Potential energy surface transition structures

Potential Energy Surface Molecular Structure, Transition States, and Reaction Paths... 

Jensen F 1994 Transition structure modeling by intersecting potential energy surfaces J. Comput. Chem. 15 1199... 

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. 

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. 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

This type of calculation does reliably find a transition structure. However, it requires far more computer time than any of the other techniques. As such, this is generally only done when the research requires obtaining a potential energy surface for reasons other than just finding the transition structure. 

Obtain the transition structure from the entire potential energy surface. It is questionable that there will be any case where this is the only option, but it should work as a desperate last resort. 

As mentioned earlier, a potential energy surface may contain saddle points , that is, stationary points where there are one or more directions in which the energy is at a maximum. Asaddle point with one negative eigenvalue corresponds to a transition structure for a chemical reaction of changing isomeric form. Transition structures also exist for reactions involving separated species, for example, in a bimolecular reaction... 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

Geometry optimizations usually attempt to locate minima on the potential energy surface, thereby predicting equilibrium structures of molecular systems. Optimizations can also locate transition structures. However, in this chapter we will focus primarily on optimizing to minima. Optimizations to minima are also called minimizations. 

The optimization facility can be used to locate transition structures as well as ground states structures since both correspond to stationary points on the potential energy-surface. However, finding a desired transition structure directly by specifying u reasonable guess for its geometry can be chaUenging in many cases. 

Another use of frequency calculations is to determine the nature of a stationary point found by a geometry optimization. As we ve noted, geometry optimizations converge to a structure on the potential energy surface where the forces on the system are essentially zero. The final structure may correspond to a minimum on the potential energy surface, or it may represent a saddle point, which is a minimum with respect to some directions on the surface and a maximum in one or more others. First order saddle points—which are a maximum in exactly one direction and a minimum in all other orthogonal directions—correspond to transition state structures linking two minima. 

An IRC calculation examines the reaction path leading down from a transition structure on a potential energy surface. Such a calculation starts at the saddle point and follows the path in both directions from the transition state, optimizing the geometry of the molecular system at each point along the path. In this way, an IRC calculation definitively connects two minima on the potential energy surface by a path which passes through the transition state between them. 

We have already considered two reactions on the H2CO potential energy surface. In doing so, we studied five stationary points three minima—formaldehyde, trans hydroxycarbene, and carbon monoxide plus hydrogen molecule—and the two transition structures connecting formaldehyde with the two sets of products. One obvious remaining step is to find a path between the two sets of products. 

The IRC calculation verifies that the transition structure does indeed connect these two minima. Here is an illustration of the potential energy surface for this reaction ... 

Chapter 3, Geometry Optimizations, describes how to locate equilibrium structures of molecules, or, more technically, stationary points on the potential energy surface. It includes an overview of the various commonly used optimization techniques and a consideration of optimizing transition strucmres as well as minimizations. 

Part 3, Applications, begins with Chapter 8, Studying Chemical Reactions and Reactivity, which discusses using electronic structure theory to investigate chemical problems. It includes consideration of reaction path features to investigate the routes between transition structures and the equilibrium structures they connect on the reaction s potential energy surface. 

A minimum on a potential energy surface represents an equilibrium stracture. There will invariably be a number of such local minima, and we can imagine a number of paths on the surface that connect one particular minimum to another. If the highest-energy point on each path is considered, the transition structure can be defined as the lowest of these maxima. The reaction path is the lowest-energy route between two minima. 

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