Collinear reactions

Figure A3.7.1. Two-dimensional contour plot for direct collinear reaction A + BC —> AB + C. Transition state is indicated by J.

The close-coupling approach works readily and simply if the reaction is purely melastic . The method can also be made to work very simply for a single product arrangement (as in collinear reactions), by using a twisted coordinate system, most conveniently reaction path coordinates [37, 38 and 39] as shown in figure B3.4.3. 

For example, for the collinear reaction A+BC this would be the probability that if initially the diatom BC is in a vibrational state then after the reaction a diatom AB is fonned (in any product vibrational state). In... 

As an illustration, let us consider the collinear reaction AB -I- C -> A -I- BC. It is known that the collinear motion of the linear system ABC relative to its center-of-mass reduces to the motion of the... 

For example, the rate constant of the collinear reaction H -f- H2 has been calculated in the temperature interval 200-1000 K. The quantum correction factor, i.e., the ratio of the actual rate constant to that given by CLTST, has been found to reach 50 at T = 200 K. However, in the reactions that we regard as low-temperature ones, this factor may be as large as ten orders of magnitude (see introduction). That is why the present state of affairs in QTST, which is well suited for flnding quantum contributions to gas-phase rate constants, does not presently allow one to use it as a numerical tool to study complex low-temperature conversions, at least without further approximations such as the WKB one. ... 

Table 4-1. Quantum correction factor k for the collinear reaction between H and H2...

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J.Phys.Chem., 83 (1979), 1052-1079... 

Fig. 2.5 Schematic diagram of a potential energy surface for a collinear reaction A + BC — AB + C.

A function, which is similar to the London equation and based on the diatomic-in-molecules approach was first used by Kuntz to fit the ab initio surface for collinear reaction... 

Consider a model PES for a collinear reaction, A + BC — AB + C, on which a typical reactive trajectory has been shown (Fig. 9.25). The motion along rAB would correspond to reactant translation/product vibrational and similarly motion along rBC would correspond to reactant vibration/product translation. 

The fraction of released energy that passes into translational and vibrational energies of product depends to a quite significant extent on the mass combination of reactant atoms. This mass effect is referred as kinematic effect. In order to understand mass effect, at least for a collinear reaction, we can transform the motion of the three particles on PES to that of a single... 

Jacobi Coordinates The Skew Angle in Three Center Collinear Reactions... 

Table 6.1 Skew angles for collinear reactions of interest AB+C = ABC = A+BC...

Tunneling in VTST is handled just like tunneling in TST by multiplying the rate constant by k. The initial tunneling problem in the kinetics was the gas phase reaction H -(- H2 = H2 + H, as well as its isotopic variants with H replaced by D and/or T. For the collinear reaction, the quantum mechanical problem involves the two coordinates x and y introduced in the preceding section. The quantum kinetic energy operator (for a particle with mass fi) is just... 

To illustrate the point, let us consider the collinear reaction AB + C— A + BC. It is known (c.f., Baer [1982]) that motion of the system in the center-of-mass frame is equivalent to motion of a single particle of mass... 

Consider a collinear reaction of the form A + BC —> AB + C, i.e., all atoms are assumed to move along the same line. Imagine that a calculation of the (realvalued) vibrational frequency of the activated complex, at two different levels of accuracy, gives z>i cm 1 and z>2 cm 1, respectively, and Pi > p2-... 

By dynamical effects, we mean those features governing energy disposal that arise from the motion across the surface rather than the nature of the surface itself. The relative masses of the reagents have an enormous influence on the dynamics. Returning to the collinear reaction A + BC, it is possible to represent the dynamics of the reaction by the motion of a... 

About 97% of the OH product from O + HBr is found to be in the v = 1 state [443]. This reaction is 58 kJ mole-1 exoergic, but has an activation energy of llkJmole l. Quantum mechanical calculations [445] for the collinear reaction O + HBr on an LEPS surface show that at thermal energies OH(v = 1) is the preferred product ( 62%). 

Figure 1.13 Examples of potential surfaces for collinear reactions of the type A + BC - AB + C. Energies are expressed in eV relative to separated A + BC at zero energy, and the dotted lines indicate the equilibrium internuclear distances of BC and AB.

The Toronto group [313] was concerned chiefly with finding useful definitions of the terms attractive, repulsive, and mixed, which can be used to describe either the character of the potential function or the way in which the energy of the reaction is liberated as the system passes from A + BC to AB + C. In terms of V, the attractive contribution could be defined as the energy released on following a rectilinear path across the collinear reaction surface from rAB = 00 and rBC = re-BC to the point where rAB = reAB and rBC = the energy released on going from this point to products... 

S-Matrix Propagation along Delves Radial Coordinate. J. Manz and J. Romelt, Chem. Phys. Lett., 77, 172 (1981). Dissociative Collinear Reactions Evaluated by S-Matrix Propagation along Delves Radial Coordinate. J. Manz and J. Romelt, Chem. Phys. Lett. 81,179 (1981). On the Collinear 1+ HI and 1+ Mul Reactions. (Here Mu represents a muonium isotopic variant.)... 

A long time ago. Wall and Porter have mentioned the existence of upper energy bounds for H + H2 collinear reactions. More recently, Wright et have observed quite similar... 

The idea that the vibrational enhancement of the rate is due to the attraetive potential for excited vibrational states of the reactant is closely related to the observation made long ago based on transition state theoiy [25,26]. Poliak [25] found that for vibrationally highly excited reactants the repulsive pods (periodic orbit dividing surface) is way out in die reactant valley, and the corresponding adiabatic barrier is shallow. Based on this theory one can explain why dynamical thresholds are observed in reactions with vibrationally excited reactants. The simplicity of the theory and its success for mostly collinear reactions has a real appeal. However, to reconcile the existence of a vibrationally adiabatic barrier with the capture-type behavior - which seems to be supported by the agreement of the calculated and experimental rate coefficients [23] -needs further study. 

Garrett B. C. and Truhlar D. G. (1979) Generalized Transition State Theoiy. Quantum Effects for Collinear Reactions of Hydrogen Molecules and Isotopically Substituted Hydrogen Molecules, J. P/zys. Chem. 79, 1079-1112. 

The collinear reaction Ca + HCl CaCl + H exemplifies another problem accurate potential curves are unlikely to be known for all the neutral and ionic diatomic fragments. This system has been studied by Isaacson and Muckerman ° , who were able to demonstrate that most of the prominent features of their results could not be attributed to the large uncertainties in some of the diatomic potentials. 

To illustrate the general procedure let us consider collinear reactions of type A + BC - AB + C. This means that the three atoms move on a line, e.g. the x-axis, and furthermore that velocities are also along the same line. Indicating relative atomic distances by xAB, xBC and xCA, we introduce centre-of-mass coordinates, which for reactants are x = xBC and X, the distance from A to the centre of mass of BC. Similar coordinates could be defined for products. Because of restrictions in the type of motion it is not possible to simultaneously account for the B + CA rearrangement. To do this one must proceed to planar or spatial motion and, for example, introduce bifurcation coordinates. 

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