm has been proposed for determining the reaction coordinate, transition structure, and optimized geometry all in a single calculation. The... 

The calculation of reaction rates has not seen as the widespread use as the calculation of molecular geometries. In recent years, it has become possible to compute reaction rates with reasonable accuracy. However, these calculations require some expertise on the part of the researcher. This is partly because of the difficulty in obtaining transition structures and partly because reaction rate algorithms have not been integrated into major computational chemistry programs and thus become automated. 

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

In HyperChem, two different methods for the location of transition structures are available. Both arethecombinationsofseparate algorithms for the maximum energy search and quasi-Newton methods. The first method is the eigenvector-following method, and the second is the synchronous transit method. 

Optimization—that is, minimization of the energy gradient—of a reactant, reaction intermediate (if existing), or product is usually straightforward and the only caveat is to make sure that its corresponding Hessian is positive definite. However, characterization and optimization of a transition structure constitute more difficult tasks and different algorithms [16,17] have been developed to this end. The located transition structure must fulfill the following four requirements, also known as Mclver-Komornicki conditions [18] ... 

Low levels of theory such as small basis set DFT or HF calculations are usually suitable for geometry optimizations and frequency calculations, provided an IRCMax approach [26] is used to correct transition structures and provided frequencies are scaled by their appropriate scale factors. When combinatorial explosion of the conformational space becomes a problem for larger molecules, our new semisyste-matic algorithm, energy-directed tree search, can reliably locate the global minimum conformation at a fraction of the cost of full systematic conformation search [27]. 

B. Special Features of Geometry Optimization Algorithms as Applied to Transition Structure Optimization... 

Since the subject of geometry optimization is discussed in a separate chapter by H. B. Schlegel in this volume, we shall limit our discussion to those particular features of geometry optimization algorithms that are particularly relevant to the optimization of transition structures. 

---