Transition state

The transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always go on to form products [Solomons, T.W. Graham & Fryhle, Craig B. (2004). "Organic Chemistry" (8th ed.). John Wiley & Sons, Inc. ISBN 0-471-41799-8.] . The transition state shown below occurs during the SN₂ reaction of bromoethane with a hydroxyl anion.

History of concept

The concept of a transition state has been important in many theories of the rate at which chemical reactions occur. This started with the transition state theory (also referred to as the activated complex theory), which was first developed around 1935 and which introduced basic concepts in chemical kinetics which are still used today.

Explanation

A collision between reactant molecules may or may not result in a successful reaction.The outcome depends on factors such as the relative kinetic energy, relative orientation and internal energy of the molecules.Even if the collision partners form an activated complex they are not bound to go on and form
products, and instead the complex may fall apart back to the reactants.

Observing transition states

Because of the rules of quantum mechanics, the transition state cannot be captured or directly observed; the population at that point is zero. However, cleverly manipulated spectroscopic techniques can get us as close as the timescale of the technique will allow us. Femtochemical IR spectroscopy was developed for precisely that reason, and it is possible to probe molecular structure extremely close to the transition point. Often along the reaction coordinate reactive intermediates are present not much lower in energy from a transition state making it difficult to distinguish between the two.

Locating Transition States by Computational Chemistry

Transition state structures can be determined by searching for first-order saddle points on the potential energy surface (PES) [“Introduction to Computational Chemistry”, Frank Jensen, John Wiley and Sons Ltd England, 1999] . Such a saddle point is a point where there is a minimum in all dimensions but one. Almost all quantum-chemical methods (DFT, MP2, ...) can be used to find transition states. However, locating them is often difficult and there is no method guaranteed to find the right transition state. There are many different methods of searching for transition states and different quantum chemistry program packages include different ones. Many methods of locating transition states also aim to find the minimum energy pathway (MEP) along the PES. Each method has its advantages and disadvantages depending on the particular reaction under investigation. Summaries of some of the main methods are given below.

ynchronous Transit

There are several type of synchronous transit type methods with the most common being the linear synchronous transit (LST) method and the quadratic synchronous transit (QST). The LST method generates an estimate of the transition state by finding the highest point along shortest line connecting two minima. The QST method extends this further by subsequently searching for a minimum along a line perpendicular to the previous one. The path connecting minima and the found point may then be searched for a saddle point (a maximum).

Nudged elastic band

There are many variations on the NEB (nudged elastic band) method [ [http://theory.cm.utexas.edu/vtsttools/neb/ Nudged Elastic Band - Vasp Tools - Theory - UT Austin ] ] , including the climbing image nudged elastic band and the elastic band. This method works by guessing the MEP which connects the two stable structures. A discrete number of structures (called images) are placed along the guessed-MEP. These images are moved according to: (A) the force acting on them perpendicular to the path and (B) an artificial spring force keeping the images spaced along the MEP. The highest energy image gives a good estimate of the transition state.

tring method

The string method for locating transition states is similar to the NEB in many ways. It also involves a series of images along a guess of the MEP, but in this case the images are moved in two steps. Firstly, the images are moved according to the force acting on them perpendicular to the path. Using an interpolated path, the images are moved short distances along the MEP to make sure they are evenly space. Variations on the string method include the growing string method [“A growing string method for determining transition states: Comparison to the nudged elastic band and string methods”, Baron Peters, Andreas Heyden, Alexis T. Bell, Arup Chakraborty, J. Chem. Phys. 120 (2004) 7877-7886] , in which the guess of the pathway is generated as the program progresses.

Dimer method

The dimer method [“A dimer method for finding saddle points on high dimensional potentialsurfaces using only first derivatives”, Graeme Henkelman and Hannes Jónsson, J. Chem. Phys. 111 (1999) 7010-7022] can be used to find possible transition states without knowledge of the final structure or to refine a good guess of a transition structure. The “dimer” is formed by two images very close to each other on the PES. The method works by moving the dimer uphill from the starting position whilst rotating the dimer to find the direction of lowest curvature (ultimately negative).

The Hammond-Leffler postulate

The Hammond-Leffler Postulate states that the structure of the transition state more closely resembles either the product or the starting material, depending on which is higher in enthalpy.

The Structure-correlation principle

The structure-correlation principle states that "that structural changes which occur along the reaction coordinate can reveal themselves in the ground state as deviations of bond distances and angles from normal values along the reaction coordinate". ["From crystal statics to chemical dynamics " Hans Beat Buergi, Jack D. Dunitz Acc. Chem. Res.; 1983; 16(5); 153-161. DOI| 10.1021/ar00089a002] . According to this theory if one particular bond length on reaching the transition state increases then this bond is already longer in its ground state compared to a compound not sharing this transition state. One demonstration of this principle is found in the two bicyclic compounds depicted below ["Manifestations of the Alder-Rickert Reaction in the Structures of Bicyclo [2.2.2] octadiene and Bicyclo [2.2.2] octene Derivatives" Yit Wooi Goh, Stephen M. Danczak, Tang Kuan Lim, and Jonathan M. White J. Org. Chem.; 2007; 72(8) pp 2929 - 2935; (Article) DOI|10.1021/jo0625610] . The one on the left is a bicylco [2.2.2] octene which at 200°C extrudes ethylene in a retro-Diels-Alder reaction.

:

Compared to the compound on the right (which, lacking an alkene group, is unable to give this reaction) the bridgehead carbon-carbon bond length is expected to be shorter if the theory holds because on approaching the transition state this bond gains double bond character. For these two compounds the prediction holds up based on X-ray crystallography and ¹³C coupling constants (inverse linear relationship with bond length).

Implications for enzymatic catalysis

One way in which enzymatic catalysis proceeds is by stabilizing the transition state through electrostatics. By lowering the energy of the transition state, it allows a greater population of the starting material to attain the energy needed to overcome the transition energy and proceed to product.

References