Reaction coordinate, definition

In the context of association reactions, an algorithm in which the reaction coordinate definition is optimized along with the dividing surface along a one-parameter sequence of paths is called variable reaction coordinate (VRC) variational transition state theory... 

The first requirement is the definition of a low-dimensional space of reaction coordinates that still captures the essential dynamics of the processes we consider. Motions in the perpendicular null space should have irrelevant detail and equilibrate fast, preferably on a time scale that is separated from the time scale of the essential motions. Motions in the two spaces are separated much like is done in the Born-Oppenheimer approximation. The average influence of the fast motions on the essential degrees of freedom must be taken into account this concerns (i) correlations with positions expressed in a potential of mean force, (ii) correlations with velocities expressed in frictional terms, and iit) an uncorrelated remainder that can be modeled by stochastic terms. Of course, this scheme is the general idea behind the well-known Langevin and Brownian dynamics. 

In order to define how the nuclei move as a reaction progresses from reactants to transition structure to products, one must choose a definition of how a reaction occurs. There are two such definitions in common use. One definition is the minimum energy path (MEP), which defines a reaction coordinate in which the absolute minimum amount of energy is necessary to reach each point on the coordinate. A second definition is a dynamical description of how molecules undergo intramolecular vibrational redistribution until the vibrational motion occurs in a direction that leads to a reaction. The MEP definition is an intuitive description of the reaction steps. The dynamical description more closely describes the true behavior molecules as seen with femtosecond spectroscopy. 

The reaction coordinate is calculated in a number of steps. If too few steps are used, then the points that are computed will follow the reaction coordinate less closely. Usually, the default number of points computed by software packages will give reasonable results. More points may be required for complex mechanisms. This algorithm is sometimes called the IRC algorithm, thus creating confusion over the definition of IRC. 

A photochemical reaction coordinate has two branches an excited state branch and a ground state branch that is reached after decay at a conical intersection. Thus a conical intersection between ground and excited states of a molecule is a precursor to ground state reactivity, and conforms to the above definition of a reactive intermediate. The main focus of our article will be to develop this idea. In Figure 9.1b, we show the energy profile for a photochemical reaction with a conical intersection... 

However, the pathways for these reactions, particularly in the gas phase, have been only -.rtially characterized. In a wide variety of these reactions, coordinatively unsaturated, highly reactive metal carbonyls are produced [1-18]. The products of many of these photochemical reactions act as efficient catalysts. For example, Fe(C0)5 can be used to generate an efficient photocatalyst for alkene isomerization, hydrogenation, and hydrosilation reactions [19-23]. Turnover numbers as high as 3000 have been observed for Fe(C0)5 induced photocatalysis [22]. However, in many catalytically active systems, the active intermediate has not been definitively determined. Indeed, it is only recently that significant progress has been made in this area [20-23]. 

Note Refer to the text for definitions of conformations. AC is the relative energy for conformations of a given isomer, AE is the energy measured relative to the Bda conformation of the adduct formed by trans addition of the syn isomer. The reaction coordinates R, a, 3, Ys 5, and e are defined in Figure 3. 

Equation (5.86c), written as a strict equality, may also be taken to define the NRT transition state as an alternative to (and slightly different from) the usual definitions based on energetic, saddle-point-curvature, or density-of-states criteria. Note that this NRT alternative definition can be employed for non-IRC choices of reaction coordinate, and remains valid even in the case of barrierless processes (such as many ion-molecule or radical-recombination reactions) for which the reaction profile does not exhibit an energy maximum as in Fig. 5.52. The NRT definition is practically identical to the usual saddle-point definition of the transition state in the present examples. 

Figure 1. Reaction coordinate for the gas-phase displacement reaction X + CHSY -> XCHS + Y and definitions of the quantities in Eqs. 1-3.

If there is no pathway independent of the chloride, that is, if extrapolation to very low chloride concentration of chloride exchange reaction led to a zero intercept and no free ion pathway, then we would have a bimolecular reaction. This definition of bimolecularity only requires chloride to be a component of the second coordination sphere for chloride exchange to occur. 

At the transition state the reaction coordinate is defined to be in the direction of the one normal coordinate which has a negative eigenvalue. Fukui (22) suggested that the reaction coordinate be defined as the line of steepest descents from the transition state to reactant or product regions on the potential surface. However, this definition fails to acknowledge the non-orthogonality of the internal coordinates and it would appear more satisfactory to define the reaction coordinate with respect to normal coordinates Q for all points on its path so that the line of steepest descent will be that for which (9r/9(2r) is a maximum (correspondingly all other derivatives (9V/ds r will be zero). 

The definition of the reactant coordinate used in the MC pushing method may be derived from a separation into participant and bystander degrees of freedom, or it may be arrived at intuitively or empirically. Generally speaking, the more cleanly a reaction coordinate separates the two peaks of a bimodal distribution, the higher the conversion coefficient that can be achieved with it. 

Assume that equilibrium is maintained between and the reactants despite a unidirectional decomposition of M+. Then if the activated complex, M+, is regarded as an ordinary molecule, possessing the usual thermodynamic properties, with the exception that motion in one direction, i.e. along the reaction coordinate, leads to decomposition at a definite rate (Glasstone et al., 1941b), it can be shown hy classical statistical methods that the rate of decomposition of is equal to kTjh, a universal frequency factor dependent only on temperature and... 

---